2019 cfa® program exam prep ift study notes · the cfa program curriculum is important and all ift...

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2019 CFA® Program Exam Prep

IFT Study Notes

Volume 1

Ethical and Professional Standards

Quantitative Methods

This document should be read in conjunction with the corresponding reading in the 2019 Level I CFA® Program curriculum. Some of the graphs, charts, tables, examples, and figures are copyright 2018, CFA Institute. Reproduced and republished with permission from CFA Institute. All rights reserved. Required disclaimer: CFA Institute does not endorse, promote, or warrant the accuracy or quality of the products or services offered by IFT. CFA Institute, CFA®, and Chartered Financial Analyst® are trademarks owned by CFA Institute.

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Ethical and Professional Standards and Quantitative Methods 2019 Level I Notes

© IFT. All rights reserved 1

Copyright © 2018 IFT.

All rights reserved. This book or any portion thereof may not be reproduced or used in any manner

whatsoever without the express written permission of the publisher except for the use of brief

quotations in a book review.

Published in 2018 by IFT

Errata information can be found at: https://ift.world/errata

ISBN



Preface

IFThashelpedthousandsofcandidatessuccessfullyprepareforallthreelevelsoftheCFA®Programexamsince2011.IFTprovidesacompletelearningsystemandpreparationstrategy.AllIFTmaterialsremainclosetotheCFA®Programcurriculum.Wehelpstudentsdevelopathoroughunderstandingoffundamentalconceptsviaactivelearningandexampractice.IFTStudyNotesandDetailedLectureVideoshelpyouunderstandandretaincurriculumconcepts.PracticeusingIFTQuizzesandQuestionBankisessentialtotestyourgraspofthematerials.Closetotheexamdate,IFTHigh‐YieldVideos,High‐YieldNotesandHigh‐YieldQuestionBankalongwithmockexamswillhelpyouachievesuccess.

RecommendedExamPreparationStrategy

TheCFAProgramcurriculumisimportantandallIFTproductsfocusonitscoreconcepts.Startyourpreparationasearlyaspossible.Giveyourselfatleast6monthsforathoroughpreparationandbeginbymakingaschedule.Foreachreadinginthecurriculum,youshoulddothefollowing:

1. ReadIFTStudyNotesforeachreading.IFTrecommendsstartingwithQuantitativeMethods.Dothequestionsattheendofeachreadingtohelpreinforceandretaintheconcepts.

2. Ifyouneedadditionalhelp,watchIFTDetailedVideoLectures.Pause,rewind,andreviewwhereyouneedmoretimetounderstand.Printouttheslidesandtakeyourownnotesasyouarewatching.

3. Readtheexamplesinthecurriculum(alsoknownasblue‐boxexamples)anddothemonyourown.WatchIFTexamplevideostofurthergraspconceptsandpracticethem.

4. Dothepracticeproblemsfromthecurriculumattheendofeachreading.

5. DotheIFTQuestionBankforthatreading.

6. Afterdoingallthereadingsinatopic,taketheIFTTopicExam.

7. Twomonthspriortotheexamorwhenyouhavedonetheabovestepsforeveryreading,youshouldstartyourrevisionusingtheIFTHigh‐YieldCourse.

8. OnemonthbeforetheexamyoushouldattempttheCFAInstituteandIFTmockexams.Theseshouldbedoneinamannertoreplicateyourrealexamexperience.

BelowaresomefurtherdetailsaboutIFTresourcesforLevelIexampreparation.

IFTDetailedLectureVideos:Thesevideoscloselyfollowthecurriculumandcoverallsectionsandlearningoutcomesofareading.LecturesslidesareavailableinPDFformat.Youcanprinttheseslidesandmakenotesonthemasyoufollowthevideolecture.Thispracticeispartofactivelearningwherebyyoumakenotesandcarefullyfollowexamples.Thetotaldurationofthevideosisover70hours.



IFTStudyNotes:IFTStudyNotesarecloselyalignedwiththeDetailedLectureVideosandpresentinformationinaneasilyunderstandablemanner.Themostimportantpoints,formulas,andexamplesarehighlightedandexplained.Readingthenoteshelpsreinforceyourunderstandingandgraspofconcepts.Bothnotesandvideosareorganizedtomatchthecurriculum(readingnumber/sectionnumber)soyoucanstayclosetoit.

IFTExampleVideos:Thesevideospresentexamplesandtheirworkedsolutions.Theyaresimilarbutnotexactlythesameastheblue‐boxexamplesfromthecurriculum.Theunderlyingconceptsarethesame,butthenumbersmightbedifferent.Thetotaldurationofthesevideosisapproximately30hours.

IFTQuestionBank:Practicinglotsofexam‐likequestions(andsolvingthemcorrectly!)isthekeytoyourexamsuccess.TheIFTQuestionBankhasover3,000questionswithdetailedexplanations.Questionsareavailableforeverylearningoutcome,reading,andtopic.Thequestionsarearrangedintestsof20‐25questionseach.

IFTTopicExams:Thesewilltestyourpreparationatthetopiclevel.Atopicexamshouldbetakenafteryouhavestudiedallreadingsofagiventopicandhavecompletedpracticequestionsforeachreading.Thisisanessentialstepinpreparingfortheexam.

IFTMockExams:IFThasfulllengthmockexamstogetyouexam‐ready.Answersanddetailedexplanationsareprovidedforself‐grading.

IFTHigh‐YieldNotes:IFTHigh‐YieldNotesarebasedonPareto’s80‐20ruleaccordingtowhich80%oftheexamquestionsarelikelytobebasedon20%ofthecurriculum.Hencethesenotesfocusonthe20%materialwhichismosttestable.Theysummarizethemostimportantconceptsfromeachreadingintwotofivepages.

IFTHigh‐YieldVideos:ThesearevideolecturesbasedontheHigh‐YieldNotes.Eachreadingiscoveredin10to20minutes.Totaldurationisapproximately15hours.

IFTHigh‐YieldQ‐Bank:TheIFTHigh‐YieldQ‐Bankhasbetween600and700questionscoveringconceptswhicharemostlikelytoshowupontheexam.Alllearningoutcomesarecoveredandthereisminimumoverlapofthequestions.

Q&AwithIFT:Whenareyouarestuckonaconcept,example,orquestion,thenthe‘Q&AwithIFT’serviceiswheretoturnto.Submityourquery,andanIFTinstructorwillprovideanindividualizedresponse.

Finally,besuretofollowIFTonsocialmediaandvisitwww.ift.worldformylatestblogsandstudyadvice.DoreachouttotheIFTteamifyouneedanyhelporhavequestions.Iwishyouallthebestinyourstudies.

Warmregards,

ArifIrfanullah,CFA



TableofContentsR01EthicsandTrustintheInvestmentProfession..........................................................................8

1.Introduction .............................................................................................................................. 8 2.Ethics .......................................................................................................................................... 8 3.EthicsandProfessionalism ...................................................................................................... 9 4.ChallengestoEthicalConduct .................................................................................................. 9 5.TheImportanceofEthicalConductintheInvestmentIndustry ........................................ 10 6.Ethicalvs.LegalStandards ..................................................................................................... 11 7.EthicalDecision‐MakingFramework .................................................................................... 12 Summary ...................................................................................................................................... 14 PracticeQuestions ...................................................................................................................... 16

R02CodeofEthicsandStandardsofProfessionalConduct.......................................................19

Introduction ................................................................................................................................ 19 CFAInstituteProfessionalConductProgram ........................................................................... 19 CodeofEthics .............................................................................................................................. 20 StandardsofProfessionalConduct ........................................................................................... 20 Summary ...................................................................................................................................... 25

R03GuidanceforStandardsI‐VII...............................................................................................................26

Introduction ................................................................................................................................ 26 StandardI:Professionalism ....................................................................................................... 26 StandardII:IntegrityofCapitalMarkets .................................................................................. 32 StandardIII:DutiestoClients .................................................................................................... 34 StandardIV:DutiestoEmployers ............................................................................................. 40 StandardV:InvestmentAnalysis,Recommendations,andActions ....................................... 44 StandardVI:ConflictsofInterest............................................................................................... 48 StandardVII:ResponsibilitiesasaCFAInstituteMemberorCFACandidate ....................... 52 Summary ...................................................................................................................................... 55 PracticeQuestions ...................................................................................................................... 57

R04IntroductiontoGIPS................................................................................................................................66

Introduction ................................................................................................................................ 66 1.WhyWeretheGIPSStandardsCreated? ............................................................................... 66 2.WhoCanClaimCompliance? .................................................................................................. 66 3.WhoBenefitsfromCompliance? ........................................................................................... 67 4.Composites .............................................................................................................................. 67 5.Verification .............................................................................................................................. 68 6.TheStructureoftheGIPSStandards ..................................................................................... 68



Summary ...................................................................................................................................... 69 PracticeQuestions ...................................................................................................................... 70

R05TheGIPSStandard....................................................................................................................................72

Introduction ................................................................................................................................ 72 GoalsoftheGIPSExecutiveCommittee .................................................................................... 72 KeyFeaturesoftheGIPSStandards .......................................................................................... 72 HistoricalPerformanceRecord ................................................................................................. 73 Compliance .................................................................................................................................. 73 ImplementingaGlobalStandard ............................................................................................... 74 NineMajorSectionsoftheGIPSStandards .............................................................................. 74 SamplePresentation ................................................................................................................... 78 Summary ...................................................................................................................................... 81 PracticeQuestions ...................................................................................................................... 82

R06TimeValueofMoney..............................................................................................................................84

IntroductoryNote ....................................................................................................................... 84 1.Introduction ............................................................................................................................ 84 2.InterestRates:Interpretation ................................................................................................ 85 3.TheFutureValueofaSingleCashFlow ................................................................................ 87 4.TheFutureValueofaSeriesofCashFlows .......................................................................... 92 5.ThePresentValueofaSingleCashFlow .............................................................................. 94 6.ThePresentValueofaSeriesofCashFlows ......................................................................... 97 7.SolvingforRates,NumberofPeriods,orSizeofAnnuityPayments ................................ 103 Summary .................................................................................................................................... 106 PracticeQuestions .................................................................................................................... 109

R07DiscountedCashFlowApplications.............................................................................................113

1.Introduction .......................................................................................................................... 113 2.NetPresentValueandInternalRateofReturn .................................................................. 113 3.PortfolioReturnMeasurement ............................................................................................ 117 4.MoneyMarketYields ............................................................................................................ 120 Summary .................................................................................................................................... 125 PracticeQuestions .................................................................................................................... 127

R08StatisticalConceptsandMarketReturn....................................................................................131

1.Introduction .......................................................................................................................... 131 2.SomeFundamentalConcepts ............................................................................................... 131 3.SummarizingDataUsingFrequencyDistributions ............................................................ 132 4.TheGraphicPresentationofData ........................................................................................ 133 5.MeasuresofCentralTendency............................................................................................. 135



6.OtherMeasuresofLocation:Quantiles ............................................................................... 138 7.MeasuresofDispersion ........................................................................................................ 139 8.SymmetryandSkewnessinReturnDistributions ............................................................. 143 9.KurtosisinReturnDistributions ......................................................................................... 144 10.UsingGeometricandArithmeticMeans ........................................................................... 145 Summary .................................................................................................................................... 146 PracticeQuestions .................................................................................................................... 150

R09ProbabilityConcepts............................................................................................................................157

1.Introduction .......................................................................................................................... 157 2.Probability,ExpectedValue,andVariance ......................................................................... 157 3.PortfolioExpectedReturnandVarianceofReturn ............................................................ 163 4.TopicsinProbability ............................................................................................................. 165 Summary .................................................................................................................................... 170 PracticeQuestions .................................................................................................................... 174

R10CommonProbabilityDistributions..............................................................................................179

1.Introduction .......................................................................................................................... 179 2.DiscreteRandomVariables .................................................................................................. 179 3.ContinuousRandomVariables ............................................................................................ 183 4.MonteCarloSimulation ........................................................................................................ 188 Summary .................................................................................................................................... 189 PracticeQuestions .................................................................................................................... 193

R11SamplingandEstimation...................................................................................................................198

1.Introduction .......................................................................................................................... 198 2.Sampling ................................................................................................................................ 198 3.DistributionoftheSampleMean ......................................................................................... 200 4.PointandIntervalEstimatesofthePopulationMean ....................................................... 201 5.MoreonSampling ................................................................................................................. 206 Summary .................................................................................................................................... 208 PracticeQuestions .................................................................................................................... 211

R12HypothesisTesting................................................................................................................................216

1.Introduction .......................................................................................................................... 216 2.HypothesisTesting ............................................................................................................... 216 3.HypothesisTestsConcerningtheMean .............................................................................. 221 4.HypothesisTestsConcerningVariance ............................................................................... 225 5.OtherIssues:NonparametricInference .............................................................................. 229 Summary .................................................................................................................................... 230 PracticeQuestions .................................................................................................................... 234



R13TechnicalAnalysis..................................................................................................................................238

1.Introduction .......................................................................................................................... 238 2.TechnicalAnalysis:DefinitionandScope ........................................................................... 238 3.TechnicalAnalysisTools ...................................................................................................... 239 4.ElliotWaveTheory ............................................................................................................... 252 5.Inter‐marketAnalysis ........................................................................................................... 253 Summary .................................................................................................................................... 254 PracticeQuestions .................................................................................................................... 258

R01 Ethics and Trust in the Investment Profession 2019 Level I Notes


R01EthicsandTrustintheInvestmentProfession

1.Introduction

Toillustratetheimportanceofethicalbehavior,thecurriculumcitestheexampleofananalyst’sactionatafinancialservicesfirm.Theresearchdepartmentatthefirmisresponsibleformakinginvestmentrecommendationstoclientsaftersoundanalysisandvaluationofcompanies.Oneoftheanalystsatthefirmmisrepresentsfactsinhisreportwiththeobjectiveofpleasingthemanagementofthesubjectcompany.Hehopedthiswouldleadtofinancialbenefitsforhisemployerandhimself.Clientswhoactedontherecommendationincurheavylossesandspreadanegativewordonseveralonlineforumsaboutthefirm.Thiseventuallyaffectsthereputationofthefirm,forcingittodownsizeandmanyemployeeslosetheirjob.Thisexampleillustrateshowonemember’sunethicalactionshaveaspiralingeffectonthefirmandotheremployeesfornofaultoftheirs.

Thefoundationoftheinvestmentmanagementindustryistrust.Thetopthreeattributesofaninvestmentmanagementfirmareasfollows:

Hastransparentandopenbusinesspractices. Takesresponsibleactionstoaddressanissueorcrisis. Hasethicalbusinesspractices.

Ethicalbehaviorisnotjustaboutadheringtothelaw,rules,andregulations.Itisaboutidentifyingpotentialconflictsandactingrighteouslyinsituationswheretherearenostatedrules.

2.Ethics

ThewordethicscomesfromtheGreekword“ethos”meaningcharacter,guidingbeliefs,orideals.Thereareseveraldefinitionsofethicsallofwhichessentiallyconveythesamemeaning.

Ethicscanbedescribedasasetofmoralprinciplesandrulesofconductthatprovideguidanceforourbehavior.Ethicalprinciplesdefinewhatisgood,acceptablebehaviorandwhatisforbiddenorunacceptablebehavior.Examplesofethicalprinciplesincludehonesty,diligence,justice,beingopenaboutthecostsinvolvedinaninvestment,fairness,andrespectfortherightsofothers.

Anotherdefinitionofethicalconductisbehaviorthatbalancesone’sowninterestwiththedirectandindirectconsequencesofthebehavioronothers.

Instructor’sNote:The‘others’areoftenreferredtoasstakeholders,i.e.groupsofpeopleorindividualswhoaredirectlyorindirectlyimpactedbyourdecisions.

Specificcommunitiesformallydefinetherulesforacceptableandforbiddenbehaviorintoawrittensetofprinciplescalledthecodeofconduct.Professionalassociations,universities



andcompaniesoftenadoptacodeofethicsandexpecttheirmemberstoadheretothoserules,attheveryleast.Themembersmaychoosetodisplayhigherstandardsofbehaviorthanwhatisstipulatedinthecodeofethics.

Somecommunitiesmayalsoexpandontheircodeofethicsandadoptexplicitrulesorstandardsthatidentifyspecificbehaviorsrequiredofcommunitymembers.Thesestandardsofconductserveasabenchmarkoftheminimallyacceptablebehaviorexpectedfrommembersofacommunity.

CFAInstituteisanexampleofacommunitythathaslaiddownacodeofethicsandstandardsofconductforitsmembersandcandidatestofollow.ThesetofprinciplescomprisingtheCodeofEthicsandStandardsofProfessionalConductisclearlydocumentedintheCFAInstituteStandardsofPracticeHandbook.

MembersandcandidatesarerequiredtopledgetheircommitmenttoabidebytheCodeandStandardseachyear.TheyarealsorequiredtodiscloseanyviolationsoftheCodeandStandardsintheirProfessionalConductStatementeachyear.MemberswhoviolatetheCodeandStandardsfacedisciplinaryaction.

3.EthicsandProfessionalism

Anoccupationcanbedividedinto:job,vocation,andprofession.Ajobisworkonedoestoearnalivelihood,orearnmoney.Avocationisajobthatoneispassionateaboutdoing;onederivesasenseofsatisfactionormeaningfromit,asitishis/hercalling.Aprofessionistheultimateevolutionofoccupation.It:

1) requiresspecializedtrainingandskills,2) isbasedonservicetoothers,and3) ispracticedbymemberswhoshareandadheretoacommoncodeofethics.

Professionalsusetheiracquiredskillstoservetheirclients.Clientsdifferfromcustomers.Acustomerisonewhoengagesinasingleoraseriesoftransactionstobuyagoodorservice.Thisrelationshipistransactionalinnature.Aclient,ontheotherhand,usestheservicesofaprofessionalonanongoingbasis,forafee.Thebasisofthisrelationshipistrustandtheclient’sintereststakepriorityoverpersonaloremployer’sinterests.

Inanygivenprofession,thecodeofethicsopenlycommunicatestheestablishedprinciplesoftheprofessionandhowitsmembersareexpectedtobehave.Ithelpsinbuildingpublicconfidencethatmembersoftheprofessionwillusetheirskillsandknowledgeforthebenefitoftheirclients.

4.ChallengestoEthicalConduct

Someofthechallengestoethicalconductincludethefollowing:

Overestimatingone’smorality:Peoplebelievetheyaremoreethicalthantheyactuallyare.Thisoverconfidenceinthemselvescansometimesleadtofaultydecision‐making.Itisoften



seenthatemotionscloudrationalthinking,promptingonetomakedecisionsthatmaynotbethemostethicalchoice.

Situationalinfluences:Theseareexternalfactorssuchascultural,social,andenvironmentalfactorsthatinfluenceone’sthinking,behavior,anddecision‐making.Someofthecommonsituationalinfluencesare: Moneyandprestige:Bothmoneyandprestigepushpeopletoactintheirownself‐

interestsandtakeactionsthatarelessethical.Thepromiseofalargefinancialbonusorapromotion,canimpactpeople’sthinkingabilityandcausethemtoactintheirownshort‐terminterestsandignorethelong‐termconsequencesoftheiractions.

Loyaltytoemployer,employee,andcolleagues:Loyaltycanhavebothpositiveandnegativeeffects.Forinstance,somecolleaguesmayencourageyoutobehavemoreethicallyandenrollintheCFAProgramtoadvanceyourcareer.Ontheotherhand,colleagueswhodonotadheretotheCodeandStandardsmayencourageyoutosimplyactinaccordancewiththelocallaw,eventhoughitmayfallshortofethicalconduct.

Complianceculture:Astrongcompliancepolicyisimportantforethicaldecision‐making;however,processesfocusedsolelyoncomplianceoversimplifydecision‐makinganddonothelpthelargercause.ThecurriculumcitestheexampleofEnron,whichengagedintransactionswiththird‐partyentitieswhereEnron’sCFO,AndrewFastow,hadapersonalinterest.Inkeepingwiththespiritofcompliance,FastowsoughtapprovalsfromtheboardofdirectorsforalltheproposedtransactionswithEnron.TheboardfailedtoseebeyondthecompliancerequirementsanddidnotquestionFastow’svestedintereststhatwerenotalignedwiththatofEnron’sshareholders.

5.TheImportanceofEthicalConductintheInvestmentIndustry

Theinvestmentindustryconnectstwoparties:investorsandborrowers.Borrowersarethosewhoareinneedofcapitaltofundtheirlong‐termgoalsortheirregularoperations.Long‐termgoalsmayincludebuildingschools,factories,bridges,etc.Investorsarethosewhosupplycapitalandseekareturn.Theinvestmentindustrybridgesthegapbetweenthosewhoareinneedofcapitalandthosewhoarewillingtoprovidecapital.

Thefoundationoftheinvestmentindustryisbuiltontrust.Alltheparticipantsinthesystemmustactethicallytobuildanenvironmentoftrust.Forinstance,ifinvestorstrusttheirfinancialadvisersandfinancialmarkets,ingeneral,thentheywillbewillingtolendcapital,takerisks,andnotpanicoverpricefluctuationsintheshortterm.Thiswillencouragemoreparticipationinthefinancialmarketsandensurecapitalflowtofundthegrowthofseveralprojectsthatwilllargelybenefitsociety.Similarly,organizationsinneedofcapitalwillbemorewillingtoexpandtheirbusinessesiftheyarereasonablyassuredofattractingfunds.

Whiletrustisimportantinanybusiness,itisparticularlyimportantintheinvestmentprofessionbecauseofthefollowingreasons:

Natureoftheclientrelationship:Investorsparktheirassetswithfinancialinstitutionsbecausetheytrustthefirmstosafeguardtheirassets.Ifthefirmandits



employeesbreachthistrustandfailtoprotecttheirclient’sassets,theywilleventuallylosebusinessasclientswillnolongerentrustthefirmwiththeirassets.

Differenceinknowledgeandaccesstoinformation:Investmentmanagershavemoreaccesstoinformationandmorespecializedknowledgethantheirclients.Clientstrustthattheprofessionalswillusetheinformationandknowledgeforthebenefitoftheclient’sinterestsandwillinnowayacttotheirdisadvantage.

Natureofinvestmentproductsandservices:Unlikeotherindustries,theproductsandservicesintheinvestmentindustryareintangible.Theycannotbetouchedorphysicallyfelttojudgetheirquality.Intheinvestmentindustry,assetsareoftennotionalwithvaluesmeasuredintheformofnumbers.Forinstance,thevalueoftheinvestmentsaspresentedbyone’sfinancialadviserismerenumbersprintedelectronically.Investorstrustthattheinformationpresentedtothemiscomplete,accurate,andpresentsafairpicture.

6.Ethicalvs.LegalStandards

Thereisagreyareabetweenwhatislegallyacceptedandwhatisethical.Actinginaccordancewiththelawandactingethicallyarenotnecessarilythesame.Therearefourpossibleoutcomesforanyactionfromalegalandethicalperspective:

Notlegalbutethical:Forexample,civildisobedienceorprotestingpeacefullyagainstanissuemaynotbelegal,butitisethical.Anotherexampleofanillegalbutethicalactisthatofwhistleblowing.Whistleblowingisraisingthecurtainoffanillegalorcorruptactivity.

Notlegalandnotethical. Legalandethical. Legalbutnotnecessarilyethical:Somecountriesdonothavelawsthatprohibit

tradingwhileinpossessionofmaterialnonpublicinformation.Whilethisactoftradingislegalfromthelocalcountry’sperspective,itisconsideredunethicalbytheCFAInstituteandotherinvestmentprofessionals.

Thereareseveralreasonswhylawsarenotsufficienttoensureethicalconductamongmarketparticipants,asdiscussedbelow:

Lawsandregulationsareoftencreatedinresponsetoexistingmarketpractices.Anewlawmightaddressanexistingethicalproblembutcreateanopportunityforotherunethicalbehaviorinfuture.

Lawscanbeinterpreteddifferently.Marketparticipantsmaychoosetointerpretthelawtotheiradvantageordelaycompliancewherethereisnopunitiveaction.

Lawscanvaryacrossjurisdictions.Thismayencouragequestionablepracticetomovetoplacesthatarelessrestrictiveinnature.

Ethicalconductencouragesusto: Gobeyondwhatislegallyrequired. Considertheimpactonallstakeholders.



Makegoodchoices,evenintheabsenceofclearlawsandregulations.

7.EthicalDecision‐MakingFramework

Firmsmuststrivetodevelopastrongethicalcultureandencourageinvestmentprofessionalstoapplyethicaldecision‐makingskillseveryday;somuchsothatitbecomessecondnature.Workingandoperatinginanenvironmentthatfostersintegrityandmotivatesitsemployeestodotherightthingwillgoalongwayinpreventingunethicalactions.

Settingupanethicalframeworkreinforcesinvestmentprofessionalstodotherightthing.Theethicalframework:

Helpsinevaluatingasituationfrommultipleperspectivesafterconsideringthelargerpictureinsuchawaythatitbenefitsstakeholdersinthelongterm.Often,theimpactofadecisionorallaspectsofasituationisnotclearintheshorttermanddecisionstakeninhastemayharmstakeholdersunintentionally.

Helpsdecisionmakersjustifyactionstoabroadergroupofstakeholders.

Thefollowingethicaldecision‐makingframeworkispresentedinthecurriculum.

Identificationphase:Identifyalltherelevantfacts.Thisincludesinformationonehasandwhatonewouldliketohave.o Identifyrelevantfactssuchasdetailsoftheemployer,informationonanIPOora

deal,rulesandregulationsoftheindustry,etc.o Identifythestakeholderssuchasemployer,marketparticipants,clients,

supervisor,investors,family,etc.o Identifyrelevantethicalprinciplesforthesituation.Thismayincludeloyaltyto

employer,clients’intereststakingprecedencebeforeeverythingelse,andmaintainingtheconfidentialityofinformation.

o Identifyanypotentialconflictsofinterest,orconflictsinyourdutiestoemployers/clients.Examplesofpotentialconflictofinterestincludedutiestooneclientversusotherclientsofthefirm,financialrewardslinkedtothesuccessofadealversusdutytoemployer,anddutytosupervisorversustheneedtoimpress.

Considerationphase:Seekguidancetonavigatethroughsituationalinfluencesandpersonalbiasesthatmayaffectdecision‐making.o Examplesofsituationalinfluencesincludehowmuchfeesthefirmwillearnfrom

adeal,howmuchbonusorcompensationoneexpectstoreceivebecauseofworkingonanIPO/deal,orassociatingone’sself‐worthtoworkingonaprestigiousaccount/deal.

o Examplesofwhereonecouldseekguidanceincludethefirm’scompliancedepartment,peers,theCFAInstituteCodeandStandards,orasupervisor.

Decideandact:Makeadecisionandact. Reflect:Oncethedecisionismade,assessthedecisiontoseeifithadthedesired

outcome.Ifnot,thenanalyzethereasons:werethestakeholdersidentified,wasthere



anyconflictofinterest,weretheethicalprinciplesidentified,didyouseekguidanceonhowtodealwithsituationalinfluencesandpersonalbehavioralbiases?

Sometimestheinformationisnotsufficienttomakeadecisioninwhichcasetheprocessbecomesiterativeasyouseekguidancetogathermorerelevantinformation.



Summary

LO.a:Explainethics.

ThewordethicsisderivedfromtheGreekword‘ethos,’whichmeanscharacter.Ethicsmeansmakinggoodchoices. Ethicsincludesasetofmoralprinciplesandrulesofconductthathelpusinourbehavior.

LO.b:Describetheroleofacodeofethicsindefiningaprofession.

Professionisthefinaldevelopmentofanoccupation.Professionis:

basedonspecializedknowledgeandskills. basedonservicetoothers. practicedbymemberswhoshareandagreetoadheretoacommoncodeofethics.

Inanygivenprofession,thecodeofethicsopenlycommunicatestheestablishedprinciplesoftheprofessionandhowitsmembersareexpectedtobehave.

Ithelpsinbuildingpublicconfidencethatmembersoftheprofessionwillusetheirskillsandknowledgeforthebenefitoftheirclients.

LO.c:Identifychallengestoethicalbehavior.

Onechallengeisthatpeopletendtobelievethattheirethicalstandardsareaboveaverage.Thisleadstooverconfidencebiasandthereforepeopleplacetoomuchimportanceontheirinternaltraits.However,studiesshowthatexternalfactors(situationalinfluence)arethemaindeterminantofethicalbehavior.Theyshiftourfocustotheimmediateratherthanlong‐termimpactsofadecision.Thethreemaintypesofsituationalinfluencesare:

Money&Prestige. Loyaltytoemployerand/orcolleagues. Strongcomplianceculture.

LO.d:Describetheneedforhighethicalstandardsintheinvestmentindustry.

Highethicalstandardsarealwaysimportant.However,theyareofparticularimportanceintheinvestmentindustry,becausethisindustryisbasedalmostentirelyontrust.Alsotheproductsandservicesofthisindustryareintangibleinnature.

Clientstrustinvestmentprofessionalstousetheirskillsandknowledgefortheirbenefitandtoprotecttheirassets.

Ifinvestmentprofessionalsadheretohighethicalstandards,allstakeholdersgainlong‐termbenefits.

LO.e:Distinguishbetweenethicalandlegalstandards.

Legalandethicalconductisnotalwaysthesame.



Lawsarenotalwaysthebestmechanismtoreduceunethicalbehaviorbecause: Legalstandardsareoftencreatedtoaddresspastethicalfailings.Theydonotprovide

directionforaneverchangingandincreasinglycomplexworld. Lawsareoftenrule‐based. Lawswillvaryacrosscountries.

Ethicalconductgoesbeyondlegalstandards.

LO.f:Describeandapplyaframeworkforethicaldecision‐making.

Aframeworkforethicaldecision‐makingcanhelppeoplelookatandassessadecisionfromdifferentperspectives.Thisenablesthemtomakegooddecisions,andtolimitunplannedconsequences.

Ageneralethicaldecision‐makingframeworkhasthefollowingfoursteps.1. Identify:Relevantfacts,stakeholdersanddutiesowed,ethicalprinciples,conflictsof

interest.2. Consider:Situationalinfluences,additionalguidance,alternativeactions.3. Decideandact.4. Reflect:Wastheoutcomeasanticipated?Whyorwhynot?



PracticeQuestions

1. Whichofthefollowingstatementsismostlikelycorrect?A. Ethicscanbedescribedasasetofmoralprinciplesthatprovideguidanceforour

behavior.B. Ethicalconductisbehaviorthatbalancesone’sowninterestwithonlythedirect

consequencesofthebehavioronothers.C. Professionalassociationsadoptacodeofethicstoprotecttheirownprofessional

community.2. Whichoneofthefollowingisleastlikelyareasonforaprofessiontoestablishacodeof

ethics?A. Acodeofethicsservesasanaidindecision‐making.B. Acodeofethicshelpsinstillconfidenceamongclientsandprospectiveclients.C. Acodeofethicshelpsensurethatmembersoftheprofessionwillfollowthelaw.

3. Whichofthefollowingisleastlikelyachallengefacedbyprofessionalstodisplayethical

behavior?A. Peopletendtobelievetheyaremoreethicalthantheyactuallyare.B. Peopletendtounderestimatetheirownmorality.C. Peopletendtounderestimatetheimpactofsituationalinfluences.

4. Whichofthefollowingstatementsisleastlikelyaccurate?Trustisparticularlyimportant

intheinvestmentprofessionbecause:A. investmentprofessionalshavespecializedknowledgeandaccesstoinformationis

asymmetrical.B. productsandservicesintheinvestmentindustrytendtobeintangible.C. returnscannotbeguaranteedformosttypesofinvestments.

5. Whichofthefollowingisleastlikelyareasonforlawsbeinginsufficienttoensureethical

conductamongmarketparticipants?A. Lawscanbeinterpreteddifferently.B. Lawsarelargelythesameacrossjurisdictions.C. Passingalawtakessignificanttime.

6. Whichofthefollowingstatementsaboutethicaldecisionframeworkis/aremostlikely

accurate? Statement1:Anethicaldecisionframeworkhelpsdecisionmakersjustifyactions

tostakeholders. Statement2:Toomanychoicescanatbestleadtoinaction.



Statement3:Anethicaldecisionframeworkservesasatoolforinvestmentprofessionalstochoosethebestpossiblealternative.

A. Statement1and3.B. Statement3only.C. Statement1,2,and3.



Solutions1. Aiscorrect.StatementBisincorrectbecauseethicalconductisbehaviorthatbalances

one’sowninterestwiththedirectandindirectconsequencesofthebehavioronothers.StatementCisincorrect.

2. Ciscorrect.Thecodeofethicscannotensurethatmembersoftheprofessionwillfollow

thelaw.StatementsAandBaretrue.3. Biscorrect.Challengesfacedbyprofessionalstodisplayethicalbehaviorinclude:1)

overestimatingone’smoralityand2)underestimatingtheeffectofsituationalinfluences.4. Ciscorrect.StatementAandBarevalidreasonsfortrustbeingimportantinthe

investmentprofession.Cdoesnotrepresentareasonforwhytrustisparticularlyimportantintheinvestmentindustry.

5. Biscorrect.Lawscanvaryacrossjurisdictions.Thismayencouragequestionable

practicetomovetoplacesthatarelessrestrictiveinnature.StatementsAandCarevalidreasonsforwhythelawalonemightbeinsufficienttoensureethicalbehavior.

6. Ciscorrect.Allthreestatementsregardingethicaldecisionframeworksarecorrect.

R02 Code of Ethics and Standards of Professional Conduct 2019 Level I Notes


R02CodeofEthicsandStandardsofProfessionalConduct

Introduction

TheCodeofEthicsandStandardsofProfessionalConduct(CodeandStandards)stipulaterulesandguidelinesforCFAInstitutemembersandcandidatesonhowtoconductthemselvesinaprofessionalandethicalmanner,withintegrity,underallcircumstancesforthebenefitofsociety.

CFAInstituteProfessionalConductProgram

AllCFAInstitutemembersandcandidatesenrolledintheCFAprogramarerequiredtocomplywiththeCodeandStandards.TheProfessionalConductProgram(PCP),inconjunctionwiththeDisciplinaryReviewCommittee(DRC),isresponsibleforenforcementoftheCodeandStandards.

TheDRCisavolunteercommitteeofCFAcharterholderswhoserveonpanelstoreviewconductandpartnerwithprofessionalconductstafftoestablishandreviewprofessionalconductpolicies.

TheCFAInstituteBylawsandRulesofProcedureforProfessionalConductformthebasicstructureforenforcingtheCodeandStandards.

ProfessionalConductinquiriescanbepromptedbyseveralreasons: Self‐disclosure:OntheannualProfessionalConductStatement,membersdiscloseif

theyhavebeenasubjectofcivillitigationorcriminalinvestigation. Writtencomplaints:ThePCPstaffmayreceivewrittencomplaints. Evidenceofmisconduct:ThePCPstaffmaycomeacrossviolationsthroughmediaor

anypublicsource. ReportbyaCFAexamproctor:Ifacandidateviolatedanyrulesonexamdayandis

reportedbytheproctor. CFAInstitutemayconductanalysisofscoresandexammaterialsaftertheexam,as

wellasmonitoronlineandsocialmediatodetectdisclosureofconfidentialexaminformation.Forinstance,ifafriendsitsfortheexaminAustraliaanddiscussesspecificquestionsonlineaftertheexamwhileyouareintheUnitedStateswheretheexamhasn’tstarted,itcanbeconsideredaviolationoftheCodeandStandards.

Afteraninquiryisinitiated,theprofessionalconductteamconductsaninvestigation.IftheprofessionalconductstaffbelievesaviolationoftheCodeandStandardshasoccurred,theyproposesanctionswhichcaninclude:publiccensure,suspensionofmembershipanduseoftheCFAdesignation,andrevocationoftheCFAcharter.CandidatesmaybesuspendedorprohibitedfromfurtherparticipationintheCFAprogram.

Thememberorcandidatehastheopportunitytoacceptorrejectanychargesandtheproposedsanctions.Ifthemember/candidateacceptstheviolation,thenthesanctionswillbeimposed.Ifthemember/candidatedoesnotacceptthechargesortheproposedsanctions,



thematterisreferredtotheDRC,whichreviewsmaterialsandpresentationsfromprofessionalconductstaffandfromthememberorcandidate.Thepanel’staskistodeterminewhetheraviolationoftheCodeandStandardsortestingpolicieshasoccurredand,ifso,whatsanctionshouldbeimposed.

CodeofEthics

MembersoftheCFAInstitute(includingCFAcharterholders)andcandidatesfortheCFAdesignation(“Membersandcandidates”)must:

1. Actwithintegrity,competence,diligence,andrespectandinanethicalmannerwiththepublic,clients,prospectiveclients,employers,employees,colleaguesintheinvestmentprofession,andotherparticipantsintheglobalcapitalmarkets.

2. Placetheintegrityoftheinvestmentprofessionandinterestsofclientsabovetheirownpersonalinterests.

3. Usereasonablecareandexerciseindependentprofessionaljudgmentwhenconductinginvestmentanalysis,makinginvestmentrecommendations,takinginvestmentactions,andengaginginotherprofessionalactivities.

4. Practiceandencourageotherstopracticeinaprofessionalandethicalmannerthatwillreflectcreditonthemselvesandtheprofession.

5. Promotetheintegrityandviabilityoftheglobalcapitalmarketsfortheultimatebenefitofsociety.

6. Maintainandimprovetheirprofessionalcompetenceandstrivetomaintainandimprovethecompetenceofotherinvestmentprofessionals.

Instructor’sNote:ThesixcomponentsofCodeofEthics,outlinedabove,areimportantandshouldbememorized.

StandardsofProfessionalConduct

TherearesevenStandardsofProfessionalConduct.Eachstandardhassub‐sections.Thestandardsarecoveredindetailinthenextreading.

I. ProfessionalismII. IntegrityofCapitalMarketsIII. DutiestoClientsIV. DutiestoEmployersV. Investmentanalysis,Recommendations,andActionsVI. ConflictsofInterestVII. ResponsibilitiesasaCFAInstituteMember,orCFACandidate

I. Professionalism



A. KnowledgeoftheLawMembersandCandidatesmustunderstandandcomplywithallapplicablelaws,rules,andregulations(includingtheCFAInstituteCodeofEthicsandStandardsofProfessionalConduct)ofanygovernment,regulatoryorganization,licensingagency,orprofessionalassociationgoverningtheirprofessionalactivities.Intheeventofconflict,MembersandCandidatesmustcomplywiththemorestrictlaw,rule,orregulation.MembersandCandidatesmustnotknowinglyparticipateorassistinandmustdissociatefromanyviolationofsuchlaws,rules,orregulations.

B. IndependenceandObjectivityMembersandCandidatesmustusereasonablecareandjudgmenttoachieveandmaintainindependenceandobjectivityintheirprofessionalactivities.MembersandCandidatesmustnotoffer,solicit,oracceptanygift,benefit,compensation,orconsiderationthatreasonablycouldbeexpectedtocompromisetheirownoranother’sindependenceandobjectivity.

C. MisrepresentationMembersandCandidatesmustnotknowinglymakeanymisrepresentationsrelatingtoinvestmentanalysis,recommendations,actions,orotherprofessionalactivities.

D. MisconductMembersandCandidatesmustnotengageinanyprofessionalconductinvolvingdishonesty,fraud,ordeceitorcommitanyactthatreflectsadverselyontheirprofessionalreputation,integrity,orcompetence.

II. IntegrityofCapitalMarkets

A. MaterialNonpublicInformationMembersandCandidateswhopossessmaterialnonpublicinformationthatcouldaffectthevalueofaninvestmentmustnotactorcauseotherstoactontheinformation.

B. MarketManipulationMembersandCandidatesmustnotengageinpracticesthatdistortpricesorartifciallyinflatetradingvolumewiththeintenttomisleadmarketparticipants.

III. DutiestoClients

A. Loyalty,prudence,andcareMembersandCandidateshaveadutyofloyaltytotheirclientsandmustactwithreasonablecareandexerciseprudentjudgment.MembersandCandidatesmustactforthebenefitoftheirclientsandplacetheirclients’interestsbeforetheiremployer’sortheirowninterests.

B. FairDealingMembersandCandidatesmustdealfairlyandobjectivelywithallclientswhenprovidinginvestmentanalysis,makinginvestmentrecommendations,takinginvestmentaction,orengaginginotherprofessionalactivities.



C. Suitability1. WhenMembersandCandidatesareinanadvisoryrelationshipwithaclient,they

must:a. Makeareasonableinquiryintoaclient’sorprospectiveclient’sinvestment

experience,riskandreturnobjectives,andfinancialconstraintspriortomakinganyinvestmentrecommendationortakinginvestmentactionandmustreassessandupdatethisinformationregularly.

b. Determinethataninvestmentissuitabletotheclient’sfinancialsituationandconsistentwiththeclient’swrittenobjectives,mandates,andconstraintsbeforemakinganinvestmentrecommendationortakinginvestmentaction.

c. Judgethesuitabilityofinvestmentsinthecontextoftheclient’stotalportfolio.

2. WhenMembersandCandidatesareresponsibleformanagingaportfoliotoaspecificmandate,strategy,orstyle,theymustmakeonlyinvestmentrecommendationsortakeonlyinvestmentactionsthatareconsistentwiththestatedobjectivesandconstraintsoftheportfolio.

D. PerformancePresentationWhencommunicatinginvestmentperformanceinformation,MembersandCandidatesmustmakereasonableeffortstoensurethatitisfair,accurate,andcomplete.

E. PreservationofConfidentialityMembersandCandidatesmustkeepinformationaboutcurrent,former,andprospectiveclientsconfidentialunless:

1. Theinformationconcernsillegalactivitiesonthepartoftheclientorprospectiveclient,

2. Disclosureisrequiredbylaw,or

3. Theclientorprospectiveclientpermitsdisclosureoftheinformation.

IV. DutiestoEmployers

A. LoyaltyInmattersrelatedtotheiremployment,MembersandCandidatesmustactforthebenefitoftheiremployerandnotdeprivetheiremployeroftheadvantageoftheirskillsandabilities,divulgeconfidentialinformation,orotherwisecauseharmtotheiremployer.

B. AdditionalCompensationArrangementsMembersandCandidatesmustnotacceptgifts,benefits,compensation,orconsiderationthatcompeteswithormightreasonablybeexpectedtocreateaconflictofinterestwiththeiremployer’sinterestunlesstheyobtainwrittenconsentfromallpartiesinvolved.

C. ResponsibilitiesofSupervisors



MembersandCandidatesmustmakereasonableeffortstoensurethatanyonesubjecttotheirsupervisionorauthoritycomplieswithapplicablelaws,rules,regulations,andtheCodeandStandards.

V. InvestmentAnalysis,Recommendations,andActions

A. DiligenceandReasonableBasisMembersandCandidatesmust:

1. Exercisediligence,independence,andthoroughnessinanalyzinginvestments,makinginvestmentrecommendations,andtakinginvestmentactions.

2. Haveareasonableandadequatebasis,supportedbyappropriateresearchandinvestigation,foranyinvestmentanalysis,recommendation,oraction.

B. CommunicationwithClientsandProspectiveClientsMembersandCandidatesmust:

1. Disclosetoclientsandprospectiveclientsthebasicformatandgeneralprinciplesoftheinvestmentprocessestheyusetoanalyzeinvestments,selectsecurities,andconstructportfoliosandmustpromptlydiscloseanychangesthatmightmateriallyaffectthoseprocesses.

2. Disclosetoclientsandprospectiveclientssignificantlimitationsandrisksassociatedwiththeinvestmentprocess.

3. Usereasonablejudgmentinidentifyingwhichfactorsareimportanttotheirinvestmentanalyses,recommendations,oractionsandincludethosefactorsincommunicationswithclientsandprospectiveclients.

4. Distinguishbetweenfactandopinioninthepresentationofinvestmentanalysisandrecommendations.

C. RecordRetentionMembersandCandidatesmustdevelopandmaintainappropriaterecordstosupporttheirinvestmentanalyses,recommendations,actions,andotherinvestment‐relatedcommunicationswithclientsandprospectiveclients.

VI. ConflictsofInterest

A. DisclosureofConflictsMembersandCandidatesmustmakefullandfairdisclosureofallmattersthatcouldreasonablybeexpectedtoimpairtheirindependenceandobjectivityorinterferewithrespectivedutiestotheirclients,prospectiveclients,andemployer.MembersandCandidatesmustensurethatsuchdisclosuresareprominent,aredeliveredinplainlanguage,andcommunicatetherelevantinformationeffectively.

B. PriorityofTransactions



InvestmenttransactionsforclientsandemployersmusthavepriorityoverinvestmenttransactionsinwhichaMemberorCandidateisthebeneficialowner.

C. ReferralFeesMembersandCandidatesmustdisclosetotheiremployer,clients,andprospectiveclients,asappropriate,anycompensation,consideration,orbenefitreceivedfromorpaidtoothersfortherecommendationofproductsorservices.

VII. ResponsibilitiesasaCFAInstituteMemberorCFACandidate

A. ConductasparticipantsinCFAInstituteProgramsMembersandCandidatesmustnotengageinanyconductthatcompromisesthereputationorintegrityofCFAInstituteortheCFAdesignationortheintegrity,validity,orsecurityofCFAInstituteprograms.

B. ReferencetoCFAInstitute,theCFAdesignation,andtheCFAprogramWhenreferringtoCFAInstitute,CFAInstitutemembership,theCFAdesignation,orcandidacyintheCFAProgram,MembersandCandidatesmustnotmisrepresentorexaggeratethemeaningorimplicationsofmembershipinCFAInstitute,holdingtheCFAdesignation,orcandidacyintheCFAProgram.



Summary

LO.a:DescribethestructureoftheCFAInstituteProfessionalConductProgramandtheprocessfortheenforcementoftheCodeandStandards.

TheProfessionalConductProgram(PCP),inconjunctionwiththeDisciplinaryReviewCommittee(DRC),isresponsibleforenforcementoftheCodeandStandards.TheCFAInstituteBylawsandRulesofProcedureforProfessionalConductformthebasicstructureforenforcingtheCodeandStandards.ProfessionalConductinquiriescanbepromptedby:self‐disclosure,writtencomplaintsandevidenceofmisconduct,andreportbyaCFAexamproctor.

IftheprofessionalconductstaffbelievesaviolationoftheCodeandStandardshasoccurred,sanctionsareproposed.Ifthemember/candidatedoesnotacceptthechargesorthesanctions,thematterisreferredtotheDRC,whichreviewsmaterialsandpresentationsfromprofessionalconductstaffandfromthememberorcandidate.TheDRCmakesafinaldecisiononwhethertherewasaviolationandifsowhatsanctionsmustbeimposed.

LO.b:StatethesixcomponentsoftheCodeofEthicsandthesevenStandardsofProfessionalConduct.

MembersoftheCFAInstitute(includingCFAcharterholders)andcandidatesfortheCFAdesignation(“Membersandcandidates”)must:

1. Actwithintegrity,competence,diligence,andrespectandinanethicalmannerwiththepublic,clients,prospectiveclients,employers,employees,colleaguesintheinvestmentprofession,andotherparticipantsintheglobalcapitalmarkets.

2. Placetheintegrityoftheinvestmentprofessionandinterestsofclientsabovetheirownpersonalinterests.

3. Usereasonablecareandexerciseindependentprofessionaljudgmentwhenconductinginvestmentanalysis,makinginvestmentrecommendations,takinginvestmentactions,andengaginginotherprofessionalactivities.

4. Practiceandencourageotherstopracticeinaprofessionalandethicalmannerthatwillreflectcreditonthemselvesandtheprofession.

5. Promotetheintegrityandviabilityoftheglobalcapitalmarketsfortheultimatebenefitofsociety.

6. Maintainandimprovetheirprofessionalcompetenceandstrivetomaintainandimprovethecompetenceofotherinvestmentprofessionals.

LO.c:ExplaintheethicalresponsibilitiesrequiredbytheCodeandStandards,includingthesub‐sectionsofeachStandard.

Coveredinthenextreading.

R03 Guidance for Standards I-VII 2019 Level I Notes


R03GuidanceforStandardsI‐VII

Introduction

Thisisalongreading,whichprovidesguidanceandrecommendedcomplianceproceduresforeachstandard.Severalexamplesarealsogivenonhowthestandardsshouldbeapplied.IFTNotesfocusontheguidanceandrecommendedcomplianceprocedures.Readtheexamples(applicationsofthestandards)fromthecurriculum.

StandardI:Professionalism

Standard1(A)KnowledgeoftheLaw

MembersandCandidatesmustunderstandandcomplywithallapplicablelaws,rules,andregulationsofanygovernment,regulatoryorganization,licensingagency,orprofessionalassociationgoverningtheirprofessionalactivities.Intheeventofconflict,MembersandCandidatesmustcomplywiththemorestrictlaw,rule,orregulation.MembersandCandidatesmustnotknowinglyparticipateorassistinandmustdissociatefromanyviolationofsuchlaws,rules,orregulations.

Interpretation:

You,asamemberorcandidate,mustbeawareofalllawswhereyouconductbusiness.Statingthatyouarenotawareofthelawsandhenceaviolationoccurred,willnotbeacceptable.

Guidance: RelationshipbetweentheCodeandStandardsandApplicableLaw:Assumeyouarean

investmentadviserbasedinMalaysia.YouareaMalaysiancitizenandyourclientsarealsobasedinMalaysia.HeretheMalaysianlawisthe‘applicablelaw’.AsaLevelIcandidate,theCodeandStandardsmustalsobeconsidered.Let’sassumethatMalaysianlawsprohibitparticipationofinvestmentadvisersinIPOsbuttheCodeandStandardsallowparticipationunderspecifiedcircumstances,thenyouhavetofollowthestricterlaw–theMalaysianlawinthiscase.Ifthereisnoapplicablelaworregulation,thenMembersandCandidatesmustfollowtheCodeandStandards.

Investmentproductsandapplicablelaws:Followthemorestrictlaw. Participationinorassociationwithviolationsbyothers:Youareresponsiblefor

violationsinwhichyouknowinglyparticipateorassist.Knowinglyisthekeywordhere.Assumeyouarepartofagroupandyouhavereasonablegroundstobelieveaviolationistakingplace.Undersuchcircumstances:o First,makeanattempttostopthebehaviorbybringingittothenoticeofyour

supervisor/compliancedepartment.o Seektheadviceofindependentlegalcounselifthecompliancedepartmentwasnot

helpful.



o Dissociateyourselfwiththatactivity.Dissociationvariesbasedonyourroleintheorganization;itcouldbe: Removingyournamefromtheinvestmentreportsandrecommendations. Askingforadifferentassignment. Refusingtoacceptanewclientorcontinuingtoadvisethecurrentclient.

o Inextremecases,leavetheorganization. Nottakinganactionafterreportingaviolation(andcontinuingassociationwiththe

illegalactivity),canbeconsideredasparticipatingintheillegalorunethicalconduct. Ifyouarenotsurethataviolationistakingplace,thentheappropriateactionwouldbe

toseektheadviceoflegal/compliancecounsel. CFAInstitutedoesnotcompelyoutoreportviolationstothegovernmentorregulatory

organizationunlessrequiredbylaw.

Recommendedproceduresforcompliance: Stayinformed:Haveaprocedureorregulartrainingtokeepemployeesinformedofthe

changesinapplicablelaws,rules,regulationsetc. Reviewprocedures:Periodicallyreviewfirm’swrittencomplianceprocedurestoensure

itconformstotheapplicablelaw. Maintaincurrentfiles:Latestcopiesofapplicablerulesandregulationsshouldbe

availableforreference. Legalcounsel:Ifindoubthowtorespondtoapossibleviolation,seektheadviceof

legal/compliancepersonnel. Dissociation:Documenttheviolationifyouaredissociatingfromanillegalactivity;urge

thefirmtotakestepstoceasetheactivity,andresigninextremecases. Advise/encourageyourfirmto:

o Developand/oradoptacodeofethics.o Provideinformationonapplicablelaws:makealltheinformationregardinglaws

andrulesavailableinacentrallocation.o Establishproceduresforreportingviolations:makeiteasytoreportviolations.

Standard1(B)IndependenceandObjectivity

MembersandCandidatesmustusereasonablecareandjudgmenttoachieveandmaintainindependenceandobjectivityintheirprofessionalactivities.MembersandCandidatesmustnotoffer,solicit,oracceptanygift,benefit,compensation,orconsiderationthatreasonablycouldbeexpectedtocompromisetheirownoranother’sindependenceandobjectivity.

Interpretation:

Maintainindependenceandobjectivity.Donotcompromiseyourindependenceandobjectivityunderanycircumstanceasitcanhurtnotjustyourfirm,butthewholeindustry.Forinstance,assumeyouarewritingaresearchreportandthefirmyouarecoveringgives



youanexpensivegift.Acceptingthegiftmayshroudyourjudgmenttobeimpartialandgiveanobjectivereport.

Guidance: Buy‐sideclients:Assumeyouworkintheresearchdepartmentofalargebrokerage(buy‐

side)firmandyoucoverpharmaceuticalfirms.Yourresearchreportsaredisseminatedtoinstitutionalclients(buy‐sideclients)suchasmutualfunds.Mutualfundswithlargepositionsinpharmastocksmighttrytoinfluenceyoutowritepositivereports.However,itisimportantforyou,nottosuccumbtopressure.Independenceandobjectivitymustbemaintained.

Investmentbankingrelationships:Nowassumeyourfirmalsohasaninvestmentbanking(IB)division.Pfizerisaclientofthefirm,andtheIBdivisionisworkingcloselyonPfizer’ssecondaryoffering.TheIBdivisionmayinfluenceresearchanalyststoissuefavorableresearchreports.But,asananalyst,youmustmaintainyourobjectivity.

Publiccompanies:Publiccompaniesmaytrytoinfluenceanalyststowritepositiveresearchreports.

Issuer‐paidresearch:Assumeacompanyisnotbeingwidelyfollowed.Ifthiscompanyapproachesyoutowritearesearchreportforthem,andcompensatesyou,thenthereisapotentialconflictofinterest.Thebestpracticeforindependentanalystsistonegotiateaflatfeeforthereport.Thefeeshouldbeindependentoftheeventualrecommendation.Disclosureofthetypeofcompensationisalsoimportant.

Travelfunding:Itisbestforcandidatestousecommercialtransportationpaidforbytheirfirm,andnottheclient.Ifcommercialtransportationisunavailable,membersandcandidatesmayacceptmodestlyarrangedtravel,toparticipateinappropriateinformation‐gatheringevents,suchasapropertytour.

Creditratingagencyopinions:Creditratingagenciesprovideratingsforfixed‐incomeproducts.Ifyouareworkingataratingagency,youmaybeofferedincentivesandcompensationbythesponsoringcompany(companiesissuingbonds)toissueafavorablerating.However,youshouldbeobjectiveabouttheanalysisandensuretheprocessesatyouragencydonotresultinaconflictofinterest.

Influenceduringthemanagerselection/procurementprocess:Assumealargepensionfundisintheprocessofselectinganassetmanagementcompany(AMC)tomanagetheirassets.Inordertogetthisbusiness,AMCsmaytrytoinfluencethehiringmanageratthepensionfundbygivinggifts,etc.Irrespectiveofwhichsideyouareintheprocess(pensionfundorAMCwhichisseekingbusiness),donotsolicitgiftsorcontributionseitherdirectlyorindirectlythatmayaffectyourindependence.

Brokeragehouses:Membersandcandidateshiresecondaryfundmanagerstomanagespecificassets,fortradingandreporting.Theremaybeattemptstoinfluencethemwithgiftsorcompensation.Itisimportantformemberstonotacceptsuchgiftsandstayobjectiveaboutthehiringdecision.



RecommendedProceduresforCompliance: Protecttheintegrityofopinions. Createarestrictedlistforcompanieswhereafirmwantstodisseminateonlyfactual

information,andnonegativeorpositiveopinion. Restrictspecialcostarrangements:usecorporateaircraftonlyifcommercial

transportationisnotavailable. Limitgifts:astrictlimitfortokengiftsthatcanbeacceptedmustbeestablished. Restrictinvestments:Enforcepriorapprovalforemployeespurchasingequityorequity‐

relatedIPOs. Reviewprocedures. Establishanindependencepolicy. Appointedofficer:appointaseniorofficertoensurecompliancewiththefirm’scodeof

ethics.

Standard1(C)Misrepresentation

MembersandCandidatesmustnotknowinglymakeanymisrepresentationsrelatingtoinvestmentanalysis,recommendations,actions,orotherprofessionalactivities.

Amisrepresentationisanyuntruestatement,oromissionoffact,oranystatementthatisotherwisefalseormisleading.

Interpretation:

Thefoundationofanyclient‐customerrelationshipistrust.Iftrustislostbecauseofmisrepresentingfacts,itnotonlyhurtsyou,butalsohurtsconfidenceintheentireprofessionandintegrityofcapitalmarketsaswell.

Guidance: Impactoninvestmentpractice:Assumeyourfirmhasbeenmanagingalargecapequity

fundforseveralyearsandhasaddedasmallcapfundlastyear.Ifthefirmclaimsithasyearsofexperiencemanagingsmallcapfunds/stocks,thenitwouldbemisrepresentingfacts.o Membersandcandidatesmustnotmisrepresentfactsincludingtheirqualifications,

orcredentials.Forinstance,ifyouhaveclearedonlytwolevelsoftheCFAprogram,youcannotclaimtobeaCFAcharterholder.

o Whenissuingaresearchreport,youmaybeusingthird‐partyinformation.Youmustexercisecareanddiligencewhenusingthird‐partyinformationsuchascreditratings,research,ormarketingmaterials,toensurethereisnomisrepresentation.

o Ifyouareusingexternalmanagerstomanagespecificareas,youmustnotrepresenttheirinvestmentpracticesasyourown.



Performancereporting:o Ifyouhavechosenabenchmarkforyourportfolio,arethestrategiesofboth

comparable?Areyouchoosingabenchmarkbecauseitmakestheportfolio’sperformancelookbetter?

o Youmustensuretheperformanceevaluationofyourportfoliohasareasonablebasis.

o Providepricinginformationofsecuritiestoclientsonaconsistentbasis.Donotchangepricingproviderssolelyonthebasisofhighervalueofasecurity.Thisisespeciallytrueofilliquidsecurities.Thiswillbemisrepresentinginformationasinvestorsmakethedecisionofwhetherornottoholdanilliquidsecuritybasedontheinformationprovided.

Socialmedia:ThelanguageusedonsocialmediaplatformssuchasFacebookandTwitterisofteninformal.However,membersandcandidatesmustensuretheinformationprovidedisthesameasintraditionalmodesofcommunication.TheformatmustadheretotheCodeandStandards,eventhoughthereisagreatdealofanonymity.

Omissions:Factsoroutcomesmustnotbeomitted,especiallywhenitcomestoperformancemeasurementandattribution.Forexample,assumeamanagerhadexceptionalperformanceinthepastthreeyears,butnegativereturnsinthethreeyearsprecedingit.Hemustpresenttheperformancefortheentireperiodandnotomityearsofbadperformance;thatiscalledcherrypicking(orselectivepresentation).

Plagiarism:Plagiarismisusingtheworkofotherswithoutacknowledgingorattributingthesourceofinformation.Examplesinclude:o Usingtheresearchreportofanotherfirm,andthenredistributingitbychangingthe

names.o Aresearchreportbasedonmultiplesourcesofinformationwithoutnamingthe

sources.o Excerptsfromarticleswithlittleornochangeinwording.o Notnamingspecificreferences,butinsteadattributingto“leadinginvestment

analysts”.o Usingchartsandgraphswithoutnamingtheirsources.

MembersandCandidatesmustdisclosethesourceofinformationusedintheirreports.Ifitispaidfor,thenitmustbedisclosed.Sentencesreproducedmustbewithinquotesandtheauthornamedspecifically.

Workcompletedforemployer:Work(models/reports/research)donewithinafirmmaybeusedbyothersinthefirmwithoutattribution.Ifthepersonwhodevelopedamodelhasleftthefirm,thefirmcancontinueusingitasitisapropertyofthefirmwithoutnamingtheperson.However,noonecanclaimthattheworkdonebythepersonwhohasquitthefirmhasbeendonebytheonewhoisnowusingit.



RecommendedProceduresforCompliance: Factualpresentations:Eachmemberandcandidatemustbeawareofthefirm’sandthe

individual’scapabilitiesandlimitations.Awrittenlistofthefirm’savailableservicesshouldguidetheemployeeswhopresenttoclients.

Qualificationsummary:Eachmemberandcandidateshouldprepareasummaryofhis/herqualificationsandexperiencetopresenttoclients.Thesemustbeperiodicallyreviewed.

Verifyoutsideinformation:Ensurematerialfromathird‐partyisaccuratebeforepresentingittoclients.

Maintainwebpages:Anyinformationpublishedonawebpagemustbecurrent,andaccurate.

Plagiarismpolicy:Maintaincopiesofresearchreports/articlesusedinmakingyourresearchreport,attributequotationstotheirsource,andattributesummariestotheirsources.

Standard1(D)Misconduct

MembersandCandidatesmustnotengageinanyprofessionalconductinvolvingdishonesty,fraud,ordeceitorcommitanyactthatreflectsadverselyontheirprofessionalreputation,integrity,orcompetence.

Guidance:

Anyactthatinvolveslying,cheating,stealing,orotherdishonestconductisaviolationofthisstandardiftheoffensereflectsadverselyonamember’sorcandidate’sprofessionalactivities.AlthoughCFAInstitutediscouragesanysortofunethicalbehaviorbymembersandcandidates,theCodeandStandardsareprimarilyaimedatconductandactionsrelatedtoamember’sorcandidate’sprofessionallife.Someimportantpointsbasedonexamplesseenoften: Usingalcoholduringbusinesshours,thoughnotillegalimpairsaperson’sabilitytothink

objectively. Ifamemberorcandidatedeclarespersonalbankruptcy,itisnotmisconduct.But,ifthe

circumstancesthatledtobankruptcyincludedeceitorfraud,thenitwouldbeaviolationanddeemedasmisconduct.

RecommendedProceduresforCompliance: Codeofethics:Adoptacodeofethicsthateverymembermustadhereto. Listofviolations:Communicatetoallemployeesalistofpotentialviolationsandthe

associatedsanctions. Employeereferences:Dobackground(reference)checksofemployeestoensurethey

havenothadabrushwiththelawinthepastandareeligibletoworkintheinvestmentprofession.



StandardII:IntegrityofCapitalMarkets

StandardII(A)MaterialNonpublicInformation

MembersandCandidateswhopossessmaterialnonpublicinformationthatcouldaffectthevalueofaninvestmentmustnotactorcauseotherstoactontheinformation.

Guidance: Whatismaterialinformation?:Thisisinformationthat,ifdisclosed,canhaveanimpact

onthepriceofasecurity,orinformationthatinvestorswouldwanttoknowbeforemakinganinvestmentdecision.Forexample,informationthattheCEOofacompanywasinvolvedinascandaltomanipulatefinancialstatementsandisgoingtobearrested,ismaterialinformation.Othercommonexamplesincludemergersandacquisitions,newproductlicenses,changesinmanagement,bankruptcies,legaldisputes,etc.

Whatconstitutes“nonpublic”information?:Asthenameimplies,informationthathasnotbeenmadepubliciscallednonpublicinformation.Forinstance,ifapharmaceuticalcompanyhasjustreceivednewsthataparticulardrughasbeenapprovedbyFDAanditisnotmadepublicyet,thenitconstitutesnonpublicinformation.Thisisalsomaterialinformationasitissomethinginvestorswouldliketoknowbeforeinvestinginthecompany.

Mosaictheory:AspertheMosaictheory,analystsarefreetoactonpublicandnonmaterialnonpublicinformationwithoutriskingviolation.Let’stakeanexamplefromthecurriculum.Ananalystisresearchingacompanyinthefurnitureindustry.Heanalyzesthepublicdisclosures,andspeakswithmanyfurnitureretailersonwhichhebaseshisrecommendationreport.Theinformationgatheredfromfurnitureretailersisanexampleofnonmaterialnonpublicinformationbecausetheinformationisnotpublic,andnotmaterialbyitselftoinfluencethestockpricesinanyway.

Socialmedia:Membersandcandidatesmustensurethatinformationobtainedfromclosedgroupsonsocialmedia(Facebook,LinkedIn)isaccessibletothepublicthroughothersources.

Usingindustryexperts:Usingexpertsisappropriateaslongasmembersarenotrequestingoractingonmaterialnonpublicinformation.

Investmentresearchreports:Assumeyouareawell‐knownanalystandyourrecommendationreportsmightimpactstockprices.Sinceyouarenotaninsideranddidnotbaseyourreportoninsiderinformation,StandardII(A)doesnotapply.Inthiscase,youarenotrequiredtomakethereportpublic.Ifthepublicwantsaccesstothereport,theycanbeaskedtopayforyourservices.

RecommendedProceduresforCompliance: Achievepublicdissemination:Takestepstopubliclydisseminatematerialnonpublic

information.Ensurenoinvestmentactionistakenbasedontheinformation.



Adoptcomplianceprocedures:Adoptcomplianceprocedurestopreventthemisuseofmaterialnonpublicinformation.Ex:reviewemployeetrading,investmentrecommendations,andinterdepartmentalrecommendations.

Adoptdisclosureprocedures:Sameinformationshouldbecommunicatedtothemarketinanequitablemanner.Theinformationreceivedbybuy‐sideclientsshouldbethesameassell‐sideclients,andthesamegoesforlargefirmsandsmallfirms.

Issuepressreleases:Pressreleasesmustbemadebeforeconferencecallsandanalystmeetingssothatnewinformationisdisclosedatsuchgatherings.

Firewallelements:Afirewallisaninformationbarriercreatedtopreventtheflowofmaterialnonpublicinformationwithinafirm;forinstance,betweenthebrokerageandinvestmentbankingdepartmentsofafirm.Listedbelowareafewwaysafirewallisimplemented:o Reviewofemployeetrading.o Routeinterdepartmentalcommunicationsthroughthecomplianceorlegal

department.o Documenthowtoenforceprocedurestolimitinformationflowwithinthefirm.o Review/restrictproprietarytradingwhenafirmisinpossessionofmaterial

nonpublicinformation. Appropriateinterdepartmentalcommunications:Documentproceduresforhow

interdepartmentalcommunicationsmustoccur,reviewtradingactivity,andwhatactionstotakeifviolationsoccur.

Physicalseparationofdepartments:Topreventsensitiveinformationflowingfromonedepartmenttoanother.Ex:IB/corporatefinancetobephysicallyseparatedfromsalesandresearchofabrokeragefirm.

Preventionofpersonneloverlap:Anemployeeshouldbeononlyonesideofthefirewall.Forinstance,anemployeeworkinginthecommerciallendingdepartmentofabankmustnotbeassociatedwithitstrust/researchdepartments.

Areportingsystem:Haveareportingsysteminwhichauthorizedpeoplecanreviewandapprovecommunicationsbetweendepartments.Ifsharingofcertaininformationisnecessaryacrossthefirewall,thenadesignatedofficermustascertainwhethersharingisessentialandmustmonitortheprocess.

Personaltradinglimitations:Enforcerestrictionsonpersonaltradingbyemployees.Monitorbothproprietaryandpersonaltrading.

Recordmaintenance:Maintainrecordsofinterdepartmentalcommunication. Proprietarytradingprocedures:Outlineproceduresforunderwhatsituationsthere

shouldberestrictionsonproprietarytrading:o Marketmaking:Restrictionsontradingifthefirmisamarketmakercanbe

counterproductiveasitmaybeasignaltotradersthatthefirmisinpossessionofsomematerialnonpublicinformation.Thefirmmusttakethecontrasideofunsolicitedcustomertrades.



o Arbitragetrading:Mustnotengageinproprietarytradingifitisinpossessionofsensitiveinformation.

Communicatetoallemployees:Educateemployeesthroughtrainingsonhowtoidentifymaterialnonpublicinformationandhowtoact(consultasupervisor/complianceofficer)iftheypossesssuchinformation.Circulatewrittencompliancepoliciesandprocedurestoallemployees.

StandardII(B)MarketManipulation

MembersandCandidatesmustnotengageinpracticesthatdistortpricesorartificiallyinflatetradingvolumewiththeintenttomisleadmarketparticipants.

Whatitincludes: Disseminatingfalseinformationintothemarket. Misleadingmarketparticipantsbydistortingprices.

Guidance: Information‐basedmanipulation:Spreadingfalserumorstoinducetradingbyothers.For

example,ananalystmaypumpfalseinformationintothemarketthroughblogsorsomeothermediatoartificiallyinflatestockprices.

Transaction‐basedmanipulation:Transactionsthatartificiallyaffectthepricesorvolumeofasecurity.Forexample,iftransactionsshowasecuritytobemoreliquid,thenmarketparticipantsperceiveitfavorablyandmaybuy.Forexample,alargefirmmayhaveofficesinTokyoandChicago.Oneofficemaysellalargenumberofsharesandtheotherofficemaybuy.Whileitmayappearasiftheliquidity/tradingvolumeofthesecurityisup.But,inreality,thetradingwaswithinthefirm.

StandardIII:DutiestoClients

StandardIII(A)Loyalty,Prudence,andCare

MembersandCandidateshaveadutyofloyaltytotheirclientsandmustactwithreasonablecareandexerciseprudentjudgment.MembersandCandidatesmustactforthebenefitoftheirclientsandplacetheirclients’interestsbeforetheiremployer’sortheirowninterests.

Interpretation:

Clientinterestscomefirst,followedbytheemployerand,then.personalinterestsofthememberorcandidate.Theonlyexceptionisthattheintegrityofcapitalmarketsmusttakeprecedenceovertheclient’sinterestsifthereisaconflict.Prudencerequirescautionanddiscretion.Whenhandlingfundsofaclient,prudencerequiresthatyoutreatthemwiththesameskill,care,anddiligenceasyouwouldtreatyourownfunds.



Guidance: Understandingtheapplicationofloyalty,prudence,andcare:Investmentadvisershave

differentjobroles;somehavefiduciaryresponsibilitiesthatareimposedbylawandrequireahigherleveloftrustthanotherbusinessroles.Irrespectiveofwhetherornottheyareinafiduciaryrole,membersandcandidatesareexpectedtoworkintheclient’sbestinterest,andbeloyal,prudent,andexercisecareinmanagingtheclient’sportfolio.

Identifyingtheactualinvestmentclient:Identifywhoistheactualclient.It’softeneasytodefineaclientbutthereareinstanceswhenitmaynotbeclear.Forexample,ifapensionplanhiresaninvestmentmanager,thentheclientisnotthepensionplanbutthebeneficiariesoftheplan.Inthiscasethehiringentityisnotyourclient.Insomecases,theremaynotbeanydirectclientsorbeneficiaries.Ex:afundmanagermanagingthefundtoanindex.Insuchcases,fundmanagersshouldinvestaccordingtothestatedmandate.

Developingtheclient’sportfolio:Caremustbetakenindevelopingportfolios,whichareconsistentwiththeclients’objectives,circumstances,constraints,andrisks.Investmentdecisionsshouldbebasedontheoverallportfolio,ratherthanthecharacteristicsofanindividualinvestment.

Softcommission(dollar)policies:Assumeaclienthashiredyoutomanagehisfunds.Youhavediscretionovertheselectionofbrokerstoexecutetransactions.Conflictsmayariseifyouuseclientbrokerage(moneypaidbytheclientfortradeexecution)topurchaseresearchservicesfromthebroker.Thispracticeiscalled“softdollars”or“softcommissions.”Ifyoupayahigherbrokeragecommissionthanyouwouldnormallypay,toallowforthepurchaseofgoodsorservices,withoutacorrespondingbenefittotheclient,youhaveviolatedthedutyofloyaltytoyourclient.

Proxyvotingpolicies:Assumeyouareaninvestmentmanagerandyouhavepurchased1millionsharesofGeneralElectriconbehalfofyourclient.Sinceyouaremanagingyourclient’sportfolio,youcanvoteonbehalfoftheclient.Youshouldperformasimplecost‐benefitanalysistodecidewhetherornottovote.Whenyouvoteitshouldbeinthebestinterestoftheclient(shareholder),notthecompanymanagement.Yourfirm’sproxyvotingpoliciesshouldbedisclosedtoclients.

RecommendedProceduresforCompliance: Regularaccountinformation:Submitaquarterlystatementtotheclientthatincludes

credits,debits,securitiesholdings,andtransactionsduringtheperiod.Indicatewhethertheclientmustholdorsellassets.Andifsold,wheretheproceedsshouldbeinvestedinandwhen.

Clientapproval:Ifunsureofwhatcourseofactiontotakewithrespecttoaclient,membersandcandidatesmustdiscusswiththeclientinwritingandtakeapproval.

Firmpolicies:Encouragefirmstoadoptthesepolicies:o Followallapplicablerulesandlaws.



o Establishtheinvestmentobjectivesoftheclient:returnrequirements,riskprofile,experiences,andconstraints.

o Consideralltheinformationwhentakingactions:theclient’sneedsandcircumstances,theclient’sportfolio,andaninvestment’sindividualcharacteristics.

o Carryoutregularreviews:Ifaclient’scircumstanceshavechanged(suddenneedforlargesumsofmoney,oranunexpectedinflowofmoney),thentheymustbeaddressed.

o Dealfairlywithallclientswithrespecttoinvestmentactions.o Discloseconflictsofinterest.o Disclosecompensationarrangements:Ifamanageriscompensatedbasedonthe

returnsgeneratedforaclient,thenitmustbedisclosedtotheclient.o Maintainconfidentiality.

StandardIII(B)FairDealing

MembersandCandidatesmustdealfairlyandobjectivelywithallclientswhenprovidinginvestmentanalysis,makinginvestmentrecommendations,takinginvestmentaction,orengaginginotherprofessionalactivities.

Interpretation:Thestandardfocusesondealingfairlyandobjectivelywithallclients.Itdoesnotmeanequallybecausethecircumstancesofeveryclientwillbedifferent.Also,afirmmayofferdifferentlevelsofservices.Aclientpayingahigherfeeforapersonalizedservicecannotbetreatedinanequitablemannerwithonewhoisnot.Moreover,itisalsonotpossibletocommunicateinformationtoallclientsatthesametimeasthemodesofcommunicationmayvary(e‐mail,phone,andfax).

Guidance: Investmentrecommendationisanyopiniontobuy,sell,orholdasecurity/investment.

Guidelinesonhowrecommendationsmustbedisseminatedtoclients:o Allyourclientsmusthaveafairopportunitytoactontheinvestment

recommendation.o Thereshouldnotbeselectivedisclosuresuchthatyourlargeclientsreceivea

reportfirstandthesmallerclientslater.Theremaybepracticaldifficultiesinreachingallclientsattheexactsametimebecauseoftimedifferencesandmodesofcommunication,butaneffortmustbemadetocommunicateinanequitablemanner.

o Theremaybeinstanceswhenyoumaychangeyourrecommendation.Let’sassumeyouissuedabuyrecommendationforastockerroneously.Youchangeditlatertosellandifthereareclientswhohaveactedonthebuyorderbutarenotawareofthechangetosell,youmustadvisethemofthechangebeforeacceptingtheorder.

Guidelinesformembersandcandidateswhoseprimaryroleistotakeactionsbasedoninvestmentrecommendationsreceivedeitherfromwithinthefirmorexternalsources:



o Takecaretotreatallclientsfairly.o IPOandsecondaryofferings:Distributetoallclientsforwhomtheinvestmentsare

appropriate.Allocationofthestockshouldbeconsistentwiththepoliciesofthefirm.

o Oversubscribedissues:Distributeonaprorataandround‐lotbasis.Refrainfrombuyingforindividualandfamilyaccounts.But,ifafamily‐memberisafee‐payingclient,thenthefamilymembermustbetreatedonanequalbasisasanyotherclient.

o Blocktrade:Allaccountsofclientsinablocktrademustbegiventhesameexecutionpriceandchargedthesamecommissionfee.

o Ordersmustbetimestamped.o Ordersaretobeexecutedonafirst‐inandfirst‐outbasis.o Disclosetotheclienttheallocationproceduresthatthefirmfollows.o MembersandcandidatesmustnotwithholdsecuritiesofIPOs,tradingatapremium

inthesecondarymarket,fortheirbenefit.

Recommendedproceduresforcompliance: Developfirmpolicies.

o Limitthenumberofpeoplewhoknowthatarecommendationisgoingtobedisseminated.

o Shortenthetimeframebetweenthedecisiontomakeaninvestmentrecommendationandactualdissemination.

o Publishguidelinesforpre‐disseminationbehavior:Firmsmustbeencouragedtohaveguidelinesthatprohibitpersonnel,whoknowabouttherecommendation,fromtakingactionordiscussing.

o Simultaneousdissemination:Oncedisseminationtoallclientshashappened,membersandcandidatesmayfollowupwithindividualclients.

o Maintainalistofclientsandtheirholdings.o Developanddocumenttradeallocationprocedures(discussedabove).

Disclosetradeallocationprocedures. Establishsystematicaccountreview:Conductperiodicreviewtoensurenoclientis

receivingpreferentialtreatmentandtradesarebasedontheaccount’sobjectives.Ifthemanagerissellingfromoneaccountandbuyingitforanotheraccount,hemustdocumentthereasonsforboththetransactions.

Disclosethelevelsofserviceandtheassociatedfeestoallclients.

StandardIII(C)Suitability

1. Whenmembersandcandidatesareinanadvisoryrelationshipwithaclient,theymust:a. Makeareasonableinquiryintoaclient’sorprospectiveclient’sinvestment

experience,riskandreturnobjectives,andfinancialconstraintspriortomakinganyinvestmentrecommendationortakinginvestmentaction,andmustreassessandupdatethisinformationregularly.



b. Determinethataninvestmentissuitabletotheclient’sfinancialsituationandconsistentwiththeclient’swrittenobjectives,mandates,andconstraintsbeforemakinganinvestmentrecommendationortakinginvestmentaction.

c. Judgethesuitabilityofinvestmentsinthecontextoftheclient’stotalportfolio.

2. Whenmembersandcandidatesareresponsibleformanagingaportfoliotoaspecificmandate,strategy,orstyle,theymustmakeonlyinvestmentrecommendationsortakeonlyinvestmentactionsthatareconsistentwiththestatedobjectivesandconstraintsoftheportfolio.

Interpretation:

Determinethesuitabilityofaninvestmentbeforetakingactionbasedontheclients’circumstancesandotherfactors.Itistheresponsibilityofmembersandcandidateswhoprovideinvestmentadvicetoaclienttodeterminethesuitabilityofaninvestment.Sell‐sideanalystsandothermemberswhoexecuteinstructionsarenotresponsibleforsuitabilityanalysis.

Guidance: Developinganinvestmentpolicy:Gatherclientinformation(personaldata,objectives,

risk,andcircumstances)atthestartoftherelationship.DevelopanIPSthatoutlinesreturnrequirements,risktolerance,andallinvestmentconstraints.IPSalsooutlinestherolesandresponsibilitiesofthepartiesintheadvisoryrelationship,whenperiodicreviewswillbeconductedandtheIPSreevaluated.

Updatinganinvestmentpolicy:IPSistobeupdatedatleastannuallytoreflectchangesinmarketexpectationsandcircumstancesoftheclient.Needsandcircumstancesoftheclientscanchangeatanytimeandtheinvestmentrecommendations/decisionsmusttakenoteofthis.Examplesofchangesinanindividual’scircumstances:taxstatus,numberofdependents,liquidityneeds,lossofjob/changeincurrentincome,etc.

Theneedfordiversification:Combiningdifferentinvestmentsreducestheriskofaportfoliohavingallassetsinasingleinvestment.Aninvestmentthatisrelativelyriskyonitsownmaybesuitableinthecontextoftheentireportfolio.

Addressingunsolicitedtradingrequestso Requestsfromclientsfortradesthatdonotalignwiththeriskandreturnobjectives

ofaclient’sIPS:Membersandcandidatesmusttakeeffortstobalancetheclient’srequestwhilenotdeviatingfromtheIPS.

o Unsolicitedrequeststhatarenotsuitableinvestments:IfyourclientsaskyoutomakeatradethatisnotinaccordancewiththeIPS,thenrefrainfrommakingthetradeuntilyoudiscussitwiththeclient.EducatetheclientaboutthedeviationfromthecurrentIPS.

o Iftheclientinsistsonmakingthetradeandifyouthinkitwillhaveamaterialimpactontheportfolio,updatetheIPS.IftheclientrefusestohavetheIPSmodified,thendeterminethefutureoftheadvisoryrelationship.



Managingtoanindexormandate:Investaccordingtothemandate.Forexample,assumeyouareaportfoliomanagerforasmallcapfundandyourmandateistoincludestocksbelowacertainmarketcapitalization.Youwouldbedeviatingfromthemandateifyoubuylargecapstocksevenifyouexpectlargecapstoperformexceptionallywell.

RecommendedProceduresforCompliance: Investmentpolicystatement:Bothindividualandinstitutionalinvestorsmusthavean

IPS.TheIPSshouldoutlinethefollowing:clientidentification,investorobjectives,investorconstraints,andperformancemeasurementbenchmarks.

Regularupdates:IPSistobeupdatedonaregularbasis(atleastannually)toreflectchangingcircumstancesandcapitalmarketexpectations.

Suitabilitytestpolicies:Firmsmustbeencouragedtohavetestprocedurestodeterminethesuitabilityofinvestmentsfordifferenttypesofclients.

StandardIII(D)PerformancePresentation

Whencommunicatinginvestmentperformanceinformation,membersandcandidatesmustmakereasonableeffortstoensurethatitisfair,accurate,andcomplete.

Guidance: Providecredibleperformanceinformationtoclientsandprospectiveclients.Shouldnot

statethatpastperformancecanbeobtainedagain. Avoidmisstatingperformanceormisleadingclients. Ifthepresentationisbrief,makedetailedsupportinginformationavailabletoclientsand

prospectsonrequest.

RecommendedProceduresforCompliance:ApplyingtheGIPSstandardsisrecommended,butnotrequired.FirmsthatclaimcompliancewithoutapplyingGIPSstandardsmustdothefollowing: Considertheknowledgeandsophisticationoftheaudience. Presenttheperformanceoftheweightedcompositeofsimilarportfoliosratherthan

usingasinglerepresentativeaccount.Assumetherearethreeportfolioswithsimilarmandatesworth2million,10million,and8million.Iftheygeneratedreturnsof9%,2%,and2%,respectively,thentakeaweightedaverageofreturns.

Includeterminatedaccountsaspartofperformancehistory.Alsostatewhenthoseaccountswereterminated.

Includedisclosuresthatfullyexplaintheperformanceresultsbeingreported. Maintainthedataandrecordsusedtocalculatetheperformancebeingpresented.

StandardIII(E)PreservationofConfidentiality

MembersandCandidatesmustkeepinformationaboutcurrent,former,andprospectiveclientsconfidentialunless:

1. Theinformationconcernsillegalactivitiesonthepartoftheclient.



2. Disclosureisrequiredbythelaw.

3. Theclientorprospectiveclientpermitsdisclosureoftheinformation.

Guidance: Statusofclient:Evenifanentityisnolongeraclient,membersandcandidatesmust

maintaintheconfidentialityofclientrecords. Compliancewithlaws:Complywithapplicablelaw.Ifaclientisinvolvedinillegal

activitiesandtheapplicablelawrequiresmembersandcandidatestomaintainconfidentiality,thentheinformationmustnotbedisclosed.

Electronicinformationandsecurity:Membersandcandidatesneedtobeawareofpossibleaccidentaldisclosures.Theyshouldtakecarewhencommunicatingsensitiveclientinformation.Forinstance,assumetwoclientsaninvestmentmanagerisdealingwith,havesimilarnames.Whensendingane‐mailwithupdatedIPS,theinvestmentmanagertypesinthenameoftheintendedrecipientanddoesn’trealizethatitgoestotheotherclientinsteadoftheintendedrecipient.Suchmistakescanhavedireconsequences.

ProfessionalconductinvestigationsbyCFAInstitute:Ifpermissibleunderlaw,membersandcandidatesmustcooperatewithPCPandprovideinformationaboutaclientinsupportofaninvestigation.AnyinformationgiventoPCPstaysconfidential.

RecommendedProceduresforCompliance: Thesimplest,mostconservative,andmosteffectivewaytocomplywithStandardIII(E)

istoavoiddisclosinganyinformationreceivedfromaclient,excepttoauthorizedfellowemployeeswhoarealsoworkingfortheclient.

Communicatingwithclients:Followfirm‐supportedcommunicationmethodsandcomplianceprocedureswhencommunicatingconfidentialinformation.

StandardIV:DutiestoEmployers

StandardIV(A)Loyalty

Inmattersrelatedtotheiremployment,MembersandCandidatesmustactforthebenefitoftheiremployerandnotdeprivetheiremployeroftheadvantageoftheirskillsandabilities,divulgeconfidentialinformation,orotherwisecauseharmtotheiremployer.

Interpretation: Assumeyouworkforaninvestmentmanagementfirmandhavecommittedtowork45

hoursaweek.Duringthistime,you’llnotindulgeinanyactivitythatwilldepriveyouremployerofyourskillsandabilities.

Now,assumeyouareabouttoplacealargebuyorderforastockforaclient.Youaretemptedtoplaceanorderforyourownaccountbeforebuyingfortheclient.Thisis



calledfrontrunninganditmustbeavoided,asyoumustplaceyourclientandemployer’sinterestsbeforeyourowninterests.

Everythingelsetakesprecedencebeforedutytoyourownself.Ofcourse,it’snotablanketstatementthatrequiresmembersandcandidatestoalwaysputworkaheadofpersonalcommitmentsandimportantfamilyobligations.Thestandardrecommendsmemberstoenterintoadialoguewithemployerstostrikeabalancebetweenworkandpersonallife.

Guidance: Theemployermustnothaverules/writtenpoliciesthatconflictwithresponsibilitiesof

membersandcandidates.Ifthereareany,thenyoumustencourageyouremployertochangethosepolicies.

Independentpractice:Independentpracticeisengaginginabusinessactivitywhereyougetpaid,andtheworkisnotrelatedtotheemployer.Assumeyouarethinkingofstartinganindependentpracticetoworkovertheweekendsorafter‐workhours.Therearecertainrulesthatgovernthis:o Youmustnotstartapracticethatconflictswiththeinterestsofyouremployer.o Obtainconsentfromyouremployerbeforestartingthepractice.Disclosethetypes

ofservicesyouwillrender,theexpecteddurationoftheservices,andthecompensation.

Leavinganemployer:Assumeyouhavesubmittedyourresignationanddecidedtoleaveyouremployer.Thereisaonemonthnoticeperiod.Duringthisperiod:o Youmustcontinuetoactinthebestinterestsofyourcurrentemployer.o Youmustnotrevealtradesecretstoyournewemployer.o Youmustnotmisuseclientlists.o Youmustnotsolicitexistingclientstoshifttheirbusinesstothenewemployer.o Onceyouhaveleftyourcurrentemployerandarebeingpaidbythenewemployer,

youmayseekbusinessfromoldclientsifyouhavenotsignedanon‐competeagreementwiththepreviousemployer.

Guidelinesforwhatisacceptableafterstartingworkatanewfirm:o Itisokaytouseskillsandexperiencegainedatthepreviousemployerastheyare

notconsideredconfidential.Knowledgeofthenamesofformerclientsisnotconsideredconfidential.

o Onemustnotuseanything(records/work)storedinpaperorelectronicformatfromthepreviousfirm.Ex:Excelmodelforthepharmaceuticalindustrydevelopedatthepreviousemployer.

Useofsocialmedia:o Followfirmpolicieswithrespecttosocialmediaforinteractingwithclientsand

prospectiveclients.Ex:whenemployeesareleavinganorganization,itmaynotbeappropriatetoannounceitonsocialmediaasfirmsmayhaverulesonhowandwhentoannouncethistoclients.



o Therecommendedpracticeistohaveseparateaccountsforpersonalandprofessionalsocialmediaactivities.

o Iftherearenofirmrules,it’sbesttoactinthespiritoftheStandardandnotengageinanyactivitythatwouldharmtheemployer.

Whistle‐blowing:Bringinginsiderknowledgeofillegal/unethicalactivitiesinanorganizationtotheattentionoflawenforcementactivitiesiscalledwhistle‐blowing.Whistle‐blowingisnotacceptableiftheintentisforpersonalgain.

Natureofemployment:Understandthenatureofemployment(full‐timeemployeeoracontractor).Youneedtobeawareofthetermsoftherelationship:numberofhours,compensation,benefits,worklocation,clientexpectations,etc.

Recommendedproceduresforcompliance: Competitionpolicy:Relatestotheindependentpractice,wesawintheguidelinessection.

Youmustunderstandtherules/proceduresofyourfirmwithrespecttopursuinganindependentpractice.

Terminationpolicy:Understandtheterminationpoliciesofyouremployer. Incident‐reportingprocedures:Beawareofincident‐reportingproceduresatyourfirm.

Ifthereisnone,encourageyourfirmtoadoptone. Employeeclassification:Understandyourstatuswithinthefirm:part‐time,full‐time,or

contractor.Beawareofthepoliciesthatapplytoyourclass.

StandardIV(B)AdditionalCompensationArrangements

MembersandCandidatesmustnotacceptgifts,benefits,compensation,orconsiderationthatcompeteswithormightreasonablybeexpectedtocreateaconflictofinterestwiththeiremployer’sinterest,unlesstheyobtainwrittenconsentfromallpartiesinvolved.

Interpretation: Assumeyouareaportfoliomanagerworkingforaninvestmentmanagementfirm.

Assumeaclienthasbenefitedimmenselyfromyourwork,andwouldliketogiftanexpensivecruiseforyouandyourfamilyasatokenofappreciation.Thisisanexampleofadditionalcompensation.

Assumeyouuseabrokeragefirmtoexecuteordersforyourclients.Ifthebrokeragewantstosendagiftsothatyoucontinuetodirectbusinesstotheminthefuture,itisanexampleofadditionalcompensation.

Guidance: Obtainpermissionbeforeacceptingcompensationthatmightcreateaconflict.Youmust

firstdisclosetoyouremployerandobtainwrittenconsentforanycompensationthatmaycreateaconflict.

“Writtenconsent”includesanyformofcommunicationthatcanbedocumented.



Notallgiftsneedtobereported.Forexample,ifabrokeragefirmsendsyouadesktopcalendar,orifaclientsendsyouapenasatokengift(notofsignificantvalue),thenitneednotbereported.

Discusspossiblelimitationstotheirabilitiestoprovideservicesthatmaybecompetingwithyouremployer’sduringthenegotiationandhiringprocess.

Recommendedproceduresforcompliance: Makeanimmediatewrittenreporttoyoursupervisorandcomplianceofficerspecifying

anycompensationyouproposetoreceive. Thedetailsofthereportshouldbeconfirmedbythepartyofferingtheadditional

compensation,includingperformanceincentivesofferedbyclients.Inourearlierexample,wheretheclientofferedanexpensivevacation,whenyoudisclosethesametoyouremployer,itmustbevalidatedbytheclient.Thiswrittenreportshouldstatethetermsofanyagreement.

StandardIV(C)ResponsibilitiesofSupervisors

MembersandCandidatesmustmakereasonableeffortstoensurethatanyonesubjecttotheirsupervisionorauthoritycomplieswithapplicablelaws,rules,regulations,andtheCodeandStandards.

Interpretation: Thisstandardappliestoanyonewhohassupervisoryresponsibilities,irrespectiveof

whetherornottheemployeesundertheirsupervisionareCFAInstitutemembers,CFAcharterholders,orcandidates.

Ifthenumberofemployeesundersupervisionislarge,thensupervisorsmaydelegateresponsibilitiestosubordinates,butthatdoesnotabsolvethemofresponsibilityincaseaviolationhappens.Supervisorsmustensuretheirsubordinatesareawareoftherules,applicablelaws,firmpolicies,CodeandStandards,etc.

Theymusthaveregulartrainingprogramsoncompliancepoliciesforemployeesundertheirsupervision.

Ifthecomplianceproceduresatafirmareinadequate,theymustbringittotheattentionofthefirm’sseniormanagers.

Ifthecomplianceproceduresareinadequateornon‐existent,thenmembersandcandidatesshoulddeclinesupervisoryresponsibility.

Guidance: Systemforsupervision

o Understandthecomplianceproceduresofthefirm.o Ensureadequatecomplianceproceduresareinplacethatcoverallpossible

violations.Itisnotpossibletocovereverypotentialviolationthatmayoccur.



o Onceaviolationisdetected,asupervisormustimmediatelyreportthemisconductandinitiateanassessmenttodeterminetheextentofwrongdoing.Itisnotsufficienttowarntheemployeeorrelyonhis/herstatementsthatitwillnotrecur.

o Hemustalsoensurethattheactisnotrepeateduntiltheinvestigationiscomplete. Supervisionincludesdetection

o Supervisorsareresponsiblefordetectingviolations.o Supervisorsareresponsibleforensuringcomplianceproceduresareimplemented

andthattheyarefollowedthroughperiodicreview.o Assumeyouasasupervisorhavetakenadequatestepstoensurecompliance

proceduresareinplace.Despitethis,aviolationoccurs.Sinceadequatestepsweretaken,youasamembermaynotbeinviolationofthestandardunderthesecircumstances.However,itisanindicationthattheexistingcomplianceproceduresarenotsufficient.

RecommendedProceduresforCompliance: Encouragefirmstoadoptacodeofethicsforstrongethicalfoundation. HaveadequatecomplianceprocedurestoensurethepoliciesintheCodeandStandards,

andsecuritieslawsareimplementedatthefirm,andadheredto,onadailybasis. Distinguishbetweenthecodeofethicsandcomplianceprocedures.Keepingthem

separatehelpsservetheirindividualpurpose.o Complianceproceduresmustbewritteninplainlanguagesuchthatanyaverage

personcanunderstandandassimilatethemeasily.o Assignacomplianceofficerwhohastheauthoritytoimplementthefirm’s

complianceprocedures.o Establishthehierarchyofsupervisionandassigndutiesamongsupervisors.o Oncethecompliancesystemisinplace,supervisorsmustperiodicallymonitorto

detectviolationsand,ifdiscovered,musttakethenecessaryactions. Implementationofcomplianceeducationandtraining. Establishanappropriateincentivestructure.

o Supervisorsandfirmsmustanalyzethecompensationstructuretoseeifitencouragesprofitsattheexpenseofethicalbehavior.

o Is“how”profitsaregeneratedgivenlessimportancethan“howmuch”profitsaremadeforthefirm?

StandardV:InvestmentAnalysis,Recommendations,andActions

StandardV(A)DiligenceandReasonableBasis

MembersandCandidatesmust:

1. Exercisediligence,independence,andthoroughnessinanalyzinginvestments,makinginvestmentrecommendations,andtakinginvestmentactions.



2. Haveareasonableandadequatebasis,supportedbyappropriateresearchandinvestigation,foranyinvestmentanalysis,recommendation,oraction.

Interpretation:

Thelevelofdiligenceandthoroughnessofresearchdependsontheinvestmentphilosophythemember/firmisfollowingandtheroleofthememberintheinvestmentdecision‐makingprocess.

Guidance: Definediligenceandreasonablebasis. Whenusingsecondaryorthird‐partyresearch(researchconductedbysomeoneoutside

themember’sfirm)makereasonableeffortstoensurethird‐partyresearchissound. Ensurethefirmhasapolicyaboutperiodicreviewofapprovedthird‐partyresearch

providers.Ifnot,youmustencouragethefirmtoadoptaformalreviewpractice. Youmayrelyonthejudgmentofothers(seniormanagers)inyourfirmifyoubelievethe

duediligencedonebythemwasadequate. Whenusingquantitativelyorientedresearch,ensurethesoundnessofmodels.Youare

notexpectedtobecomeanexpertineverytechnicalaspectofthemodels,butyoumustunderstandthedata,parameters,assumptions,andlimitationsofthesemodels.Testtheoutputofthesemodelsundervariousscenariosbeforedistributingtheproduct.Ensurethatthemodelincludesabroadrangeofscenarios–evenhigh‐riskandpotentiallynegativeoutcomesthatarenotcommonlyencountered.

Developingquantitativelyorientedtechniques:Ifyouareinvolvedindevelopingnewmodels/algorithms,thenyoumustexercisehigherdiligenceinreviewingnewproductsthanindividualswhowouldusethesemodels.Includedataforbothpositiveandnegativeeconomiccycles.Testmodelsusingadversevolatilityandperformanceexpectations.Testthemodelforawiderangeofinputexpectations.

Selectingexternaladvisersandsub‐advisers:Ifyouareusingexternaladviserstomanageaspecificmandate,thenyoumustdiligentlyreviewthemjustasyouwouldanindividualfund/security.Reviewifthepublishedreturninformationisaccurate.Understandtheadviser’scomplianceprocedures,investmentprocess,andifhe/sheadherestothestatedstrategy.

Groupresearchanddecisionmaking:Often,membersandcandidatesarepartofagroupthatcollectivelyproducesaninvestmentanalysisorresearch.Thegrouparrivesataconsensusandgivesarecommendation.Thenamesofthemembersareincludedinthereport.Ifyoudonotagreetothefinalrecommendation,butbelievethatconsensusopinionhasareasonableandadequatebasis,andisindependentandobjective,thenyouneednotdissociateyourselforaskthatyournameberemovedfromthereport.



RecommendedProceduresforCompliance: Establishapolicythatresearchreportsmusthaveareasonableandadequatebasis.

Eitheranindividualorareviewcommitteeconsistingofagroupofemployeesmustbeappointedtoreviewthereportbeforeitiscirculatedtotheoutsideworld.

Developwrittenguidanceforanalysts,supervisoryanalysts,andreviewcommitteethatoutlineduediligenceproceduresifarecommendationhasareasonableandadequatebasis.

Developcriteriaforassessingthequalityofresearch. Developwrittenguidancefortestingofallcomputer‐basedmodels. Developmeasurablecriteriaforassessingoutsideproviders.Thisrelatestothe

guidelinesforusingexternal/thirdpartyresearch(wesawthisintheprevioussection).

StandardV(B)CommunicationwithClientsandProspectiveClients

MembersandCandidatesmust:

1. Disclose to clients and prospective clients the basic format and general principles of theinvestment processes they use to analyze investments, select securities, and constructportfolios, and must promptly disclose any changes that might materially affect thoseprocesses.

2. Disclosetoclientsandprospectiveclientssignificantlimitationsandrisksassociatedwiththeinvestmentprocess.

3. Use reasonable judgment in identifying which factors are important to their investmentanalyses, recommendations, or actions, and include those factors in communicationwithclientsandprospectiveclients.

4. Distinguish between fact and opinion in the presentation of investment analyses andrecommendations.

Interpretation:

Thisstandardemphasizestheneedforcommunicatingclearlyandfrequentlywithclients.Itisimportanttocommunicatetoclientswhatfactorstheyconsideredwhilemakingtherecommendation.Ifthereisachangeintheriskcharacteristicsofasecurityorasset,thenthismustalsobecommunicated.

Guidance: Informingclientsoftheinvestmentprocess:Describeyour/firm’sinvestmentdecision‐

makingprocesstotheclient.Thismustincludetheprosandcons,risksandlimitationsoftheprocess.o Justcommunicatingthefinalrecommendation(forinstance,buy/sellasecurity)to

theclientisnotsufficient.Youmustexplaininsimplelanguagetheinvestmentprocess.

o Ifthereisanychangeintheprocess,informtheclient.o Communicatetotheclientifanyexternaladvisersarebeingusedfortheirexpertise

tomanageaspecificstrategy.



Differentformsofcommunication:Communicationisnotrestrictedtotraditionalwrittenreport.Itcouldbein‐personmeetings,e‐mail,telephoneconversation,etc.o Careshouldbetakenwhencommunicatingthroughsocialmedia.o Iftherecommendationisconcise(stock‐list),thenyoumustnotifyclientsthat

additionalinformationwillsoonbemadeavailable. Identifyingriskandlimitations:Disclosetoclientstherisksandlimitationsofthe

investmentprocess/product. Reportpresentation:Inthereportincludethoseelementsthatwereimportantfor

analysisandconclusion. Distinctionbetweenfactsandopinionsinreports:Assumeyouarerecommendinga

sugarstockbecauseyoubelievethatthegovernmentwillraisetheexportquotalimit.But,thishasnotbeendoneyet;so,itisjustyouropinion.Youmustdistinguishbetweenfactsandopinionbystatingthisisanopinion.However,forinstance,ifyouwerepresentingtheperformanceofthepastthreequarters,thenthiswouldbeafact.

RecommendedProceduresforCompliance:

Theinformationincluded/excludedinresearchreportsvariesgiventhediversenatureofclientsandinvestmentassets.Thereisnospecificchecklistforwhatmustbeincluded.But,firmsmusthavearigorousmethodologytoreviewresearchmeantfordisseminationtoclients.

StandardV(C)RecordRetention

MembersandCandidatesmustdevelopandmaintainappropriaterecordstosupporttheirinvestmentanalyses,recommendations,actions,andotherinvestment‐relatedcommunicationswithclientsandprospectiveclients.

Interpretation:

Membersandcandidatesmustretainrecordsthatsupporttheirresearch,analysis,andconclusion.Whatrecordstomaintaindependsonthememberinvolvedinthedecision‐makingprocess.Recordscanbemaintainedeitherinhardcopyorelectronicformat.

Guidance: Newmediarecords:Itisthemember’s/candidate’sresponsibilitytomaintainarecordof

informationposted/discussedinsocialmediaevenifthefirmdoesnothavearecordretentionpolicyyet.Examplesincludetwitter/blogposts,Facebookupdates,etc.

Recordscreatedaspartofanyprofessionalactivityarethepropertyofthefirm;ifamemberdecidestoleavethefirm,he/shecannottaketherecordsorsupportingdocumentswithouttheconsentofthepreviousemployer.

Memberscannotreusehistoricalresearchreportsifthesupportingdocumentationisnotavailable.

Everycountry/jurisdictionwhereyouoperatemayhavecertainrulesforhowmuchdatatoretain.Forinstance,acountry’sregulatormaycallforretainingdataforthepastfive



years.Similarly,firmsmayalsohavepoliciesforretainingresearch/communicationrecords.CFAInstituterecommendsretainingrecordsforatleastsevenyears.

RecommendedProceduresforCompliance: Theresponsibilitytomaintainrecordsthatsupportinvestmentactiongenerallyfalls

withthefirmratherthanindividuals. Youshouldarchiveresearchnotesandotherdocumentsthatsupportinvestment‐related

communications. Ifthefirmhaspoliciesandprocedurestofacilitaterecordretention,thenyoumustfollow

them.Ifnot,youmustencourageyourfirmtoadoptpoliciesforpreservingrecords.

StandardVI:ConflictsofInterest

StandardVI(A)DisclosureofConflicts

MembersandCandidatesmustmakefullandfairdisclosureofallmattersthatcouldreasonablybeexpectedtoimpairtheirindependenceandobjectivityorinterferewithrespectivedutiestotheirclients,prospectiveclients,oremployer.MembersandCandidatesmustensurethatsuchdisclosuresareprominent,aredeliveredinplainlanguage,andcommunicatetherelevantinformationeffectively.

Interpretation:

Conflictsoccuroftenintheinvestmentprofession.Theyoccurbetweentheinterestsofclients,interestsofemployers,ortheycouldbeyourownpersonalinterests.Disclosetheconflictofinterestinplainlanguagetoemployer,clients,orprospectiveclients.

Guidance: Disclosureofconflictstoemployers.Someexamples:

o Assumeyouareworkinginaninvestmentmanagementfirm.Youmanageaclient’sportfoliothathasperformedextremelywell.Theclientishappyandwishestocompensateyouforthisperformance.Thisisaconflictofinterestwithotherclientsandyoumustdisclosethistoyouremployer.

o Assumeyouvolunteeratacharityorganizationthatisinnowayrelatedtoyourwork,andyouarenotpaidforit.However,youarepassionateabouttheworkyoudoatthischaritywhichkeepsyoubusyonweekendsandmentallyoccupiedduringtheweek,andisdeprivingyouremployerofyourskills.Youmustdisclosethispotentialconflictofinteresttoyouremployer.

o Assumeyouholdstocksinyourpersonalaccountforwhichyourfirmhasabuyrecommendationandissuitableformanyclients.Thismaycreateaconflictofinterest.

Firmscreatepoliciestopreventactionsthatmayappearasaconflictofinterest.Policiesincluderestrictionsonpersonaltrading,outsideboardmembership,etc.



Disclosuretoclients:Therearenumerousinstanceswhereaconflictofinterestexists;theseshouldbedisclosedtoclientssothattheyunderstandthecostoftheirinvestmentsandthebenefitsreceivedbythefirm.Afewinstancesarehighlightedbelow:o AssumeyouholdstocksofGeneralElectric(GE).Youareaskingyourclienttobuy

sharesofGE;itmaycreateapotentialconflictofinterestas,ifyourclientbuysandthestockpriceincreases,youwillbenefitfromthemovement.

o Youreceivecompensation(1%commission)fromyouremployerwhenyourecommendcertainmutualfunds.Youmustdisclosethistotheclientastheclientmaybelievethisrecommendationiskeepingtheclient’sbestinterestsinmind.Followingthedisclosure,theclientmaydecidewhetherthemutualfundissuitableornot.

o AssumeyouissueabuyrecommendationonGeneralElectricandrecommendyourclienttobuythestock.Ifyourfirmalsohasaninvestmentbankingrelationship,forinstance,thenitmustbedisclosedtotheclient.Theclientcanthendecideifitisinhisbestinterest,ortheinterestofthefirmandGE.

Cross‐departmentalconflicts:Assumeyouarearesearchanalyst(sell‐sideanalyst)workingatabrokeragefirm.Yourfirmhasaninvestmentbankingdepartment,andmaypressurizeyoutowritefavorablereportsforcompanieswithwhomtheyhaveanexistingrelationshiporaretryingtoforgeone.Ideally,existingcompaniesshouldbeonarestrictedlist.But,ifthatisnotpossible,thenyoumustmakeadisclosureoftheinvestmentbankingrelationshipintherecommendationreport.Anotherexamplewheresuchconflictsmayariseisbuy‐sideanalyst/bankswithunderwritingpowers.

Conflictswithstockownership:Membersandcandidatesmustdiscloseanymaterialownershipinastock/investmentthattheyarerecommendingtoclients.

Conflictsasadirector:Therearethreepossibleconflictsofinterestifyouareaninvestmentprofessionalandservingasadirectorofacompany:o Dutiesowedtoclientsanddutiesowedtoshareholdersofthecompany.o Asadirector,youmayreceivesecurities/optionstopurchasesecuritiesofthe

companyascompensation.Aconflictmayariseiftradinginthesesecuritiesincreasesthevalueofthesecurity.

o Asadirector,youmaybeprivytomaterialnonpublicinformationaboutthecompany.Theremaybeaperceptionthatthedirectorcommunicatesthisinformationtohisfirmandinvestmentrecommendationsarebasedonthatinformation.

Recommendedproceduresforcompliance: Disclosespecialcompensationarrangementswiththeemployerthatmightconflictwith

clientinterests,suchasbonusesbasedonshort‐termperformancecriteria,commissions,incentivefees,performancefees,andreferralfees.

Ifthefirmdoesnotpermitsuchdisclosure,youshoulddocumenttherequestandconsiderdissociatingfromtheactivity.Forexample,ifyoureceivea1%bonusfromyour



firmforsellingcertainmutualfundsandyourfirmdoesnotpermitdisclosingthiscompensation,thenyoushouldconsiderdissociatingfromtheactivity.

StandardVI(B)PriorityofTransactions

InvestmenttransactionsforclientsandemployersmusthavepriorityoverinvestmenttransactionsinwhichaMemberorCandidateisthebeneficialowner.

Interpretation:

Ifyouaretradingforyourownaccount,thenyouarethebeneficialowner.But,assumethetransactionhappensinyourchildren’sorspouse’saccount.Eventhoughthoseaccountsarenotinyourname,youbenefitfromthemandyouarethebeneficialowner.Theaccounthereappliestoanyaccountwithwhomyouhaveadirectrelationship.

Guidance: Avoidingpotentialconflicts:Conflictsbetweenclient’sinterestandinvestment

professional’sinterestmayoccur.Thereisnothingunethicalaboutmanagers,advisers,ormutualfundemployeesmakingmoneyfrompersonalinvestmentsaslongastheyfollowthesethreerules:o Theclientisnotdisadvantagedbythetrade.Forexample,ifyouareexecutingasell

trade,thenitshouldnotaffectyourclientsinanyway.o Theinvestmentprofessionaldoesnotbenefitpersonallyfromtradesundertaken

forclients.o Theinvestmentprofessionalcomplieswithapplicableregulatoryrequirements.

Personaltradingsecondarytotradingforclients:Theorderofexecutingtradesis:clients,employers,andthenyourpersonalaccount,oroneinwhichyouarethebeneficialowner.Therationaleistopreventpersonaltransactionsfromadverselyaffectingtheinterestsofclientsoremployers.

Impactonallaccountswithbeneficialownership:MembersandCandidatesmayundertaketransactionsinaccountsforwhichtheyareabeneficialowner,onlyaftertheirclientsandemployershavehadanadequateopportunitytoactonarecommendation.Forexample,assumeyouareworkingasaninvestmentmanagerandyourgroupmadeabuyrecommendationonastock.Theclientmustgetthefirstopportunitytoactontherecommendation,thentheemployer,andthenyou.

Howshouldfamilyaccountsbetreated?:Assumeaclosefamilymemberisaclient.He/sheshouldreceivethesamelevelofserviceasanyotherclient.Ifyouhaveabeneficialrelationshipinthefee‐payingaccount,thenyoumaybesubjecttopreclearanceorreportingrequirementsoftheemployer.

RecommendedProceduresforCompliance: LimitedparticipationinequityIPOs:SomeIPO(initialpublicofferings)issuesarehighly

soughtafterandthesharepricerisesinvaluesignificantlyaftertheissueisbroughttothemarket.Usually,itisahotIPOifthesupplyislimitedandthedemandishigh.



PurchaseoftheIPObyinvestmentprofessionalscreatesaconflictofinterestintwoways:o Itmayappearasifinvestmentpersonnelaretakingtheopportunityawayfrom

clientsforpersonalgain.Forexample,assumebothyouandyourclientareallotted200sharesinanIPO.Theclienthadappliedfor400butonlygot200.Allotmenttoyouraccountwillmakeitseemasifsomeopportunitywastakenawayfromtheclientforyourgain.

o ThepartythatisgivingtheinvestmentprofessionalthisopportunitytoparticipateintheIPOispossiblytryingtoinfluencehim/herinthefutureinvestmentdecisions.

Itisrecommendedthatmembersandcandidatesshouldpre‐clearparticipationinIPOsevenwherethereisnoappearanceofconflictofinterest,andstayawayfromequityIPOs.Fromafirm’sperspective,itmaynotberighttofollowablanketpolicythatbansemployeesfromIPOs.Instead,itwouldbeappropriatetohavereliableandsystematicproceduresinplacetoidentifyanyconflictofinterest,anddealtwithbysupervisors.

Restrictionsonprivateplacements:Privateplacementsaretransactionswhereyougetsharesofacompanythroughaprivateoffering,andnotthroughapublicoffering.TheconflictofinteresthereissimilartothatofIPOsasitmayseemthatthisparticipationinprivateplacementisafavorforfuturebusinessdeals.Assumeyouhaveparticipatedinaprivateplacement.Whentheinvestmentgoespublic,itmayseemasifyouhaveavestedinterestifyourecommendtheinvestmenttoclientsregardlessofitssuitability.

Establishblackout/restrictedperiods:Topreventfrontrunning(thepracticeoftradingforone’spersonalaccountbeforeclientaccounts),firmshaveblackoutperiodsduringwhichinvestmentpersonnelcannottradefortheirpersonalaccounts.Thisistosafeguardtheinterestsoftheclients.Thepolicyonblackoutandrestrictedperiodsvariesfromfirmtofirmdependingontheirsize.Itcanrangefromatotalbanontradingtopreventingtheinvestmentmanagerfromfrontrunning.

Supervisorsmustestablishreportingproceduresforinvestmentpersonnel.Forexample:o Disclosureofholdingsinwhichtheemployeehasabeneficialinterest:Thisshould

bedoneatthebeginningofemploymentandatleastannuallythereafter.o Providingduplicateconfirmationsoftransactions:Investmentpersonnelmust

directtheirbrokerstoprovideduplicatecopiesofallthesecuritiestransactionsdonewiththem.Itservestwopurposes:a)discouragesunethicalbehaviorbecausethereisanindependentverificationb)acleartransactionhistoryandflowofmoneyisavailable,andnotjusttheholdings.

o Preclearanceprocedures:Obtainingclearanceforplannedtradeshelpsreduceconflictofinterest.

Membersandcandidatesmustdisclosetoinvestorstheirfirm’spoliciesaboutpersonalinvesting/trading.Itshouldbeinsimplelanguagethatinvestorscanunderstand.



StandardVI(C)ReferralFees

MembersandCandidatesmustdisclosetotheiremployer,clients,andprospectiveclients,asappropriate,anycompensation,consideration,orbenefitreceivedfromorpaidtoothersfortherecommendationofproductsorservices.

Interpretation: Assumeyouprovideequityinvestmentadvisoryservicetoaclient.Theclientisnow

interestedinmakingfixedincomeinvestmentsaswell.So,yourefersomeoneprovidingthisservicetotheclient.Youreceiveafeeforthisfromtheperson/firmgivingfixedincomeadvice.Asperthisstandard,youmustdisclosethefeeyougetforthereferral.

Anotherexampleiswhereyourecommendyourclienttopurchaseamutualfund,andthefundpaysyouacommission.Youmustdisclosethisarrangementtotheclientsothathe/shecanunderstandthefullcostoftheinvestmentandthebenefityouarereceiving.

Sayyoureceiveareferencefromsomeone/firm,andyoupayareferralfeetothepartyintroducingtheclient.Youmustdisclosetotheclientthefeepaidforthisreferral.

Guidance: Advisetheclientorprospectiveclientaboutanyreferralfeesbeforeenteringintoany

formalagreement. Disclosethenatureoftheconsiderationorbenefit.Forexample,flatfeeorpercentage

basis,one‐timefee,orcontinuingbenefitbasedonperformancemustbedisclosed.

RecommendedProceduresforCompliance: Encourageyouremployertodevelopproceduresrelatedtoreferralfees.Thefirmmay

completelyrestrictsuchfees. Provideclientsnotificationofapprovedreferralfeeprogramsandprovidetheemployer

regular(atleastquarterly)updatesontheamountandnatureofcompensationreceived.

StandardVII:ResponsibilitiesasaCFAInstituteMemberorCFACandidate

StandardVII(A)ConductasParticipantsinCFAInstitutePrograms

MembersandCandidatesmustnotengageinanyconductthatcompromisesthereputationorintegrityofCFAInstituteortheCFAdesignationortheintegrity,validity,orsecurityofCFAInstituteprograms.

Interpretation: ThisstandardcoverstheconductofCFAInstituteandMembersinvolvedwiththeCFA

Program. CFAInstituteprogramsincludetheCFAprogram,certificateininvestmentperformance

measurement(CIPM),andtheClaritas®InvestmentCertificate.



ThestandardcoversmanyaspectssuchascheatingonanyCFAInstituteexaminations,violatingthetestingpolicies,disclosingconfidentialexaminformationtothepublic,andimproperlyusinganyassociationwiththeCFAInstitutetofurtherpersonalorprofessionalgoals.

Guidance: Confidentialprograminformation:Candidatesmaydiscussnon‐confidentialinformation

andcurriculummaterialwithotherswhilepreparingfortheexam.Examplesofinformationthatcannotbedisclosedinclude:o Specificdetailsofquestionsappearingintheexam.o Discussingwhatareasorformulasweretestedontheexam.

AdditionalCFAprogramrestrictions:o Thereareadditionalpoliciesthatdefineallowedanddisallowedactionsduringthe

exam.Testingpoliciesincludecalculatorpolicy(onlytwocalculatorsareallowed)andthepersonalbelongingspolicy.

o MembersmayparticipateasvolunteersinvariousaspectsoftheCFAprogramsuchasgrading,administering,ordevelopingtheexam.Buttheyarenotallowedto: Discloseanymaterialappearingontheexam. Howquestionsarescored. Anyinformationontheexamprocess.

Expressinganopinion:MembersarefreetoexpresstheiropinionordiscontentwithCFAInstituteregardingitspoliciesandprocedures.Forexample,ifyousaytheexamwasnotagoodrepresentationofthecurriculum,thenitisnotaviolationofthestandard.However,ifyoudiscussspecifictopicsorquestions,thenitisaviolation.

StandardVII(B)ReferencetoCFAInstitute,CFADesignation,andCFAProgram

WhenreferringtoCFAInstitute,CFAInstitutemembership,theCFAdesignation,orcandidacyintheCFAprogram,MembersandCandidatesmustnotmisrepresentorexaggeratethemeaningoforimplicationsofmembershipinCFAInstitute,holdingtheCFAdesignation,orcandidacyintheCFAprogram.

Interpretation: ItisnotintendedtoprohibitfactualstatementsrelatedtothebenefitsofearningtheCFA

designation. However,themeritsofCFAInstitute,theCFAProgram,andtheCodeandStandardsmust

beexpressedastheopinionofthespeaker. Thisstandardappliestoallformsofcommunication. ItisnotallowedtostatethatsomeonewithaCFAdesignationwillexhibitsuperior

performance.



Guidance: CFAInstitutemembership:CFAInstitutememberreferstoregular/affiliatemembersof

theCFAInstitutewhohavefulfilledthefollowingmembershiprequirements:o RemitannuallytoCFAInstituteacompletedProfessionalConductStatement.o AnnuallypayCFAInstitutemembershipdues.

UsingtheCFAdesignation:OnceyouhaveearnedtherighttousetheCFAdesignation,youmustfollowtherulesassociatedwiththeusageofthedesignation.CFAcharterholdersareindividualswhohaveearnedthisrightbycompletingtheCFAprogramandhavetherequiredyearsofworkexperience.Theymustalsosatisfythemembershiprequirementsinordertousethedesignation.

ReferringtocandidacyintheCFAprogram:CandidatesmayrefertotheirparticipationintheCFAprogram.Apersonisacandidateifthepersonappearsforaspecifiedexaminationaftercompletingtheregistrationprocessorthepersonhasappearedforaspecifiedexamination,buttheresultsareyettobeannounced.

MembersandcandidatesmustencouragetheirfirmstocreatetemplatesconsistentwithstandardVII(B).

Instructor’sNote:ThisisthemostimportantreadinginEthicsandwillrepresentamajorpercentageoftheEthicsquestionsontheExam.Todowellonthistopicyoushouldcarefullystudyalltheexamples(ApplicationsoftheStandard)inthecurriculumandalsodoasmanypracticequestionsaspossible.



Summary

LO.a:DemonstratetheapplicationoftheCodeofEthicsandStandardsofProfessionalConducttosituationsinvolvingissuesofprofessionalintegrity.

Readthe“ApplicationoftheStandard”segmentforeachstandardinthecurriculum.

LO.b:DistinguishbetweenconductthatconformstotheCodeandStandardsandconductthatviolatestheCodeandStandards.

LO.c:RecommendpracticesandproceduresdesignedtopreventviolationsoftheCodeofEthicsandStandardsofProfessionalConduct.

1.A.Knowledgeofthelaw

Understandapplicablelawandrules.Complywiththemorestrictlaw.Donotknowinglyparticipate/disassociatefromsuchactivity.

1.B.Independenceandobjectivity

Usereasonablecareandjudgment.Maintainindependenceandobjectivity.Donotoffer/solicitgifts.

1.C.Misrepresentation Donotmisrepresentfacts/performancereports.Avoidplagiarism.Donotomitfacts.

1.D.Misconduct Aimedatprofessionallife;actslikelying,cheating,andstealingaffectprofessionalreputation/integrity.

2.A.MaterialNonpublicInformation

Donotactorcauseotherstoactonmaterialnonpublicinformation.Achievepublicdissemination.Notaviolation:MosaicTheory=materialpublicinformation+nonmaterialnonpublicinformation.

2.B.MarketManipulation

Information‐basedmanipulation:Blogs,othermediatoinflatestockprices.Transaction‐basedmanipulation:Makeasecuritytoappearmoreliquid.

3.A.Loyalty,PrudenceandCare

Usereasonablecareandexerciseprudentjudgment.Placeclient’sinterestsbeforeyouremployeroryourinterests.Softdollarsshouldbenefittheclient.Striveforbestexecution.

3.B.FairDealing Dealfairlyandobjectivelywithallclients.Note:itdoesnotstateequallybecauseofdifferentlevelsofservice.Fee‐payingfamilymembershouldbetreatednodifferentthananyotherclient.Disseminatereportswithoutbeingpartial.Sametimeisnotpossiblebecauseofdifferentmodesofcommunication.

3.C.Suitability DevelopIPS.Understandclient’sriskprofile.UpdateIPSperiodically.

3.D.PerformancePresentation

Donotmisstateperformance.Ensureperformanceinformationisfair,accurateandcomplete.



3.E.PreservationofConfidentiality

Maintainconfidentialityofcurrent,formerandprospectiveclientsunless:a)lawmandatesdisclosureb)illegalactivitiesbyclientc)clientpermitsdisclosure.

4.A.Loyalty Avoidfrontrunning.Getwrittenconsentfromemployerbeforestartinganindependentpractice.Youcannottakeproprietaryinformation,clientlistsofthepreviousemployer.

4.B.AdditionalCompensationArrangements

Donotacceptgifts,benefits,orcompensationthatwillcreateaconflictofinterest.

4.C.ResponsibilitiesofSupervisors

Ensureanyoneunderyoursupervisioncomplieswithapplicablelaws,rules,regulations,andCodeandStandards.

5.A.DiligenceandReasonableBasis

Exercisediligence,independence,andthoroughnessinanalyzinginvestmentsandmakingrecommendations.Bediligentandhaveareasonablebasis,evenwhenusingsecondaryorthird‐partyresearch.

5.B.CommunicationwithClientsandProspectiveClients

Disclosetoclientstheinvestmentprocess.Identifyrisksandlimitations.Distinguishbetweenfactandopinion.

5.C.RecordRetention Maintainrecordsthatsupportyouranalysisandresearch.CodeandStandardsrecommendstoringrecordsforatleastsevenyears.

6.A.DisclosureofConflicts

Makefullandfairdisclosureofmattersthatmayimpairindependenceandobjectivity.Disclosuretobemadeinplainlanguage.Exofconflicts:stockownership,director,crossdepartmental(IB/research)conflicts.

6.B.PriorityofTransactions

Anyaccountfromwhichyoubenefitmakesyouthebeneficialowner.Personaltradingsecondarytotradingforclients.Establishblackoutperiodstopreventfrontrunning.LimitparticipationinIPO.

6.C.ReferralFees Disclosereferralfeetoclients,prospectiveclients,andemployers.

7.A.ConductasparticipantsinCFAInstitutePrograms

Keepquestions,examinformationconfidential.Complywithprogramrestriction.Youmayexpressanopiniononthedifficultyofexam,curriculumetc.

7.B.ReferencetoCFAInstitute,theCFAdesignation,andtheCFAprogram

Payannualduesandfillprofessionalconductstatementtoclaimmembership.Referencestopartialdesignationnotallowed(CFA,Level1).CFAmarkcanbeusedifyou’veclearedallthreelevelsandfulfilledthemembershiprequirements.



PracticeQuestions

1. NargisDilawez,CFA,worksasanindependentresearchanalystandusesvariousonlinesocialmedia sites tomake announcements, recommendations, and analyses of varioussecurities.SheisaresidentofCountrySwherethereisnolawagainstpostingofcommentsandopinions, but since her views are read globally she isworried about regulators incertaincountrieswhoimposerestrictionsandrequirementsononlinecommunications.AccordingtotheStandards,Dilawezshould:A. continue to post her comments since her resident country does not impose any

regulatoryrestrictions.B. discontinue immediately and wait for the restrictions to ease in the nonresident

countries.C. seek guidance from appropriate, knowledgeable, and reliable sources to diligently

followlegalandregulatorytrendsaffectingherprofessionalresponsibilities.2. WynonaFritzworksforBradyBrokerageasafixedincomeanalyst.Sheisalsoregistered

to take the Level III examination.After analyzing both the qualitative andquantitativeaspectsofSaberInc.,Fritzconcludesthatthecompanyisnotcorrectlyratedbythecreditratingagencyandshouldbedowngradeddue to the leverage in itscapital structure.AseniormanagerfromtheinvestmentbankingdepartmentinformsherthatSaberInc.haschosenBradyBrokerageasoneof the firms tounderwriteandmarket theirnewbondissue. Fritz is concerned that her report will cause the company to terminate theirrelationshipwith Brady and affect her employment. According to the Standards, Fritzshould:A. dissociatefromthereport,theunderwriting,andtheclient.B. be independent and objective in her analysis based solely on the company’s

fundamentals.C. changeherrecommendationaboutthecreditratingtoremovetheconflict.

3. JulieGrosky,CFA,worksforHarvestMutualFundwhereshemanagesafixed‐incomefund.

Inahastilycompiledperformancereview,Groskyreportstoherclientsthatherfundhasexceededthebenchmarkby0.20%.StuartBrennanisaclientofHarvest,whowritesbackto inform Grosky that the fund actually underperformed the benchmark. Groskyincorrectly blames the error on a computer program newly implemented at Harvest.GroskyleastlikelyviolatedtheStandardrelatingto:A. Misrepresentation.B. Misconduct.C. IndependenceandObjectivity.

4. SteveMiller is enrolled as a candidate in the CFA Program. Heworks as an assistant

manager in Trust Investment Bank. He enjoys drinking liquor during his lunch break.



Miller’scolleagueshavenoticedthatheisvisiblyintoxicatedafterthelunchbreakandisnot in a position tomake rational investment decisions.Millermost likely violates theStandardof:A. Misconduct.B. KnowledgeoftheLaw.C. DisclosureofConflicts.

5. Isaac Dobrogost, a candidate in the CFA Program,works as an investment advisor for

ZenithMutualFund.Heisinvitedbyoneofhisclients,SaharaInc.(SI),amanufacturingcompany,tomeetwiththefinancedirectoralongwithafewlargestakeholdersofSI.InthemeetingDobrogostfindsoutthatthecompanyisgoingthroughaleanperiodandwillannounceadecreaseinearningsintheirnextquarterfinancialresults.CanDobrogostusethisinformationtochangetheratingofthecompanyfrom“buy”to“sell”?A. No.B. Yes,becausethisinformationisgivendirectlybythecompany.C. Yes,becauseithasbeendisseminatedtotheotherstakeholdersaswell.

6. Weinberg Inc., a global asset management company, has a large position in Wessner

Pharma.Thetradingvolumeofthisstockislow.Inordertoboosttheliquidityofthestock,multiple tradingdesksatWeinburgstartbuyingandsellingWessnershares fromeachother.TheCFAInstituteStandardmostlikelyviolatedbyWeinbergis:A. MarketManipulation.B. Misconduct.C. ActingonNonPublicInformation.

7. JaniceMcDowell,CFA,isthechiefinvestmentofficerofZenithInvestmentBankandwants

toimprovethediversificationofoneofitsbalancedfundsinordertoimproveitsreturns.Theinvestmentpolicystatementofthefundmentionslowriskinvestmentsinlarge‐capequities,governmentbondsofAAratings,andcorporatebondsofhighinvestmentgraderatings.However,anewIPOofferingofasmallpharmaceuticalcompanywithhighgrowthpotential promises high returns since the issue is being offered at a discount. Heimmediatelyallocatessomeportionoftheissuetohisfundwithoutexceedingthelimitonthe equity exposure of this fund. McDowell has least likely violated the CFA InstituteStandardsofProfessionalConductrelatingto:A. Loyalty,prudenceandcare.B. Suitability.C. Fairdealing.

8. EileenConnorsisachieftraderforAscotInvestments,amoneymanagementfirm.Shehas

beentoldrecentlybyhermostlucrativeclient,ShelbyCompany,thatiftheperformanceofitsaccountsdidnotimprovetheywillbeforcedtochangetheirmoneymanagers.Connors



haspurchasedcertainsecuritiesafewdaysback,whosepricehasgoneupsignificantly.Shehas failed to allocate these trades due to her busy schedule. After the threat fromShelby,shedecidestoallocatetheprofitabletradestoShelby’saccount,whilespreadingthelosingtradestootherAscot’saccounts.HasConnorsviolatedanyStandard?A. Yes,relatedtoFairDealing.B. No.C. Yes,relatedtoDiligenceandReasonableBasis.

9. JessicaMoralesworks as an investment adviser for Chris Crosby, amiddle‐aged, risk‐

averseinvestor.Aspertheinvestmentpolicystatement,Moralesinvestsinlow‐risk,high‐incomeequities forCrosbykeeping inmindhis currentneedsandobjectives.RecentlyCrosby’s mother passed away leaving him with a significant inheritance. Moralescontinuestoinvestasbeforewithoutanychangeintheinvestmentstrategy.AccordingtotheCFAInstituteStandardsofProfessionalConduct,Moralesshould:A. stayabreastofchangesintheclient’snetworthandaccordinglyupdatetheinvestment

policytoreflectchangesininvestmentobjectives.B. considerthelong‐termaspectofMorales’investmentsandcontinuewiththecurrent

strategy.C. keepchangingtheassetallocationsinlinewithmarketchanges.

10. SaminaHaq a CFA candidate,works for SuperiorTrust Company.While reviewing the

performanceofoneofthetrustfunds,shefindsoutthatthetrustfundhasonanaverageperformedat5%forthelastthreeyears,yetthebrochureofherfundadvertisesanannualcompoundgrowthrateof20%whichhappenedonlyinthepastyear.Italsoboastsofaconsistent increment in the investmentvalueabove theentiremarket,whichalso tookplaceduringlastyear.Haq’shighestpriorityinavoidingaviolationoftheCFAInstituteStandardsofProfessionalConductisto:A. correcttheperformancecalculationandlengthoftime.B. continuewiththeadvertisementsinceitdidriseabovethemarket.C. usethefirm’saveragerateofreturninhermarketingmaterialforallaccounts.

11. PenelopeCoxisemployedbyJameasonInvestment,andprovidesinvestmentadvicetothe

trusteesofSYUUniversityinordertorecommendinvestmentsthatwouldgeneratecapitalappreciationinendowmentfunds.Coxhasbeengiveninternalreportsbythetrusteesthathighlight theexpansionof theuniversity.Cox isapproachedbyBradleyCooper,a localphilanthropistwhoisconsideringagenerouscontributiontoSYUandanotheruniversityinthearea,buthewouldliketoseetheexpansionplansofSYUbeforemakingthedonation.CoxknowsthathedoesnotwanttospeaktothetrusteeshenceshegivesacopyoftheinternalreporttoCooper.HasCoxviolatedtheCodeandStandards?A. No.B. Yes,preservationofconfidentiality.



C. Yes,loyalty.12. LaraWhitman,CFA,workedforRapidResultsBrokerageCompany(RRBC)asatrader.She

recently resigned her position as a trader to join another competing investment andbrokerage firm.Whitmandidnotsignanynon‐competeagreementwhileatRRBC thatwouldhavepreventedherfromsolicitingformerclients.Whitman,however,hadsavedherclientlistandrecords,whileworkingatRRBC,inherpersonalcomputerathomeasasecond copy. She accesses this file to contact her former clients in her new job. TheStandardmostlikelyviolatedis:A. Loyalty.B. DutiestoClients.C. CommunicationswithClientsandProspectiveClients.

13. RobertBlakeisontheboardofdirectorsofRiceIndustriesandreceivesfreeticketsatthe

endofeachquarterforhisentirefamilytotraveltoanycityoftheirchoiceinEuropeforhisservicestotheboard.Blakedoesnotdisclosethisinformationtohisemployersinceitis not a monetary compensation. Has Blake violated any CFA Institute Standards ofProfessionalConduct?A. No.B. Yes,hehastoinformhisemployerofthebenefithereceives.C. Yes,becausehehasboughtstockofRiceforsomeofhisclientswhereappropriate.

14. AnnaBeckerisemployedbyJergenInvestmentManagementCompany(JIMC).Beckerisa

Level II candidate and is the only CFA candidate employed by JIMC. Becker is givensupervisoryresponsibilitiesofthecompliancedepartmentandaskedtoreviewthefirm’scompliancepoliciesandprocedures,whichshefindsinadequate.ShevoicesherconcernsduringameetingwiththeCEOwhotellshertosubmitherrecommendationsinareport,butthesewillnotbeimplementedsincethefirmisundergoingachangeinstructureandnocompliancechangeswillbeentertainedtillthen.AccordingtotheCodeandStandards,Beckershould:A. declinetoacceptsupervisoryresponsibilities.B. accept supervisory responsibilities and lay down the compliance policies and

proceduresforfuture.C. waittillanewstructureisimplementedandthenreviewtheentirefirm.

15. GregLouhasbeenaskedbyhisfirm,BinkleyInvestmentManagement,tofindanadviser

foroneof its fundswhich invests inderivativesandcomplexsecurities.Louselects12firmsbasedontheirannualtotalreturnperformanceandfinalizesontheadviserwiththehighestannualtotalreturn.WhichCFAInstituteStandardsofProfessionalConductdidLouviolate?A. CommunicationswithClientsandProspectiveClients.



B. ProfessionalMisconduct.C. DiligenceandReasonableBasis.

16. AlexKarachanis,CFA,isanindependentfinancialadvisorwitharosterofover100clients.

Alongwithadvisoryservices,healsofacilitatesinexecutingthetradesforhisclientsandmanagestheirportfolio.AdoniaPapadakissignedupAlexinNovember2013toadviseandmanageher portfolio.After detaileddiscussions onAdonia’s circumstances and returnrequirements,itwasagreedthatonlylarge‐capequityinvestmentswillbemade.Inmid‐2013Alexfeltthatlarge‐capstockswereexcessivelyovervaluedandshifted50%oftheportfolio to small‐cap stocks. Over the next six months, small‐cap stocks significantlyoutperformedlarge‐capstocks.ItisnowJanuary2014andAdoniahasjustreceivedheraccount statement for 2013. She is very happywith the performance of her portfolio.WhichStandarddidAlexleastlikelyviolate?A. PerformancePresentation.B. CommunicationwithClientsandProspectiveClients.C. Loyalty,PrudenceandCare.

17. Raza Jafferyworks as an independent analyst for themedical equipment industry.His

reportsarebasedonananalysisofcustomerinterviews,manufacturers,on‐sitecompanyvisits,andsecondaryresearchfromotheranalysts.Jafferydoesnotmaintainanyrecordsorfilesfortheinformationhecollectsbuthementionsthesourceofhisresearchinhisreports.Iftheclientsneedinformationonthespecificwebsites,Jafferyalwaysprovidesthemwith the relevant information. Jafferymost likely violatedwhich of the followingStandards?A. RecordRetention.B. DiligenceandReasonableBasis.C. Misrepresentation.

18. Carla Simone, a CFA candidate and a research analyst, follows firms in the beverage

industry.ShehasbeenrecommendingthepurchaseofCitrusbecauseofitsintroductionof a popular new drink for athletes and exercise enthusiasts. Simone’s husband hasinherited,fromarelative,thestockofCitrusworth$3.5million.Simonehasbeenaskedtowrite a follow up report on Citrus. She writes the report and gives a strong buyrecommendation.Thereportdoesnotmentionherhusband’sownershipofthestock.HasSimoneviolatedtheCFAInstituteStandards?A. No.B. Yes,disclosureofconflicts.C. Yes,independenceandobjectivity.

19. IzzyZubeika,CFA,works forTopworthMutualFundand is aportfoliomanager foran

aggressivegrowthequityfund.Sheisplanningtosellalargeportionofherinvestmentto



meet themedical costsofher ailinghusband.Zubeikawants to sell her stake inRoyalBeverages, but her firm has recently upgraded the stock from “hold” to “buy”.Nevertheless, after receiving approval from her employer she informs her broker toconduct the trade. Has Zubeika violated any CFA Institute Standards of ProfessionalConduct?

A. YesrelatedtoMarketManipulation.B. Yes,relatedtoPriorityofTransactions.C. No.

20. DaveDaisuke,CFA,works in thecorporate financedepartmentofAdvileSecurities.He

receives a non‐cash compensation for every referral he makes to the brokeragedepartment.Thisarrangementisanacceptednormwithinthecompanybuttheclientsare not informed because no cash is given out within the firm for interdepartmentalreferrals.AccordingtotheCFAInstituteStandards,themostappropriateactiontotakeforthefirmtoavoidaviolationisto:A. adjustthenon‐cashcompensationinthesalariesofthepersonnelincludingDaisuke

whoarereferringclientstothebrokeragedepartment.B. disclosetoclientsatthetimeofareferral,thereferralarrangementswithinAdvile’s

departments.C. stopthereferralpolicytoremoveanyconflictsofinterest.

21. LaurenCrawley is enrolled to take the Level I exam. As he tries hard to remember a

formulatocompleteaquestionhenoticesthatthepersoninfrontofhimgetsuptodrinkwaterandapieceofpaperslipsfromhispocketandfallsonCrawley’stable.Inordertoavoid a violation of the CFA Institute Standards of Professional Conduct, the leastappropriateactiontakenbyCrawleyisto:A. removeitwithoutlookingatitandcalltheproctor.B. immediatelycalltheproctortohertableandhavethepaperremoved.C. lookatthepaperandthenremoveitbeforeanyoneelsenoticesit.

22. Ankit Aacharya, CFA,whilemaking themarketingmaterial for his firmAakash Capital

writesinthebrochure,“AakashCapitaliscommittedtoachievingexcellentperformanceforitsclients.Ithiresthemosteligiblepersonnelinthefieldofinvestmentmanagement.Most of the employees have either completed the CFA Program or are enrolled ascandidatesintheCFAProgram.AsaCFAcharterholder,Iamthemostqualifiedtomanageclientinvestments.”AacharyamostlikelyviolatedtheStandardwithimproperreferencestothe:A. CFAdesignation.B. CFAProgram.C. CFAInstitute.



Solutions1. Ciscorrect.AccordingtoStandardI(A)KnowledgeoftheLawDilawezshouldadoptthe

stricterlaw.2. Biscorrect.Fritzshouldbeindependentandobjectiveinherreport.Alternatively,Brady

BrokeragecouldplaceSaber Inc.onarestricted listand issueonly factual information.StandardI(B)IndependenceandObjectivity.

3. Ciscorrect.StandardI(B)IndependenceandObjectivityinvolvesmembersandcandidates

not accepting any gifts or benefits that could be expected to compromise theirindependence and objectivity. Since no benefits were received Grosky has least likelyviolatedI(B).GroskymostlikelyviolatedtheStandardsI(C)Misrepresentation,andI(D)Misconductbecausesheknowinglymisrepresentsthecauseoftheerror.

4. Aiscorrect.RefertoStandardI(D)Misconduct.5. Aiscorrect.IftheinformationisnotpubliclydisseminatedbythecompanyandDobrogost

uses it, then it becomesmaterial nonpublic information, hence a violation of StandardII(A). A small group of stakeholders does not qualify as the public. He cannot use theinformation.

6. Aiscorrect.RefertoStandardII(B)MarketManipulation.Weinbergcreatedanappearance

ofgreaterliquidityofstockthroughitstradingstrategyandwasabletomanipulatethemarket.

7. C is correct. The Standards related to III(A) Loyalty, Prudence, and Care and III(C)

Suitability are violated. The IPSmentions low‐risk securities, and describes the assetclasses.Thereforeinvestmentinthepharmastockmaynotbesuitableforthisportfolio.

8. Aiscorrect.ConnorshasviolatedStandardIII(B)FairDealingbyfailingtodealfairlywith

allherclientsintakingtheseinvestmentactions.9. Aiscorrect.RefertoStandardIII(C)Suitability.10. Aiscorrect.AccordingtoStandardIII(D)PerformancePresentation,Haqneedstocorrect

thecalculationandlengthoftimespecifyingtheperformanceofhertrustfund.11. Biscorrect.Coxwasgiventheinternalreportsbythetrustees;becausetheinformation

wasconfidentialCoxshouldhaverefusedtodivulgeittoCooper.ThereforebyhandingtheinternalreportstohimCoxviolatesStandardIII(E)PreservationofConfidentiality.



12. Aiscorrect.StandardIV(A)Loyaltyismostlikelyviolated.Amembercannottakerecordsor work performed on behalf of the firm in paper copy or electronically withoutpermissiontoanotherfirm.Inthiscaseshecannotusethefirm’srecordsofclientswithoutthefirm’spermission.

13. Biscorrect.BlakehasviolatedStandardIV(B)AdditionalCompensationArrangementsby

failing todisclose tohisemployerbenefitsreceived inexchange forhisserviceson theboard.

14. A is correct.According to Standard IV(C)Responsibilities of Supervisors, amemberor

candidateshoulddeclineinwritingtoacceptsupervisoryresponsibilitiesuntilreasonablecompliance procedures are laid down by a firm for her to assume and exerciseresponsibility.

15. Ciscorrect.LouviolatedStandardV(A)DiligenceandReasonableBasisbynotconducting

sufficientreviewofpotentialfirms.16. A is correct. Standard III(D) Performance Presentation is not violated as Alex sends a

quarterly itemized statement of the funds and securities in his custody and thetransactionsthatoccurredduringthisperiod.StandardV(B)CommunicationwithClientsandProspectiveClientsisviolatedbecauseAlexshouldhavediscussedthechangewiththeclientbeforemovingtosmall‐capstocks.StandardIII(A)Loyalty,Prudence,andCareisviolatedbecausesmall‐capstocksmightnotcorrespondtoclient’sriskprofile.

17. Aiscorrect.RefertoStandardV(C)RecordRetention.Jafferymustcarefullydocumentand

maintaincopiesofall informationthatgoesinhisreportsinordertoavoidviolationofStandardV(C).

18. Biscorrect.Simonemustdiscloseherhusband’sownershipofthestocktoavoidviolation

ofStandardVI(A)DisclosureofConflicts.19. C is correct. No violation has occurred because she has received approval from her

employer. Standard VI(B) Priority of Transactions does not limit transactions ofemployeeswhicharedifferentfromthecurrentrecommendationsaslongastheydonotdisadvantagethecurrentclients.

20. B is correct.Disclosure to clients is important even if the referrals result in anoncash

compensation.RefertoStandardVI(C)ReferralFees21. Ciscorrect.RefertoStandardVII(A)ConductasParticipantsinCFAInstitutePrograms.



22. A is correct. CFA Institute and CFA designationwere improperly referenced. Refer toStandardVII(B)ReferencetoCFAInstitute,theCFAdesignation,andtheCFAProgram.

R04 Introduction to GIPS 2019 Level I Notes


R04IntroductiontoGIPS

Introduction

Thisreadingfocuseson: WhytheGIPSstandardswerecreatedandwhomdotheyapplyto? Whatarecompositesandwhatistheirpurposeinperformancereporting? WhocanclaimcompliancewithGIPS,andisthereaverificationprocess?

Note:mostofthematerialpresentedhereistakenfromthecurriculum.

1.WhyWeretheGIPSStandardsCreated?

GIPSstandardswerecreatedtomakeiteasiertocomparedifferentinvestmentmanagementfirms.Withoutastandard,differentfirmswouldselectthemethodwhichwouldmaketheirperformancelookbetter.

TheGIPSstandardsareapractitioner‐drivensetofethicalprinciplesthatestablishastandardized,industry‐wideapproachforinvestmentfirmstofollowincalculatingandpresentingtheirhistoricalinvestmentresultstoprospectiveclients.TheGIPSstandardsensurefairrepresentationandfulldisclosureofinvestmentperformance.Inotherwords,theGIPSstandardsleadinvestmentmanagementfirmstoavoidmisrepresentationsofperformanceandtocommunicateallrelevantinformationthatprospectiveclientsshouldknowinordertoevaluatepastresults.

MisleadingpracticesintheabsenceofGIPSincluded: Representativeaccounts:Showcasingonlythetop‐performingportfolioto

representthefirm’soverallinvestmentresults. Survivorshipbias:Excludingpoorlyperformingportfoliosandpresentingan

averageperformancehistory. Varyingtimeperiods:Presentingperformanceforaselectedtime‐periodduring

whichthemandateproducedexcellentreturns.

2.WhoCanClaimCompliance?

Anyinvestmentmanagementfirmcanclaimcompliance.ComplyingwiththeGIPSstandardsisvoluntary.Onlyinvestmentmanagementfirmsthatactuallymanageassetscanclaimcompliance.Plansponsorsandconsultantscannotclaimcomplianceunlesstheymanageassetsforwhichtheyclaimcompliance.

Complianceisafirm‐wideprocessthatcannotbeachievedonasingleproductorcomposite.AfirmhasonlytwooptionswithregardtocompliancewiththeGIPSstandards:

FullycomplywithallrequirementsoftheGIPSstandardsandclaimcompliancethroughtheuseoftheGIPSComplianceStatement;or

NotcomplywithallrequirementsoftheGIPSstandardsandnotclaimcompliancewith,ormakeanyreferenceto,theGIPSstandards.



3.WhoBenefitsfromCompliance?

TwogroupsbenefitfromGIPScompliance:investmentmanagementfirmsandprospectiveclients.

FollowingtheGIPSstandardsallowsinvestmentmanagementfirmstoassureprospectiveclientsthatthehistoricaltrackrecordtheyreportisbothcompleteandfairlypresented.ComplianceenablestheGIPS‐compliantfirmtoparticipateincompetitivebidsagainstothercompliantfirmsthroughouttheworld.Achievingandmaintainingcompliancemayalsostrengthenthefirm’sinternalcontrolsoverperformance‐relatedprocessesandprocedures.

InvestorshaveagreaterlevelofconfidenceintheintegrityofperformancepresentationsofaGIPS‐compliantfirm.Investorscaneasilycompareperformancepresentationsfromdifferentinvestmentmanagementfirms.

CompliancewiththeGIPSstandardsdoesnoteliminatetheneedfordue‐diligence,butitenhancesthecredibilityofinvestmentmanagementfirmsthathavechosentoundertakethisresponsibility.

4.Composites

OneofthekeyrequirementsoftheGIPSstandardsistheuseofcomposites.Acompositeisanaggregationofoneormoreportfoliosmanagedaccordingtoasimilarinvestmentmandate,objective,orstrategy.Assumeafirmmanagesportfoliosbasedononeofthefollowingstrategies:

StrategyA:Aggressivegrowth.Underthisstrategythefirmselectssmall‐capstockswithstronggrowthpotentialoverthenextfewyears.

StrategyB.Largecapvalue.Underthisstrategylarge‐capvaluestocksareselected.

GivethisscenariothefirmshouldcreateacompositeforStrategyA,andanothercompositeforStrategyB.

Acompositemustincludeallactual,fee‐paying,discretionaryportfoliosmanagedinaccordancewiththesameinvestmentmandate,objective,orstrategy.By“actual”wemeantheseshouldberealandnotdummy/modelportfoliostosimulatethereturns.Portfoliosforwhichtheclientdoesnotpayafeemustnotbeincluded.Forinstance,theremaybecharitableorganizationsthatdonotpayafeefortheirassetsbeingmanaged.Theseshouldnotbeincluded.By“discretionary”,wemeantheinvestmentmanagementfirmhastherighttodetermineandpurchasesuitablesecuritiesforaportfolio.Ifthereisaportfoliowheretheclientdetermineswhatsecuritiesshouldbepurchased,thenitisnon‐discretionary.

Thedeterminationofwhichportfoliostoincludeinthecompositeshouldbedoneaccordingtopre‐establishedcriteria(i.e.onanex‐antebasis),notafterthefact.Thispreventsafirmfromincludingonlythebest‐performingportfolios.Thisisimportantbecauseperformancenumbersarereportedbasedoncomposites.



5.Verification

FirmsthatclaimcompliancewiththeGIPSstandardsareresponsiblefortheirclaimofcomplianceandmaintainingthatcompliance.OnceafirmclaimscompliancewithGIPS,theymayvoluntarilyhireanindependentthird‐partytoperformverification.JustasGIPScomplianceisvoluntary,verificationisalsovoluntary.Verificationisperformedwithrespecttoanentirefirm.Itisnotdoneoncomposites,orindividualdepartments.

Verificationmustbeperformedbyanindependentthirdparty.Afirmcannotperformitsownverification.Third‐partyverificationbringsadditionalcredibilitytoafirm’sclaimofcompliance.Tounderstandwhyafirmwouldpaytobeverifiedifitisvoluntary,assumetherearetwofirms,AandB.FirmAclaimsGIPScomplianceandfirmBclaimsGIPScompliancewiththird‐partyverificationfromareputedfirm.Asaninvestor,whichfirmwouldyoubemorecomfortablewith?ObviouslyfirmB,andthatgivesfirmBanadvantageoverfirmA.

Verificationtestsinclude: Whethertheinvestmentfirmhascompliedwithallthecompositeconstruction

requirementsoftheGIPSstandardsonafirm‐widebasis,and Whetherthefirm’spoliciesandproceduresaredesignedtocalculateandpresent

performanceincompliancewiththeGIPSstandards.

6.TheStructureoftheGIPSStandards

Theprovisionswithinthe2010editionoftheGIPSstandardsaredividedintoninesections:

0. FundamentalsofCompliance

1. InputData

2. CalculationMethodology

3. CompositeConstruction

4. Disclosure

5. PresentationandReporting

6. RealEstate

7. PrivateEquity

8. WrapFee.SeparatelyManagedAccount(SMA)Portfolios



Summary

LO.a:ExplainwhytheGIPSstandardswerecreated,whatpartiestheGIPSstandardsapplyto,andwhoisservedbythestandards.

TheGIPSstandardswerecreatedtoavoidmisrepresentationofperformance.Theyapplytoinvestmentmanagementfirms.Theyareintendedtoserveprospectiveandexistingclientsoftheinvestmentfirms.

LO.b:Explaintheconstructionandpurposeofcompositesinperformancereporting.

Acompositeisanaggregationofoneormoreportfoliosmanagedaccordingtoasimilarinvestmentmandate,objective,orstrategy.Whenusedinperformancereporting,compositeshelpclientsevaluatehowwellacompanyhasperformedwithdifferentinvestmentstyles.

LO.c:Explaintherequirementsforverification.

Verificationisperformedwithrespecttoanentirefirm.Itisnotdoneoncomposites,orindividualdepartments.

Verificationmustbeperformedbyanindependentthird‐party.Afirmcannotperformitsownverification.



PracticeQuestions

1. WhocanmostlikelyclaimcompliancewithGIPSStandards?A. CFAcharterholders.B. Individuals.C. Investmentmanagementfirms.

2. According to the Global Investment Performance Standards (GIPS), the criteria for

includingportfoliosincompositesis:A. all actual fee‐paying, discretionary portfolios must be included in at least one

composite.B. alldiscretionaryportfoliosmustbeincludedinacomposite.C. allactualfee‐payingportfoliosmustbeincludedinacomposite.

3. VerificationofGIPScomplianceis:

A. donebyanindependentthird‐party.B. mandatorytoclaimcompliance.C. donevoluntarilybythefirmunderthesupervisionoftheCFAInstitute.



Solutions1. C is correct. Only investment management firms can claim compliance. Individuals,

charterholders,andsoftwaretoimplementtheStandardscannotclaimcompliance.2. Aiscorrect.Allactualfee‐paying,discretionaryportfoliosmustbeincludedinatleastone

composite.3. Aiscorrect.VerificationofGIPScomplianceisdonebyanindependentthirdparty.Afirm

cannotperformitsownverification.

R05 The GIPS Standard 2019 Level I Notes


R05TheGIPSStandard

Introduction

Inthisreadingwefocuson: GoalsoftheGIPSExecutiveCommittee. KeyfeaturesoftheGIPSstandardsandthefundamentalsofcompliance. Howhistoricalperformancerecordmustbepresented. TheninemajorsectionsoftheGIPSstandard.

Note:mostofthematerialpresentedhereistakenfromthecurriculum.

GoalsoftheGIPSExecutiveCommittee

ThegoalsoftheGIPSExecutiveCommitteearepresentedbelow: Toestablishinvestmentindustrybest‐practicesforcalculatingandpresenting

investmentperformancethatpromoteinvestorinterestsandinstillinvestorconfidence.

Toobtainworldwideacceptanceofasinglestandardforthecalculationandpresentationofinvestmentperformancebasedontheprinciplesoffairpresentationandfulldisclosure.

Topromotetheuseofaccurateandconsistentperformancedata. Toencouragefairglobalcompetitionamonginvestmentfirmswithoutcreating

barrierstoentry;and Tofosterthenotionofindustry“self‐regulation”onaglobalbasis.

KeyFeaturesoftheGIPSStandards

ThekeyfeaturesofGIPSareasfollows: TheGIPSstandardsaretheethicalstandardsforinvestmentperformance

presentationtoensurefairrepresentationandfulldisclosureofinvestmentperformance.Inordertoclaimcompliance,firmsmustadheretotherequirementsincludedintheGIPSstandards.

MeetingtheobjectivesoffairrepresentationandfulldisclosureislikelytorequiremorethansimplyadheringtotheminimumrequirementsoftheGIPSstandards.Firmsshouldalsoadheretotherecommendationstoachievebestpracticeinthecalculationandpresentationofperformance.

TheGIPSstandardsrequirefirmstoincludeallactual,discretionary,fee‐payingportfoliosinatleastonecompositedefinedbyinvestmentmandate,objective,orstrategyinordertopreventfirmsfromcherry‐pickingtheirbestperformance.Thismeansfirmsmustcreatecompositesandeachactual,fee‐paying,discretionaryportfoliomustbeinatleastonecomposite.Ifaportfolioisnotincludedinanycomposite,thenthereturnsassociatedwithitwillnotbeincluded.



TheGIPSstandardsrelyontheintegrityofinputdata.Theaccuracyofinputdataiscriticaltotheaccuracyofperformancepresentation.Theunderlyingvaluationsofportfolioholdingsdrivetheportfolio’sperformance.Itisessentialthattheseandotherinputsareaccurate.TheGIPSstandardsrequirefirmstoadheretocertaincalculationmethodologiesandtomakespecificdisclosuresalongwiththefirm’sperformance.

FirmsmustcomplywithallrequirementsoftheGIPSstandards.

HistoricalPerformanceRecord

Afirmisrequiredtoinitiallypresent,ataminimum,fiveyearsofannualinvestmentperformancethatarecompliantwiththeGIPSstandards.Ifthefirmorthecompositehasbeeninexistenceforlessthanfiveyears,thefirmmustpresentperformancesincethefirm’sinceptionorthecomposite’sinceptiondate.

Laterthefirmmustpresentanadditionalyearofperformanceeachyear,buildinguptoaminimumof10yearsofGIPS‐compliantperformance.

Firmsmaylinknon‐GIPScompliantperformancetotheirGIPS‐compliantperformanceprovidedthatonlyGIPS‐compliantperformanceispresentedforperiodsafter1January,2000andthefirmdisclosestheperiodsofnon‐compliance.

Firmsthatmanageprivate‐equity,realestate,and/orwrapfee/separatelymanagedaccount(SMA)portfoliosmustalsocomplywithsections6,7,and8respectively,oftheprovisionsoftheGIPSstandardsthatbecameeffectiveasof1January,2006.

ConsiderFirmAwhichwasestablishedin2013anddecidestobecomeGIPScompliantin2014.Initially,itmustpresentperformanceinformationfor2013and2014.Later,itmustkeepaddingperformancedataeveryyearuntilitbuildsuptoaminimumof10years.

ConsiderFirmBwhichwasestablishedin2008anddecidestobecomeGIPScompliantin2014.Initially,itmustpresentperformanceinformationforfiveyearsfromtheperiodendingin2010totheperiodendingin2014.Later,itmustalsoaddanadditionalyearuntilithas10yearsofGIPS‐compliantperformance.

Compliance

Thedefinitionofthefirmisthefoundationforfirm‐widecomplianceandcreatesdefinedboundarieswherebytotalfirmassetscanbedetermined.

FirmsmusttakeallstepsnecessarytoensurethattheyhavesatisfiedalltherequirementsoftheGIPSstandardsbeforeclaimingcompliance.

Firmsarestronglyencouragedtoperformperiodicinternalcompliancechecks. Firmsmaychoosetohaveanindependentthird‐partyverificationthatteststhe

constructionofthefirm’scompositesaswellasthefirm’spoliciesandproceduresastheyrelatetocompliancewiththeGIPSstandards.Verificationisrecommended,butitisvoluntaryandmustbedonebyathird‐partyverifier.



Inadditiontoverification,firmsmayalsochoosetohavespecificallyfocusedcompositetesting(performanceexamination)performedbyanindependentthird‐partyverifiertoprovideadditionalassuranceregardingaparticularcomposite.

Theeffectivedateforthe2010editionoftheGIPSstandardsis1January,2011.Compliantpresentationsthatincludeaperformanceforperiodsthatbeginonorafter1January,2011mustbepreparedinaccordancewiththe2010editionoftheGIPSstandards.

ImplementingaGlobalStandard

ThepresenceofalocalsponsoringorganizationforinvestmentperformancestandardsisessentialforeffectiveimplementationandongoingsupportoftheGIPSstandardswithinacountry.ThecurriculumlistsGIPScountrysponsorsforafewcountries.

Countrysponsorensuresthatthecountry’sinterestsaretakenintoaccountastheGIPSstandardsaredeveloped.

TheGIPSexecutivecommitteestronglyencouragescountrieswithoutaninvestmentperformancestandardtopromotetheGIPSstandardsasthelocalstandard.Ifthereisnolocalstandardinacountry,thenitisidealforthecountrytopromoteandadoptGIPSasitisaglobalstandard,andwhenrequiredtranslatethemintothelocallanguage.

CompliancewithapplicablelawandrulesdoesnotnecessarilymeancompliancewithGIPS.

Incasesinwhichlawsand/orregulationsconflictwiththeGIPSstandards,firmsarerequiredtocomplywiththelawsandregulationsandmakefulldisclosureoftheconflictinthecompliantpresentation.FirmscanstillclaimcompliancewithGIPSbuttheymustdisclosewhereverthereisadeviationthatthelawofthelandisbeingfollowed.

NineMajorSectionsoftheGIPSStandards

Theprovisionswithinthe2010editionoftheGIPSstandardsaredividedintoninesections:0. FundamentalsofCompliance1. InputData2. CalculationMethodology3. CompositeConstruction4. Disclosure5. PresentationandReporting6. RealEstate7. PrivateEquity8. WrapFee/SeparatelyManagedAccount(SMA)portfolios



Theprovisionsarecategorizedintorequirementsandrecommendations.Alltherequirementsmustbeimplementedtoclaimcompliance.

0.FundamentalsofCompliance

SeveralcoreprinciplescreatethefoundationfortheGIPSstandards,includingproperlydefiningthefirm,providingcompliantpresentationstoallprospectiveclients,adheringtoapplicablelawsandregulations,andensuringthatinformationpresentedisnotfalseormisleading.TwoimportantissuesthatafirmmustconsiderwhenbecomingcompliantwiththeGIPSstandardsarethedefinitionofthefirmandthefirm’sdefinitionofdiscretion.Thedefinitionofthefirmisthefoundationforfirm‐widecomplianceandcreatesdefinedboundarieswherebytotalfirmassetscanbedetermined.Thefirm’sdefinitionofdiscretionestablishescriteriatojudgewhichportfoliosmustbeincludedinacompositeandisbasedonthefirm’sabilitytoimplementitsinvestmentstrategy.

Samplefirmdefinition:XYXInvestmentFirmisabalancedportfolioinvestmentmanagerthatinvestssolelyinUS‐basedsecurities.XYZInvestmentFirmisdefinedasanindependentinvestmentmanagementfirmthatisnotaffiliatedwithanyparentorganization.

TherequirementsofProvision0arepresentedbelow(reproducedfromthecurriculum).

0.A.1:FirmsmustcomplywithalltherequirementsoftheGIPSstandards,includinganyupdates,GuidanceStatements,interpretations,Questions&Answers(Q&As),andclarificationspublishedbyCFAInstituteandtheGIPSExecutiveCommittee,whichareavailableontheGIPSstandardswebsite(www.gipsstandards.org)aswellasintheGIPSHandbook.

0.A.2:Firmsmustcomplywithallapplicablelawsandregulationsregardingthecalculationandpresentationofperformance.

Iftherearenoapplicablelawsandrules,thenGIPScompliantfirmsmustfollowtheGIPSstandards.But,ifacountryhasapplicablelawsandregulationsregardingthecalculationandpresentationofperformance,thenthecountrylawsmustbefollowedandanydifferenceswithGIPSmustbedocumented.

0.A.3:Firmsmustnotpresentperformanceorperformance‐relatedinformationthatisfalseormisleading.

0.A.4:TheGIPSstandardsmustbeappliedonafirm‐widebasis.

0.A.5:FirmsmustdocumenttheirpoliciesandproceduresusedinestablishingandmaintainingcompliancewiththeGIPSstandards,includingensuringtheexistenceandownershipofclientassets,andmustapplythemconsistently.

0.A.6:IfthefirmdoesnotmeetalltherequirementsoftheGIPSstandards,thefirmmustnotrepresentorstatethatitis“incompliancewiththeGlobalInvestmentPerformanceStandardsexceptfor...”ormakeanyotherstatementsthatmayindicatepartialcompliancewiththeGIPSstandards.



FirmsarenotallowedtoclaimpartialcompliancewiththeGIPSstandards.

0.A.7:Statementsreferringtothecalculationmethodologyasbeing“inaccordance,”“incompliance,”or“consistent”withtheGlobalInvestmentPerformanceStandards,orsimilarstatements,areprohibited.

0.A.8:Statementsreferringtotheperformanceofasingle,existingclientportfolioasbeing“calculatedinaccordancewiththeGlobalInvestmentPerformanceStandards”areprohibited,exceptwhenaGIPS‐compliantfirmreportstheperformanceofanindividualclient’sportfoliotothatclient.

0.A.9:Firmsmustmakeeveryreasonableefforttoprovideacompliantpresentationtoallprospectiveclients.Firmsmustnotchoosetowhomtheypresentacompliantpresentation.Aslongasaprospectiveclienthasreceivedacompliantpresentationwithintheprevious12months,thefirmhasmetthisrequirement.

0.A.10:Firmsmustprovideacompletelistofcompositedescriptionstoanyprospectiveclientthatmakessucharequest.Firmsmustincludeterminatedcompositesonthefirm’slistofcompositedescriptionsforatleastfiveyearsafterthecompositeterminationdate.Acompositemustbeclearlydescribedastowhatmandateorstrategyitisfollowing:Forexample,small‐capequityvalue,Japan‐equity,fixed‐incomeetc.Ifacompositewasterminated,thenitsperformancemustbepresentedforatleastfiveyearsafterterminationtoovercomesurvivorshipbias.

0.A.11:Firmsmustprovideacompliantpresentationforanycompositelistedonthefirm’slistofcompositedescriptionstoanyprospectiveclientthatmakessucharequest.

AcompliantpresentationisonethatcomplieswithalltheGIPSprovisions.

0.A.12:Firmsmustbedefinedasaninvestmentfirm,subsidiary,ordivisionheldouttoclientsorprospectiveclientsasadistinctbusinessentity.

Scenario:AssumethereisafirmcalledUBLandithasasubsidiarycalledUBL‐AssetManagement(UBL‐AM).IfinvestorsapproachUBL‐AMtotradeandinvestinsecurities/funds,thenUBM‐AMisthefirmhere,andmustcomplywiththeGIPSstandards.

0.A.13:Forperiodsbeginningonorafter1January2011,totalfirmassetsmustbetheaggregatefairvalueofalldiscretionaryandnon‐discretionaryassetsmanagedbythefirm.Thisincludesbothfee‐payingandnon‐fee‐payingportfolios.

Donotconfusethiswithacomposite.Acompositemustincludeonlyactual,fee‐payingdiscretionaryportfolios.But,whenafirmreportsitstotalassets,itmustincludethefairvalueofalldiscretionaryandnon‐discretionaryassetsandallfee‐payingandnon‐feepayingportfolios.

0.A.14:Totalfirmassetsmustincludeassetsassignedtoasub‐advisorprovidedthefirmhasdiscretionovertheselectionofthesub‐advisor.



0.A.15:Changesinafirm’sorganizationmustnotleadtoalterationofhistoricalcompositeperformance.

0.A.16:Whenthefirmjointlymarketswithotherfirms,thefirmclaimingcompliancewiththeGIPSstandardsmustbesurethatitisclearlydefinedandseparaterelativetootherfirmsbeingmarketed,andthatitisclearwhichfirmisclaimingcompliance.

Outlinedabovearerequirements.TheGIPSstandardsalsoincluderequirements.Forexample,assumeaninvestmentmanagementcompany,HS,hasdifferentgeographicaloffices,whichoperateunderthesamebrandnamebutasindividualinvestmentmanagementcompaniessuchasHSMaltaplc,HSSpain,HSIndiaLimited,HSMalaysiaLimited.Thefirmdefinitionshouldbebroadenoughtoincludeallgeographicalofficesunderoneumbrella.Thisisjustarecommendation,notarequirement.

Instructor’sNote:AtLevelIyouarerequiredtoknowthedetailsofProvision0(FundamentalsofCompliance).Forprovisions1–8youjustneedtoknowthebasicdescriptionswhicharegivenbelow:

1. InputdataConsistencyofinputdatausedtocalculateperformanceiscriticaltoeffectivecompliancewiththeGIPSstandardsandestablishesthefoundationforfull,fair,andcomparableinvestmentperformancepresentations.Forperiodsbeginningonorafter1January2011,allportfoliosmustbevaluedinaccordancewiththedefinitionoffairvalueandtheGIPSvaluationprinciples.

2. CalculationMethodologyAchievingcomparabilityamonginvestmentmanagementfirms’performancepresentationsrequiresuniformityinthemethodsusedtocalculatereturns.TheGIPSstandardsmandatetheuseofcertaincalculationmethodologiestofacilitatecomparability.

3. CompositeConstructionAcompositeisanaggregationofoneormoreportfoliosmanagedaccordingtoasimilarinvestmentmandate,objective,orstrategy.Thecompositereturnistheasset‐weightedaverageoftheperformanceofallportfoliosinthecomposite.Creatingmeaningfulcompositesisessentialtothefairpresentation,consistency,andcomparabilityofperformanceovertimeandamongfirms.Assumetherearetwoportfoliosinacomposite:portfolio1withavalueof$10millionandportfolio2withavalueof$90million.Thereturnsofthetwoportfoliosare10%and12%respectively.Theoverallreturnofthecompositemustbecloserto12%asthe12%returnhasa90%weightage.

4. DisclosureDisclosureallowsfirmstoelaborateonthedataprovidedinthepresentationandgivethereaderthepropercontextinwhichtounderstandtheperformance.TocomplywiththeGIPSstandards,firmsmustdisclosecertaininformationinallcompliantpresentationsregardingtheirperformanceandthepoliciesadoptedbythefirm.Oneoftheessentialdisclosuresfor



everyfirmistheclaimofcompliance.OnceafirmmeetsalltherequirementsoftheGIPSstandards,itmustappropriatelyusetheclaimofcompliancetoindicatecompliancewiththeGIPSstandards.Theallowedformatforfirmsthatclaimcomplianceis:<<Nameoffirm>>claimscompliancewiththeGlobalInvestmentPerformanceStandards(GIPS)andhaspreparedandpresentedthisreportincompliancewiththeGIPSStandards.

5. PresentationandReportingAfterconstructingthecomposites,gatheringtheinputdata,calculatingreturns,anddeterminingthenecessarydisclosures,thefirmmustincorporatethisinformationinpresentationsbasedontherequirementsintheGIPSstandardsforpresentinginvestmentperformance.Nofinitesetofrequirementscancoverallpotentialsituationsoranticipatefuturedevelopmentsininvestmentindustrystructure,technology,products,orpractices.Whenappropriate,firmshavetheresponsibilitytoincludeinGIPS‐compliantpresentationsinformationnotaddressedbytheGIPSstandards.

6. RealEstateUnlessotherwisenoted,thissectionsupplementsalloftherequiredandrecommendedprovisionsinSections0‐5.Realestateprovisionswerefirstincludedinthe2005editionoftheGIPSstandardsandbecameeffective1January,2006.The2010editionoftheGIPSstandardsincludesnewprovisionsforclosed‐endrealestatefunds.Firmsshouldnotethatcertainprovisionsofsections0‐5donotapplytorealestateinvestmentsoraresupersededbytheprovisionswithinsection6.Theprovisionsthatdonotapplyhavebeennotedwithinsection6.

7. PrivateEquityUnlessotherwisenoted,thissectionsupplementsalloftherequiredandrecommendedprovisionsinsections0‐5.Privateequityprovisionswerefirstincludedinthe2005editionoftheGIPSstandardsandbecameeffective1January2006.Firmsshouldnotethatcertainprovisionsinsections0‐5donotapplytoprivateequityinvestmentsoraresupersededbytheprovisionswithinsection7.Theprovisionsthatdonotapplyhavebeennotedwithinsection7.

8. WrapFee/SeparatelyManagedAccount(SMA)PortfoliosUnlessotherwisenoted,thissectionsupplementsalloftherequiredandrecommendedprovisionsinsections0‐5.Firmsshouldnotethatcertainprovisionsinsections0‐5oftheGIPSstandardsdonotapplytowrapfee/SMAportfoliosoraresupersededbytheprovisionswithinsection8.Theprovisionsthatdonotapplyherehavebeennotedwithinsection8.

SamplePresentation

AsampleGIPS‐compliantpresentationreportispresentedbelow.Someoftheimportantaspectsthatyoucantakenoteofare:

Nameoffirm:Sample1InvestmentFirm;Composite:BalancedGrowth Grossreturn,netreturn,andno.ofportfoliosarerequireddatawhicharepresented.



Sample1 InvestmentFirmBalancedGrowthComposite(fromthecurriculum)

1January2002through31December2011

Year CompositeGrossReturn(%)

CompositeNetReturn(%)

CustomBenchmarkReturn(%)

Composite3‐YrStDev(%)

Benchmark3‐YrStDev(%)

NumberofPortfolios

InternalDispersion(%)

CompositeAssets($M)

FirmAssets($M)

2002 ‐10.5 ‐11.4 ‐11.8 31 4.5 165 236

2003 16.3 15.1 13.2 34 2.0 235 346

2004 7.5 6.4 8.9 38 5.7 344 529

2005 1.8 0.8 0.3 45 2.8 445 695

2006 11.2 10.1 12.2 48 3.1 520 839

2007 6.1 5.0 7.1 49 2.8 505 1,014

2008 ‐21.3 ‐22.1 ‐24.9 44 2.9 475 964

2009 16.5 15.3 14.7 47 3.1 493 983

2010 10.6 9.5 13.0 51 3.5 549 1,114

2011 2.7 1.7 0.4 7.1 7.4 54 2.5 575 1,236

Sample1InvestmentFirmclaimscompliancewiththeGlobalInvestmentPerformanceStandards(GIPS®)andhaspreparedandpresentedthisreportincompliancewiththeGIPSstandards.Sample1InvestmentFirmhasbeenindependentlyverifiedfortheperiods1January2000through31December2010.Theverificationreportisavailableuponrequest.Verificationassesseswhether(1)thefirmhascompliedwithallthecompositeconstructionrequirementsoftheGIPSstandardsonafirm‐widebasisand(2)thefirm’spoliciesandproceduresaredesignedtocalculateandpresentperformanceincompliancewiththeGIPSstandards.Verificationdoesnotensuretheaccuracyofanyspecificcompositepresentation.

Notes:

1. Sample1InvestmentFirmisabalancedportfolioinvestmentmanagerthatinvestssolelyinUS‐basedsecurities.Sample1InvestmentFirmisdefinedasanindependentinvestmentmanagementfirmthatisnotaffiliatedwithanyparentorganization.Policiesforvaluingportfolios,calculatingperformance,andpreparingcompliantpresentationsareavailableuponrequest.

2. TheBalancedGrowthCompositeincludesallinstitutionalbalancedportfoliosthatinvestinlarge‐capUSequitiesandinvestment‐gradebondswiththegoalofprovidinglong‐termcapitalgrowthandsteadyincomefromawell‐diversifiedstrategy.Althoughthestrategyallowsforequityexposurerangingbetween50–70%,thetypicalallocationisbetween55–65%.Theaccountminimumforthecompositeis$5million.



3. Thecustombenchmarkis60%YYYUSEquityIndexand40%ZZZUSAggregateBondIndex.Thebenchmarkisrebalancedmonthly.

4. ValuationsarecomputedandperformanceisreportedinUSdollars.

5. Gross‐of‐feesreturnsarepresentedbeforemanagementandcustodialfeesbutafteralltradingexpenses.Compositeandbenchmarkreturnsarepresentednetofnon‐reclaimablewithholdingtaxes.Net‐of‐feesreturnsarecalculatedbydeductingthehighestfeeof0.83%fromthemonthlygrosscompositereturn.Themanagementfeescheduleisasfollows:1.00%onthefirst$25million;0.60%thereafter.

6. ThiscompositewascreatedinFebruary2000.Acompletelistofcompositedescriptionsisavailableuponrequest.

7. Internaldispersioniscalculatedusingtheequal‐weightedstandarddeviationofannualgrossreturnsofthoseportfoliosthatwereincludedinthecompositefortheentireyear.

8. Thethree‐yearannualizedstandarddeviationmeasuresthevariabilityofthecompositeandthebenchmarkreturnsoverthepreceding36‐monthperiod.



Summary

LO.a:DescribethekeyfeaturesoftheGIPSstandardsandthefundamentalsofcompliance.

Refertosections‘KeyFeaturesoftheGIPSStandards’and‘0.FundamentalsofCompliance’.

LO.b:DescribethescopeoftheGIPSstandardswithrespecttoaninvestmentfirm’sdefinitionandhistoricalperformancerecord.

InvestmentFirm’sDefinition Firmsmustbedefinedasaninvestmentfirm,subsidiary,oradivisionthatisheldout

toclientsandprospectsasa‘distinctbusinessentity’. Ifafirmhasdifferentgeographiclocations,alldoingbusinessunderthesamename,

thenthedefinitionofthefirmmustincludebranchesfromalllocations.

HistoricalPerformanceRecord

Initially, Afirmmustpresentaminimumoffiveyearsofcompliantpresentation. Ifthefirmorcompositehasbeeninexistenceforlessthanfiveyears,the

presentationshouldincludeperformancesinceinception.

Afterinitialcompliance, Thefirmmustaddoneyearofcompliantpresentationeachyear,

Sothatthefirmeventuallypresentsaminimumperformancehistoryof10years.

LO.c:ExplainhowtheGIPSstandardsareimplementedincountrieswithexistingstandardsforperformancereportinganddescribetheappropriateresponsewhentheGIPSstandardsandlocalregulationsconflict.

Incountrieswheretherearenoinvestmentperformanceregulations,useandpromotetheGIPSstandard.

Incountrieswherethereareexistinglawsandregulationsregardingperformancepresentation,adheretoGIPSinadditiontothelocallaws.

Incaseofaconflictwiththelocallaws,followthelocallawbutdisclosetheconflict

LO.d:DescribetheninemajorsectionsoftheGIPSstandards.

Refertosection‘NineMajorSectionsoftheGIPSStandards’.



PracticeQuestions

1. WhichofthefollowingisnotakeyfeatureoftheGIPSstandards?A. Allactual,discretionary,fee‐paying,andnon‐feepayingportfoliosmustbeincluded

inatleastonecomposite.B. Firmsmustuseaccurateinputdata,followcertaincalculationmethodologies,and

disclosethemethodused.C. FirmsmustcomplywithallrequirementsoftheGIPSstandards.

2. Ifacompositehasbeeninexistenceforlessthanfiveyears,thenforwhatperiodisthe

firmmostlikelyrequiredtopresentGIPS‐compliantperformance?A. Twoyears.B. Oneyear.C. Sinceinceptiondate.

3. EritbaisasmallislandnationinthePacificwherelawsandregulationsexistforcalculation

andpresentationofinvestmentperformance.AccordingtotheGIPSstandards,whatlawsare firms in Eritba encouraged to complywith for the calculation and presentation ofinvestmentperformance?

A. GIPSstandardsonly.B. Applicablelaw,regulations,andGIPSstandards.C. Applicablelawandregulationsonly.

4. Which of the following is not one of the nine sections of the provisions of the Global

InvestmentPerformanceStandards?A. Disclosure.B. ProcessedData.C. RealEstate.



Solutions1. Aiscorrect.Itisnotmandatoryfornon‐feepayingportfoliostobeincludedinatleastone

composite.2. Ciscorrect.Ifafirmhasbeeninexistenceforlessthanfiveyears,thenafirmisrequired

to present compliant presentation since the firm’s inception date, or the compositeinceptiondate.

3. B is correct. Firms are encouraged to comply with applicable laws and regulatory

requirements in addition to the GIPS Standards. This is because compliance withapplicablelawdoesnotimplycompliancewiththeGIPSStandards.

4. Biscorrect. ‘InputData’,not ‘ProcessedData’, isasectionoftheprovisionsoftheGIPS

standards.

R06 Time Value of Money 2019 Level I Notes


R06TimeValueofMoney

IntroductoryNote

FinancialCalculator:CFAInstituteallowsonlytwocalculatormodelsduringtheexam: TexasInstrumentsBAIIPlus(includingBAIIPlusProfessional)and

HewlettPackard12C(includingtheHP12CPlatinum,12CPlatinum25thanniversaryedition,12C30thanniversaryedition,andHP12CPrestige)

UnlessyouarealreadycomfortablewiththeHPfinancialcalculator,werecommendusingtheTexasInstrumentsfinancialcalculator.ExplanationsandkeystrokesinourstudymaterialsarebasedontheTexasInstrumentsBAIIPluscalculator.Beforeyoustartusingthecalculatortosolveproblems,werecommendthatyousetthenumberofdecimalplacesto‘floatingdecimal’.1.Introduction

Ifyouhave$100today,versusanoptiontoreceive$100afterthreeyears,whatwouldyouprefer?

Obviously,youwouldprefer$100today.Eventhoughyouhavethesameamount($100)inbothcases,youprefer$100today.Thismeansthattherehastobesomevalueassociatedwithtime,becauseyouareputtingmorevalueonthe$100thatyouaregettingtoday,relativetothe$100atalaterpointintime.Thisisknownas‘timevalueofmoney.’

Letussaythatyouareindifferentbetween$100dollarstodayversus$110afteroneyear.

Presentvalue(PV):Themoneytodayorthevaluetodayiscalledthepresentvalue(PV=100).Thiscouldbeaninvestmentwhichyoumakeattime0.

Futurevalue(FV):Thevalueatafuturepointintimeiscalledthefuturevalue(FV=110).

Interestrate(I):Therelationshiporthelinkbetweenpresentvalueandfuturevalueisestablishedthroughaninterestrate(I=10%).

Inthisreading,weareessentiallygoingtotalkabouttheseconcepts:presentvalue(PV),futurevalue(FV),andthewaywelinkthesetwoconceptsusinginterestrates(I).



2.InterestRates:Interpretation

Let’sdiscussthedifferentinterpretationsofinterestratesusinganexample.Sayyoulend$900todayandreceive$990afteroneyear(–vesignindicatesoutflow).

Interestratescanbeinterpretedas:

1. Requiredrateofreturn:Thefactthatyouarewillingtogive$900todayontheconditionthatyouget$990afteroneyearmeansthattoengageinthistransaction,yourequireareturnof10%.(Simplecalculationwillshowyouthattheinterestrateinthistransactionis10%).

2. Discountrate:Youcandiscountthemoneythatyouwillreceiveafteroneyeari.e.$990at10%togetthepresentvalueof$900(990/1.1=900).Therefore,the10%canalsobethoughtofasadiscountrate.

3. Opportunitycost:Let’ssayinsteadoflendingthe$900,youspentitonsomethingelse.Youhavethenforgonetheopportunitytoearn10%interest.Therefore,10%canalsobethoughtofasanopportunitycost.

InterestRates:InvestorPerspective

Asaninvestor,wecanthinkoftheinterestrateasasumofthefollowingcomponents:

Interestrate=Realrisk‐freeinterestrate+Inflationpremium+Defaultriskpremium+Liquiditypremium+Maturitypremium

Let’slookatthedifferentcomponents.

Realrisk‐freeinterestrate:Thisistheratethatyougetonasecuritythathasnoriskandisextremelyliquid.Wemakeanassumptionherethatthereisnoinflation.

Inflationpremium:Wecanthenaddonaninflationpremium.Inflationpremiumistheexpectedannualinflationintheupcomingperiod.

Defaultriskpremium:Wecanalsothenaddadefaultriskpremium.Thisistheadditionalpremiumthatinvestorsrequirebecauseoftheriskofdefault.Example:Let'ssaythatyoulend$100eachtopersonAandpersonB.However,Bhasahighriskofdefault,soyouareworriedthathemightnotpay.ThereforeyoumightdemandahigherreturnfromBascomparedtoA,becauseoftheriskofdefault.Thisadditionalreturnthatyoudemandiscalledthedefaultriskpremium.

Liquiditypremium:Nextwehaveliquiditypremium.Thisisthepremiumthatinvestorsdemandbecauseofthelackofliquidityofaninvestment.



Example:ThinkoftwoinvestmentsCandDwhicharesimilarinallregards.TheonlydifferenceisthatinvestmentCisextremelyliquid,whereasinvestmentDisnotthatliquid.Clearlyasinvestors,wewilldemandahigherreturnonDbecauseitisnoteasytosell.Thisadditionalreturnthatwedemandiscalledtheliquiditypremium.

Maturitypremium:Finallywehavethematuritypremium.Thisisthepremiumthatinvestorsdemandonasecuritywithlongmaturity.Thematuritypremiumcompensatesinvestorsfortheincreasedsensitivityofthemarketvalueofdebttoachangeinmarketinterestratesasmaturityisextended.Example:Let’ssaywehavetwosecurities,EandF.SecurityEhasamaturityof1yearandsecurityFhasamaturityof4years.Becauseofthelongermaturity,Fhasmorerisk,intermsofitspricebeingmoresensitivetochangesininterestrate.Instructor’sNote:Youwillunderstandthisconceptbetterwhenyoustudyfixedincomesecurities.Butfornow,youcantakeitasagiventhatFhashigherriskbecauseofthelongermaturity.Obviously,investorswilldemandsomecompensationforthehigherlevelofrisk.Thisadditionalreturnthatinvestorsdemandiscalledthematuritypremium.

Nominalriskfreerate:Nominalrisk‐freerate=Realrisk‐freeinterestrate+Inflationpremium.Soiftherealrisk‐freerateis3%andtheinflationpremiumis2%,thenthenominalrisk‐freerateis5%.Instructor’sNote:Ontheexamifyougetaterm‘risk‐freerate’withnomentionofwhethertherateisrealornominal,thentheassumptionisthatwearetalkingaboutthenominalrisk‐freerate.Example

InvestmentsMaturity(inyears)

Liquidity Defaultrisk InterestRates(%)

A 1 High Low 2.0B 1 Low Low 2.5C 2 Low Low rD 3 High Low 3.0E 3 Low High 4.0

1. ExplainthedifferencebetweentheinterestratesonInvestmentAandInvestmentB.

2. Estimatethedefaultriskpremium.

3. CalculateupperandlowerlimitsfortheinterestrateonInvestmentC,r.

Solution:

1. InvestmentsAandBhavethesamematurityandthesamedefaultrisk.However,BhasalowerliquidityascomparedtoA.Hence,investorswilldemandaliquiditypremiumonB.



Thedifferencebetweentheirinterestratesi.e.2.5–2.0=0.5%isequaltotheliquiditypremium.

2. ConsiderinvestmentsDandE,theyhavethesamematurity,butdifferentliquidityanddifferentdefaultrisk.Let’smakeliquiditythesameandcreateanewlowliquidityversionofD.Thisversionwillhaveahigherinterestrate,becausenowinvestorswilldemandaliquiditypremium.Wehavealreadydeterminedthattheliquiditypremiumis0.5%.Therefore,thelowliquidityversionofDwillhaveaninterestrateof3.0+0.5=3.5%.NowcomparethisversionofDwithinvestmentE.Theonlydifferencebetweenthetwoisdefaultrisk.Ehasahigherdefaultrisk.Therefore,thedifferencebetweentheirinterestratesi.e.4.0–3.5=0.5%mustbeequaltothedefaultriskpremium.

3. NoticethatbetweenBandC,theonlydifferenceisthatChasalongermaturity.Therefore,interestrateofCmustbehigherthanB(2.5%).AlsonoticethatbetweenCandthelowliquidityversionofD,theonlydifferenceisthatChasashortermaturity.Therefore,interestrateonChastobelowerthanthelowliquidityversionofD(3.5%).SotherangeforCis2.5<r<3.5.

3.TheFutureValueofaSingleCashFlow

Let’sunderstandthisconceptwithasimpleexample.Saypresentvalue(PV)=$100andinterestrate(r)=10%.Whatisthefuturevalue(FV)afteroneyear?Whatisthefuturevalue(FV)aftertwoyears?

Thefuturevalueofasinglecashflowcanbecomputedusingthefollowingformula:

FV PV 1 r

where:FVN=futurevalueoftheinvestmentN=numberofperiodsPV=presentvalueoftheinvestmentr=rateofinterest

Therefore,

FV 100 1 0.1 $110

FV 100 1 0.1 $121



Noticethatwithcompoundinterest,aftertwoyearswehave$121.Whereas,withsimpleinterest,aftertwoyearswewouldhave$120.Thedifferencebetweenthetwovalues($1)representstheinterestoninterestcomponent.InYear2,wenotonlyreceiveinterestonthe$100principal,butwealsoreceiveinterestonthe$10interestearnedinYear1thathasbeenreinvested.

Example

CyndiaRojersdeposits$5millioninhersavingsaccount.Theaccountholdersareentitledtoa5%interest.IfCyndiawithdrawscashafter2.5years,howmuchcashwouldshemostlikelybeabletowithdraw?

Solution:

FV PV 1 r

FV . 5 1 0.05 . $5.649million

FVCalculationusingaFinancialCalculator

YouwilloftenusethefollowingkeysonyourTIBAIIPluscalculator:N=numberofperiodsI/Y=rateperperiodPV=presentvalueFV=futurevaluePMT=paymentCPT=compute

OneimportantpointtonoteisthesignsusedforPVandFV.IfthevalueforPVisnegative“‐”,thenthevalueforFVispositive“+”.Aninflowisoftenrepresentedasapositivenumber,whileoutflowsaredenotedbynegativenumbers.Beforeyoubegin,setthenumberofdecimalpointsonyourcalculatorto9toincreaseaccuracy.

Keystrokes Explanation Display

[2nd][FORMAT][ENTER] Getintoformatmode DEC=9

[2nd][QUIT]Returntostandardcalcmode

0

Question:Youinvest$100todayat10%compoundedannually.Howmuchwillyouhavein5years?

Thekeystrokestocomputethefuturevalueofasinglecashflowareillustratedbelow.


[2nd][QUIT] Returntostandardcalcmode 0

[2nd][CLRTVM] ClearsTVMWorksheet 0



5[N] Fiveyears/periods N=5

10[I/Y] Setinterestrate I/Y=10

100[PV] Setpresentvalue PV=100

0[PMT] Setpayment PMT=0

[CPT][FV] Computefuturevalue FV=‐161.05

3.1.TheFrequencyofCompounding

Whenourcompoundingfrequencyisnotannual,weusethefollowingformulatocomputefuturevalue:

FV PV 1rm

where:rs=thestatedannualinterestrateindecimalformatm=thenumberofcompoundingperiodsperyearN=thenumberofyears

Let’sunderstandthisconceptusinganexample.

Youinvest$80,000ina3‐yearcertificateofdeposit.ThisCDoffersastatedannualinterestrateof10%compoundedquarterly.Howmuchwillyouhaveattheendofthreeyears?

Solution:Therearetwomethodstosolvethisquestion.FormulaMethodPVis$80,000.Thestatedannualrateis10%.Thenumberofcompoundingperiodsperyearis4.Thetotalnumberofperiodsis4x3=12.Thereforefuturevalueafter12quarters(3years)is

FV $80,000 1 0.025 $107,591

CalculatorMethodYoucanalsosolvethisproblemusingafinancialcalculator;thekeystrokesaregivenbelow:N=12,I/Y=2.5%,PV=$80,000,PMT=0,CPTFV=‐$107,591PMTis0becausetherearenointermediatepaymentsinthisexample.Example

Donaldinvested$3millioninanAmericanbankthatpromisestopay4%compoundeddaily.WhichofthefollowingisclosesttotheamountDonaldreceivesattheendofthefirstyear?Assume365daysinayear.A. $3.003millionB. $3.122million



C. $3.562million

SolutionThecorrectanswerisB.FormulaMethod

FV PV 1

FV 3million 1 . $3.122million

CalculatorMethodN=365,I/Y=4/365%,PV=$3million,PMT=0;CPTFV=‐$3.122million

3.2.ContinuousCompounding

Wesawexampleswithannualcompounding.Thenwediscussedquarterlycompoundingandintheaboveexamplewelookedatdailycompounding.Ifwekeepincreasingthenumberofcompoundingperiodsuntilwehaveinfinitenumberofcompoundingperiodsperyear,thenwecansaythatwehavecontinuouscompounding.

Theformulaforcomputingfuturevalueswithcontinuouscompoundingis:

FV PVe

where:r=continuouslycompoundedrateN=thenumberofyears

Let’slookatanexample.

Aninvestmentworth$50,000earnsinterestthatiscompoundedcontinuously.Thestatedannualinterestis3.6%.Whatisthefuturevalueoftheinvestmentafter3years?

Solution:

PV=$50,000;r=0.036;N=3

FV 50,000e . $55,702

ConceptBuildingExercise

Assumethatthestatedannualinterestrateis12%.Whatisthefuturevalueof$100atdifferentcompoundingfrequencies?Whatisthereturn?

Frequency Futurevalueof$100 ReturnAnnual 112.00 12.00%Semiannual 112.36 12.36%Quarterly 112.55 12.55%Monthly 112.68 12.68%Daily 112.75 12.75%Continuous 112.75 12.75%



Instructor’sNote:

1.Forthesamestatedannualrate,thereturnskeepgettingbetteraswecompoundmoreoften.

2.IfyouhavetwobanksthatofferthefollowingratesA:12.5%compoundedannuallyB:12%compoundeddailyWhichofferisbetter?

EventhoughA’s12.5%looksbetter,B’s12%compoundeddailywilleffectivelygiveyouareturnof12.75%.ThereforetheofferfrombankBisbetter.

3.3.StatedandEffectiveRates

Nowwecometotherelatedconceptofstatedversuseffectiverates.Intheaboveconcept‐buildingexercise,thestatedratewas12%acrosstheboard,buttheeffectiveratethataninvestoractuallyearnsdependsonthecompoundingfrequency.Theeffectiveratesweredifferentfordifferentcompoundingfrequencies.

Ifwearegivenacompoundingfrequency,wecancomputeeffectiveratesusingthefollowingformulae:

Effectiveannualratefordiscretecompounding:

EAR 1 periodicinterestrate – 1

where:m=numberofcompoundingperiodsinoneyear Fordailycompounding,m=365 Formonthlycompounding,m=12 Forquarterlycompounding,m=4 Forsemiannualcompounding,m=2

Forexample,forastatedannualrateof12%andquarterlycompounding,theEARwillbeequalto:

EAR=(1+0.12/4)4–1=1.1255–1=0.1255=12.55%

Instructor’sNote:Alotofpeoplegetconfusedaboutthe‐1attheendoftheformula.Theideaisactuallyfairlystraightforward.Basicallywehave1.034whichistellingushowmuch$1willbecomeattheendof4periods.$1isgoingtobecome$1.1255.Butthisisnotarate.Tofigureouttheratewehavetosubtracttheoriginal$1thatweinvested.Soweareleftwith0.1255whichisoureffectiverate.

EffectiveAnnualRateforcontinuouscompounding:EAR e 1



wherer =statedannualinterestrate

Forexample,forastatedannualrateof12%andcontinuouscompounding,theEARwillbeequalto:

EAR=e0.12–1=1.1275–1=0.1275=12.75%

4.TheFutureValueofaSeriesofCashFlows

Thedifferenttypesofcashflowsbasedonthetimeperiodsoverwhichtheyoccurinclude: Annuity:Afinitesetofequalsequentialcashflows.Thetwotypesare

o Ordinaryannuity:Thefirstcashflowoccursoneperiodfromnow(indexedatt=1).

o Annuitydue:Thefirstcashflowoccursimmediately(indexedatt=0). Perpetuity:Asetofequalnever‐endingsequentialcashflowswiththefirstcashflow

occurringoneperiodfromtoday.(Theperiodisfiniteincaseofanannuitywhereasinperpetuityitisinfinite.)

4.1.EqualCashFlows–OrdinaryAnnuity

Let’ssaythatwehaveanordinaryannuitywithA=$1,000,r=5%andN=5,i.e.wearegoingtoreceiveapaymentof$1,000attheendofeachyearforthenext5yearsandourdiscountrateis5%.WecancomputetheFVofthisannuityusingthefollowingthreemethods:

Brute‐ForceMethod

Wecantakeeachindividualcashflowandseehowmucheachofthesewillbeworthattheendoffiveyears.ThenwecanaddallthevaluestocomputethetotalFVoftheannuity.

Forinstance,thefirst$1,000depositmadeatt=1willcompoundoverfourperiods;theseconddepositof$1,000willcompoundoverthreeperiodsandsoon.Wethenaddthefuturevaluesofallpaymentstoarriveatthefuturevalueoftheannuitywhichis$5,525.63.



FormulaMethod

Thefuturevalueofanannuitycanalsobecomputedusingthefollowingformula:

FV A1 r – 1

r

where:A=annuityamountN=numberofyears

Theterminsquarebracketsisknownasthe‘futurevalueannuityfactor’(FVAF).Thisfactorgivesthefuturevalueofanordinaryannuityof$1perperiod.Hencetheformulagivenabovecanalsobewrittenas:FV=AxFVAF.

Therefore,usingtheformula:

FV 1,000 . –

.$5,525.63

CalculatorMethod

Givenbelowarethekeystrokesforcomputingthefuturevalueofanordinaryannuity.






0[PV] 0becausethereisnoinitialinvestment PV=0

1000[PMT] Setannuitypayment PMT=1000

[CPT][FV] Computefuturevalue FV=‐5525.63

Ontheexamyoushouldusethecalculatormethod,becausethisisthefastestmethodanddoesnotrequireyoutomemorizetheannuityformula.

Example

Haleydeposits$24,000inherbankaccountattheendofeveryyear.Theaccountearns12%perannum.Ifshecontinuesthispractice,howmuchmoneywillshehaveattheendof15years?

Solution:N=15,I/Y=12%,PV=0,PMT=$24,000;CPTFV=‐$894,713.15



4.2.UnequalCashFlows

Ifcashflowstreamsareunequal,thefuturevalueannuityfactorcannotbeused.Inthiscase,wefindthefuturevalueofaseriesofunequalcashflowsbycompoundingthecashflowsoneatatime.

Thisconceptisillustratedinthefigurebelow.Weneedtofindthefuturevalueoffivecashflows:$1,000attheendofYear1;$2,000attheendofYear2;$3,000attheendofYear3;$4,000attheendofYear4;and$5,000attheendofYear5.

Thefuturevalueis$5,000+$4,000x1.05+$3,000x1.052+$2,000x1.053+$1,000x1.054

=$16,038.

5.ThePresentValueofaSingleCashFlow

Let'ssaythatoneyearfromtodayyouwillreceiveacashflowof$110.Whatisthevalueofthat$110today?(Assumethattheinterestrateis10%)

PVFV

1 0.1$110

1 0.1$100

The$110oneyearfromtodayhasapresentvalueof$100.Inotherwords,youwillbeindifferentbetween$100todayand$110oneyearfromtoday.

Whatifyouweregoingtoreceive$121attheendoftwoyears,whatisitspresentvalue?



PVFV

1 0.1$121

1 0.1$100

UsingthesetwoexampleswecanwriteageneralformulaforcomputingPV.GivenacashflowthatistobereceivedinNperiodsandaninterestrateofrperperiod,thePVcanbecomputedas:

PVFV1 r

where:N=numberofperiodsr=rateofinterestFV=futurevalueofinvestment

Instructor’sNoteNoticethatthisformulacanalsobeobtainedbysimplyrearrangingtheformulaforFVthatwestudiedearlier.

FV PV 1 r PV

Basedonthisformulawecanmaketwoobservations

1. Foragivendiscountrate,thefartherinthefuturetheamounttobereceived,thesmallertheamount’spresentvalue.

Mathematicalexplanation:InthefirstcasethePVis$110/1.1,whereasinthesecondcasePVis$110/1.12.SincewearedividingbyalargernumberthePVwillbelowerinthesecondcase.

Intuitiveexplanation:Clearlyreceivingacertainamountofmoneysoonerisbetterthanreceivingthesameamountofmoneylatter.



2. Holdingtimeconstant,thelargerthediscountrate,thesmallerthepresentvalueofafutureamount.

InthefirstcasePVis$110/1.1,whereasinthesecondcasePVis$110/1.2.ClearlythePVisgoingtobelowerinthesecondcase,becausewearedividingbyalargernumber.

Example

Liampurchasesacontractfromaninsurancecompany.Thecontractpromisestopay$600,000after8yearswitha5%return.WhatamountofmoneyshouldLiammostlikelyinvest?SolveusingtheformulaandTVMfunctionsonthecalculator.

Solution:FormulaMethod

PVFV1 r

$600,0001.05

$406,104

CalculatorMethod

N=8,I/Y=5%,PMT=0,FV=$600,000;CPTPVPV=‐$406,104Example

Mathewswishestofundhisson,Nathan’s,collegetuitionfee.Hepurchasesasecuritythatwillpay$1,000,000in12years.Nathan’scollegebegins3yearsfromnow.Giventhatthediscountrateis7.5%,whatisthesecurity’svalueatthetimeofNathan’sadmission?

Solution:

PV$1,000,0001.075

$521,583.47

ExampleOrlandoisamanageratanAustralianpensionfund.5yearsfromtodayhewantsalumpsumamountofAUD40,000.Giventhatthecurrentinterestrateis4%ayear,compoundedmonthly,howmuchshouldOrlandoinvesttoday?



Solution:

Wehavemonthlycompounding,thereforetheinputstoourcalculatorwillbeN=5x12=60I=4/12%PMT=0FV=$40,000CPTPV=‐$32,760.12

6.ThePresentValueofaSeriesofCashFlows

6.1.ThePresentValueofaSeriesofEqualCashFlows

OrdinaryAnnuity

Anordinaryannuityisaseriesofequalpaymentsatequalintervalsforafiniteperiodoftime.Examplesofordinaryannuity:mortgagepayments,pensionincomeetc.

ConsideranordinaryannuitywithA=$10,r=5%andN=5.

WecancomputethePVofthisannuityusingthreemethods

Brute‐ForceMethod:

SimplytakeeachcashflowandcomputethePV.AddallvaluestogetthePVfortheannuity.

PV=$43.29.



FormulaMethod:

Thepresentvaluecanalsobecomputedusingthefollowingformula:

PV A1

r

where:A=annuityamountr=interestrateperperiodcorrespondingtothefrequencyofannuitypaymentsN=numberofannuitypaymentsTheterminsquarebracketsiscalledthepresentvalueannuityfactor(PVAF).Hencetheequationabovecanalsobewrittenas:PV=AxPVAF.

Therefore,usingtheformulaweget,

PV 101

.

0.05$43.29

CalculatorMethod:

Thekeystrokestosolvethisusingafinancialcalculatoraregivenbelow:






0[FV]Setto0becausethereisnofinalpaymentotherthantheperiodicannuityamounts

FV=0

10[PMT] Setannuitypayment PMT=10

[CPT][PV] Computepresentvalue PV=‐43.29

AnnuityDueWithanannuityduethefirstpaymentisreceivedatthestartofthefirstperiod.SoifwehaveanannuityduewithA=$10,r=5%andN=5.Thecashflowswillbe



Again,therearethreemethodstocalculatethePVofthisannuitydue.

Brute‐Forcemethod

TakeeachcashflowandcomputethePV.AddallvaluestogetthePVfortheannuity.

PV=$45.46.

Noticethatwithanannuitydueyouarereceivingmoneyfaster,whichmeansthatthe

PVannuitydue($45.46)>PVordinaryannuity($43.29).

Formulamethod:

Wecanalsousethefollowingformula:

PV A1

r1 r

where:A=annuityamountr=interestrateperperiodcorrespondingtothefrequencyofannuitypaymentsN=numberofannuitypayments

Thereforeusingtheformula,

PV 101

.

0.051 0.05 $45.46

Instructor’sNote:

NoticethatA isbasicallytheformulaforcomputingthePVofanordinaryannuity.

IfyouusetheordinaryannuityformulathePVthatyougetwillbeattimeperiod‐1.Sothisneedstobetakenforwardoneperiodbymultiplyingitby(1+r)



CalculatorMethod:

SetthecalculatortoBGNmode.Thistellsthecalculatorthatpaymentshappenatthestartofeveryperiod.(ThedefaultcalculatorsettingisENDmodewhichmeansthatpaymentshappenattheendofeveryperiod).Thekeystrokesareshownbelow:


[2nd][BGN][2nd][SET] Setpaymentstobereceivedatbeginningratherthanend

BGN

[2nd][QUIT] Returntostandardcalcmode BGN0

[2nd][CLRTVM] ClearsTVMWorksheet BGN0

5[N] Fouryears/periods BGNN=5

5[I/Y] Setinterestrate BGNI/Y=5

10[PMT] Setpayment BGNPMT=10

0[FV] Setfuturevalue BGNFV=0

[CPT][PV] Computepresentvalue BGN PV=‐45.46

[2nd][BGN][2nd][SET]Setpaymentstobereceivedattheend

END


AlwaysremembertoputyourcalculatorbackintheENDmodeafteryouaredonewiththecalculations.

6.2.ThePresentValueofanInfiniteSeriesofEqualCashFlows–Perpetuity

Aperpetuityisaseriesofneverendingequalcashflows.Thepresentvalueofperpetuitycanbecalculatedbyusingthefollowingformula:

PVAr

where:A=annuityamountr=discountrate

Let’ssaythatwehaveareallysimpleperpetuitywherewereceive$10attheendofeveryyearforever,andlet’ssaythattheinterestrateis5%.

ThePVofthisperpetuitycanbecomputedas:



PV100.05

$200

Instructor’sNote:Keepinmindthatthepresentvalueof$200isoneperiodbeforethefirstcashflow.Manystudentsshowthepresentvalueof$200atthesametimeasthefirstcashflow,whichisincorrect.

6.3.PresentValuesIndexedatTimesOtherThant=0

Anannuityorperpetuitybeginningsometimeinthefuturecanbeexpressedinpresentvaluetermsoneperiodpriortothefirstpayment.Thatvaluecanthenbediscountedbacktotoday’spresentvalue.Let’ssayyouareofferedacashflowof$10attheendofyear5,endofyear6,andsoonforever.WhatisthePVofthesecashflows,assumingadiscountrateof10%?

ThePVoftheperpetuityattheendofyear4canbecomputedas:

PV100.1

$100

ThisvaluehastobediscountedbackfourperiodstogetthePVattimeperiod0.

PV0=$100/1.14=$68.30

ExampleBillGrahamiswillingtopayforaperpetualpreferredstockthatpaysdividendsworth$100peryearindefinitely.Thefirstpaymentwillbereceivedatt=4.Giventhattherequiredrateofreturnis10%,howmuchshouldMr.Grahampaytoday?

Solution:Thetimelineforthisscenariois

ThePVoftheperpetuityattheendofyear3canbecomputedas

PV1000.1

$1,000

Thisvaluehastobediscountedback3periodstogetthePVattimeperiod0.



PV0=$1,000/1.13=$751.31

6.4.ThePresentValueofaSeriesofUnequalCashFlows

Whenwehaveunequalcashflows,wecanfirstfindthepresentvalueofeachindividualcashflowandthensumtherespectivepresentvalues.

Let’ssaythatwehavethefollowingcashflows:

Timeperiod CashFlow1 $1002 $2003 $300

Assumingadiscountrateof10%,thePVofthesecashflowscanbecomputedas:

PV=100/1.1+200/1.12+300/1.13=$481.59

Example

Andymakesaninvestmentwiththeexpectedcashflowshowninthetablebelow.Assumingadiscountrateof9%whatisthepresentvalueofthisinvestment?

TimePeriod CashFlow($)

1 50

2 100

3 150

4 200

5 250Solution:PV=50/1.09+100/1.092+150/1.093+200/1.094+250/1.095=$550.03

Wecanalsousethecashflowregisteronourfinancialcalculatortosolvethisproblemquickly.Thekeystrokesareasfollows:




[2nd][QUIT] Returntostandardmode 0

[CF][2nd][CLRWRK] ClearCFRegister CF=0

0[ENTER] Nocashflowatt=0 CF0=0

[↓]50[ENTER] EnterCFatt=1 C01=50

[↓][↓]100[ENTER] EnterCFatt=2 C02=100




[↓][NPV][9][ENTER] Enterdiscountrate I=9

[↓][CPT] ComputeNPV 550.03

7.SolvingforRates,NumberofPeriods,orSizeofAnnuityPayments

7.1.SolvingforInterestRatesandGrowthRates

Aninterestratecanalsobeconsideredagrowthrate.Wecancomputetherateusingtheformulamethodorthecalculatormethod.Example:A$100deposittodaygrowsto$121in2years.Whatistheinterestrate?Useboththeformulaandthecalculatormethod.Usingtheformula100(1+r)2=121.Thereforer=0.1or10%Usingthecalculatormethod,inputstothecalculatorarePV=‐$100(WhenweenterbothPVandFV,theyshouldbegivenoppositesignstoavoidacalculatorerror.)FV=$121N=2PMT=0CPTII=10%Example:Thepopulationofasmalltownis100,000on1Jan2000.On31December2001thepopulationis121,000.Whatisthegrowthrate?InputstothecalculatorarePV=‐$100,000FV=$121,000N=2PMT=0CPTII=10%



Example:Youinvest$900todayandreceivea$100couponpaymentattheendofeveryyearfor5years.Inaddition,youreceive$1,000andtheendofyear5.Whatistheinterestrate?InputstothecalculatorarePV=‐$900FV=$1,000N=5PMT=100CPTII=12.83%

7.2.SolvingfortheNumberofPeriods

Similarly,wecandeterminethenumberofperiodsgivenotherinformationsuchasfuturevalue,presentvalueandinterestrate.Example:Youinvest$2,500.Howmanyyearswillittaketotripletheamountgiventhattheinterestrateis6%perannumcompoundedannually?Useboththeformulaandthecalculatormethod.FormulaMethod:FV PV 1 r 7,500 2,500 1 0.06 1.06 3Nx ln 1.06 ln 3

Nln 3

ln 1.0618.85

CalculatorMethod:Usingthecalculator:I/Y=6%,PV=$2,500,PMT=0,FV=‐$7,500,CPTN=18.85.

7.3.SolvingfortheSizeofAnnuityPayments

Giventhenumberofperiods,interestrateperperiod,presentvalue,andfuturevalue,itiseasytosolvefortheannuitypaymentamount.Thisconceptcanbeappliedtomortgagesandretirementplanning.Considerthefollowingexample.

Example:Freddieboughtacarworth$42,000today.Hewasrequiredtomakea15%downpayment.Theremainderwastobepaidasamonthlypaymentoverthenext12monthswiththefirstpaymentdueatt=1.Giventhattheinterestrateis8%perannumcompoundedmonthly,whatistheapproximatemonthlypayment?

Loanamount=85%of$42,000=0.85x42,000=$35,700PV=$35,700N=12I/Y=8/12%FV=0 CPTPMTPMT=$3,105.48



7.4.ReviewofPresentandFutureValueEquivalence

Let’ssaythatwehaveanordinaryannuitywithA=10,r=5%andN=5.

Asperourdiscussionsofar,wecancomputethePVandFVofthisannuityPV(attime0)=$43.29andFV(attime5)=$55.26Accordingtotheconceptofpresentandfuturevalueequivalence,alumpsumof$43.29attime0isequivalenttoanannuityof$10overfiveyears.Further,boththeseoptionsareequivalenttoalumpsumof$55.26attime5.Givenaninterestrateof5%,youwouldbeindifferentbetweenthesechoices.

7.5.TheCashFlowAdditivityPrinciple

Amountsofmoneyindexedatthesamepointintimeareadditive.Forexample,ifyouhavethefollowingcashflows:

Youcannotsimplyaddthesethreenumbers.Youhavetotakeeachofthesenumbersandbringthemtoaparticularpointintime.Let’ssaythatwefindthepresentvaluesattimezeroforeachofthesecashflows.Accordingtothisprinciple,thesepresentvaluesthatareallindexedtotimezerocanbeadded.



Summary

LO.a:Interpretinterestratesasrequiredratesofreturn,discountrates,oropportunitycosts.

Aninterestrateistherequiredrateofreturn.Ifyouinvest$100todayontheconditionthatyouget$110afteroneyear,therequiredrateofreturnis10%.Ifthefuturevalue(FV)attheendofYear1is$110,youcandiscountat10%togetthepresentvalue(PV)of$100.Hence,10%canalsobethoughtofasadiscountrate.Finally,ifyouspent$100ontakingyourspouseoutfordinneryougaveuptheopportunitytoearn10%.Thus,10%canalsobeinterpretedasanopportunitycost.

LO.b:Explainaninterestrateasthesumofarealrisk‐freerate,andpremiumsthatcompensateinvestorsforbearingdistincttypesofrisk.

Interestrate=Realrisk‐freeinterestrate+Inflationpremium+Defaultriskpremium+Liquiditypremium+Maturitypremium.

Nominalriskfreerate=realriskfreerate+inflationpremium

LO.c:Calculateandinterprettheeffectiveannualrate,giventhestatedannualinterestrateandthefrequencyofcompounding.

Thestatedannualinterestrateisaquotedinterestratethatdoesnotaccountforcompoundingwithintheyear.Theeffectiveannualrate(EAR)istheamountbywhichaunitofcurrencywillgrowinayearwhenwedoconsidercompoundingwithintheyear.Example:Ifthestatedannualrateis12%withmonthlycompounding,theperiodicormonthlyrateis1%.Since$1investedatthestartoftheyearwillgrowto1.0112=1.1268,theEARis12.68%.

LO.d:Solvetimevalueofmoneyproblemsfordifferentfrequenciesofcompounding.

Whenourcompoundingfrequencyisnotannual,weusethefollowingformulatocomputefuturevalue:

FV PV 1rm

where:rs=thestatedannualinterestrateindecimalformatm=thenumberofcompoundingperiodsperyearN=thenumberofyears

Ifwekeepincreasingthenumberofcompoundingperiodsuntilwehaveinfinitenumberofcompoundingperiodsperyear,thenwecansaythatwehavecontinuouscompounding.Theformulatocomputefuturevalueis:

FV PVe where:



r=continuouslycompoundedrate N=thenumberofyears

LO.e:Calculateandinterpretthefuturevalue(FV)andpresentvalue(PV)ofasinglesumofmoney,anordinaryannuity,anannuitydue,aperpetuity(PVonly),andaseriesofunequalcashflows.

Thefuturevalueandpresentvalueforasinglesumofmoneycanbecalculatedusingthefollowingformulae:

FV=PV(1+r)NandPV=FV/(1+r)N

Anannuityisafinitesetofequalsequentialcashflowsoccurringatequalintervals.Therearetwotypesofannuities:

Ordinaryannuity:Cashflowsoccurattheendofeveryperiod. Annuitydue:Cashflowsoccuratthestartofeveryperiod(hence,thePeriod1cash

flowoccursimmediately).Thefuturevalueofanordinaryannuitycanbecomputedusingthefollowingformula:

FV A1 r – 1

r

where:A=annuityamountN=numberofyears

Thepresentvalueofordinaryannuitycanbecomputedusingthefollowingformula:

PV A1

r


Withanannuityduethefirstpaymentisreceivedatthestartofthefirstperiod.Theformulatocalculatepresentvalueofannuitydueisasfollows:

PV A1

r1 r




Alternatively,youmayalsousetheTVMkeysonthecalculatorinsteadoftheformulastocomputethepresentvaluesandthefuturevaluesofannuities.

Aperpetuityisaseriesofneverendingequalcashflows.Thepresentvalueofperpetuitycanbecalculatedbyusingthefollowingformula:

PVAr

where:A=annuityamountr=discountrate

LO.f:Demonstratetheuseofatimelineinmodelingandsolvingtimevalueofmoneyproblems.

Youcansolvetimevalueofmoneyquestionsbyshowingcashflowsonatimelinesuchastheoneshownbelow:

Sayyouwillreceive$150attheendofYear4,Year5,andYear6andyouwanttocalculatethePVattime0.YoucantreatthethreepaymentsasanannuityandcalculatethePVattheendofyear3.Thisvalue,assuminga10%discountrate,is:$373.03.Wecanthenfurtherdiscount$373.03totime0.Plug:FV=$373.03,N=3,I=10%,PMT=0.ComputePV.Youshouldget$280.26.



PracticeQuestions

1. Interestratescanbeleastlikelyinterpretedas:A. discountrates.B. opportunitycosts.C. sunkcosts.

2. Thefollowinginformationisprovidedregardingasecuritywhosenominalinterestrateis

10%: Therealrisk‐freerateofreturnis4% Thedefaultriskpremiumis1% Thematurityriskpremiumis1% Theliquidityriskpremiumis2%An investor wants to determine the inflation premium in the security’s return. Theinflationpremiumisclosestto:A. 2%.B. 4%.C. 6%.

3. Which of the following fixed income instruments has thehighest effective annual rate

(EAR)? Compoundingfrequency AnnualinterestrateInstrument1 Monthly 6.20%Instrument2 Quarterly 6.25%Instrument3 Continuously 6.00%

A. Instrument1.B. Instrument2.C. Instrument3.

4. Howmuchshouldbeinvestedtodayat8%interestcompoundedquarterlytoaccumulate

$10,000fiveyearsfromtoday?Theamountthatmustbeinvestedtodayisclosestto:A. $6,210.B. $6,730.C. $6,840.

5. Theamountaninvestorwillhavein10years,if$1000isinvestedtodayatacontinuously

compoundedrateof7%,willbeclosestto:A. $2,014.B. $2,038.C. $2,044.



6. Nancy Scott is buying a house. She expects her budget to allow amonthly payment of$2000ona20‐yearmortgagewithastatedannualinterestrateof6percent.IfMs.Scottputsa15percentdownpayment,themostshecanpayforthehouseisclosestto:A. $279,160.B. $328,425.C. $336,160.

7. A tenantpays rentof $800monthlydueon the firstdayof everymonth. If theannual

interestrateis7percent,thepresentvalueofafullyear’srentisclosestto:A. $9,245.B. $9,300.C. $9,355.

8. The preferred shares of Crane Industries are expected to pay a $10 dividend forever,

startingfromtheendofthisyear.Iftherequiredrateofreturnonequivalentinvestmentsis9%,ashareofCraneIndustriespreferredstockshouldbeworth:A. $90.50.B. $111.10.C. $124.60.

9. Aninvestmentisexpectedtoproducethecashflowsof$100,$200,and$300attheend

ofthenextthreeyears.Iftherequiredrateofreturnis10%,thepresentvalueofthisinvestmentisclosestto:A. $456.65.B. $475.83.C. $481.59.

10. JamesMillerwantstosaveforhisson’scollegetuition.Hewillhavetopay$40,000atthe

endofeachyearforthefouryearsthathissonattendscollege.Hehas6yearsuntilhissonstartscollegetosaveupforhistuition.Usinga8%interestratecompoundedannually,theamountMillerwouldhavetosaveeachyearfor6yearsisclosestto:A. $16,190.B. $18,060.C. $19,530.



Solutions1. Ciscorrect.Interestratescanbeinterpretedas

Required rate of return: It is theminimum rate that the investors require tomakeinvestments.

Discountrate:Futurevaluescanbediscountedbyinterestratestoarriveatpresentvalues.

Opportunitycosts:Ifinsteadofinvesting,youspendthemoneyonsomethingelse,thenyouhavegivenuptheopportunitytoearninterest.

Sunkcostisacostthathasalreadybeenincurredandcannotberecovered.2. Aiscorrect.Nominalinterestrate=realrisk‐freerateofreturn+inflationpremium+risk

premiums(default,liquidity,maturitypremiums)Therefore,Inflationpremium=10%‐4%‐1%‐1%‐2%=2%

3. Biscorrect.UsetheEAR(effectiveannualrate)tocomparetheinvestments:

Instrument Formula EARInstrument1 (1+.062/12)^12–1 6.379%Instrument2 (1+.0625/4)^4–1 6.398%Instrument3 e^(0.060×1)–1 6.183%

4. Biscorrect.EnterintoyourfinancialcalculatorFV=10,000,N=5x4=20,I/Y=8/4=2,

PMT=0,andsolveforPV.PV=‐6,729.715. Aiscorrect.Thefuturevalueofanamountcalculatedusingcontinuouscompoundingis:

FV Pv e Thus:FV 1000 e . $2,013.75

6. Biscorrect.Theconsumer’sbudgetwillsupportamonthlypaymentof$2,000.Givena

20‐yearmortgageat6percent,theloanamountwillbe$279,161(N=20x12=240,%I=6/12=0.5,PMT=2,000,FV=0solveforPV).Ifshemakesa15%downpayment,thenthemostshecanpayforthenewhouse=$279,161/(1–0.15)=$328,424.7.

7. Biscorrect.Usingafinancialcalculator:PMT=800,I=7/12=0.583,n=12Computeannuity

duePV,PV=$9299.6(PutthecalculatorinBGNmodeforannuityduecalculations)8. Biscorrect.

PV/

$

.$111.11



9. Ciscorrect.Usingyourcashflowkeys,(CF0=0),CF1=100,CF2=200,CF3=300,I=10

ComputePV,PV=$481.59

10. Biscorrect.Usingafinancialcalculator,wefirstneedtocalculatethetotalvalueofthetuitionfeesneededattheendof6years.Notethatthefirstpaymentof40,000needstobemade7yearsfromtoday.N=4,I/Y=8,PMT=40,000,FV=0ComputePV:PV=$132,485.07.Thisistheamountofmoneyneededattheendof6years.Using$132,485.07astheFVforthesavingphaseannuity,wecomputeyearlydepositswiththeinputs:N=6,I/Y=8,PV=0,FV=132,485.07ComputePMT:PMT=$18059.75~$18060.

R07 Discounted Cash Flow Applications 2019 Level I Notes


R07DiscountedCashFlowApplications

1.Introduction

Thisreadingcovers: Decisiontools:netpresentvalue(NPV)andinternalrateofreturn(IRR). DecisionrulesforNPVandIRR. ConflictingsituationsunderIRR,andwhatruletouseinsuchcases. Calculatingreturnsofaportfolio:money‐weightedreturnandtime‐weightedreturn. Calculatingdifferentyieldmeasuresformoneymarketinstruments.

2.NetPresentValueandInternalRateofReturn

Netpresentvalueandinternalrateofreturnareoftenappliedinallfieldsoffinance.Butperhapsthemostcommonandwellknownapplicationoftheseconceptsisinthefieldofcapitalbudgeting,wherecompaniesneedtomakedecisionsonwhichprojectstopursueandwhichprojectstoreject.

2.1NetPresentValueandtheNetPresentValueRule

Thenetpresentvalue(NPV)ofaninvestmentisthepresentvalueofitscashinflowsminusthepresentvalueofitscashoutflows.ThestepstocalculateNPVareasfollows:

Identifyallthecashflowsassociatedwithaninvestment(bothinflowsandoutflows). Determinetheappropriatediscountrate‘r’fortheinvestmentproject.‘r’isalso

knownasthecostofcapitalortheopportunitycost. Usingthediscountrate‘r’,findthepresentvalueofeachcashflow. Inflowsarepositiveandoutflowsarenegative.Sumthepresentvaluesofallcash

flows,includingtheinitialinvestment.Thisvaluerepresentstheinvestment’snetpresentvalue.

FormulaforcomputingNPVis:

NPV presentvalueofcashinflows– presentvalueofcashoutflows

NPVCF1 r

where:CFt=theexpectednetcashflowattimetN=theinvestment’sprojectedlifer=thediscountrateoropportunitycost

TounderstandtheNPVconcept,letusconsiderasimpleexample.



Example

Aprojectrequiresaninitialoutlayof$750,000.Itisexpectedtoproduce$200,000inthefirstyear,$300,000inthesecondyear,and$400,000inthethirdyear.Thecostofcapitalforthisprojectis10%.WhatistheNPV?Shouldtheprojectbeaccepted?

Solution:FormulaMethod:

UsingtheformulaforNPV,

NPV CF0 CF11 r

CF21 r

CF31 r

NPV 750,000200,0001.1

300,0001.1

400,0001.1

NPV=‐19,722

Whilethismethodisconceptuallysimple,itcanbetediousifthenumberofcashflowsislarge.Itismucheasiertousethefinancialcalculator.Thestepsareoutlinedbelow:

CalculatorMethod:Keystrokes Explanation Display[2nd][QUIT] Returntostandardmode 0[CF][2nd][CLRWRK] ClearCFRegister CF=0750[+/‐][ENTER] InitialOutlay(in000’s) CF0=‐750[↓]200[ENTER] EnterCFatt=1 C01=200[↓][↓]300[ENTER] EnterCFatt=2 C02=300[↓][↓]400[ENTER] EnterCFatt=3 C03=400[↓][NPV][10][ENTER] Enterdiscountrate I=10[↓][CPT] ComputeNPV ‐19.722Thepresentvalueofcashinflowsis$730,278whichislessthanthecostof$750,000.Valueisbeingdestroyed.TheNPVisnegativeandhencethisprojectshouldberejected.

NPVDecisionRule

Forindependentprojects(whereyoucanmakeadecisiononeachprojectindependently): IftheNPVispositiveAccepttheproject. IftheNPVisnegativeRejecttheproject.

Formutuallyexclusiveprojects(whereonlyoneprojectcanbeaccepted): AccepttheprojectwiththehigherNPVaslongastheNPVispositive.

2.2TheInternalRateofReturnandtheInternalRateofReturnRule

Theinternalrateofreturn(IRR)isthediscountratethatmakesthenetpresentvalueequaltozero.Itis‘internal’becauseitdependsonlyonthecashflowsoftheinvestment;noexternaldataisneeded.TheformulaforIRRisasfollows:



NPV CF CF

1 IRR

CF1 IRR

… CF

1 IRR0

where:CF usuallytheinitialinvestmentwhichisacashoutflowCFt=theexpectednetcashflowattimetNPV=netpresentvalueoftheinvestmentIRR=internalrateofreturn

TheIRRisasinglenumberwhichrepresentsthereturngeneratedbyaproject.Consideraverysimpleprojectwheretheinitialinvestmentis$100.Oneyearlatertheamountreceivedfromthisprojectis$110.Therearenoothercashflows.IfweapplytheformulaforIRRweget:

100110

1 IRR0

SolvingthisequationshowsthatIRR=0.1or10%.

Example

Consideraprojectthatrequiresaninitialinvestmentof$150,000.Estimatedcashflowsforthefollowingthreeyearsare$50,000,$100,000and$40,000respectively.WhatistheIRR?

Solution:WecansetupanequationwiththeinitialoutflowequaltothepresentvalueoffuturecashflowsandsolvefortheIRR:

CF0 CF1

1 IRR

CF21 IRR

CF3

1 IRR

Plugginginthevalues,weget:

$150,000 $50,0001 IRR

$100,0001 IRR

$40,0001 IRR

Whileitistheoreticallypossibletosolvetheaboveequation,itismuchsimplertousethefinancialcalculator.Keystrokes Explanation Display[2nd][QUIT] Returntostandardmode 0[CF][2nd][CLRWRK] ClearCFRegister CF=0150[+/‐][ENTER] Initialoutlay(in000’s) CF0=‐150[↓]50[ENTER] EnterCFatt=1 C01=50[↓][↓]100[ENTER] EnterCFatt=2 C02=100[↓][↓]40[ENTER] EnterCFatt=3 C03=40[↓][ÌRR][CPT] ComputeIRR 13.11%

TheIRRRule

Forindependentprojects:



IfIRR>OpportunitycostAccepttheproject. IfIRR<OpportunitycostRejecttheproject.

Formutuallyexclusiveprojects: AccepttheprojectwiththehigherIRR,aslongastheIRR>Opportunitycost.

IRRusestheopportunitycostofcapitalasthehurdlerate.Forexample,ifatagivencompanythecostofcapital(opportunitycost)is10%,thenonlyprojectswithIRR>10%willbeaccepted.

Example

Billisinterestedinaprojectwhichrequiresaninvestmentof$1.5million.Theprojectshallpay$200,000peryearinperpetuity.Thefirstcashflowwillbereceived1yearfromtoday.Thecostofcapitalis8%.WhatistheIRR?ShouldBillinvestinthisproject?

Solution:IRRcanalsobethoughtofasthediscountratewhichmakestheinitialoutlayequaltothepresentvalueoffuturecashflows.Heretheinitialoutlayis$1,500,000.Becausetheproject’scashflowsareaperpetuity,thepresentvalueoffuturecashflowscanbewrittenas:$200,000/IRR.Hencetheequationbecomes:

1,500,000200,000IRR

WecansolveforIRRas:

IRR200,000

$1,500,0000.133or13.3%

SincetheIRRof13.3%isgreaterthanthecostofcapitalof8%,Billshouldinvestinthisproject.

2.3ProblemswiththeIRRRule

NPVandIRRrulesgivethesameacceptorrejectdecisionwhenprojectsareindependent.However,whendealingwithmutuallyexclusiveprojects,itispossiblethatthehighestNPVprojectisnotthesameasthehighestIRRproject.Thisiscalledarankingconflict.

IRRandNPVcanrankprojectsdifferentlywhen: Thesizeorscaleoftheprojectsdiffers. Timingoftheprojects’cashflowsdiffers.

Toillustratethefirstpoint(differenceinsize),consideracompanywith$100millionavailabletoinvest.Ithastwoinvestmentprojectsasshownbelow:

Project Investmentatt=0 Cashflowatt=1 IRR(%) NPVat10%A ‐100 120 20% 10D ‐1,000 1,150 15% 45



TheIRRruleranksProjectAfirstbecauseofthehigherIRR.TheNPVrule,however,ranksProjectDfirstbecauseofthehigherNPV.

Toillustratethesecondpoint(differenceincashflowtiming),considerProjectsAandCasshowninthetablebelow:

Project CF0 CF1 CF2 CF3 IRR(%)NPVat10%

A ‐100 120 0 0 20 10C ‐100 0 0 170 19 28

TheIRRruleranksProjectAfirstbecauseofthehigherIRR.TheNPVrule,however,ranksProjectCfirstbecauseofthehigherNPV.

WheneverthereisaconflictinrankingbetweentheIRRruleandtheNPVrule,theNPVruleshouldbeusedtodecidebetweenmutuallyexclusiveprojects.ThisisbecausetheNPVrepresentstheexpectedadditiontoshareholderwealthfromaninvestment.Themaximizationofshareholderwealthisabasicfinancialobjectiveofacompanyandhence,theNPVrulemustbegivenpreference.

Therefore,inthefirstcaseyoushouldselectProjectDoverProjectA.Similarly,inthesecondcaseyouselectProjectCoverProjectA.

3.PortfolioReturnMeasurement

Portfolioperformancemeasurementinvolvescalculatingreturnsinalogicalandconsistentmanner.Forinstance,determiningthereturnsofaportfoliohelpsincomparingandrankingdifferentmutualfunds.Inthissection,wecoverthefollowingreturnmeasuresandidentifysituationswhenthesemeasuresaretobeused:

Holdingperiodreturn Money‐weightedrateofreturn(MWRR) Time‐weightedrateofreturn(TWRR)

HoldingPeriodReturnHoldingperiodreturn(HPR)isthereturnthataninvestorearnsoveraspecifiedholdingperiod.Theholdingperiodcanrangefromdaystoyears.TheformulaforcalculatingHPRforaninvestmentthatmakesone‐timecashpaymentattheendoftheholdingperiodisgivenbelow:

HPRP –P D

Pendingvalue– beginningvalue cashflow

beginningvalue

where:P0=initialinvestmentP1=pricereceivedattheendoftheholdingperiodD1=cashpaidbytheinvestmentattheendoftheholdingperiod



Example

Assumewebuyastockfor$50.Sixmonthslater,thestockpricegoesupto$53andwereceiveadividendof$2.Calculatetheholdingperiodreturn.Solution:Thereturnforthesix‐monthholdingperiodisgivenbelow:

HPR= =0.10=10%

3.1Money‐WeightedRateofReturn

Themoney‐weightedrateofreturnistheinternalrateofreturn(IRR)ofaprojectoraninvestment.

Letusconsiderasimpleexampletoillustratethispoint.Attimet=0,aninvestorbuysasharefor$20.00.AttheendoftheYear1,hereceivesadividendof$0.50andpurchasesanothersharefor$22.50.AttheendoftheYear2,hesellsbothsharesfor$23.50eachafterreceivinganotherdividendof$0.50pershare.Whatisthemoney‐weightedreturn?

Sincethemoney‐weightedreturnistheIRR,wecanuseafinancialcalculator.Thefirststepistodeterminethenetcashflowsforeveryperiod.Thisisillustratedinthetablebelow:

Time(endofperiod)

Outflow(‐) Inflow(+)Netcashflow

0 ‐$20.00Topurchasethefirstshare

‐$20.00

1 ‐$22.50Topurchasethesecondshare

$0.50Dividendreceivedonfirstshare

‐$22.00

2 Dividendreceived=$0.50x2shares=$1.00Fromsalesof2shares=$47

+48.00

Afterenteringthesecashflows,usethecalculator’sIRRfunctiontofindthemoney‐weightedrateofreturnas9.39%.

3.2Time‐weightedRateofReturn

Thetime‐weightedrateofreturnmeasuresthecompoundgrowthrateof$1initiallyinvestedintheportfoliooverastatedmeasurementperiod.Thetime‐weightedreturncanbecalculatedusingthefollowingsteps:1. Breaktheoverallevaluationperiodintosub‐periodsbasedonthedatesofcashinflows

andoutflows.2. Calculatetheholdingperiodreturnontheportfolioforeachsub‐period.3. Linkorcompoundholdingperiodreturnstoobtainanannualrateofreturnfortheyear

(thetime‐weightedrateofreturnfortheyear).4. Iftheinvestmentisformorethanayear,takethegeometricmeanoftheannualreturns

toobtainthetime‐weightedrateofreturnoverthatmeasurementperiod.



Considerthesameexamplewediscussedabovewiththefollowingcashflows:TimeOutflow Inflow0 $20.00topurchasethefirstshare

1$22.50topurchasethesecondshare

$0.50dividendreceivedonfirstshare

$1.00dividends($0.50x2shares);$47.00fromselling2shares@$23.50pershare

CalculatingtheTWRRforthisexampleisrelativelysimplebecausecashflowsonlyoccuratthestart/endofeveryyear.Wewillfollowthestepsmentionedearlier:

Steps1:Breakintoevaluationperiodandvaluetheportfolioatstart/endofeveryperiod. ValueoftheportfolioatthestartofYear1(t=0)is$20.00. ValueofportfolioattheendofYear1(t=1)beforethepurchaseofthenewshareis

22.50+0.50=$23.00.Notethatthedividendof$0.50onthefirstshareisreceivedattheendofYear1.

ValueoftheportfolioatthestartofYear2(t=1)afterthepurchaseofthesecondshareis22.50+22.50=$45.00.Thedividendof$0.50fromthefirstshareispaidoutandisnotconsideredaspartoftheportfolio.

ValueoftheportfolioattheendofYear2(t=2)is23.50+23.50+0.50+0.50=$48.00.Bothsharespayadividendof$0.50attheendofthesecondyear.

Step2:Calculatetheholdingperiodreturnontheportfolioforeachsub‐period. Inthisquestionthecashflowsaretakingplaceatthestart/endofeachperiod.Hence

therearenosub‐periods.Scenariosinvolvingsub‐periodswillbecoveredinthenextexample.

Step3:Linkorcompoundholdingperiodreturnstoobtainanannualrateofreturnfortheyear. Theannualrateofreturnisbasedontheportfoliovalueatthestartandendofeach

period. TheportfoliovalueatthestartofYear1was$20.00andthevalueattheendofYear1

was$23.00.Hencetheholdingperiodreturnwas15.00%. TheportfoliovalueatthestartofYear2was$45.00andthevalueattheendofYear2

was$48.00.Hencetheholdingperiodreturnwas6.67%.

Step4:Iftheinvestmentisformorethanayear,takethegeometricmeanoftheannualreturnstoobtainthetime‐weightedrateofreturnoverthatmeasurementperiod.

TheTWRRiscalculatedas: 1.15 ∗ 1.067 – 1=0.1077=10.77%.



Example

Consideraninvestmentwherecashflowsoccuratthestart/endofeveryquarter.Hereeachquarterisconsideredasub‐period.Thereturnforeachsub‐periodhasalreadybeencalculatedandisshownbelow:

Calculatethetime‐weightedreturn.

Solution:

Step1(breakevaluationintosub‐periods)andstep2(calculateHPRforsub‐periods)havebeendoneforyou.

Step3:LinkthequarterlyreturnstodeterminethereturnforYears1and2respectively.Foryear1:(1+0.10)(1–0.05)(1+0.15)(1–0.10)=1.0816Foryear2:(1–0.20)(1+0.30)(1+0.20)(1+0)=1.2480

Step4:Determinetheannualizedreturnbytakingthegeometricmean.TWRR=(1.0816x1.2480)1/2‐1=0.1618=16.18%.

Money‐weightedv/stime‐weightedreturns

Themoney‐weightedrateofreturnisimpactedbythetimingandamountofcashflows.

Thetime‐weightedrateofreturnisnotimpactedbythetimingandamountofcashflows.

Thetime‐weightedreturnisanappropriateperformancemeasureiftheportfoliomanagerdoesnotcontrolthetimingandamountofinvestment.

Ontheotherhand,money‐weightedreturnisanappropriatemeasureiftheportfoliomanagerhascontroloverthetimingandamountofinvestment.

4.MoneyMarketYields

Themoneymarketisthemarketforshort‐termdebtinstruments(oneyearmaturityorless).Someinstrumentsrequiretheissuertorepaythelendertheamountborrowedplustheinterest.Othersarepurediscountinstrumentsthatpayinterestasthedifferencebetweentheamountborrowedandtheamountpaidback.

Thefollowingyieldmeasuresareusedwhendealingwithmoneymarketinstruments: Bankdiscountyield Holdingperiodyield Effectiveannualyield Moneymarketyield



Bondequivalentyield

BankDiscountYieldThebankdiscountyieldiscomputedasfollows:

BDYDFx360t

where:BDY=theannualizedyieldonabankdiscountbasisD=thedollardiscount,whichisequaltothedifferencebetweenthefacevalueofthebillandthepurchasepriceF=facevalueofthebillt=theactualnumberofdaysuntilmaturity

Example

ConsideraT‐billwithafacevalue(orparvalue)of$100,000and150daysuntilmaturitywhichissellingfor$98,000.Thedollardiscount,D,is$2,000.Calculatethebankdiscountyield.

Solution:

BDY2,000100,000

x360150

0.048 4.8%

Thebankdiscountyield(BDY)istheindustrystandardmeasureforquotingT‐bills.However,theBDYisnotanaccuratemeasureofinvestors’returnsforthefollowingthreereasons:1. Theyieldisbasedonthefacevalueofthebond,notonitspurchaseprice.Intheabove

example,thedollardiscountof$2,000isdividedthebythefacevalueof$100,000.Amoreaccuratemeasureofreturncanbeobtainedifwedividebytheinvestmentamount(ortheT‐billprice)of$98,000.

2. Theyieldisannualizedbasedona360‐dayyearratherthana365‐dayyear.3. Thebankdiscountyieldannualizeswithsimpleinterest.Intheaboveexamplethe150‐

dayreturnismultipliedby360/150.Thisignorestheopportunitytoearninterestoninterest(compoundinterest).

HoldingPeriodReturnItisthereturnaninvestorwillearnbyholdingtheinstrumenttomaturity.Itisalsoknownasholdingperiodyield(HPY).

HPYP –P D

P

where:P0=initialpurchasepriceoftheinstrumentP1=pricereceivedfortheinstrumentatmaturity



D1=cashpaidbytheinstrumentatmaturity

Note:ThisconcepthasbeendiscussedearlierinSection3.

Example

ConsideraT‐billwithafacevalueof$100,000and150daysuntilmaturitywhichissellingfor$98,000.Determinetheholdingperiodyield.

Solution:

HPY=(100,000–98,000+0)/98,000=0.0204=2.04%

MoneyMarketYieldThemoneymarketyieldiscomputedbyannualizingtheHPYassumingsimpleinterestanda360‐dayyear.Theformulaisasfollows:

MMYHPYx360

t

where:HPY=holdingpriceyield360=numberofdaysinayeart=theactualnumberofdaysuntilmaturity

Example

ConsideraT‐billwithafacevalue(orparvalue)of$100,000and150daysuntilmaturitywhichissellingfor$98,000.Calculatethemoneymarketyield.

Solution:

Weearliercalculatedtheholdingperiodyieldas2.04%.

MMY0.0204x360

1500.0490 4.90%

EffectiveAnnualYieldThemostaccuratemeasureofinvestors’returnsistheeffectiveannualyield(EAY).Theeffectiveannualyieldiscalculatedasfollows:

EAY 1 HPY – 1

where:

HPY=holdingpriceyield365=numberofdaysinayeart=theactualnumberofdaysremainingtomaturity

Theeffectiveannualyieldaddressesthethreeweaknessofthebankdiscountyield:1. TheHPYcorrectlygivesareturnwithrespecttotheinvestmentamountandnottheface

value.



2. TheHPRisannualizedbasedona365‐dayyear,nota360‐dayyear.3. Byusinganexponent,compoundinterestisbeingusedratherthansimpleinterest.

ExampleConsideraT‐billwithafacevalue(orparvalue)of$100,000and150daysuntilmaturitywhichissellingfor$98,000.Determinetheeffectiveannualyield.

Solution:

Inanearlierexample,wecalculatedtheholdingperiodyieldas2.04%.

EAY 1 0.0204 – 1 0.0504 5.04%

BondEquivalentYield

Bondequivalentyieldiscomputedas:

Bondequivalentyield=2xsemiannualyield

Mostbondsmakecouponpaymentseverysixmonths.Considerabondworth$100andwhichmakesacouponpaymentof$4semi‐annually.Thesemi‐annualorsix‐monthyieldonthisbondis4/100=4%.Thebondequivalentyieldistwotimesthesix‐monthyield:2x4%=8%.Notethatforthisbondtheeffectiveannualyieldwillbe1.042–1=0.0816or8.16%.

Instructor’sNote:

Hereisasuggestiononhowtorememberthevariousmoneymarketyields.

Bankdiscountyield(BDY)=D/Fx360/t.Rememberfromthenamethatthereisadiscountinvolved.Thediscountisrelativetothefacevalue.HencewehaveD/FintheBDYexpression.NextD/Fneedstobeannualizedusingsimpleinterestsowemultiplyby360/twheretisthenumberofdaystomaturity.Sotheoverallformulabecomes:BDY=D/Fx360/t.Alsorememberthethreelimitationsofthismeasure:1)thediscountisdividedbyfacevalueratherthanprice,2)theuseof360daysinayearratherthan365days,and3)theuseofsimpleinteresttoannualizeratherthancompoundinterest.

Holdingperiodyield(HPY)=(Increaseinprice+anyothercashflow)/Investmentamount.Asthenameimpliesthisistheyieldorreturnforagivenholdingperiod.Itisdefinedasthegain(increaseinpriceplusanydividendorcouponpayment)overtheholdingperioddividedbytheoriginalinvestmentamount.Bydefinitionthisyieldmeasureisnotannualized.

Moneymarketyield(MMY)=HPYx360/t.HereweareannualizingtheHPYusinga360‐dayyearandsimpleinterest.SincetheHPYisbasedonthegaindividedbytheinvestmentamount,MMYaddressesthefirstandmostsignificantlimitationoftheBDY.Theothertwolimitationsremain.

Effectiveannualyield(EAY)=(1+HPY)365/t–1.ThismeasurecompoundstheHPYusinga365‐dayyear.HenceitaddressesallthreelimitationsoftheBDY.



Convertingbetweenyieldmeasures

Thetablebelowsummarizeshowtoconvertbetweendifferentyieldmeasures:Thecurriculumoutlinesaformulaforconvertingabankdiscountyieldtoamoneymarketyield,butitiseasierandmoreintuitivetousetheprocessshowninthetablebelow:

Conversion Formula/MethodHPYtoMMY MMY=

HPYtoEAY EAY 1 HPY – 1HPYtoBDY(bankdiscountyield)

GiventhefacevalueandHPY,computepriceandthediscount.Usingthediscount,facevalueandnumberofdaystomaturity,computethebankdiscountyield.

BDYtoEAY FromtheBDY,computethediscount.Fromthediscount,computetheHPY.FromtheHPY,computetheEAY.

BDYtoMMY FromtheBDY,computethediscountandtheprice.Fromthediscountandtheprice,computetheHPY.FromtheHPY,computetheMMY.

ExampleConsideraT‐billwithafacevalueof$100,000and150daysuntilmaturity.Assumethebankdiscountyieldisgivenas4.80%.Determinetheholdingperiodyieldandthemoneymarketyield.

Solution:

1. Computethediscount:0.048x$100,000x $2,000andtheprice:

$100,000– $2,000 $98,0002. Fromthediscountandprice,wecancomputetheHPY:

$2,000$98,000

0.0204

3. FromtheHPY,computetheMMY:0.0204x =0.04896=4.90%



Summary

LO.a:Calculateandinterpretthenetpresentvalue(NPV)andtheinternalrateofreturn(IRR)ofaninvestment.

Thenetpresentvalue(NPV)ofaninvestmentisthepresentvalueofitscashinflowsminusthepresentvalueofitscashoutflows.

Theinternalrateofreturn(IRR)isthediscountratethatmakesthenetpresentvalueequaltozero.

LO.b:ContrasttheNPVruletotheIRRrule,andidentifyproblemsassociatedwiththeIRRrule.

TheNPVruleforindependentprojectsistoaccepttheprojectiftheinvestment’sNPVispositiveandrejecttheprojectifNPVisnegative.However,formutuallyexclusiveprojectstheinvestormustchoosetheprojectwiththehighestpositiveNPV.

TheIRRruleforindependentprojectsistoaccepttheprojectiftheinvestment’sIRRisgreaterthanthecostofcapitalandrejecttheprojectifitislessthanthecostofcapital.Incaseofmutuallyexclusiveprojects,theprojectwiththehighestIRRmustbeselected.

ThereisatheoreticallimitationofIRR,wherebyinterimcashflowsareassumedtobereinvestedattheIRRrateandnotatthecostofcapital.Thisleadstoarankingconflict,i.e.whendecidingbetweenprojectswhicharenotindependent,theNPVandIRRrulesdonotalwaysleadtothesamedecision.WheneverthereisaconflictinrankingbetweentheIRRruleandtheNPVrule,theNPVruleshouldbeusedtodecidebetweenmutuallyexclusiveprojects.

LO.c:Calculateandinterpretaholdingperiodreturn(totalreturn).

HoldingPeriodReturn(HPR)isthereturnthataninvestorearnsoveraspecifiedholdingperiod.

HPRP –P D

P

where:P0=initialinvestment,P1=pricereceivedattheendoftheholdingperiod,D1=cashpaidbytheinvestmentattheendoftheholdingperiod.

LO.d:Calculateandcomparethemoney‐weightedandtime‐weightedratesofreturnofaportfolioandevaluatetheperformanceofportfoliosbasedonthesemeasures.

Themoney‐weightedrateofreturnaccountsforthetimingandamountofallcashflowsintoandoutofaportfolio.Itissimplytheinternalrateofreturn.

Thetime‐weightedrateofreturnmeasuresthecompoundrateofgrowthof$1initiallyinvestedintheportfoliooverastatedmeasurementperiod.

Money‐weightedv/stime‐weightedreturns



Themoney‐weightedrateofreturnisimpactedbythetimingandamountofcashflows.

Thetime‐weightedrateofreturnisnotimpactedbythetimingandamountofcashflows.

Thetime‐weightedreturnisanappropriateperformancemeasureiftheportfoliomanagerdoesnotcontrolthetimingandamountofinvestment.

Ontheotherhand,money‐weightedreturnisanappropriatemeasureiftheportfoliomanagerhascontroloverthetimingandamountofinvestment.

LO.e:Calculateandinterpretthebankdiscountyield,holdingperiodyield,effectiveannualyield,andmoneymarketyieldforUSTreasurybillsandothermoneymarketinstruments.

BDY DF

∗360t

HPY P –P D

P

EAY 1 HPY 365/t 1

MMYHPY ∗ 360

t

LO.f:Convertamongholdingperiodyields,moneymarketyields,effectiveannualyields,andbondequivalentyields.

HPYtoBDY(bankdiscountyield)

GiventhefacevalueandHPY,computepriceandthediscount.

Usingthediscount,facevalue,andnumberofdaystomaturity,computethebankdiscountyield.

BDYtoEAY FromtheBDY,computethediscount.

Fromthediscount,computetheHPY.

FromtheHPY,computetheEAY.

BDYtoMMY FromtheBDY,computethediscountandtheprice.

Fromthediscountandtheprice,computetheHPY.

FromtheHPY,computetheMMY.

Bond‐equivalentyield=2xsemi‐annualYTM



PracticeQuestions

1. Theincrementalafter‐taxcashflowsofaprojectaregivenbelow:Year 0 1 2 3 4Cashflow(€) ‐100,000 50,000 40,000 20,000 6,000

Thediscountrateforevaluatingtheprojectistakenas10%.TheNPV(in€)oftheprojectisclosestto:A. ‐2,363.B. 1,586.C. 2,458.

2. TheIndiangovernmentwishestoinvestinaprojectthatshallrequireaninitialinvestment

of$20million,andwillproducepositivecashflowsof$5millionforthefirstthreeyears,and$4millionforthenexttwoyears.Whatistheapproximateinternalrateofreturn(IRR)fortheinvestment?A. 3%.B. 4%.C. 5%.

3. As a projectmanager, Ronald Parker has to choose between threemutually exclusive

projects:A,B,andC.Hehasthefollowinginformationfromhisstaffregardingthethreeprojects:

NPV IRRA $11,000 8%B $15,000 10%C $10,000 12%

Basedon the informationgiven,whichprojectwouldbemostappropriate forParker’sdepartment?A. ProjectA.B. ProjectB.C. ProjectC.

4. NancyMillerpurchased100sharesofacompanyataprice$15pershareon1January.

Shesoldallthestockson30Juneofthesameyearatprice$18pershare.Shealsoreceiveddividendstotaling$80on30June.Theholdingperiodreturnontheinvestmentisclosestto:A. 20%.B. 25%.C. 30%.



5. Aninvestorpurchasesoneshareofacompanyfor$50.Exactlyoneyearlater,thecompanypaysadividendof$5.00pershare.Thisisfollowedbytwomoreannualdividendsof$6.00and$6.50 in successiveyears.Uponreceiving the thirddividend, the investor sells thesharefor$60.Themoney‐weightedrateofreturnonthisinvestmentisclosestto:A. 15%.B. 16%.C. 17%.

6. Aninvestorpurchases100sharesofacompany.Thetablebelowoutlinesthehistoryofhis

investment:

Time Activity PriceperShare DividendperShare

StartofYear1 Buy100shares $10

EndofYear1 Buy10shares $11 $1EndofYear2 $13 $1.5EndofYear3 Sell110shares $12

Assumingthattheinvestordoesnotreinvesthisdividends,whicharetax‐free,thetime‐weightedrateofreturnontheinvestmentisclosestto:A. 12.2%.B. 13.7%.C. 14.8%.

7. AT‐Billwithaparvalueof$1,000and120daystomaturityistradingatapriceof$980.

ThebankdiscountyieldoftheT‐Billisclosestto:A. 5%.B. 6%.C. 7%.

8. A 180‐day U.S. Treasury bill with a face value of $1,000 sells for $990 when issued.

Assuming an investor holds the bill tomaturity, the investor’s moneymarket yield isclosestto:A. 1.19%.B. 2.02%.C. 3.50%.

9. ATreasury bill offers a bank discount yield of 5% and has 180 days tomaturity. The

effectiveannualyieldontheinstrumentisclosestto:A. 4.88%.B. 5.26%.C. 5.79%.



Solutions1. Aiscorrect.

NPV of a project = Present value of the expected cash inflows – Present value of theexpectedcashoutflows.EnterthegivencashflowsandthegivendiscountrateintoafinancialcalculatorandsolveforNPV.CF0=–100,000,CF1=50,000,CF2=40,000,CF3=20,000,CF=6,000,i=10%.ComputePV.TheNPVis–2,363.

2. Ciscorrect.IRRisdefinedastherateofreturnthatequatesthePVofthecashinflowsto

thePVofthecashoutflows.Ciscorrect.EnterthegivencashflowsinthefinancialcalculatorCF0=‐20millionCF1=5millionCF2=5millionCF3=5millionCF4=4millionCF5=4millionIRRComputed=5.07%

3. Biscorrect.ProjectBhasthehighestNPVamongthethreeprojectsandthusresultsinthe

greatestadditiontoshareholderwealth.WhilethereisaconflictbetweentheNPVandIRRrulesforprojectsBandC,NPVruleistobegivenpreferenceforitssuperiorityoverIRRandhenceBwouldbethemostappropriatechoice.

4. Biscorrect.

HPRP P D

P

(18–15+80/100)/15=0.2533=25.33%.5. Ciscorrect.Themoney‐weightedrateofreturnistheinternalrateofreturn(IRR)ofthe

cashflowsassociatedwiththeinvestment.Usethecashflow(CF)functionofafinancialcalculatorandenterCF0=–50,CF1=5,CF2=6,andCF3=66.5.Calculate the IRR.Theansweris17.15%

6. Biscorrect.TWR=3√{[(11+1)/10]x[(13+1.5)/11]x[(12/13)]}–1=0.1344=13.45%.7. Biscorrect.Thebankdiscountyield=Discount/FaceValuex360/Noofdaystomaturity

=20/1000x360/120=0.06=6%.8. Biscorrect.Themoneymarketyieldis:2.02%=[(1,000/990)–1]x(360/180).



MMY HPY360t

9. Biscorrect.First,calculatetheinitialprice(P0)oftheT‐bill:

0.05=D/100x360/180D=2.5P0=100–2.5=97.5Then, calculate the holding period yield (HPY) (recall that T‐bills are pure discountinstrumentsanddonotpaycoupons):HPY=(P1–P0)÷P0HPY=(100–97.5)÷97.5=0.0256Finally,converttheHPYintoeffectiveannualyield:EAY=(1+HPY)365/t–1EAY=(1+0.0256)365/180–1=0.05259=5.26%.

R08 Statistical Concepts and Market Return 2019 Level I Notes


R08StatisticalConceptsandMarketReturn

1.Introduction

Statisticsisapowerfultoolforanalyzingdataanddrawingconclusions.Asinvestors,weareconcernedaboutthereturnsonourinvestmentsandthedistributionofthosereturns.Weneedthisinformationtoevaluateourinvestments.

Forexample,weoftenlookforcentraltendency.Let’ssaythatthestockmarkethasreturnedonaverage14%overthelast10years.Obviously,weareconcernedwiththisaveragenumberbutwearealsoconcernedwiththedispersionwhichtellsushowspreadoutthereturnshavebeen.Oneofthesimplestmeasuresofdispersionisrange.Let’ssaythatoverthelast10yearsthestockmarkethasrangedbetween‐20%and+35%.Thistellsusabouttheriskinessofourinvestments.

Inthisreading,wewillstudystatisticalmethodsthatallowustosummarizereturndistributions.

Specifically,wewillexplorefourpropertiesofreturndistributions: Wherethereturnsarecentered(centraltendency). Howfarreturnsaredispersedfromtheircenter(dispersion). Whetherthedistributionofreturnsissymmetricallyshapedorlopsided(skewness). Whetherextremeoutcomesarelikely(kurtosis).

2.SomeFundamentalConcepts

2.1TheNatureofStatistics

Thetermstatisticscanhavetwobroadmeanings,onereferringtodataandtheothertoamethodusedtoanalyzedata.Statisticalmethodsinclude:

Descriptivestatistics:Itreferstohowlargedatasetscanbesummarizedeffectivelytodescribetheirimportantcharacteristics.

Inferentialstatistics:Itreferstomakingforecasts,estimatesorjudgmentsaboutalargedatasetbasedonasmallrepresentativeset.

Thefocusofthisreadingisondescriptivestatistics.Wewillcoverinferentialstatisticsinalaterreading.

2.2PopulationsandSamples

A‘population’isdefinedasallmembersofaspecifiedgroup.A‘parameter’describesthecharacteristicsofapopulation.

A‘sample’isasubsetdrawnfromapopulation.A‘samplestatistic’describesthecharacteristicofasample.

Allstockslistedontheexchangeofacountryisanexampleofpopulation.If30stocksareselectedfromamongthelistedstocks,thenthisisasample.



2.3MeasurementScales

Thedifferenttypesofmeasurementscalesare:

Nominalscales:Thesescalescategorizedatabutdonotrankthem.Hence,theyareoftenconsideredtheweakestlevelofmeasurement.Anexamplewouldbetheclassificationofmutualfundsaccordingtotheinvestmentstrategyfollowed–growthfund,valuefund,incomefund,emergingequityfundetc.

Ordinalscales:Thesescalessortdataintocategoriesthatareorderedwithrespecttosomecharacteristic.AnexampleisStandard&Poor’sstarratingsformutualfunds.Onestarrepresentsthegroupofmutualfundswiththeworstperformance.Similarly,groupswithtwo,three,four,andfivestarsrepresentgroupswithincreasinglybetterperformance.

Intervalscales:Thesescalesnotonlyrankdata,butalsoensurethatthedifferencesbetweenscalevaluesareequal.TheCelsiusandFahrenheitscalesareexamplesofsuchscales.Thedifferenceintemperaturebetween10oCand11oCisthesameamountasthedifferencebetween40oCand41oC.However,thesescalesdonothaveatruezero.Forexample,0oCdoesnotrepresenttheabsenceoftemperature.Itissimplythefreezingpointofwater;itisnotatruezero.

Ratioscales:Thesescaleshaveallthecharacteristicsofintervalscalesaswellasatruezeropointastheorigin.Thisisthestrongestlevelofmeasurement.Therateofreturnonaninvestmentismeasuredonaratioscale.Areturnof0%meanstheabsenceofanyreturn.

3.SummarizingDataUsingFrequencyDistributions

Afrequencydistributionisatabulardisplayofdatasummarizedintoarelativelysmallnumberofintervals.Inordertoconstructafrequencydistribution,wecanfollowthefollowingprocedure:

1. Definetheintervals.2. Tallytheobservationsi.e.assignobservationstointervals.3. Counttheobservationsineachinterval.

Example

Sayyouareevaluating100stockswithpricesrangingfrom46to65thataredividedintothefollowingfourintervalsofstockpriceeachhavingawidthof5:

46‐50,51‐55,56‐60and61‐65.Assumethenumberofstockswhosepricesfallineachoftheseintervalsare25,35,29,and11respectively.

Calculatethecumulativefrequency,relativefrequency,andthecumulativerelativefrequencyforthestockpricesgiventhesetofintervalsabove.

Solution:



StockPrice AbsoluteFrequency

CumulativeFrequency

RelativeFrequency

CumulativeRelativeFrequency

46‐50 25 25 0.25 0.2551‐55 35 60 0.35 0.6056‐60 29 89 0.29 0.8961‐65 11 100 0.11 1.00

Absolutefrequency:Theactualnumberofobservationsinagivenintervaliscalledtheabsolutefrequency,orsimplythefrequency,whichisgivenhere.

Cumulativefrequency:Foraninterval,itiscalculatedasthesumoftheabsolutefrequenciesofallintervalslowerthanandincludingthatinterval.

Relativefrequency:Itistheabsolutefrequencyofeachintervaldividedbythetotalnumberofobservations.

Cumulativerelativefrequency:Foraninterval,itiscalculatedasthesumoftherelativefrequenciesofallintervalslowerthanandincludingthatinterval.

4.TheGraphicPresentationofData

4.1TheHistogram

Itisabarchartofdatathathasbeengroupedtogetherintoafrequencydistribution.Theheightofeachbarisequaltotheabsolutefrequencyofeachinterval.

Theadvantageofthevisualdisplayisthatwecanquicklyseewheremostoftheobservationslie.



4.2TheFrequencyPolygonandtheCumulativeFrequencyDistribution

AfrequencypolygonplotsthemidpointsofeachintervalontheX‐axisandtheabsolutefrequencyofthatintervalontheY‐axis.Eachpointisthenconnectedwithastraightline.

Anothergraphicaltoolisthecumulativefrequencydistribution.Suchagraphcanploteitherthecumulativefrequencyorcumulativerelativefrequencyagainsttheupperintervallimit.Thecumulativefrequencydistributionallowsustoseehowmanyorwhatpercentoftheobservationsliebelowacertainvalue.Thefigurebelowisanexampleofacumulativefrequencydistribution.



5.MeasuresofCentralTendency

5.1TheArithmeticMean

Thearithmeticmeanisthesumoftheobservationsdividedbythenumberofobservations.Itisthemostfrequentlyusedmeasureofthemiddleorcenterofdata.

ThePopulationMean

Thepopulationmeanisthearithmeticmeancomputedforapopulation.Itisexpressedas:

μ∑ XN

where:NisthenumberofobservationsintheentirepopulationandXiistheithobservation

Considerthestockreturnsofacompanyoverthelast10years:2%,5%,4%,7%,8%,8%,12%,10%,8%,and5%.

Forthisdataset,thepopulationmeancanbecomputedas:

μ2 5 4 7 8 8 12 10 8 5

106.9%

TheSampleMeanThesamplemeaniscalculatedlikethepopulationmean,exceptthatweusethesamplevalues.Itisexpressedas:

X∑ Xn

where:nisthenumberofobservationsinthesample.

Ifthesampledatais:8,12,10,8and5,thesamplemeancanbecalculatedas:

X8 12 10 8 5

58.6

5.2TheMedian

Themedianisthemidpointofadatasetthathasbeensortedintoascendingordescendingorder.

Foroddnumberofobservations:2,5,7,11,14Median=7

Forevennumberofobservations:3,9,10,20Median=(9+10)/2=9.5

Ascomparedtoamean,amedianislessaffectedbyextremevalues(outliers).

5.3TheMode

Themodeisthemostfrequentlyoccurringvalueinadistribution.



Forthefollowingdataset:2,4,5,5,7,8,8,8,10,12Mode=8

Adistributioncanhavemorethanonemode,orevennomode.Whenadistributionhasonemodeitissaidtobeunimodal.Ifadistributionhastwoorthreemodes,itiscalledbimodalortrimodalrespectively.

5.4OtherConceptsofMean

TheWeightedMeanHeredifferentobservationsaregivendifferentproportionalinfluenceonthemean.Theformulafortheweightedmeanis:

X w X

where:thesumoftheweightsequals1;thatis∑ w 1

ExampleConsideraninvestorwithaportfolioofthreestocks.$40isinvestedinA,$60inB,and$100inC.Ifreturnswere5%onA,7%onB,and9%onC,computetheportfolioreturnusingtheweightedmean.

Solution:

40200

x5% 60200

x7% 100200

x9% 7.6%

Anarithmeticmeanisaspecialcaseofaweightedmeanwhereallobservationsareequallyweightedbythefactor1/n.

TheGeometricMeanThemostcommonapplicationofthegeometricmeanistocalculatetheaveragereturnofaninvestment.Theformulais:

R 1 R 1 R … 1 R – 1

ExampleThereturnoverthelastfourperiodsforagivenstockis:10%,8%,‐5%and2%.Calculatethegeometricmean.

Solution:

1 0.10 1 0.08 1– 0.05 1 0.02 – 1 0.0358 3.58%

Giventhereturnsshownabove,$1investedatthestartofperiod1grewto:

$1.00x1.10x1.08x0.95x1.02 $1.151.Iftheinvestmenthadgrownat3.58%everyperiod,$1.00investedatthestartofperiod1wouldhaveincreasedto:

$1.00x1.0358x1.0358x1.0358x1.0358 $1.151.Asexpected,bothscenariosgivethesameanswer.3.58%issimplytheaveragegrowthrateperperiod.



Instructor’sNoteInthereadingonDiscountedCashFlowApplications,weusedthegeometricmeantocalculatethetime‐weightedrateofreturn.

TheHarmonicMean

Theharmonicmeanisaspecialtypeofweightedmeaninwhichanobservation’sweightisinverselyproportionaltoitsmagnitude.Theformulaforaharmonicmeanis:

Xn

∑

where:Xi>0fori=1,2…n,andnisthenumberofobservations

Theharmonicmeanisusedtofindaveragepurchasepriceforequalperiodicinvestments.

ExampleAninvestorpurchases$1,000ofasecurityeachmonthforthreemonths.Thesharepricesare$10,$15and$20atthethreepurchasedates.Calculatetheaveragepurchasepricepershareforthesecuritypurchased.

Solution:

Theaveragepurchasepriceissimplytheharmonicmeanof$10,$15and$20.

Theharmonicmeanis:

3

$ $ $

$13.85.

Amoreintuitivewayofsolvingthisistotalmoneyspentpurchasingthesharesdividedbythetotalnumberofsharespurchased.

Totalmoneyspentpurchasingtheshares=$1,000x3=$3,000

Totalsharespurchased=sumofsharesboughteachmonth

$1,00010

$1,00015

$1,00020

=100+66.67+50=216.67

Averagepurchasepricepershare$3,000216.67

$13.85

ComparisonofAM,GMandHM Ifthereturnsareconstantovertime:AM=GM=HM. Ifthereturnsarevariable:AM>GM>HM. Thegreaterthevariabilityofreturnsovertime,themorethearithmeticmeanwill

exceedthegeometricmean.



6.OtherMeasuresofLocation:Quantiles

Aquantileisavalueatorbelowwhichastatedfractionofthedatalies.Someexamplesofquantilesinclude:

Quartiles:Thedistributionisdividedintoquarters. Quintiles:Thedistributionisdividedintofifths. Deciles:Thedistributionisdividedintotenths. Percentile:Thedistributionisdividedintohundredths.

Theformulaforthepositionofapercentileinadatasetwithnobservationssortedinascendingorderis:

Ln 1 y100

where:yisthepercentagepointatwhichwearedividingthedistribution.nisthenumberofobservations.Lyisthelocation(L)ofthepercentile(Py)inanarraysortedinascendingorder.

Someimportantpointstorememberare: Whenthelocation,Ly,isawholenumber,thelocationcorrespondstoanactual

observation. WhenLyisnotawholenumberorinteger,Lyliesbetweenthetwoclosestinteger

numbers(oneaboveandonebelow)andweuselinearinterpolationbetweenthosetwoplacestodeterminePy.

ExampleConsiderthedataset:

47 35 37 32 40 39 36 34 35 3144

1. Findthe75thpercentilepoint2. Findthe1stquartilepoint3. Findthe5thdecilepoint4. Findthe6thdecilepoint.

Solutionto1:Firstarrangethedatainascendingorder:

31,32,34,35,35,36,37,39,40,44,47

Locationofthe75thpercentileisthe:L75=(11+1)(75/100)=9thvalue.i.e.P75=40

Withasmalldataset,suchasthisone,thelocationandthevalueisapproximate.Asthedatasetbecomeslarger,thelocationandpercentilevalueestimatesbecomemoreprecise.

Solutionto2:



Locationofthe1stquartileisthe:

L25=(11+1)(25/100)=3rdvalue.i.e.P25=34

Solutionto3:Locationofthe5thdecileisthe:

L50=(11+1)(50/100)=6thvalue.i.e.P50=36

Solutionto4:L60=(11+1)(60/100)=7.2

Uselinearinterpolation,whichestimatesanunknownvalueonthebasisoftwoknownvaluesthatsurroundit.

Inthiscase,the7thvalueis37andthe8thvalueis39.The6thdecileis:P60=37+0.4(0.2timesthelineardistancebetween37and39).P60=37.4

7.MeasuresofDispersion

Inthissegmentwelookatmeasuresthattellushowspreadoutordispersedourdatamightbe.

7.1TheRange

Therangeisthedifferencebetweenthemaximumandminimumvaluesinadataset.Itisexpressedas:

Range=Maxvalue–MinValue

Iftheannualreturnsdatais:10%,‐5%,10%,25%.Whatistherange?

Herethemaximumreturnis25%andtheminimumreturnis‐5%.Therangeis25%–(‐5%)=30%.

7.2TheMeanAbsoluteDeviation

Itistheaverageoftheabsolutevaluesofdeviationsfromthemean.Itisexpressedas:

MAD |X X| /n

where:Xisthesamplemeanandnisthenumberofobservationsinthesample.

Example

Considerthefollowingdataset:8,12,10,8and5.Calculatethemeanabsolutedeviation.

Solution:

X=(8+12+10+8+5)/5=8.6

MAD|8 8.6| |12 8.6| |10 8.6| |8 8.6| |5 8.6|

5



MAD0.6 3.4 1.4 0.6 3.6

51.92

7.3PopulationVarianceandPopulationStandardDeviation

Populationvarianceisthemeanofthesquareddeviationsfromthemean.Thepopulationvarianceiscomputedusingallmembersofapopulation.Itisexpressedas:

σ X μ /N

where:µisthepopulationmeanandNisthesizeofthepopulation

Populationstandarddeviationisdefinedasthepositivesquarerootofthepopulationvariance.

ExampleCalculatethepopulationvarianceandstandarddeviationforthisdataset:2%,5%,4%,7%,8%,8%,12%,10%,8%,and5%.

Solution:σ

. . . . . . . . . .

σ 7.89%

Populationstandarddeviation σ √7.89=2.81%

7.4SampleVarianceandSampleStandardDeviation

Samplevarianceapplieswhenwearedealingwithasubset,orsample,ofthetotalpopulation.Itisexpressedas:

s X X / n 1

where:Xisthesamplemeanandnisthenumberofobservationsinthesample.

Samplestandarddeviationisdefinedasthepositivesquarerootofthesamplevariance.

Example

Calculatethesamplevarianceforthefollowingdataset:8,12,10,8and5.

Solution:

s8 8.6 12 8.6 10 8.6 8 8.6 5 8.6

5 1

s 6.80%



Thesamplestandarddeviationisthepositivesquarerootofthesamplevariance.Forthesampledatagivenabove, √6.80=2.61%

Usingafinancialcalculatortocalculatevarianceandstandarddeviations

Thepopulationandsamplestandarddeviationcaneasilybecomputedusingafinancialcalculator.Assumethefollowingdataset:10%,‐5%,10%,25%,thecalculatorkeystrokesareshownbelow:

Keystrokes Description Display[2nd][DATA] Entersdataentrymode [2nd][CLRWRK] Clearsdataregister X0110[ENTER] X01=10[↓][↓]5+/‐[ENTER] X02=‐5[↓][↓]10[ENTER] X03=10[↓][↓]25[ENTER] X04=25[2nd][STAT][ENTER] Putscalculatorintostatsmode [2nd][SET] Pressrepeatedlytillyousee 1‐V[↓] Numberofdatapoints N=4[↓] Mean X=10[↓] Samplestandarddeviation Sx=12.25[↓] Populationstandarddeviation σx=10.61

Noticethatthecalculatorgivesboththesampleandthepopulationstandarddeviation.Ontheexamwewillhavetodeterminewhetherwearedealingwithpopulationorsampledataandchoosetheappropriatevalue.

7.5Semivariance,Semideviation,andRelatedConcepts

Instructor’sNote:SemivarianceandsemideviationarenotemphasizedinthelearningoutcomesandhaveaverylowprobabilityofbeingtestedontheLevelIexam.Nevertheless,abriefexplanationisgivenbelow.

Varianceandstandarddeviationofreturnstakeaccountofreturnsaboveandbelowthemean,butofteninvestorsareconcernedonlywithdownsiderisk,forexamplereturnsbelowthemean.Asaresult,analystshavedevelopedsemivariance,semideviationandrelateddispersionmeasuresthatfocusondownsiderisk.Semivarianceisdefinedastheaveragesquareddeviationbelowthemean.Semideviationisthepositivesquarerootofsemivariance.

7.6Chebyshev’sInequality

AccordingtoChebyshev’sinequality,theproportionoftheobservationswithinkstandard

deviationsofthearithmeticmeanisatleast: – forallk>1.



Tofindoutwhatpercentoftheobservationsmustbewithintwostandarddeviationsofthe

meanwesimplyplugintotheformulaandget: – – ¼ 0.75=75%.Hence,at

least75%ofthedatawillbebetweentwostandarddeviationsofthemean.

Chebyshev’sinequalitycanbeusedtomeasuremaximumamountofdispersion,regardlessoftheshapeofthedistribution.Noticethatherewedonotmakeanyassumptionsaboutwhetherthedistributionisnormalornotnormal.Thisinequalityappliesacrossalldistributions.

7.7CoefficientofVariation

Coefficientofvariationexpresseshowmuchdispersionexistsrelativetothemeanofadistributionandallowsfordirectcomparisonofdispersionacrossdifferentdatasets.Itisusedininvestmentanalysistocomparerelativerisks.Whenevaluatinginvestments,alowervalueisbetter.Coefficientofvariationisexpressedas:

CVsX

where:s=samplestandarddeviationofasetofobservationsandX=samplemean

ExampleInvestmentAhasameanreturnof7%andastandarddeviationof5%.InvestmentBhasameanreturnof12%andastandarddeviationof7%.Calculatethecoefficientsofvariation.

SolutionThecoefficientsofvariationcanbecalculatedasfollows:

CV5%7%

0.71

CV7%12%

0.58

ThismetricshowsthatInvestmentAisriskierthanInvestmentB.

7.8TheSharpeRatio

TheSharperatioistheratioofexcessreturntostandarddeviationofreturnforaportfolio.Excessreturnreferstothereturnabovetherisk‐freerate.Whenevaluatinginvestments,ahighervalueisbetter.TheformulaforcalculatingtheSharperatiois:

S R R

s

where:R =MeanreturntotheportfolioR =Meanreturntoarisk‐freeassets =Standarddeviationofreturnontheportfolio



Example

Thetablebelowprovidesdatafortwoportfolios.Giventhatthemeanannualriskfreerateis10.5%,whichportfoliohasthehigherSharperatio?Portfolio Arithmeticmeanreturn(%) Varianceof(%)PortfolioA 16.4% 4.9%PortfolioB 12.6% 3.5%

Solution:

PortfolioA:16.4 10.5

√4.92.665

PortfolioB:12.6 10.5

√3.51.122

PortfolioAoffersahigherexcessreturnperunitofriskrelativetoPortfolioB.

8.SymmetryandSkewnessinReturnDistributions

SymmetricaldistributionAdistributionissaidtobesymmetricalwhenthedistributiononeithersideofthemeanisamirrorimageoftheother.

Inanormaldistribution,mean=median=mode.

Ifadistributionisnon‐symmetrical,itissaidtobeskewed.Skewnessisameasureoftheasymmetryoftheprobabilitydistribution.Skewnesscanbenegativeorpositive.

PositivelyskeweddistributionApositivelyskeweddistributionhasalongtailontherightside,whichmeansthattherewillbefrequentsmalllossesandfewlargegains.

Herethemean>median>mode.Theextremevaluesaffectthemeanthemostwhichispulledtotheright.Theyaffectthemodetheleast.



Negativelyskeweddistribution

Anegativelyskeweddistributionhasalongtailontheleftside,whichmeansthattherewillbefrequentsmallgainsandfewlargelosses.

Herethemean<median<mode.Theextremevaluesaffectthemeanthemostwhichispulledtotheleft.Theyaffectthemodetheleast.

9.KurtosisinReturnDistributions

Kurtosisisameasureofthecombinedweightofthetailsofadistributionrelativetotherestofthedistribution.

Excesskurtosis=kurtosis‐3.Anexcesskurtosiswithanabsolutevaluegreaterthanoneisconsideredsignificant.

Aleptokurticdistributionhasfattertailsthananormaldistribution.Ithasanexcesskurtosisgreaterthan0.

Aplatykurticdistributionhasthinnertailsthananormaldistribution.Ithasanexcesskurtosislessthan0.

Amesokurticdistributionisidenticaltoanormaldistribution.Ithasanexcesskurtosisequalto0.

Thefollowingfigureshowsaleptokurticdistribution.Ascomparedtoanormaldistribution,aleptokurticdistributionismorelikelytogenerateobservationsinthetailregion.Itisalso



morelikelytogenerateobservationsnearthemean.However,tohavethetotalprobabilitiessumto1,itwillgeneratefewerobservationsintheremainingregions(i.e.regionsbetweenthecentralandthetwotailregions)

10.UsingGeometricandArithmeticMeans

Thegeometricmeanisappropriatetomeasurepastperformanceovermultipleperiods.

ExampleTheportfolioreturnsforthepasttwoyearswere100%inyear1and‐50%inyear2.Whatwasthemeanreturn?

Solution:Pastreturn=geometricmean=(2x0.5)0.5–1=0%

Thearithmeticmeanisappropriateforforecastingsingleperiodreturns.

ExampleTwopossiblereturnsforthenextyearare100%and‐50%.Whatistheexpectedreturn?

Solution:Expectedreturn=Arithmeticmean=(100–50)/2=25%



Summary

LO.a:Distinguishbetweendescriptivestatisticsandinferentialstatistics,betweenapopulationandasample,andamongthetypesofmeasurementscales.

TheNatureofStatistics Descriptivestatistics:Itreferstohowlargedatasetscanbesummarizedeffectivelyto

describetheirimportantcharacteristics. Inferentialstatistics:Itreferstomakingforecasts,estimates,orjudgmentsabouta

largedatasetbasedonasmallrepresentativeset.

PopulationandSample Population:Itincludesallmembersofaparticulargroup. Sample:Itisasubsetdrawnfromapopulation.

MeasurementScales:Datacanbemeasuredusingthefollowingscales: Nominalscale:Theyputdataincategoriesbutdonotrankthem. Ordinalscale:Nominalscale+datacanberankedwithrespecttosomecharacteristic. Intervalscale:Ordinalscale+thedifferencesinthedatavaluesaremeaningful. Ratioscale:Intervalscale+theratiosofvalue,suchastwiceorhalfasmuchare

meaningful.

LO.b:Defineaparameter,asamplestatistic,andafrequencydistribution.

Parameter:Adescriptivemeasureofapopulationiscalledaparameter.

Samplestatistic:Adescriptivemeasureofasampleiscalledasamplestatistic.

Frequencydistribution:Afrequencydistributionisatabulardisplayofdatacategorizedintoarelativelysmallnumberofintervalsorclasses.Itallowsustoevaluatehowdataisdistributed.

LO.c:Calculateandinterpretrelativefrequenciesandcumulativerelativefrequencies,givenafrequencydistribution.

Relativefrequency:Itiscalculatedastheabsolutefrequencyofanintervaldividedbythetotalnumberofobservations.

Cumulativerelativefrequency:Foraninterval,itiscalculatedasthesumoftherelativefrequenciesofallintervalslowerthanandincludingthatinterval.

LO.d:Describethepropertiesofadatasetpresentedasahistogramorafrequencypolygon.

Histogramisabarchartofdatathathasbeengroupedtogetherintoafrequencydistribution.Theheightofeachbarisequaltotheabsolutefrequencyofeachinterval.

AfrequencypolygonplotsthemidpointsofeachintervalontheX‐axisandtheabsolutefrequencyofthatintervalontheY‐axis.Eachpointisthenconnectedwithastraightline.



LO.e:Calculateandinterpretmeasuresofcentraltendency,includingthepopulationmean,samplemean,arithmeticmean,weightedaverageormean,geometricmean,harmonicmean,median,andmode.

Arithmeticmeanissimplythesumofalltheobservationsdividedbythetotalnumberofobservations.

Medianisthemidpointofadatasetthathasbeensortedfromlargesttosmallestorvise‐versa.

Modeisthevaluethatoccursmostfrequentlyinadataset.

Thegeometricmeanisusedtocalculatecompoundgrowthrate.Itiscomputedas:

R 1 R 1 R …… . 1 R / 1

Inaweightedmean,differentobservationsaregivendifferentweightsaspertheirproportionalinfluenceonthemean.Itiscomputedas:

X w X

Harmonicmeanisusedtofindaveragepurchasepriceforequalperiodicinvestments.Itiscomputedas:

X n/1X

LO.f:Calculateandinterpretquartiles,quintiles,deciles,andpercentiles.

Aquantileisavalueatorbelowwhichastatedfractionofthedatalies.Someexamplesofquantilesinclude:

Quartiles:Thedistributionisdividedintoquarters. Quintiles:Thedistributionisdividedintofifths. Deciles:Thedistributionisdividedintotenths. Percentile:Thedistributionisdividedintohundredths.

Theformulaforthepositionofapercentileinadatasetwithnobservationssortedinascendingorderis:

Ly=(n+1)y/100

LO.g:Calculateandinterpret1)arangeandameanabsolutedeviationand2)thevarianceandstandarddeviationofapopulationandofasample.

Rangeisthedifferencebetweenthemaximumandminimumvaluesinadataset.Itiscalculatedas:

Range=Maximumvalue–Minimumvalue



Meanabsolutedeviation(MAD)istheaverageoftheabsolutevaluesofdeviationsfromthemean.Itisexpressedas:

MAD |X X| /n

Varianceisdefinedasthemeanofthesquareddeviationsfromthearithmeticmean.Itiscalculatedas:

PopulationVarianceσ ∑ X μ /N

SampleVariances ∑ X X / n 1

Standarddeviationisthepositivesquarerootofthevariance.Itisoftenusedasameasureofrisk.

LO.h:CalculateandinterprettheproportionofobservationsfallingwithinaspecifiednumberofstandarddeviationsofthemeanusingChebyshev’sinequality.

AccordingtoChebyshev’sinequality,theproportionoftheobservationswithinkstandarddeviationsofthearithmeticmeanisatleast1‐1/k2forallk>1.

LO.i:CalculateandinterpretthecoefficientofvariationandtheSharperatio.

Coefficientofvariationmeasurestheriskperunitofreturn.Whenevaluatinginvestments,alowervalueisbetter.Itisexpressedas:

CVsX

Sharperatiomeasuresexcessreturnperunitofrisk.Whenevaluatinginvestments,ahighervalueisbetter.Itisexpressedas:

S R R

s

LO.j:Explainskewnessandthemeaningofapositivelyornegativelyskewedreturndistribution.

Skewdescribesthedegreetowhichadistributionisnotsymmetricaboutitsmean.Areturndistributionwithpositiveskewnesshasfrequentsmalllossesandafewextremegains.Areturndistributionwithnegativeskewnesshasfrequentsmallgainsandafewextremelosses.Zeroskewnessindicatesasymmetricdistributionofreturns.

LO.k:Describetherelativelocationsofthemean,median,andmodeforaunimodal,nonsymmetricaldistribution.

Forthepositivelyskewedunimodaldistribution,themodeislessthanthemedian,whichislessthanthemean.Forthenegativelyskewedunimodaldistribution,themeanislessthanthemedian,whichislessthanthemode.



LO.l:Explainmeasuresofsampleskewnessandkurtosis.

Kurtosisisameasureofthecombinedweightofthetailsofadistributionrelativetotherestofthedistribution.

Excesskurtosis=kurtosis‐3.Anexcesskurtosiswithanabsolutevaluegreaterthanoneisconsideredsignificant.

Aleptokurticdistributionhasfattertailsthananormaldistribution. Aplatykurticdistributionhasthinnertailsthananormaldistribution. Amesokurticdistributionisidenticaltoanormaldistribution.

LO.m:Comparetheuseofarithmeticandgeometricmeanswhenanalyzinginvestmentreturns.

Toestimatetheaveragereturnsovermorethanoneperiod(timeseriesdata),youshouldusethegeometricmeanbecauseitcaptureshowthetotalreturnsarelinkedovertime.Ifyouwanttoestimatetheaveragereturnofmultipleinvestmentsoveraone‐periodhorizon(cross‐sectionaldata),youshouldusethearithmeticmean.



PracticeQuestions

1. Ananalystratesstocksasunderweight,marketweight,oroverweight,referringtothesuggestedweightingofthestockinaportfolio.Themeasurementscaleusedbytheanalystcanbestbedescribedas:A. nominalscale.B. ordinalscale.C. intervalscale.

2. Aparameterdescribesthecharacteristicofa:

A. population.B. sample.C. populationandasample.

3. Forthefollowingfrequencydistribution,thenumberofintervals,thesamplesize,andthe

relativefrequencyofthethirdintervalareclosestto:

Returns Frequency‐10%upto0% 40%upto10% 1310%upto20% 520%upto30% 3

A. 4,25,20%.B. 1,20,10%.C. 3,30,15%.

4. Thefollowingtenobservationsareasampledrawnfromanormalpopulation:20,15,12,

6,4,‐11,19,14,‐3,and19.Thearithmeticmeanofthesampleisclosestto:A. 8.6.B. 9.5.C. 10.2.

5. Aportfolio has the following annual returns: 6%, 10%, ‐5%, 0%. The geometricmean

acrossthefour‐yearperiodisclosestto:A. 2.37%.B. 2.48%.C. 2.59%.

6. Considerthefollowingsetofnumbers:

‐20 ‐11 ‐3 0 13 5 6 9 10



12 18 21 23 2528 39 40 54 60

Themedianvalueoftheaboveitemsisclosestto:A. 10.B. 11.C. 12.

7. Considerthefollowingsetofnumbers:

20 24 21 35 20 2424 22 20 26 28 2219 21 20 21 22 28

Themodeofthesampleisclosetto:A. 20.B. 21.C. 22.

8. Followingdataisprovidedonreturnsofaseriesoffunds:

Fund Returns(%)Fund1 6.15%Fund2 7.25%Fund3 8.95%Fund4 9.65%Fund5 10.35%Fund6 11.10%Fund7 12.35%Fund8 13.55%Fund9 14.05%Fund10 15.75%Fund11 16.95%Fund12 17.25%Fund13 18.30%

Thevalueofthesecondquintileisclosestto:A. 10.35%B. 10.80%.C. 11.30%.

9. Theannualreturnsofaportfolioaregivenbelow:

Year Portfolioreturn

Year1 6.5%



Year2 8.2%

Year3 10.5%Year4 ‐5.4%

Year5 7.7%

Theportfolio’srangeandmeanabsolutedeviationforthefive‐yearperiodareclosestto:A. 15.90%and5.10%.B. 5.10%and4.36%.C. 15.90%and4.36%.

10. Thefollowingobservationsaredrawnfromanapproximatelynormalpopulation:

Observation 1 2 3 4 5Value 11 8 ‐6 4 ‐5

Thesamplestandarddeviationisclosestto:A. 6.83and46.65.B. 7.64and58.37.C. 7.64and2.76.

11. Asampleof240observationsisrandomlyselectedfromapopulation.Themeanofthe

sample is 120 and the standard deviation is 8. Based on Chebyshev’s inequality, theendpointsoftheintervalthatmustcontainatleast75%oftheobservationsareclosestto:A. 96and144.B. 112and128.C. 104and136.

12. GeorgeBaker, an equity fundmanagerhas the following information about a common

stockportfolio:

Arithmeticmeanreturn 11.8%Geometricmeanreturn 10.6%Portfoliobeta 1.2Risk‐freerateofreturn 4.25%Varianceofreturns 196

Fromthegiveninformation,thecoefficientofvariationisclosestto:A. 1.32.B. 1.24.C. 1.18.

13. Followinginformationaboutthreeportfoliosisgiven:

Portfolio Meanreturnonportfolio(%)

Standarddeviationofthereturns(%)



A 15 28B 12 19C 10 7

Iftherisk‐freerateis4%,whichportfoliohasthehighestSharperatio?A. A.B. B.C. C.

14. Whichofthefollowingismostlikelytobetrueforapositivelyskeweddistribution?

A. Mode>Median>Mean.B. Median>Mode>Mean.C. Mean>Median>Mode.

15. Adistributionlesspeakedthanthenormaldistributionisbestdescribedasbeing:

A. platykurtic.B. mesokurtic.C. leptokurtic.



Solutions

1. Biscorrect.Thisisanordinalscale.Theratingofunderweight,marketweightor

overweightorderstheratedsecuritiesintermsoflevelsofexpectedperformance.2. Aiscorrect.Aparameterdescribesthecharacteristicofapopulation,whileasample

statisticdescribesthecharacteristicofasample.3. Aiscorrect.Anintervalisthesetofreturnvaluesthatanobservationfallswithin.There

arefourintervals.Thesamplesizeisthesumofallofthefrequenciesinthedistribution:4+13+5+3=25.Therelativefrequencyisfoundbydividingthefrequencyoftheintervalbythetotalnumberoffrequencies:5/25=20%.

4. Biscorrect.Thesumofthetennumbersis95.Dividingby10givesthemeanof9.5.5. Ciscorrect.Thegeometricmeanreturniscalculatedas[(1+0.06)×(1+0.1)×(1‐0.05)

×(1+0.00)]1/4–1=0.0259≈2.59%.6. Biscorrect.Themedianisthevalueofthemiddleitemofasetofitems.Thetotalnumber

ofitemsare20,hencethemedianisthevaluebetween10thand11thobservation.Thevalueofthe10thitemis10;thevalueofthe11thitemis12.Theaverageof10and12is11.

7. Aiscorrect.Themodeisthemostfrequentvalueinthesetofitemsandthusisequalto

20.8. Biscorrect.Quintilesdividedataintofiveparts.Hencethefirstquintilecorrespondsto

the20thpercentileandthesecondquintilecorrespondstothe40thpercentile.Thelocationcanbedeterminedusing:Ly=(n+1)×(y/100)L40=(13+1)×(40/100)=5.6.Thevaluecorrespondingtolocation5(Fund5)is10.35%.Thevaluecorrespondingtolocation6(Fund6)is11.10%.Theapproximatevaluecorrespondingtolocation5.6canbeestimatedusinglinearinterpolation:10.35%+(0.6×(11.10%–10.35%))=10.80%

9. Ciscorrect.Range=Highestvalue–Lowestvalue=10.5%‐(‐5.4%)=15.9%

TocalculateMAD,firstcomputethemean:(6.5+8.2+10.5–5.4+7.7)/5=5.5%andcomputeMAD,(|6.5–5.5|+|8.2–5.5|+|10.5–5.5|+|–5.4–5.5|+|7.7–5.5|)/5=4.36%.

10. Biscorrect.Thesamplestandarddeviationcanbefoundas:




[2nd][DATA] Enterdataentrymode

[2nd][CLRWRK] Cleardataregisters X01

11[ENTER] X01=11

[↓][↓]8[ENTER] X02=8

[↓][↓]6+/‐[ENTER] X03=‐6

[↓][↓]4[ENTER] X04=4

[↓][↓]5+/‐[ENTER] X05=‐5

[2nd][STAT] Putscalculatorintostats

[2nd][SET] Pressrepeatedlytill 1‐V

[↓] Numberofdatapoints N=5

[↓] Mean X=2.4

[↓] Samplestandard Sx=7.64

[↓] Populationstandard σx=6.83

Thesamplevarianceissimplythesquareofsamplestandarddeviation:7.642=58.37.11. Ciscorrect.AccordingtoChebyshev’sinequality,theproportionoftheobservations

withinkstandarddeviationsofthearithmeticmeanisatleast1–1/k2forallk>1.Fork=2,thatproportionis1–1/22,whichis75%.Thelowerendpointis,therefore,themean(120)minus2times8(thestandarddeviation)andtheupperendpointis120plus2times8.120–(2x8)=104;120+2(8)=136.

12. Ciscorrect.Thecoefficientofvariationis:Standarddeviationofreturn/Meanreturn=

sqrt(196)/11.8=1.1813. Ciscorrect.TheSharperatioisdefinedasSp=( p‐ F)/ p

SA=(15–4)/28=0.3928SB=(12–4)/19=0.4210SC=(10–4)/7=0.8571

SharpeRatio i.e.excessreturnsperunitofrisk.Ahighernumberispreferred.

14. Ciscorrect.Forapositivelyskeweddistribution,themeanisgreaterthanthemedian,

whichisgreaterthanthemode.



15. Aiscorrect.Platykurticdescribesadistributionthatislesspeakedthananormal

distribution.Leptokurticdescribesadistributionthatismorepeakedthanthenormaldistribution.Mesokurticisadistributionaspeakedasthenormaldistribution.

R09 Probability Concepts 2019 Level I Notes


R09ProbabilityConcepts

1.Introduction

Sincemanyinvestmentdecisionsaremadeinanenvironmentofuncertainty,itisessentialforportfoliomanagersandinvestmentmanagerstohaveafundamentalgraspofprobabilityconcepts.Inthisreading,wewillfocuson:

• Definitionsandrulesrelatedtoprobability.• Expectedvalueandvariance.• Covarianceandcorrelation.

2.Probability,ExpectedValue,andVariance

FundamentalConcepts

Arandomvariableisanuncertainquantity/number.Forexample,whenyourolladie,theresultisarandomvariable.

Anoutcomeistheobservedvalueofarandomvariable.Forexample,ifyourolla2,itisanoutcome.

Aneventcanbeasingleoutcomeorasetofoutcomes.Forexample,youcandefineaneventasrollinga2orrollinganevennumber.

Mutuallyexclusiveeventsareeventsthatcannothappenatthesametime.Forexample,rollinga2androllinga3areexamplesofmutuallyexclusiveevents.Theycannothappenatthesametime.

Exhaustiveeventsarethosethatcoverallpossibleoutcomes.Forexample,‘rollinganevennumber’or’rollinganoddnumber’areexhaustiveevents.Theycoverallpossibleoutcomes.

Thetwodefiningpropertiesofprobabilityare:• Theprobabilityofanyeventhastobebetween0and1.• Thesumoftheprobabilitiesofmutuallyexclusiveandexhaustiveeventsisequalto

1.WaysofEstimatingProbability

Themethodsofestimatingprobabilitiesare:• Empiricalprobability:Basedonanalyzingthefrequencyofanevent’soccurrencein

thepast.• Aprioriprobability:Basedonformalreasoningandinspectionratherthan

personaljudgment.• Subjectiveprobability:Informedguessbasedonpersonaljudgment.

Empiricalandaprioriprobabilitiesareoftengroupedasobjectiveprobabilitiesbecausetheydonotvaryfrompersontoperson.



ProbabilityStatedasOdds

Oddsforaneventaredefinedastheprobabilityoftheeventoccurringtotheprobabilityoftheeventnotoccurring.OddsforE=P(E)/[1–P(E)].

GivenoddsforEof“atob”,theimpliedprobabilityofEisa/(a+b).

Example

Iftheprobabilityofaneventis0.2,whataretheoddsofitoccurring?Alternatively,iftheoddsare1to4,whatistheprobabilityofthisevent?

Solution:

Theoddsoftheeventoccurringare= ..=1/4.Thisisstatedasoddsof1to4.

Giventheodds,theprobabilityoftheeventoccurringis

=0.20.

Oddsagainstaneventaredefinedastheprobabilityoftheeventnotoccurringtotheprobabilityoftheeventoccurring.OddsagainstE=[1–P(E)]/P(E).

GiveoddsagainstEof“atob”,theimpliedprobabilityofEisb/(a+b).

Example

IfP(E)=0.2,whataretheoddsagainsttheeventoccurring?Iftheoddsagainstaneventare4to1,whatistheprobabilityoftheevent?

Solution:

P(E)= ..= .HencetheoddsagainstEare4to1.

Giventheoddsagainstanevent,theprobabilityoftheeventis =0.2

Conditionalv/sUnconditionalprobabilities

Unconditionalprobabilityistheprobabilityofaneventoccurringirrespectiveoftheoccurrenceofotherevents.ItisdenotedasP(A).Unconditionalprobabilityisalsocalled‘marginal’probability.

Conditionalprobabilityistheprobabilityofaneventoccurringgiventhatanothereventhasoccurred.ItisdenotedasP(A|B),whichistheprobabilityofeventAgiventhateventBhasoccurred.

JointProbabilityandMultiplicationRule

Multiplicationruleisusedtodeterminethejointprobabilityoftwoevents.Itisexpressedas:

P(AB)=P(A|B)P(B)

Rearrangingtheequationwegettheformulaforcomputingconditionalprobabilities:

P(A|B)=P(AB)/P(B)



Example

P(interestrateswilldecrease)=P(D)=40%P(stockpriceincreases)=P(S)P(stockpricewillincreasegiveninterestratesdecrease)=P(S|D)=70%

Computeprobabilityofastockpriceincreaseandaninterestratedecrease.

Solution:

P(SD)=P(S|D)xP(D)=0.7x0.4=0.28=28%

AdditionRuleforProbabilities

Additionruleisusedtodeterminetheprobabilitythatatleastoneoftheeventswilloccur.Itisexpressedas:

P(AorB)=P(A)+P(B)–P(AB)

Example

P(priceofAincreases)=P(A)=0.5P(priceofBincreases)=P(B)=0.7P(priceofAandBincreases)=P(AB)=0.3

ComputetheprobabilitythatthepriceofstockAorthepriceofstockBincreases.

Solution

P(AorB)=0.5+0.7–0.3=0.9

IndependentandDependentEvents

Iftheoccurrenceofoneeventdoesnotinfluencetheoccurrenceoftheotherevent,thenthetwoeventsarecalledindependentevents.

i.e.P(A|B)=P(A)orP(B|A)=P(B)

Multiplicationruleforindependentevents:P(AB)=P(A)P(B)

Additionruleforindependentevents:P(AorB)=P(A)+P(B)–P(AB).(Theadditionruledoesnotchange.)

Iftheprobabilityofaneventisaffectedbytheoccurrenceofanothereventthenitiscalledadependentevent.

TotalProbabilityRule

Thetotalprobabilityruleisusedtocalculatetheunconditionalprobabilityofanevent,givenconditionalprobabilities.

Ininvestmentanalysis,weoftenformulateasetofmutuallyexclusiveandexhaustivescenariosandthenestimatetheprobabilityofaparticularevent.Forexample,let’ssaythatwehavetwoscenariosSandnon‐Sthataremutuallyexclusiveandexhaustive.



Accordingtothetotalprobabilityrule,theprobabilityofanyeventP(A)canbeexpressedas:

P(A)=P(AS)+P(ASC)

Usingthemultiplicationruleweget,

P(A)=P(A|S)P(S)+P(A|SC)P(SC)

Ifwehavemorethantwoscenarios,wecangeneralizethisequationto:

P(A)=P(AS1)+P(AS2)+…+P(ASn)=P(A|S1)P(S1)+P(A|S2)P(S2)+…+P(A|Sn)P(Sn)

ExpectedValueofaRandomVariable

Theexpectedvalueofarandomvariablecanbedefinedastheprobability‐weightedaverageofthepossibleoutcomesoftherandomvariable.ForarandomvariableX,theexpectedvalueofXisdenotedasE(X)andiscalculatedas:

E X P X X

where:Xi=OneofnpossibleoutcomesoftherandomvariableXP(Xi)=ProbabilityofXi

VarianceofaRandomVariable

Theexpectedvalueisourforecast,butwecannotcountontheindividualforecastbeingrealized.Thisiswhyweneedtomeasuretheriskweface.Varianceandstandarddeviationareexamplesofhowwecanmeasurethisrisk.Thevarianceofarandomvariableistheprobability‐weightedsumofthesquareddifferencesbetweeneachpossibleoutcomeandtheexpectedvalueoftherandomvariable.Itisexpressedas:

σ X P X X E X

Varianceisanumbergreaterthanorequalto0becauseitisthesumofsquaredterms.Ifvarianceis0,thereisnodispersionorrisk.TheoutcomeiscertainandthequantityXisnotrandomatall.Standarddeviationisthepositivesquarerootofvariance.

Wecancalculatetheexpectedvalueandvarianceofarandomvariableusingafinancialcalculatorasshownbelow:

Example

Aproject’scashflowfortheupcomingyeardependsonthestateoftheeconomy,asshowninthetablebelow.Whatisthevarianceofthecashflow?Whatisthestandarddeviation?

StateofEconomy Probability CashFlow



Good 0.3 50

Average 0.5 40

Weak 0.2 20Solution:

Usingafinancialcalculator:


[2nd][DATA] Entersdataentrymode

[2nd][CLRWRK] Clearsdataregister X01

50[ENTER] 1stpossiblevalueofrandomvariable X01=50

[↓]30[ENTER] Probabilityof30%forX01 Y01=30

[↓]40[ENTER] 2ndpossiblevalueofrandomvariable X02=40


[↓]20[ENTER] 3rdpossiblevalueofrandomvariable X03=20


[2nd][STAT] Putscalculatorintostatsmode

[2nd][SET] Pressrepeatedlytillyousee 1‐V

[↓] Totalnumberofentries N=100

[↓] Expectedvalueofrandomvariable X=39

[↓] Samplestandarddeviation Sx=10.49

[↓] Populationstandarddeviation σx=10.44

Wecanthensquarethepopulationstandarddeviationof10.44togetthevariancei.e.10.442=109.00

TotalProbabilityRuleforExpectedValue

Justlikethetotalprobabilityrulestatesunconditionalprobabilitiesintermsofconditionalprobabilities,thetotalprobabilityruleforexpectedvaluesstatesunconditionalexpectedvaluesintermsofconditionalexpectedvalues.

E(X|S)=P(X1|S)X1+P(X2|S)X2+…+P(Xn|S)Xn

Instructor’sNoteNoticethatthisformulaisexactlysimilartothetotalprobabilityruleformula.

P(A)=P(A|S1)P(S1)+P(A|S2)P(S2)+…+P(A|Sn)P(Sn)



Example

What is the expectedpriceof a stockat theendof the currentperiodgiven the followinginformation:probabilitythatinterestrateswilldecline=0.4.Ifinterestratesdeclinethereisa75%chancethatstockpricewillbe$100versusa25%chancethatthestockpricewillbe$90. If interestratesdonotdecline there isa50%chance that thestockpricewillbe$80versusa50%chancethatstockpricewillbe$70.

Solution:

Wecanplottheprobabilitiesusingatreediagram.

Considerthefirstnode(topright).Itreferstotheprobabilitythatthestockpricewillbe$100given a decline in interest rates. We can calculate the probability of that happening bymultiplyingtheprobabilityofadeclineininterestrates(0.4)bytheprobabilityofthestockpricebeing$100ifthathappens(0.75).Thisgivesusaconditionalprobabilityof0.30.Inshort,it is the joint probability of the stock price being $100 given a decline in interest rates.Similarly,probabilitiesarecalculatedforeachoftheotherthreenodes.Wecanthencalculate:

E(Price│declineininterestrates)=0.75($100)+0.25($90)=$97.50

E(Price│nodeclineininterestrates)=0.50($80)+0.50($70)=$75.00

Nowweusethetotalprobabilityruleforexpectedvalueofstockpriceattheendofthecurrentperiod:

E(Price)=E(Price│declineininterestrates)P(declineininterestrates)+E(Price│nodeclineininterestrates)P(nodeclineininterestrates)

E(Price)=$97.50(0.40)+$75.00(0.60)E(Price)=$84.00



3.PortfolioExpectedReturnandVarianceofReturn

ExpectedReturn

Aportfolio’sexpectedreturncanbecalculatedas:

E R w E R w E R … w E R

where:wn=portfolioweightofnthsecurityintheportfolioRn=expectedreturnofnthsecurityintheportfolion=numberofsecuritiesintheportfolio

Wewilldiscussportfolioexpectedreturnandvarianceofreturnusingatwo‐stockportfolio.

Example

40%oftheportfolioisinvestedinStockAand60%isinvestedinStockB.Asshowninthetablebelow,theexpectedreturnofeachstockdependsontheeconomicscenario.

Scenario P(Scenario) ExpectedreturnsofA ExpectedreturnsofB

Recession 0.25 2% 4%

Normal 0.50 8% 10%

Boom 0.25 12% 16%ThisinformationcanalsobepresentedasajointprobabilityfunctionofA’sandB’sreturns: RB=4% RB=10% RB=16%RA=2% 0.25 0 0RA=8% 0 0.50 0RA=12% 0 0 0.25

Row1andColumn1representthereturnsofAandBrespectively.Theothercellscontainprobabilities.CalculatetheexpectedreturnofAandB.

Solution:

Giventhedatapresentedabove:

TheexpectedreturnofAis:0.25x2+0.50x8+0.25x12=7.5%.

TheexpectedreturnofBis:0.25x4+0.50x10+0.25x16=10%.

Expectedreturnoftheportfolio=weightofAintheportfolioxexpectedreturnofA+weightofstockBintheportfolioxexpectedreturnofB=0.4x7.5+0.6x10=9%

Theexpectedportfolioreturnis9%.Asthetermimplies,thisistheexpectedreturn.Theactualreturnwillvaryaround9%.Theamountofvariabilityismeasuredbythevariance.Inordertodeterminethevarianceofreturn,wemustfirstcalculatethecovariance.



Covariance

Covariancetellsushowmovementsinarandomvariablevarywithmovementsinanotherrandomvariable,whereasvariancetellsushowarandomvariablevarieswithitself.AssumetherearetworandomvariablesRiandRj.ThecovariancebetweenRiandRj(usedtomeasurehowtheymovetogether)isgivenby:

Cov R , R E R –ER R –ER

where:ERi=expectedreturnforvariableRiERj=expectedreturnforvariableRj

Example

Continuingwithourpreviousexample,calculatethecovarianceofreturnsbetweenAandB.

Solution:

SayRirepresentsthereturnonAandRjrepresentsthereturnonB,wehavealreadycalculatedtheexpectedreturnsofAandBas7.5%and10%respectively.Thecovarianceofreturnsis:

E Ri– 7.5 Rj– 10

=0.25(2%‐7.5%)(4%‐10%)+0.5(8%‐7.5%)(10%‐10%)+0.25(12%‐7.5%)(16%‐10%)

=0.000825+0+0.000675=0.0015

Correlation

Theproblemwithcovarianceisthatitcanvaryfromnegativeinfinitytopositiveinfinitywhichmakes it difficult to interpret. To address this problem, we use another measure calledcorrelation. Correlation is a standardizedmeasure of the linear relationship between twovariableswithvaluesrangingbetween‐1and+1.

Acorrelationof0(uncorrelatedvariables)indicatesanabsenceofanylinear(straight‐line)relationshipbetweenthevariables.

Acorrelationof+1indicatesaperfectpositiverelationship. Acorrelationof‐1indicatesaperfectnegativerelationship.

Itiscomputedas:

ρ R , R Cov R , R /σ R σ R

WewillnowapplythisformulatocalculatethecorrelationbetweenthereturnsofAandBfromourexample.Wehavealreadyshownthatthecovarianceofreturnsis0.0015.Inorderto calculate the correlation,we need the standard deviation of A and B. Using a financialcalculator,we can determine that the standard deviation of A is 0.0357 and the standard

deviationofBis0.0424.Thecorrelation,ρ A, B , =0.0015/ 0.0357x0.0424 =0.99.



Thecorrelationof0.99 (almost1) impliesaverystrongpositive relationshipbetween thereturnsofAandB.Thisismoremeaningfulthanthecovariancenumberof0.0015whichtellsusthatthereisapositiverelationshipbetweenthereturnsofAandBbutdoesnotgiveasenseforthestrengthoftherelationship.

Definitionof Independence forRandomVariables. Two random variables X and Y areindependentifandonlyifP(X,Y)=P(X)P(Y).

For example, given independence, P(5,6) = P(5)P(6). Joint probabilities are obtained bymultiplying the individual probabilities. Independence is a stronger property thanuncorrelatednessbecausecorrelationaddressesonlylinearrelationships.

Thefollowingconditionholdsforindependentrandomvariablesand,therefore,alsoholdsforuncorrelatedrandomvariables.

Multiplication Rule for Expected Value of the Product of Uncorrelated RandomVariables.Theexpectedvalueoftheproductofuncorrelatedrandomvariablesistheproductoftheirexpectedvalues.

E(XY)=E(X)E(Y)ifXandYareuncorrelated.

Manyfinancialvariables,suchasrevenue(pricetimesquantity),aretheproductofrandomquantities.

Varianceofreturns

Onceweknowthecovariance,wecancalculatethevarianceofaportfoliousingthisformula:

σ R w σ R w σ R 2w w Cov R R

Example

Continuingwithourexample,thevarianceoftheportfoliois Weightofthefirstasset,w1=0.40 Weightofthesecondasset,w2=0.60 Standarddeviationoffirstasset=0.0357 Standarddeviationofsecondasset=0.0424 Covariancebetweenthetwoassets=0.0015

Varianceoftheportfolio=0.42x0.03572+0.62x0.04242+2x0.4x0.6x0.0015=0.00157

Standarddeviationoftheportfolio=√0.00157 0.0396

4.TopicsinProbability

4.1.Bayes’Formula

Bayes’formulaisarationalmethodforupdatingoradjustingtheprobabilityofaneventbasedonnewinformation.AccordingtoBayes’formula,theupdatedprobabilityofaneventgivennewinformationis:



P(Event│Information)=P(Information│Event)

P(Information) P(Event)

Example

Considerafactorythathasthreeassemblylines.Thepercentageofoutputproducedateachassemblylineisasfollows:LineA=45%,LineB=35%,LineC=20%.Theoutputdefectivefromeach line is estimated tobe3%,5%, and4%, respectively.Given that theproduct isdefective,whatistheprobabilitythatitcamefromLineC?

Solution:

WhendealingwithquestionsrelatedtoBayes’formula,thefirststepistoreproducetheinformationinprobabilitynotation:

P(LineA)=0.45;P(NotLineA)=0.55

P(LineB)=0.35;P(NotLineB)=0.65

P(LineC)=0.20;P(NotLineC)=0.80

P(Defective|LineA)=0.03,P(Defective|LineB)=0.05,P(Defective|LineC)=0.04

P(Defective)=0.45x0.03+0.35x0.05+0.20x0.04=0.039

NextwritedowntheBayesformula:


P(Information)xP(Event)

Wethenhavetodistinguishbetweentheeventandtheinformationandplugtherelevantvaluesintotheformula.Inthiscase,theinformationisthattheproductisdefective.Hence,theformulacanbewrittenas:

P LineC|Defective | ∗

. ∗ .

.=20.51%

4.2.PrinciplesofCounting

Incounting,enumeration(countingtheoutcomesonebyone)isthemostbasicresource.Thisprocessisdifficultandispronetoerror.Wewilldiscussshortcutsandprinciplesofcounting,whichmaketheprocesseasier.

MultiplicationRuleofCounting

Thefirstoftheseprinciplesisthemultiplicationrule.Itstatesthat‘ifonetaskcanbedoneinn1ways,andasecondtask,giventhefirst,canbedoneinn2ways,andathirdtask,giventhefirsttwotasks,canbedoneinn3waysandsoonforktasks,thenthenumberofwaysthektaskscanbedoneis(n1)(n2)(n3)…(nk).Sothemultiplicationruleforcountingcanbeexpressedas:

Numberofwaysofdoingktasks=n xn xn …n



where:n =numberofwaysofdoingthefirsttask,n =numberofwaysofdoingthesecondtaskandsoon

Example

Considerasimpleexample.Supposewehavethreestepsinaninvestmentdecisionprocess.Thefirststepcanbedonein2ways,thesecondstepcanbedonein4waysandthethirdin3ways.Inhowmanywayscantheinvestmentdecisionbemade?

Solution:

Followingthemultiplicationrule,thereare(2)(4)(3)=24waysofmakingtheinvestmentdecision.

Noticethattherearethreegroupingsinthisproblem.Fromeachgroup,onlyonestepcanbeselected.

Factorial

Another counting principle relates to the assignment of members of a group to an equalnumberofpositions.Thenumberofwayswecanassigneverymemberofagroupofsizentonslots isn!(readasnfactorial)=n(n‐1)(n‐2)(n‐3)…1.Byconvention,0!=1.Thedifferencebetweenthemultiplicationruleandfactorial isthatthereisonlyonegroupinafactorial.Itinvolvesarrangingthesetofitemswithinthegroupandtheorderinwhichtheitemsarearrangedmatters.Theformulais:

Numberofwaysofassigninggroupofsizentontasks=n!

Example

Therearefiveequityanalystscoveringfiveemergingcountries.Inhowmanywayscanthecountriesbeassignedtotheanalysts?

Solution:

Thetotalnumberofwaystheassignmentscanbemade=5!=120

Labeling

Labelingreferstothenumberofwaysthatnitemscanbelabelledwithkdifferentlabelswithn,ofthefirsttype,nofthesecondtype,andsoon.Thiscanbeexpressedas:

Numberofwaysinwhichnitemscanbelabelledusingklabels=n!

n ! n ! … n !



Example

Aportfolioconsistsofeightstocks.Thegoalistodesignatefourofthestocksas"long‐termholds,"threeofthestocksas"short‐termholds,"andonestocka"sell."Howmanywayscantheselabelsbeassignedtotheeightstocks?

Solution:

Noticethatthereareeightitems(stocks)thataretobelabelledinthreedifferentways.8!

4! 3! 1!280

Combination

Aspecialcaseofthelabellingisthecombinationformula.Itisthenumberofwaystochooserobjects froma totalofnobjects,whentheorder inwhich therobjectsare listeddoesnotmatter.Thiscanbeexpressedas:

C n!/ n r ! r!

where:n=numberofobjectsr=numberofobjectschosenfromnobjects

C =numberofwaystochooserobjectsfromnobjectswhereorderdoesnotmatter

Example

Aportfoliomanagerwantstoeliminatefourstocksfromaportfoliothatconsistsofsixstocks.HowmanywayscanthefourstocksbesoldwhentheorderofthesaleisNOTimportant?

Solution:

Usingtheformulaforcombination,wegetthenumberofwaysthefourstockscanbesold

=6!/[(6–4)!4!]=15.

Permutation

Permutationisthenumberofwaystochooserobjectsfromatotalofnobjects,whentheorderinwhichtherobjectsarelisteddoesmatter.Itisexpressedas:

P n!

n r !

where:n=numberofobjectsr=numberofobjectschosenfromnobjects



Instructor’sNote:givenaproblem,usethefollowingpointerstoidentifythecorrectcountingmethodtoapply. Factorial:ifthereisonegroupofsizenandnitems/taskstobeassigned,numberofways

=n! Labeling:usedwhentherearethreeormorelabels.Eachitem/memberofagroupmust

beappliedalabel. Combination: used when there are two groups of a certain size, say n and r. Use

combinationwhentheorderofchoosingrobjectsfromnobjectsdoesNOTmatter. Permutation: used when there are two groups of a certain size, say n and r. Use

permutationwhentheorderofchoosingrobjectsfromnobjectsdoesmatter.

Combination and permutation functions are available on the financial calculator andshouldbeusedratherthantheformula.

Example

Assumethatinaportfolioofeightstocks,wedecidetosellthreestocks.Howmanywayscanwechoosethreeoftheeighttoselliftheorderofsaledoesmatter?

Solution:

Usingtheformulaforpermutation,wecanfindthenumberofwaystosellthreeoftheeightstockswhereordermatters:8!

8– 3 !336



Summary

LO.a:Definearandomvariable,anoutcome,anevent,mutuallyexclusiveevents,andexhaustiveevents.

Arandomvariableisanuncertainquantity/number. Anoutcomeistheobservedvalueofarandomvariable. Aneventcanbeasingleoutcomeorasetofoutcomes. Mutuallyexclusiveeventsareeventsthatcannothappenatthesametime. Exhaustiveeventsarethosethatincludeallpossibleoutcomes.

LO.b:Statethetwodefiningpropertiesofprobabilityanddistinguishamongempirical,subjective,andaprioriprobabilities.

Thetwodefiningpropertiesofaprobabilityare: TheprobabilityofanyeventEisanumberbetween0and1:0≤P(E)≤1. Thesumof theprobabilitiesofanysetofmutuallyexclusiveandexhaustiveevents

equals1.

Themethodsofestimatingprobabilitiesare: Empiricalprobability:Basedonanalyzingthefrequencyofanevent’soccurrenceinthe

past. Aprioriprobability:Basedonformalreasoningandinspectionratherthanpersonal

judgment. Subjectiveprobability:Informedguessbasedonpersonaljudgment.

LO.c:Statetheprobabilityofaneventintermsofoddsforandagainsttheevent.

OddsforE=P(E)/[1–P(E)].

OddsagainstE=[1–P(E)]/P(E).

LO.d:Distinguishbetweenunconditionalandconditionalprobabilities.

Unconditional probability (marginal probability) is the probability of an event occurringirrespectiveoftheoccurrenceofotherevents.ItisdenotedasP(A).

Conditionalprobabilityistheprobabilityofaneventoccurringgiventhatanothereventhasoccurred.ItisdenotedasP(A|B),whichistheprobabilityofeventAgiventhateventBhasoccurred.

LO.e:Explainthemultiplication,addition,andtotalprobabilityrules.

Multiplicationruleisusedtodeterminethejointprobabilityoftwoevents.Itisexpressedas:

P(AB)=P(A|B)P(B)

Additionruleisusedtodeterminetheprobabilitythatatleastoneoftheeventswilloccur.Itisexpressedas:



P(AorB)=P(A)+P(B)–P(AB)

Thetotalprobabilityruleisusedtocalculatetheunconditionalprobabilityofanevent,givenconditionalprobabilities.Itisexpressedas:


LO.f:Calculateandinterpret1)thejointprobabilityoftwoevents,2)theprobabilitythatat leastoneoftwoeventswilloccur,giventheprobabilityofeachandthe jointprobabilityofthetwoevents,and3)ajointprobabilityofanynumberofindependentevents.

ConsidertheexamplethatyouhavetwostocksAandB.TheprobabilitythatstockAwillpayoutadividendthisquarteris60%andtheprobabilitythatstockBwillpayoutadividendthisquarteris50%.Assumethatthetwoeventsareindependent.ThejointprobabilityofAandBi.e.bothAandBissueadividendthisquarteris0.6x0.5=0.3.

Theprobabilitythatatleastoneoftwoevents,AorB,willoccurisP(AorB)=P(A)+P(B)–P(AB)=0.6+0.5–0.6x0.5=0.8.

LO.g:Distinguishbetweendependentandindependentevents.

Iftheoccurrenceofoneeventdoesnotinfluencetheoccurrenceoftheotherevent,thentheeventsarecalledindependentevents.

i.e.P(A|B)=P(A)orP(B|A)=P(B)

Iftheprobabilityofaneventisaffectedbytheoccurrenceofanothereventthenitiscalledadependentevent.

LO.h:Calculateandinterpretanunconditionalprobabilityusingthetotalprobabilityrule.

UsingthetotalprobabilityruletheunconditionalprobabilityofAcanbecomputedas:


WhereS1,S2..Snaremutuallyexclusiveandexhaustiveevents.

LO.i:Explaintheuseofconditionalexpectationininvestmentapplications.

The expected value is heavily used in investment applications e.g. forecasting EPS of acompany, estimating rewards of alternative investments, etc. When you refine yourexpectationsorforecasts,youaretypicallymakingadjustmentsbasedonnewinformationorevents;thisisactuallytheuseofconditionalexpectedvalues.

LO.j:Explaintheuseofatreediagramtorepresentaninvestmentproblem.

The tree diagram in an investment problem can help plot the probabilities of variousoutcomesanddepictexpectedvaluesbasedonthepathschosenandselectionmadeateachnode.Forexample:



LO.k:Calculateandinterpretcovarianceandcorrelation.

Covarianceisameasureofhowtwovariablesmovetogether.GiventworandomvariablesRiandRj,thecovariancebetweenRiandRjisgivenby:

Cov(Ri,Rj)=E[(Ri–ERi)(Rj–ERj)]Where,ERi=expectedreturnforvariableRiERj=expectedreturnforvariableRj

Correlationisastandardizedmeasureofthelinearrelationshipbetweentwovariableswithvaluesrangingbetween‐1and+1.Theformulaisgivenby:

ρ(A,B)=Cov(A,B)/σ(A)σ(B)

LO.l:Calculateandinterprettheexpectedvalue,variance,andstandarddeviationofarandomvariableandofreturnsonaportfolio.

Theformulaforcalculatingtheexpectedportfolioreturnis:

E(RP)=w1E(R1)+w2E(R2)+…+wnE(Rn)

Variancecanbecomputedas:

σ R w σ R w σ R 2w w Cov R R

LO.m:Calculateandinterpretcovariancegivenajointprobabilityfunction.

GiventworandomvariablesRiandRj,thecovariancebetweenRiandRjisgivenby:

Cov(Ri,Rj)=E[(Ri–ERi)(Rj–ERj)]

where:ERi=expectedreturnforvariableRiERj=expectedreturnforvariableRj



LO.n:CalculateandinterpretanupdatedprobabilityusingBayes’formula.

Bayes’formulaisarationalmethodforupdatingoradjustingtheprobabilityofaneventbasedonnewinformation.AccordingtoBayes’formula,theupdatedprobabilityofaneventgivennewinformationis:


P(Information) P(Event)

LO.o:Identifythemostappropriatemethodtosolveaparticularcountingproblem,andsolvecountingproblemsusingfactorial,combination,andpermutationconcepts.

Thenumberofwayswecanassigneverymemberofagroupofsizentonslotsisn!

Numberofwaysinwhichnitemscanbelabelledusingklabels= !

! ! … !

The combination formula gives the number ofways to choose r objects from a total of nobjects,whentheorderinwhichtherobjectsarelisteddoesnotmatter.

nr

n!

n r ! r!

The permutation formula gives the number ofways to choose r objects from a total of nobjects,whentheorderinwhichtherobjectsarelisteddoesmatter.

P n!

n r !



PracticeQuestions

1. IfeventsAandBaremutuallyexclusive,thenwhichofthefollowingistrue?A. P(A|B)=P(A).B. P(AB)=P(A)xP(B).C. P(AorB)=P(A)+P(B).

2. Whichofthefollowingvaluescanbetheprobabilityofanevent?

A. ‐0.23.B. 0.68.C. 1.36.

3. Whichofthefollowingismostlikelyanempiricalprobability?A. The probability of a particular outcome when exactly 6 equally likely possible

outcomesexist.B. TheprobabilitythatUSstockreturnsexceedlong‐termcorporatebondreturnsovera

5yearperiod,basedonZellerFinancialdata.C. AnupdatedprobabilityofaneventarrivedatusingBayes’formulaandtheperceived

priorprobabilityoftheevent.

4. Theprobabilitythatthestockmarketwillincreasetomorrowis3/5.Theprobabilityofanincreaseinthestockmarketstatedas'oddsfor’is:A. three‐to‐two.B. two‐to‐three.C. three‐to‐five.

5. Afundmanagerhasnotedthatduringthepastfiveyears60percentofthestocksinhisportfoliohavepaidacashdividendand20percentofthestockshavepaidastockdividend.If65percentofthestockshavepaidadividendofanykind,thejointprobabilityofastockpayingbothacashdividendandastockdividendisclosestto:A. 10%.B. 15%.C. 20%.

6. Twoeventsaresaidtobeindependentiftheoccurrenceofoneevent:A. impliesthatthesecondeventcannotoccur.B. impliesthatthesecondeventiscertaintooccur.C. doesnotaffecttheprobabilityoftheoccurrenceoftheotherevent.

7. ThecorrelationofreturnsbetweenStocksAandBis0.60.Thecovariancebetweenthesetwosecuritiesis0.0056andthestandarddeviationofthereturnsofStockBis18%.ThevarianceofreturnsforStockAis:



A. 0.0027.B. 0.0035.C. 0.0048.

8. Thefollowinginformationontwoportfoliosisgiven:

FundA FundBPortfolioweights(%) 40 60Expectedreturns(%) 15 10Standarddeviations(%) 20 16Correlation between the returnsofFundAandFundB

0.5

Theexpectedreturnandthestandarddeviationoftheportfolioarerespectivelyclosestto:A. 12.5%and22.3%.B. 12%and15.2%.C. 13%and16.5%.

9. ThejointprobabilitiesforXandYareP(X=10,Y=3)=0.4,andP(X=20,Y=6)=0.6,thentheCovarianceofXYisclosestto:A. 7.2B. 6.5.C. 6.6.

10. Aresearcherisstudyingthelinkbetweenexchangeratemovementsandthediscountrateset by the country’s bank. He uses historical data to determine that the probability ofexchangeraterisingorfallingoverthenextmonthis60%and30%respectivelywhiletheprobability that theexchangerate stays thesame is10%.Somedays later,he receivesinformationthatthecentralbankwillincreasethediscountrate.Theresearchercomesup with the following subjective probabilities that the central bank will increase thediscountrategiventhescenariosthatexchangeraterises,fallsorstaysthesame:

P(increaseddiscountrate|exchangerateincreases)=65% P(increaseddiscountrate|exchangeratestayssame)=15% P(increaseddiscountrate|exchangeratedecreases)=20%

Whatistheprobabilitythattheexchangeratewillfallgiventhenewinformationthatthecentralbankwillincreasethediscountrate?A. 18.79%.B. 15.65%.C. 12.90%

11. Aninvestorwantstopurchase7stocksforhisportfoliofromauniverseof10stocks.Iftheorderinwhichhebuysthestocksisnotimportant,thenhowmanypotential7stockcombinationsdowehave?



A. 120.B. 140.C. 160.

12. Afundmanagerwantstosell3bondsfromhisportfolioof8bonds.Iftheorderinwhichhesellsthebondsisimportant,thenhowmanypotential3‐bondcombinationsdowehave?A. 56.B. 336.C. 512.



Solutions

1. Ciscorrect.Mutuallyexclusiveeventsarethoseeventswhichcannothappentogether,i.e.thereisnointersectionbetweenthetwoevents.Therefore,bothP(A|B)andP(AB)mustbeequaltozero.

2. Biscorrect.Theprobabilityofaneventhastobebetween0and1.

3. B is correct. This is an example of empirical probability since it is basedonpast data.OptionAisAprioriprobabilitysinceitisbasedonlogicalreasoning.OptionCissubjectiveprobabilitysinceitisbasedonpersonaljudgment.

4. Aiscorrect.OddsforE=P(E)/[1–P(E)]=(3/5)/(2/5)=3/2=threetotwo.

5. Biscorrect.Theprobabilitythatat leastoneoftwoeventswilloccuristhesumoftheprobabilitiesoftheseparateeventslessthejointprobabilityofthetwoevents.P(AorB)=P(A)+P(B)–P(AB)65%=60%+20%–P(AB);thereforeP(AB)=15%

6. Ciscorrect.Twoeventsaresaidtobeindependentiftheoccurrenceofoneeventdoesnotaffecttheprobabilityoftheoccurrenceoftheotherevent.

7. Aiscorrect.

Corr A, BCov A, Bσ A σ B

0.60.0056σ A 0.18

Therefore 0.0518.ThevarianceofreturnsforstockA=0.0518 0.0027

8. Biscorrect.Theexpectedreturnontheportfoliois0.4x15%+0.6x10%=12%Calculatetheportfoliostandarddeviationofreturnsasfollows:√(.402x.202+.602x.162+2x.40x.60x.5x.20x.16)=0.152and15.2%

9. Aiscorrect.Thejointprobabilitiesinthequestionaregivenasfollows:

X,Y 3 610 0.4 20 0.6

E[X]=0.4(10)+0.6(20)=16E[Y]=0.4(3)+0.6(6)=4.8Cov[XY]=0.4(10‐16)(3‐4.8)+0.6(20‐16)(6‐4.8)=7.2



10. Ciscorrect.AccordingtoBayes’Theorem:Updatedprobabilityofeventgiventhenewinformation= (Probability of new information given event ÷ unconditional probability of newinformation)xpriorprobabilityofeventInordertoproceedwiththegivendata,weneedtocalculatetheunconditionalprobabilityofnewinformationi.e.theprobabilityofanincreaseinthediscountrate.P(increaseddiscountrate)=P(increaseddiscountrate|exchangerateincreases)xP(exchangerateincreases)+P(increaseddiscountrate|exchangeratestayssame)xP(exchangeratestayssame)+P(increaseddiscountrate|exchangeratedecreases)xP(exchangeratedecreases)=(0.65x0.60)+(0.15x0.1)+(0.2x0.3)=0.465=46.5%

P E/I P E /

Using the unconditional probability and Bayes’ Theorem, we can calculate updatedprobabilityoftheeventgiventhenewinformationaboutdiscountratesas:P(exchangeratedecreases|increaseddiscountrate)==[P(increaseddiscountrate|exchangeratedecreases)÷P(increaseddiscountrate)]xP(exchangeratedecreases)=(0.20÷0.465)x0.30=12.90

11. Aiscorrect.Sincetheorderisnotimportantwewillusecombination.10C7=120

12. Biscorrect.Sincetheorderisimportantwewillusepermutation.8P3=336.

R10 Common Probability Distributions 2019 Level I Notes


R10CommonProbabilityDistributions

1.Introduction

Innearlyallinvestmentdecisions,weworkwithrandomvariables.Tomakeprobabilitystatementsaboutarandomvariable,weneedtounderstanditsprobabilitydistribution.Aprobabilitydistributionspecifiestheprobabilitiesofallpossibleoutcomesofarandomvariable.Inthisreading,wewilllookatthefollowingfourprobabilitydistributions:

Uniform Binomial Normal Lognormal

2.DiscreteRandomVariables

Arandomvariableisavariablewhoseoutcomecannotbepredicted.Therearetwobasictypesofrandomvariables:

Adiscreterandomvariableisonewherewecanlistallthepossibleoutcomes.Forexample,thestockstradedontheNewYorkStockExchangearequotedinticksof$0.01.Quotedstockpriceisthereforeadiscreterandomvariable.

Acontinuousrandomvariableiswherethenumberofpointsbetweenthelowerandupperboundsareessentiallyinfinite.Rateofreturnisanexampleofacontinuousrandomvariable.

Probabilitydistributionspecifiestheprobabilitiesofallthepossibleoutcomesforarandomvariable.

Probabilityfunctionspecifiestheprobabilitythatarandomvariabletakesonaspecificvalue.

Probabilitydensityfunctionisusedforcontinuousrandomvariables.

2.1.TheDiscreteUniformDistribution

Thediscreteuniformdistributionhasafinitenumberofspecifiedoutcomesandeachoutcomeisequallylikely.Considerarollofadice.Theoutcomeisarandomvariableanditcantakeavalueof1to6.Theprobabilitythattherandomvariabletakesonanyofthesevaluesisthesameforalloutcomes.Withsixoutcomes,p(x)=1/6forallvaluesofX(X=1,2,3,4,5,6).Thetablebelowsummarizesthetwoviewsofthisrandomvariable–theprobabilityfunctionandthecumulativedistributionfunction.

X=x ProbabilityFunctionp(x)=P(X=x)

CumulativeDistributionFunctionF(x)=P(X≤x)

1 1/6 1/62 1/6 2/63 1/6 3/6



4 1/6 4/65 1/6 5/66 1/6 6/6

2.2.TheBinomialDistribution

ThebuildingblockofthebinomialdistributionistheBernoullirandomvariable.ABernoullitrialisonewherethereareonlytwopossibleoutcomes:successorfailure.FlippingacoinisanexampleofaBernoullitrial–youeithergetheadsortails,butnothingelse.Thiscanbeexpressedas:

P(Y=1)=pP(Y=0)=1–p

where:p=probabilitythatthetrialisasuccess

Inabinomialdistribution,therandomvariable,X,isthenumberofsuccessesinagivennumberofBernoullitrials.Continuingwiththecoinexample,sayweflipthecoin10timesandwedefinesuccessas‘Heads’.Clearlywith10flipswecanget0to10successes.

Theprobabilitydistributionofabinomialrandomvariablefortheprobabilityof"x"successin"n"trialsiscalculatedusingthefollowingformula:

P x P X x C p 1 p –

where:p=theprobabilityofsuccessoneachtrial

Example

Usingthetableabove,findthefollowingprobabilities:1. F(4)2. P(3≤X<6)3. F(9)Solutionto1:

TofindF(4),wemustfindthecumulativeprobabilityofP(X≤4)usingthecumulativedistributionfunction(thirdcolumn).Fromthetable,wecanseethatP(X≤4)=4/6=2/3.Therefore,theprobabilityis2/3.

Solutionto2:

TofindP(3≤X<6),weneedtofindthesumofthreeprobabilities:p(3),p(4),p(5).Thisis1/6+1/6+1/6=3/6=1/2.

Solutionto3:

TofindF(9),wemustfindthecumulativeprobabilityofP(X≤9).Thisincludesallpossibleoutcomes,hencetheprobabilityis1.



x=numberofsuccessesn=numberoftrials

Instructor’sNote:

Twoimportantpointshelpillustratetheintuitionbehindtheformula: Thesuccessescanbeinanyorder.Thatiswhyweusethecombinationfunctionandnot

thepermutationfunction. Theeventsareindependent.Thatiswhywesimplymultiplytheprobabilityofeach

event.ExampleIfweflipafaircoin(p=0.5)tentimes(n=10),whatistheprobabilityofsevensuccesses?

Solution:P(7)=P(X=7)=10C70.570.53=0.117

Meanandvarianceofabinomialvariable

Themeanandvarianceofabinomialvariablecanbecalculatedas:

Forourcoin‐flipexample,themeanvalueofthebinomialrandomvariableisnp=10x0.5=5.Theintuition:ifweperformthebinomialexperimentseveraltimes,whereeachexperimentrefersto10coin‐flips,onaveragewewillhave5successes.Theactualnumberofsuccesseswillbedistributedequallyoneithersideofthemeanvalue.Therandomvalueforeverytrialmovesclosertotheexpectedvalueasthenumberoftrialsgrows.

Example

Overthelast10years,Abrocorporation’sEPSincreasedyearoveryearsixtimesanddecreasedyearoveryearfourtimes.YoudecidetomodelthenumberofEPSincreasesforthenextdecadeasabinomialrandomvariable.1. IfsuccessisdefinedasanincreaseintheannualEPS,determinetheprobabilityof

success.2. WhatistheprobabilitythatEPSwillincreaseinexactly5ofthenext10years?3. CalculatetheexpectednumberofyearlyEPSincreasesduringthenext10years.4. CalculatethevarianceandstandarddeviationofthenumberofyearlyEPSincreases

duringthenext10years.

Solutionto1:Thereareonlytwopossibleoutcomes:increaseintheEPSandnoincreaseintheEPS.Probabilityofsuccess:p=6/10=0.6Probabilityoffailure:1–p=1–0.6=0.4

RandomVariable Mean VarianceBernoulli,B(1,p) p p(1‐p)Binomial,B(n,p) np np(1‐p)



Solutionto2:Usingthebinomialmodel:P X 5 C p q P X 5 C 0.6 0.4 P X 5 252 0.07776 0.01024 20.06%

Solutionto3:ExpectednumberofyearlyEPSincreases:E x np 10 0.6 6

Solutionto4:Variance=np 1– p 6 0.4 2.4StandardDeviation=√2.4=1.549 Thevarianceofthedistributioniscalculatedasnp(1–p)=10x0.5x(1–0.5)=2.5

Binomialtree

Abinomialtreecanbeusedtomodelstockpricemovements.Refertothetreediagrambelow.‘S’representstheinitialstockprice.‘u’representsanupmoveand‘d’representsadownmove.Thenodesshoweachpossiblevalueofthestockafter1,2and3timeperiods.

Theexpectedstockpriceaftereachperiodisequaltothesumofpossiblestockpricesattheendoftheperiodmultipliedbytheirrespectiveprobabilities.

Example

Consideraninitialstockpriceof$100.Inonetimeperiod,thestockcaneitherrisebyafactorof1.1orgodownbyafactorof1/1.1.Inanygiventimeperiod,theprobabilityofanupmoveis0.6andtheprobabilityofadownmoveis0.4.Aftertwoperiods,whatarethepossiblestockpricesandtheirrespectiveprobabilities?Whatistheexpectedstockprice?

Solution:

uuS=1.1x1.1x100=121withprobability0.6x0.6=0.36udS=1.1x1/1.1x100=100withprobability0.6x0.4=0.24duS=1/1.1x1.1x100=100withprobability0.4x0.6=0.24



ddS=1/1.1x1/1.1x100=82.64withprobability0.4x0.4=0.16Expectedstockprice=121x0.36+100x0.24+100x0.24+82.64x0.16=$104.78

3.ContinuousRandomVariables

3.1.ContinuousUniformDistribution

Thecontinuousuniformdistributionisdefinedoverarangefromalowerlimit‘a’toanupperlimit‘b’.Theselimitsserveastheparametersofthedistribution.

Theprobabilitythattherandomvariablewilltakeavaluebetweenx1andx2,wherex1andx2bothliewithintherangeisgivenby:

P x X x x xb a

Example

Xisauniformlydistributedcontinuousrandomvariablebetween10and20.CalculatetheprobabilitythatXwillfallbetween12and18.

Solution:

P 12 X 18 18 1220 10

0.6

Thecumulativedistributionfunctionforacontinuousrandomvariableisshownbelow:

Example

Acommodityanalystpredictsthatthepriceperounceofgoldthreeyearsfromnowwillbebetween$1,500and$1,700.Assumegoldpricesfollowacontinuousuniformdistribution.Whatistheprobabilitythatthepricewillbelessthan$1,600threeyearsfromnow?



Solution:

F(1,600)= , – ,

, ,=50%Theprobabilitythatgoldpricewillbelessthan$1,600per

ouncethreeyearsfromnowis50%.

3.2.TheNormalDistribution

Thenormaldistributionisthemostextensivelyusedprobabilitydistributioninquantitativework.Anormaldistributionissymmetricalandbell‐shapedasshowninthegraphbelow:

Inthisfigure‘m’standsformean,1smeansonestandarddeviation,2smeanstwostandarddeviations,andsoon.Wecanmakethefollowingprobabilitystatementsforanormaldistribution:

Approximately68%ofallobservationsfallintheintervalm±1s. Approximately95%ofallobservationsfallintheintervalm±2s. Approximately99%ofallobservationsfallintheintervalm±3s.

Theintervalsindicatedaboveareeasytorememberbutareonlyapproximateforthestatedprobabilities.Morepreciseintervals(confidenceintervals)are:

90%ofallobservationsareintheintervalm±1.65s. 95%ofallobservationsareintheintervalm±1.96s. 99%ofallobservationsareintheintervalm±2.58s.

Thecharacteristicsofanormaldistributionareasfollows: Thenormaldistributioniscompletelydescribedbytwoparameters–itsmean,µ,and

variance,σ2.WeindicatethisasX~N(µ,σ2). Thenormaldistributionhasaskewnessof0(itissymmetric)andakurtosis

(measureofpeakedness)of3.Duetothesymmetry,themean,medianandmodeareallequalforanormalrandomvariable.

Alinearcombinationoftwoormorenormalrandomvariablesisalsonormallydistributed.

Standardnormaldistribution



Thenormaldistributionwithmean(µ)=0andstandarddeviation(σ)=1iscalledthestandardnormaldistribution.

TheformulaforstandardizingarandomvariableXis:

ZX μσ

where:μisthepopulationmean.σisthepopulationstandarddeviation.

TheZ‐tableisusedtofindtheprobabilitythatXwillbelessthanorequaltoagivenvalue.Supposewehaveanormalrandomvariable,X,withµ=10andσ=2.IfthevalueofXis11,westandardizeXwithZ=(11–10)/2=0.5.

Theprobabilitythatwewillobserveavaluelessthan11forX~N(10,2)isexactlythesameastheprobabilitythatwewillobserveavaluelessthan0.5forZ~N(0,1).

WecananswerprobabilityquestionsaboutXusingstandardizedvaluesandprobabilitytablesforZ.Asnapshotofatableshowingcumulativeprobabilitiesforastandardnormaldistributionisshownbelow.

Tofindtheprobabilitythatastandardnormalvariableislessthanorequalto0.5,forexample,locatetherowthatcontains0.50,lookatthe0column,andfindtheentry0.6915.Thus,P(Z≤0.5)=0.6915or69.15%.

Theprobabilitythatastandardnormalvariableislessthanorequalto0is0.5000.Thisistruebydefinitionbecausethemeanofastandardnormaldistributionis0.Thetableabovevalidatesthisfact.

Foranon‐negativenumberx,wecanuseN(x)directlyfromthetable.Foranegativenumber–x,N(‐x)=1.0–N(x).Essentially,weareusingthefactthatthenormaldistributionissymmetricaroundthemean.

Example

Aportfoliohasameanreturnof15%andastandarddeviationofreturnof20%peryear.Whatistheprobabilitythattheportfolioreturnwouldbebelow18%?Wearegiventhe



followinginformationfromthez‐table:P(Z<0.15)=0.5596,P(Z>0.15)=0.4404,P(Z<0.18)=0.5714,P(Z>0.18)=0.4286.

Solution:

P ZX μσ

P Z0.18 0.15

0.20P Z 0.15 0.5596

Univariatev/smultivariatedistribution

Univariatedistribution

Aunivariatedistributiondescribestheprobabilitydistributionofasinglerandomvariable.Forexample,thedistributionofexpectedreturnofonestockfromaportfolio.

Multivariatedistribution

Amultivariatedistributiondescribestheprobabilitydistributionforagroupofrelatedrandomvariables.Forexample,thedistributionofexpectedreturnofaportfoliowithmultiplestocks.

Amultivariatenormaldistributionforthereturnsonnstocksiscompletelydefinedbythefollowingthreesetsofparameters:

Meanreturnsontheindividualstocks(nmeansintotal). Variancesoftheindividualstocks(nvariancesintotal). Pairwisereturncorrelationsbetweenthestocks(n(n‐1)/2distinctcorrelationsin

total).

3.3.ApplicationsoftheNormalDistribution

Shortfallrisk

Shortfallriskistheriskthatportfolio’sreturnwillfallbelowaspecifiedminimumlevelofreturnoveragivenperiodoftime.

Safetyfirstratio

Safetyfirstratioisusedtomeasureshortfallrisk.Itiscalculatedas:

SFRatioR –Rσ

where:Rp=ExpectedportfolioreturnRL=Thresholdlevel=Standarddeviationofportfolioreturns

TheportfoliowiththehighestSF‐Ratioispreferred,asithasthelowestprobabilityoffallingbelowthetargetreturn.

Example



AninvestorisconsideringtwoportfoliosAandB.PortfolioAhasanexpectedreturnof10%andastandarddeviationof2%.PortfolioBhasanexpectedreturnof15%andastandarddeviationof10%.Theminimumacceptablereturnfortheinvestoris8%.AccordingtoRoy’ssafetyfirstcriteria,whichportfolioshouldtheinvestorselect?

Solution:

SF 10 82

1

SF 15 810

0.7

SinceAhasahighersafetyfirstratio,theinvestorshouldselectportfolioA.

Roy’ssafetyfirstcriteria

Itstatesthatanoptimalportfoliominimizestheprobabilitythattheactualportfolioreturnwillfallbelowthetargetreturn.

3.4.TheLognormalDistribution

Ifxisarandomvariablethatisnormallydistributed,thentocreatealognormaldistributionofxwetakeexandplotthevaluesonagraph.

NormalDistribution LognormalDistribution

Thepropertiesofalognormaldistributionare: Itcannotbenegative. Theupperendofitsrangeextendstoinfinity. Itispositivelyskewed.

Instructor’sNote:Anormaldistributionismoresuitableasamodelforreturnsthanforassetprices,becausereturnsgenerallyvaryaboutthemean,withahighprobabilityofreturnsbeingclosetothemean.However,assetpricesdonotvaryequallyaboutameanprice,sincetheprobabilityofextremechangesinpricedecreasesasthepriceapproacheszero.Thismeansassetpriceswillnotformasymmetricalgraphlikethatofthenormaldistribution.Instead,assetpricesfollowalognormaldistribution,whichisskewedtotherightandcannotbenegative.

Discretelyversuscontinuouslycompoundedratesofreturn



Discretelycompoundedratesofreturnshavedefinedcompoundingperiodssuchasquarterly,monthlyetc.Aswedecreasethelengthofthecompoundingperiod,theeffectiveannualraterises.Forcontinuouscompounding,theEARisgivenby:

EAR=er–1

Ifwearegiventheholdingperiodreturnoveranytimeperiod,wecancalculatetheequivalentcontinuouslycompoundedrateofreturnforthatperiodas:

r=ln(HPR+1)

Example

Iftheholdingperiodreturnofastockwas10%foraperiodofoneyear.Whatistheequivalentcontinuouslycompoundedrateofreturnfortheyear?

Solution:r=ln(0.1+1)=0.0953=9.53%

4.MonteCarloSimulation

MonteCarlosimulationisacomputersimulationusedtosimulatepossiblesecuritypricesbasedonriskfactors.Asinput,itusesrandomlygeneratedvaluesforriskfactorsbasedontheirassumeddistributions.Itprocessesthisinformationasperthespecifiedmodelandrunsthousandsofiterations.Thenitgivesthedistributionoftheexpectedvalueofthesecurityasoutput.

Majorapplicationsinclude: financialplanning developingVARestimates valuingcomplexsecurities

Limitationsinclude: Itisfairlycomplexandwillprovideanswersthatarenobetterthantheassumptions. Simulationisnotananalyticalmethodbutastatisticalone.

MonteCarlosimulationversushistoricalsimulation

Thehistoricalsimulationusesactualpastdistributionofriskfactorsasinput.Whereas,MonteCarlosimulationusesrandomlygeneratedvaluesoftheriskfactorsbasedontheirassumeddistributions.

Thelimitationsofhistoricalsimulationare: Itcannottakeintoaccounttheeffectofsignificanteventsthatdidnotoccurduring

thesampleperiod.

Itcannotperforma‘whatif’analysiswhenthe‘if’scenariohasnothappenedinthepast.



Summary

LO.a:Defineaprobabilitydistributionanddistinguishbetweendiscreteandcontinuousrandomvariablesandtheirprobabilityfunctions.

Arandomvariableisavariablewhoseoutcomecannotbepredicted.Aprobabilitydistributionlistsallpossibleoutcomesofarandomvariablealongwiththeirassociatedprobabilities.

Adiscreterandomvariableisoneforwhichthenumberofpossibleoutcomescanbecounted.Ithasmeasurableprobabilitiesassociatedwitheachspecificoutcome.

Acontinuousrandomvariableisoneforwhichwecannotcountthenumberofpossibleoutcomes.Therefore,probabilitiescannotbeassociatedwithspecificoutcomes,instead,ithastobeassignedtoaparticularrange.

LO.b:Describethesetofpossibleoutcomesofaspecifieddiscreterandomvariable.

Thesetofpossibleoutcomesofadiscreterandomvariableisfinite. p(x)=0meansthatxcannotoccur. p(x)>0meansthatxcanoccur. p(x)=1meansthatxistheonlypossibleoutcome.

LO.c:Interpretacumulativedistributionfunction.

Thecumulativedistributionfunctiongivestheprobabilitythattherandomvariablewillbelessthanorequaltoaspecificvalue.

ItisdenotedbyF(x)=P(X≤x).

LO.d:Calculateandinterpretprobabilitiesforarandomvariable,givenitscumulativedistributionfunction.

Theprobabilitythatanoutcomewillbelessthanorequaltoaspecificvalueisrepresentedbytheareaunderthecumulativeprobabilitydistributiontotheleftofthatvalue.

LO.e:Defineadiscreteuniformrandomvariable,aBernoullirandomvariable,andabinomialrandomvariable.

Adiscreteuniformrandomvariableisonewheretheprobabilityofallthepossibleoutcomesisequal.Forexample,therollofadice.

ABernoullitrialisanexperimentthathasonlytwopossibleoutcomes:asuccessorafailure.Forexample,thetossofacoin.

Iftheexperimentiscarriedoutntimes,thenumberofsuccess(denotedbyX)iscalledaBernoullirandomvariable.

ThedistributionthatXfollowsisknownasthebinomialdistribution.



LO.f:Calculateandinterpretprobabilitiesgiventhediscreteuniformandthebinomialdistributionfunctions.

Probabilitiesforadiscreteuniformdistribution:Ifthetotalnumberofoutcomesisn,thentheprobabilityofeachoutcome=1/n.

Probabilitiesforauniformrandomvariable:Theprobabilitydistributionofabinomialrandomvariablefortheprobabilityofxsuccessesinntrialsiscalculatedusingthefollowingformula:

P(x)=P(X=x)=nCxpx(1‐p)n–x

LO.g:Constructabinomialtreetodescribestockpricemovement.

Abinomialtreecanbeusedtomodelstockpricemovements.‘S’representstheinitialstockprice.‘u’representsanupmoveand‘d’representsadownmove.Thenodesshoweachpossiblevalueofthestockafter1,2and3timeperiods.

LO.h:Definethecontinuousuniformdistributionandcalculateandinterpretprobabilities,givenacontinuousuniformdistribution.

Thecontinuousuniformdistributionisdefinedoverarangefromalowerlimit‘a’toanupperlimit‘b’.Theprobabilitythattherandomvariablewilltakeavaluebetweenx1andx2,wherex1andx2bothliewithintherangeisgivenby:

P x X x x xb a

LO.i:Explainthekeypropertiesofthenormaldistribution.

Anormaldistributionisabell‐shapedcurve,withtwoidenticalhalves.

Itiscompletelydescribedbytwoparametersitsmean(µ)anditsvariance(σ2).ThisisstatedasX~N(µ,σ2).

Ithasaskewnessof0andakurtosisof3.



Alinearcombinationoftwoormorerandomvariablesisalsonormallydistributed.

LO.j:Distinguishbetweenaunivariateandamultivariatedistribution,andexplaintheroleofcorrelationinthemultivariatenormaldistribution.

Aunivariatedistributiondescribesasinglerandomvariable.Anexampleistheexpectedreturnonaparticularstock.Amultivariatedistributionspecifiestheprobabilitiesforagroupofrelatedrandomvariables.Anexampleistheexpectedreturnonaportfolioofmultiplestocks.

Amultivariatenormaldistributionforthereturnsonnstocksiscompletelydefinedbythreelistsofparameters:

Thelistofthemeanreturnsontheindividualsecurities(nmeansintotal). Thelistofthesecurities’variancesofreturn(nvariancesintotal). Thelistofallthedistinctpairwisereturncorrelations(n(n‐1)/2distinct

correlationsintotal).

LO.k:Determinetheprobabilitythatanormallydistributedrandomvariableliesinsideagiveninterval.

Thepropertyofnormaldistributiongivesusintervalsstatedbelow: 90%ofallobservationsareintheintervalm±1.65s. 95%ofallobservationsareintheintervalm±1.96s. 99%ofallobservationsareintheintervalm±2.58s.

Thisimpliesthatifarandomvariableislessthanorequaltom±1.65s,thentheprobabilityofitlyinginsidethedistributionis90%.

LO.l:Definethestandardnormaldistribution,explainhowtostandardizearandomvariable,andcalculateandinterpretprobabilitiesusingthestandardnormaldistribution.

Thenormaldistributionwithµ=0andσ=1iscalledthestandardnormaldistribution.TheformulaforstandardizingarandomvariableXis:

Z X μσ

LO.m:Defineshortfallrisk,calculatethesafety‐firstratio,andselectanoptimalportfoliousingRoy’ssafety‐firstcriterion.

Shortfallriskistheriskthatportfoliovaluewillfallbelowsomeminimumacceptableleveloversometimehorizon.

SFRatioE R –R

σ

ToselecttheoptimalportfolioaccordingtoRoy’scriterion,wefollowthefollowingsteps:



Calculateeachportfolio’sSF‐Ratio. ChoosetheportfoliowiththehighestSF‐Ratio.

LO.n:Explaintherelationshipbetweennormalandlognormaldistributionsandwhythelognormaldistributionisusedtomodelassetprices.

Ifxisarandomvariablethatisnormallydistributed,thentocreatealognormaldistributionofxwetakeexandplotthevaluesonagraph.

Alognormaldistributionisoftenusedtomodelassetpricesbecausetheassetpricesneedtobepositive,theycannotbenegative.

LO.o:Distinguishbetweendiscretelyandcontinuouslycompoundedratesofreturn,andcalculateandinterpretacontinuouslycompoundedrateofreturn,givenaspecificholdingperiodreturn.

Discretelycompoundedratesofreturnshavedefinedcompoundingperiodssuchasquarterly,monthly.Aswedecreasethelengthofthecompoundingperiod,theeffectiveannualraterises.Forcontinuouscompounding,theEARisgivenby:EAR=er–1.

Ifwearegiventheholdingperiodreturnoveranytimeperiod,wecancalculatetheequivalentcontinuouslycompoundedrateofreturnforthatperiodas:r=ln(HPR+1)

LO.p:ExplainMonteCarlosimulationanddescribeitsapplicationsandlimitations.

MonteCarlosimulationisacomputersimulationthatproducesadistributionofpossiblesecuritypricesusingrandomlygeneratedvaluesforriskfactors,basedontheirassumeddistributions.

Limitationsinclude: Itisfairlycomplexandwillprovideanswersthatarenobetterthantheassumptions. Simulationisnotananalyticalmethodbutastatisticalone.

LO.q:CompareMonteCarlosimulationandhistoricalsimulation.

Thehistoricalsimulationusesactualpastdistributionofriskfactorsasinput.Whereas,MonteCarlosimulationusesrandomlygeneratedvaluesoftheriskfactorsbasedontheirassumeddistributions.

Thelimitationsofhistoricalsimulationare: Itcannottakeintoaccounttheeffectofsignificanteventsthatdidnotoccurduring

thesampleperiod. Itcannotperforma‘whatif’analysiswhenthe‘if’scenariohasnothappenedinthe

past.



PracticeQuestions

1. Whichofthefollowingismostlikelyanexampleofadiscreterandomvariable?A. Thereturnsonaportfolio.B. Thetimespentbyananalystonresearch.C. Thenumberofstocksinaportfolio.

2. ForacontinuousrandomvariableX,theprobabilityofanysinglevalueofXis:

A. 0.B. 1.C. determinedbythecumulativedistributionfunction.

3. TheprobabilitydistributionofadiscreterandomvariableXisgivenbelow

X 0 1 2 3 4 5 6P(X) 0.15 0.25 0.12 0.16 0.08 0.13 0.11

Whatisthecdfof4orF(4)?A. 0.08.B. 0.76.C. 0.68.

4. ThecumulativedistributionfunctionofadiscreterandomvariableXisgivenbelow:

X CumulativeDistributionFunction

0 0.151 0.402 0.523 0.684 0.765 0.896 1

TheprobabilityofXgreaterthanorequalto2andlessthanorequalto5isclosestto:A. 0.37.B. 0.52.C. 0.89.

5. Whichofthefollowingisleastlikelyaconditionofabinomialexperiment?

A. Thetrialsareindependent.B. Thereareonlytwotrials.C. Theprobabilityofsuccess+probabilityoffailure=1.



6. CastleHockeyClub,anemerginghockeyteam,hadatoughlastseasonwithawintolossrecordof1to4.Inordertocontestandincreaseitschancesofwinning,theteamsigned3newplayersanditisestimatedthatthechancesofwinningagameinthenextseasonare70%.Assumingthatwinningasinglegameisindependentofothergames,theprobabilitythattheteamwillwin3outofnext5gamesisclosestto:A. 0.3087.B. 0.3698.C. 0.4125.

7. Astock’spredictedpriceoverthenexttwoperiodsisasshownbelow.

Time=0 Time=1 Time=2S0=100 Su=104 Suu=108 Sd=96 Sud,du=101 Sdd=92

Theinitialvalueofthestockis100.Fromhistoricaldata, ithasbeenobservedthattheprobabilityofanupmoveinanygivenperiodis60%andtheprobabilityofadownmoveinanygivenperiodis40%.Usingtheabovedata,theprobabilitythatthestock’spricewillbeequalto101attheendofperiod2isclosestto:A. 24%.B. 36%.C. 48%.

8. Forafixedincomearbitragestrategy,thereturnsforasingletradeisuniformlydistributed

between3%and8%.Ifanewtradeisplacedtoday,whatistheprobabilitythatthereturnswillbemorethan5%?A. 0.4.B. 0.6.C. 0.8.

9. ForastandardnormaldistributionF(0)is:

A. 0.B. 0.5C. 1.0.

10. Forastandardnormaldistribution,P(0≤Z≤1.65)is:

A. 0.450.B. 0.475.C. 0.900.



11. GiventhatXfollowsanormaldistributionwithameanof5andstandarddeviationof1.25,thestandardizedvaluecorrespondingtoX=9wouldbeclosestto:A. 3.2.B. 4.0.C. 5.0.

12. Followingdataonthethreeportfoliosisgiven:

Portfolio ExpectedReturn StandardDeviation1 10% 3%2 15% 5%3 20% 10%

Assumingtheminimumacceptablerateofreturnis5%,underRoy’ssafety‐firstcriterion,whichofthefollowingportfoliosisthemostappropriatechoice?A. Portfolio1.B. Portfolio2.C. Portfolio3.

13. Analyst1:Normaldistributionsaresuitableforassetreturns.

Analyst2:Lognormaldistributionsaresuitablefordescribingdistributionsofassetprices.A. Analyst1iscorrect.B. Analyst2iscorrect.C. Bothanalystsarecorrect.

14. Astock’spriceatthestartoftheyearwas$10anditsyear‐endpricewas$12,thenits

continuouslycompoundedannualrateofreturnis:A. 16.45%.B. 18.23%.C. 20.00%.

15. Whichofthefollowingsimulationscanbeusedfor‘whatif’analysis?

A. MonteCarlosimulation.B. Historicalsimulation.C. BothMonteCarloandhistoricalsimulation.



Solutions1. Ciscorrect.Adiscreterandomvariableisoneforwhichthenumberofpossible

outcomescanbecounted.Acontinuousrandomvariableisoneforwhichthenumberofpossibleoutcomesisinfinite.Returnsandtimeareusuallycontinuouslyrandomvariables.Thenumberofstocksinaportfolioisadiscreterandomvariable.

2. Aiscorrect.Foracontinuousdistributionp(x)=0forallX;onlyrangesofvalueofXhave

positiveprobabilities.3. Biscorrect.Acumulativedistributionfunction(CDF)givestheprobabilitythatarandom

variablewillbelessthanorequaltospecificvalues.Therefore:F(4)=0.15+0.25+0.12+0.16+0.08=0.76.

4. Aiscorrect.P(X≤5)=0.89andP(X≤2)=0.52.Therefore,P(2≤X≤5)=0.89–0.52=

0.37.5. Biscorrect.Theremaybeanynumberofindependenttrials,eachwithonlytwopossible

outcomes.6. Aiscorrect.UsingBinomialdistributiontocalculatetheprobabilityof3winsoutof5

games:P(x)=P(X=x)=[numberofwaystochoosexfromn]×px×(1‐p)n‐xP(Win)=0.7P(Lose)=0.3P(3out5)=5C3x0.73x(0.3)2=0.3087

7. Ciscorrect.Therearefourpossibilitiesthatstockpricecantake.Itcanmoveup‐up,up‐

down,down‐upanddown‐down.Inordertoreach101,astock’spricecaneithergoupfirstandthendownortheotherway.Theprobabilityforthestockgoingupfirstandthendownis0.6x0.4=0.24Thisprobabilitywillbethesameforthestockgoingdownfirstandthenupwhichis,0.4x0.6=0.24.Therefore,theprobabilityofthestock’spricereaching101is48%(24%+24%)

8. Biscorrect.Inuniformdistribution,theprobabilitycanbefoundofarangeonlyinstead

ofapoint.Thereturnisuniformlydistributedfrom3%to8%,i.e.therangeis5%.Ifanewtradeisplacedthenreturnsgreaterthan5%leavesa3%buffer(8%‐5%=3%).Therefore,theprobabilityis3/5or0.6.

9. Biscorrect.Thenormaldistributionissymmetricaroundameanof0.F(0)=0.5since

halfofthedistributionliesoneachsideofthemean.



10. Aiscorrect.FromthetableF(1.65)=0.95,andF(0)=0.5.Thereforetheansweris0.95–

0.5=0.45.Alternatively,weknowthat90%lieswithin‐1.65and+1.65andthat0isthemidpoint,therewecansaythathalfof90%i.e45%liesbetween0and+1.65.

11. Aiscorrect.IfXfollowsanormaldistributionwithparametersμandσ,Xcanbestandardizedusingtheformula:

ZX μσ

=(9–5)÷1.25=3.2

12. Biscorrect.TheportfoliowiththehighestSFRatioispreferred.TheSFRatiois

calculatedbyE R R

σ

TheSFratiosfortheportfoliosare:Portfolio1:1.66Portfolio2:2Portfolio3:1.5

13. Ciscorrect.Anormaldistributionissuitablefordescribingassetreturns.However,the

normaldistributionisnotsuitableforassetpricesbecauseassetpricescannotbenegative.Thelognormaldistributionisboundedbyzero(skewedtotheright)andissuitablefordescribingdistributionsofassetprices.

14. Biscorrect.

Ln(EndingPrice/StartingPrice)Ln(12/10)=0.1823=18.23%

15. Aiscorrect.ComparedwithMonteCarlosimulation,thehistoricalsimulationcannotbe

usedfora“whatif”analysis.

R11 Sampling and Estimation 2019 Level I Notes


R11SamplingandEstimation

1.Introduction

Asampleisasubsetofapopulation.Wecanstudyasampletoinferconclusionsaboutthepopulationitself.Forexample,ifallthestockstradingintheUSareconsideredapopulation,thenindicessuchastheS&P500aresamples.WecanlookattheperformanceoftheS&P500anddrawconclusionsabouthowallstocksintheUSareperforming.Thisprocessisknownassamplingandestimation.

2.Sampling

Therearevariousmethodsforobtaininginformationonapopulationthroughsamples.Theinformationweobtainusuallyconcernsaparameter,aquantityusedtodescribeapopulation.Toestimateaparameter,weusesamplestatistics.Astatisticisaquantityusedtodescribeasample.

Therearetworeasonswhysamplingisused:• Timesaving:Inmanycasesitwillbeverytimeconsumingtoexamineeverymember

ofthepopulation.• Monetarysaving:Insomecases,examiningeverymemberofthepopulation

becomeseconomicallyinefficient.

2.1.SimpleRandomSampling

Simplerandomsamplingistheprocessofselectingasamplefromalargerpopulationinsuchawaythateachmemberofthepopulationhasthesameprobabilityofbeingincludedinthesample.

Samplingdistribution

Ifwedrawsamplesofthesamesizeseveraltimesandcalculatethesamplestatistic,thesamplestatisticwillbedifferenteachtime.Thedistributionofvaluesofthesamplestatisticiscalledasamplingdistribution.

Forexample,sayyouselect100stocksfromauniverseof10,000stocksandcalculatetheaverageannualreturnsofthese100stocks.Let’ssayyougetanaveragereturnof15%.Yourepeatthisprocesswithasecondsampleof100stocks.Thistime,yougetanaveragereturnof14%.Youkeeprepeatingthisprocessandeachtimeyougetadifferentaveragereturn.Thedistributionofthesesampleaveragereturnsiscalledasamplingdistribution.

Samplingerror

Samplingerroristhedifferencebetweenasamplestatisticandthecorrespondingpopulationparameter.Thesamplingerrorofthemeanisgivenby:

Samplingerrorofthemean x μ



Forexample,let’ssayyouwanttoestimatetheaveragereturnsof10,000stocks.Youdrawasampleof100stocksandcalculatetheaveragereturnofthese100stocksas15%.However,theactualaverageofthe10,000stockswas12%.Thenthesamplingerror=15%‐12%=3%.

2.2.StratifiedRandomSampling

Instratifiedrandomsampling,thepopulationisdividedintosubgroupsbasedononeormoredistinguishingcharacteristics.Samplesarethendrawnfromeachsubgroup,withsamplesizeproportionaltothesizeofthesubgrouprelativetothepopulation.Finally,samplesfromeachsubgrouparepooledtogethertoformastratifiedrandomsample.

Theadvantageofstratifiedrandomsamplingisthatthesamplewillhavethesamedistributionofkeycharacteristicsastheoverallpopulation.Thiscanhelpreducethesamplingerror.Stratifiedrandomsamplingthereforeproducesmorepreciseparameterestimatesthansimplerandomsampling

Forexample,youdividetheuniverseof10,000stocksaspertheirmarketcapitalizationsuchthatyouhave5,000largecapstocks,3,000midcapstocks,and2,000smallcapstocks.Instratifiedrandomsampling,toselectatotalsampleof100stocks,youwillrandomlyselect50largecapstocks,30midcapstocks,and20smallcapstocksandpoolallthesesamplestogethertoformastratifiedrandomsample.

Example

Paulwantstocategorizepubliclylistedstocksforhisresearchproject.Hefirstdividesthestocksinto15industries.Thenfromeachindustry,hecategorizescompaniesintothreegroups:small,medium,large.Finally,hedividestheseintovalueversusgrowthstocks.Howmanycellsorstratadoesthesamplingplanentail?A. 20B. 45C. 90

Solution:

Ciscorrect.Thisisanapplicationofthemultiplicationruleofcounting.Thetotalnumberofcellsistheproductof15,3,and2.Thustheansweris90.

2.3.Time‐SeriesandCross‐SectionalData

Time‐seriesdata

Time‐seriesdataconsistsofobservationsforasinglesubjecttakenatspecificandequallyspacedintervalsoftime.Forexample,themonthlyreturnsonMicrosoftstockfromJanuary1995toJanuary2005.



Cross‐sectionaldata

Cross‐sectionaldataconsistsofobservationsformultiplesubjectstakenataspecificpointintime.Forexample,thesampleofreportedearningspershareofallNASDAQcompaniesfor2005.

Forbothtime‐seriesandcross‐sectionaldata,therandomsamplemustberepresentativeofthepopulationwewishtostudy.

A‘longitudinal’dataor‘panel’datakeepsthesamesampleforeachobservationovertime.

3.DistributionoftheSampleMean

Thesamplemeanisarandomvariablewithaprobabilitydistributionknownasthestatistic’ssamplingdistribution.Tounderstandthisconcept,considerthefollowingpopulation:lastyear’sreturnsoneverystocktradedintheUnitedStates.Weareinterestedinthemeanreturnofallstocksbutdonothavetimetocalculatethepopulationmean.Hence,wedrawasampleof50stocksandcomputethesamplemean.Wethendrawanothersampleof50stocksandcomputethesamplemean.Thisexercisecanberepeatedseveraltimesgivingusadistributionofsamplemeans.Thisdistributioniscalledthestatistic’ssamplingdistribution.Thecentrallimittheorem,explainedbelow,helpsusunderstandthesamplingdistributionofthemean.

3.1.TheCentralLimitTheorem

Accordingtothecentrallimittheorem,ifwedrawasamplefromapopulationwithameanµandavarianceσ2,thenthesamplingdistributionofthesamplemean:

willbenormallydistributed(irrespectiveofthetypeofdistributionoftheoriginalpopulation).

willhaveameanofµ. willhaveavarianceofσ2/n.

Forexample,supposetheaveragereturnoftheuniverseof10,000stocksis12%anditsstandarddeviationis10%.Throughcentrallimittheoremwecanconcludethatifwekeepdrawingsamplesof100stocksandplottheiraveragereturns,wewillgetasamplingdistributionthatwillbenormallydistributedwithmean=12%andvarianceof102/100=1%.

Standarderrorofthesamplemean

Thestandarddeviationofthedistributionofthesamplemeansisknownasthestandarderrorofthesamplemean.

Whenweknowthepopulationstandarddeviation,thestandarderrorofthesamplemeancanbecalculatedas:

σ σ

√n



Whenwedonotknowthepopulationstandarddeviation(σ)wecanusethesamplestandarddeviation(s)toestimatethestandarderrorofthesamplemean:

s s

√n

Example

Themeanofapopulationis12andthestandarddeviationis3.Giventhatthepopulationcomprisesof64observations,whatisthestandarderrorofthesamplemean?A.0.375B.0.378C.0.667

Solution:

Aiscorrect.StandardError=σ/√n=3/√64=0.375

4.PointandIntervalEstimatesofthePopulationMean

Statisticalinferenceconsistsoftwobranches:1)hypothesistestingand2)estimation.Hypothesistestingaddressesthequestion‘Isthevalueofthisparameterequaltosomespecificvalue?’Thisisdiscussedindetailinthenextreading.Inthissection,wewilldiscussestimation.Estimationseekstoanswerthequestion‘Whatisthisparameter’svalue?’Inestimation,wemakethebestuseoftheinformationinasampletoformoneofseveraltypesofestimatesoftheparameter’svalue.

Apointestimateisasinglenumberthatestimatestheunknownpopulationparameter.

Intervalestimates(orconfidenceintervals)arearangeofvaluesthatbrackettheunknownpopulationparameterwithsomespecifiedlevelofprobability.

4.1.PointEstimators

Theformulasthatweusetocomputethesamplemeanandallothersamplestatisticsareexamplesofestimationformulasorestimators.Theparticularvaluethatwecalculatefromsampleobservationsusinganestimatoriscalledanestimate.Forexample,thecalculatedvalueofthesamplemeaninagivensampleiscalledapointestimateofthepopulationmean.

Thethreedesirablepropertiesofanestimatorare: Unbiasedness:Itsexpectedvalueisequaltotheparameterbeingestimated. Efficiency:Ithasthelowestvarianceascomparedtootherunbiasedestimatorsofthe

sameparameter. Consistency:Assamplesizeincreases,thesamplingerrordecreasesandthe

estimatesgetclosertotheactualvalue.



4.2.ConfidenceIntervalsforthePopulationMean

Aconfidenceintervalisarangeofvalues,withinwhichtheactualvalueoftheparameterwillliewithagivenprobability.Confidenceintervaliscalculatedas:

Confidenceinterval=pointestimate±(reliabilityfactorxstandarderror)

where:pointestimate=apointestimateoftheparameterreliabilityfactor=anumberbasedontheassumeddistributionofthepointestimateandthedegreeofconfidence(1‐α)fortheconfidenceintervalstandarderror=standarderrorofthesamplestatisticprovidingthepointestimate

Calculatingconfidenceintervals

Tocalculateaconfidenceintervalforapopulationmean,refertothetablebelowandselecttstatisticorzstatisticasperthescenario.

SamplingfromSmallsamplesize(n<30)

Largesamplesize(n≥30)

Normaldistribution

Varianceknown z zVarianceunknown t t(orz)

Non–normaldistribution

Varianceknown NA zVarianceunknown NA t(orz)

Usethefollowingformulaetocalculatetheconfidenceinterval:

Confidenceinterval X z / σ

√n

Confidenceinterval X t / s

√n

SamplingfromanormaldistributionwithknownvarianceThemostbasicconfidenceintervalforthepopulationmeanariseswhenwearesamplingfromanormaldistributionwithknownvariance.

Theconfidenceintervalwillbecalculatedas:

ConfidenceInterval X z / σ

√n

where:X=samplemeanz / =reliabilityfactor

σ/√n=standarderrorThereliabilityfactor(z / )dependspurelyonthedegreeofconfidence.Ifthedegreeofconfidence(1–α)is95%or0.95,thelevelofsignificance(α)is5%or0.05.α/2=0.025.α/2istheprobabilityineachtailofthestandardnormaldistribution.Thisisshowninblueinthefigurebelow:



Thereliabilityfactorsthataremostfrequentlyusedwhenweconstructconfidenceintervalsbasedonthestandardnormaldistributionare:

• 90%confidenceintervals:α=0.1,α/2=0.05.Reliabilityfactor=z0.05=1.65• 95%confidenceintervals:α=0.05,α/2=0.025.Reliabilityfactor=z0.025=1.96• 99%confidenceintervals:α=0.01,α/2=0.005.Reliabilityfactor=z0.005=2.58

Memorizetheseconfidenceintervalsandthecorrespondingreliabilityfactors.

Example

YoutakearandomsampleofstocksontheNationalStockExchange(NSE).Thesamplesizeis100andtheaverageSharperatiois0.50.AssumethattheSharperatiosofallstocksontheNSEfollowanormaldistributionwithastandarddeviationof0.30.Whatisthe90%confidenceintervalforthemeanSharperatioofallstocksontheNSE?

Solution:

ConfidenceInterval X z / σ

√n 0.50 1.65

0.30

√100=0.50 0.0495

Therefore,the90%confidenceintervalforthemeanSharperatioofallstocksontheNSEis:0.4505to0.5495.

Asweincreasethedegreeofconfidence,theconfidenceintervalbecomeswider.Ifweusea95%confidenceinterval,thereliabilityfactoris1.96.Andtheconfidenceintervalrangesfrom0.50–1.96x0.03to0.50+1.96x0.03whichis:0.4412to0.5588.Thisrangeiswiderthanwhatwehadwitha90%confidenceinterval.

Samplingfromanormaldistributionwithunknownvariance

Ifthedistributionofthepopulationisnormalwithunknownvariance,wecanusethet‐distributiontoconstructaconfidenceinterval.Letusfirstunderstandwhatat‐distributionisandcontrastitwithanormaldistribution.

Student’st‐distributionhasthefollowingproperties: Itissymmetrical,bell‐shapedandsimilartoanormaldistribution. Ithasalowerpeakandfattertailsascomparedtoanormaldistribution. Itisdefinedbyasingleparameter,degreesoffreedom(df)=n–1.



Thevalueofdegreesoffreedom,isusedtodescribehowwellthetstatisticrepresentsaz‐score.Also,thevalueofdfwilldeterminehowwellthedistributionoftapproximatesanormaldistribution.Forlargevaluesofdf,thetdistributionwillbenearlynormal,butwithsmallvaluesfordf,thetdistributionwillbeflatterandmorespreadoutthananormaldistribution.Refertothefigurebelow.

Theconfidenceintervalcanbecalculatedusingthefollowingformula:

ConfidenceInterval X t / s

√n

Thisrelationshipissimilartowhatwe’vediscussedbeforeexcepthereweusethet‐distribution.Sincethepopulationstandarddeviationisnotknown,wehavetousethesamplestandarddeviationwhichisdenotedbythesymbol‘s’.Wewillnowseehowtoreadthet‐distributiontableusinganexample.

Example

Givenasamplesizeof20,whatisthereliabilityfactorfora90%confidencelevel?

Solution:

Inordertoanswerthisquestion,weneedtorefertothet‐table.Asnapshotofthetableisgivenbelow.Thistableshowsthelevelofsignificanceforone‐tailedprobabilities.df P=0.10 P=0.05 P=0.025 P=0.01 P=0.0051 3.078 6.314 12.706 31.821 63.6572 1.886 2.920 4.303 6.965 9.9253 1.638 2.353 3.182 4.541 5.8414 1.533 2.132 2.776 3.747 4.6045 1.476 2.015 2.571 3.365 4.0326 1.440 1.943 2.447 3.143 3.707



7 1.415 1.895 2.365 2.998 3.4998 1.397 1.860 2.306 2.896 3.3559 1.383 1.833 2.262 2.821 3.25010 1.372 1.812 2.228 2.764 3.16911 1.363 1.796 2.201 2.718 3.10612 1.356 1.782 2.179 2.681 3.05513 1.350 1.771 2.160 2.650 3.01214 1.345 1.761 2.145 2.624 2.97715 1.341 1.753 2.131 2.602 2.94716 1.337 1.746 2.120 2.583 2.92117 1.333 1.740 2.110 2.567 2.89818 1.330 1.734 2.101 2.552 2.87819 1.328 1.729 2.093 2.539 2.86120 1.325 1.725 2.086 2.528 2.845Thedegreesoffreedominthiscasearen–1=20–1=19.Thelevelofsignificanceiscalculatedas:100(1‐α)%=90%andα=0.10.Inordertocalculatethereliabilityfactor

/ = . / = . ,welookattherowwithdf=19.Wethenlookatthecolumnwithp=0.05.Thevaluethatsatisfiesthesetwocriteriais1.729.Thisisthereliabilityfactor.Example

AnanalystwantstoestimatethereturnontheHangSengIndexforthecurrentyearusingthefollowingdataandassumptions: Samplesize=64stocksfromtheindex Meanreturnforthestocksinthesampleforthepreviousyear=0.12 Variance=0.081

Itisgiventhatthereliabilityfactorfora95%confidenceintervalwithunknownpopulationvarianceandsamplesizegreaterthan64is1.96.Assumingthattheindexreturnthisyearwillbethesameasitwaslastyear,whatistheestimateofthe95%confidenceintervalfortheindex’sreturnthisyear?

Solution:

ConfidenceInterval X t / √=0.12 1.96 √ .

√0.12 0.07=0.05to0.19

Instructor’sNote:Aconservativeapproachtoconfidenceintervalsreliesonthet‐distributionratherthanthenormaldistribution,anduseofthet‐distributionwillincreasethereliabilityoftheconfidenceinterval.



4.3.SelectionofSampleSize

Thechoiceofsamplesizeaffectsthewidthofaconfidenceinterval.Alargersamplesizedecreasesthewidthofaconfidenceintervalandimprovestheprecisionwithwhichwecanestimatethepopulationparameter.Thisisobviouswhenweconsidertheconfidenceintervalrelationship,shownbelow:

ConfidenceInterval X t / s

√n

Allelsebeingequal,whenthesamplesize(n)isincreased,thestandarderror(s/√ )decreasesandwehaveamoreprecise(narrower)confidenceinterval.Basedonthisdiscussionitmightappearthatweshoulduseaslargeasamplesizeaspossible.However,wemustconsiderthefollowingissues:

Increasingthesamplesizemayresultinsamplingfrommorethanonepopulation. Increasingthesamplesizemayinvolveadditionalexpensesthatoutweighthevalue

ofadditionalprecision.

5.MoreonSampling

Therearemanyissuesinsampling.Herewediscussfourmainissues.

5.1Data‐MiningBias

Data‐miningisthepracticeofanalyzingthesamedataagainandagain,tillapatternthatworksisidentified.

Therearetwosignsthatcanwarnanalystsaboutthepotentialexistenceofdatamining:• Toomuchdigging/toolittleconfidence:Manydifferentvariablesweretested,until

significantoneswerefound.Unfortunately,manyresearchersdonotdisclosethenumberofvariablesexaminedindevelopingamodel.

• Nostory/nofuture:Withoutareasonableeconomicrationaleorstoryforwhyavariableshouldwork,thevariableisunlikelytohavepredictivepower.

Thebestwaytoavoidthisbiasistotestthepatternonout‐of‐sampledatatocheckifitholds.

5.2SampleSelectionBias

Whendataavailabilityleadstocertainassetsbeingexcludedfromtheanalysis,theresultingproblemisknownassampleselectionbias.Forexample,manymutualfunddatabasesprovidehistoricalinformationaboutonlythosefundsthatcurrentlyexist.Atypeofsampleselectionbiasisthesurvivorshipbias,inwhichcompaniesareexcludedfromanalysisbecausetheyhavegoneoutofbusiness.Asamplecanalsobebiasedbecauseoftheremoval(ordelisting)ofacompany’sstockfromanexchange.



5.3Look‐AheadBias

Atestdesignissubjecttolook‐aheadbiasifitusesinformationthatwasnotavailabletomarketparticipantsatthetimethemarketparticipantsactinthemodel.Forexample,ananalystwantstousethecompany’sbookvaluepersharetoconstructtheP/Bvariableforthatparticularcompany.Althoughthemarketpriceofastockisavailableforallmarketparticipantsatthesamepointintime,fiscalyear‐endbookequitypersharemightnotbecomepubliclyavailableuntilsometimeinthefollowingquarter.

5.4Time‐PeriodBias

Atestdesignissubjecttotime‐periodbiasifitisbasedonatimeperiodthatmaymaketheresultstime‐periodspecific.Ashorttimeseriesislikelytogiveperiod‐specificresultsthatmaynotreflectalongerperiod.Ifatimeseriesistoolong,fundamentalstructuralchangesmayhaveoccurredinthattimeperiod.



Summary

LO.a:Definesimplerandomsamplingandasamplingdistribution.

Simplerandomsamplingistheprocessofselectingasamplefromalargerpopulationinsuchawaythateachelementofthepopulationhasthesameprobabilityofbeingincludedinthesample.

Ifwedrawsamplesofthesamesizeseveraltimesandcalculatethesamplestatistic,thesamplestatisticwillbedifferenteachtime.Thedistributionofvaluesofthesamplestatisticiscalledasamplingdistribution.

LO.b:Explainsamplingerror.

Samplingerroristhedifferencebetweenasamplestatisticandthecorrespondingpopulationparameter.

Samplingerrorofthemean x μ

LO.c:Distinguishbetweensimplerandomandstratifiedrandomsampling.

Instratifiedrandomsampling,thepopulationisdividedintosubgroupsbasedononeormoredistinguishingcharacteristics.Samplesarethendrawnfromeachsubgroup,withsamplesizeproportionaltothesizeofthesubgrouprelativetothepopulation.Finally,samplesfromeachsubgrouparepooledtogethertoformastratifiedrandomsample.

LO.d:Distinguishbetweentimeseriesandcross‐sectionaldata.

Timeseriesdataconsistsofobservationsforasinglesubjecttakenatspecificandequallyspacedintervalsoftime.

Cross‐sectionaldataconsistsofobservationsformultiplesubjectstakenataspecificpointintime.

LO.e:Explainthecentrallimittheoremanditsimportance.

Accordingtothecentrallimittheorem,ifwedrawasamplefromapopulationwithameanµandavarianceσ2,thenthesamplingdistributionofthesamplemean:

willbenormallydistributed(irrespectiveofthetypeofdistributionoftheoriginalpopulation).

willhaveameanofµ. willhaveavarianceofσ2/n.

LO.f:Calculateandinterpretthestandarderrorofthesamplemean.

Thestandarddeviationofthedistributionofthesamplemeansisknownasthestandarderrorofthesamplemean.

Whenweknowthepopulationstandarddeviation,thestandarderrorofthesamplemeancanbecalculatedas:σ

√



Whenwedonotknowthepopulationstandarddeviation(σ)wecanusethesamplestandarddeviation(s)toestimatethestandarderrorofthesamplemeans

√

LO.g:Identifyanddescribedesirablepropertiesofanestimator.

Thethreedesirablepropertiesofanestimatorare: Unbiasedness:Itsexpectedvalueisequaltotheparameterbeingestimated. Efficiency:Ithasthelowestvarianceascomparedtootherunbiasedestimatorsofthe

sameparameter. Consistency:Assamplesizeincreases,thesamplingerrordecreasesandthe

estimatesgetclosertotheactualvalue.

LO.h:Distinguishbetweenapointestimateandaconfidenceintervalestimateofapopulationparameter.

Apointestimateisasinglevalueestimatethatservesasanapproximationfortheactualvalueoftheparameter.

Aconfidenceintervalisarangeofvalues,withinwhichtheactualvalueoftheparameterwillliewithagivenprobability.

Confidenceinterval=Pointestimate±(reliabilityfactorxstandarderrorofpointestimate)

LO.i:DescribepropertiesofStudent’st‐distributionandcalculateandinterpretitsdegreesoffreedom.

Student’st‐distributionhasthefollowingproperties: Itissymmetrical,bell‐shaped,andsimilartoanormaldistribution. Ithasalowerpeakandfattertailsascomparedtoanormaldistribution. Itisdefinedbyasingleparameter:degreesoffreedom(df)=n‐1 Asthedegreesoffreedomincrease,theshapeofthet‐distributionstartsapproaching

theshapeofthenormaldistribution.

LO.j:Calculateandinterpretaconfidenceintervalforapopulationmean,givenanormaldistributionwith1)aknownpopulationvariance,2)anunknownpopulationvariance,or3)anunknownpopulationvarianceandalargesamplesize.

Refertothetablebelowandselecttstatisticorzstatisticasperthescenario.

Samplingfrom Smallsamplesize(n<30)


Normaldistribution




Usethefollowingformulaetocalculatetheconfidenceinterval:

Confidenceinterval X z / σ

√n



Confidenceinterval X t / s

√n

LO.k:Describetheissuesregardingselectionoftheappropriatesamplesize,data‐miningbias,sampleselectionbias,survivorshipbias,look‐aheadbias,andtime‐periodbias.

Increasingthesamplesizereducesthestandarderrorandgivesusnarrowerconfidenceintervals.However,whileincreasingsamplesizewemustconsidertwothings:

Costinvolved:Comparethecostofgettingmoredatatothepotentialbenefitsofincreasingprecision.

Riskofsamplingfromadifferentpopulation:Intheprocessofincreasingsamplesizeifwegetdatafromadifferentpopulation,thentheaccuracywillnotimprove.

Biasesobservedinsamplingmethodsare: Data‐miningbias:Analyzingthesamedataagainandagain,tillapatternthatworksis

identified.Thebestwaytoavoidthisbiasistotestthepatternonout‐of‐sampledatatocheckifitholds.

Sampleselectionbias:Excludingcertainassetsfromtheanalysisduetounavailabilityofdata.Atypeofsampleselectionbiasisthesurvivorshipbias,inwhichcompaniesareexcludedfromanalysisbecausetheyhavegoneoutofbusinessanddataforthemwasnoteasilyavailable.

Look‐aheadbias:Usinginformationthatbecameavailableatlaterperiodsintimeintheanalysis.

Time‐periodbias:Iftheselectedtimeperiodistooshort,theresultsmayonlyholdforthattimeperiod.Ifthetimeperiodistoolong,thentheresultsmightnotconsidermajorstructuralchangesintheeconomy.



PracticeQuestions

1. A simple random sample is a sample drawn in such a way that each member of thepopulationhas:A. somechanceofbeingselectedinthesample.B. anequalchanceofbeingselectedinthesample.C. isincludedinthesample.

2. Supposewetakearandomsampleof40companiesinanindustrywith100companies.

Wecalculatethesamplemeanofthedebt‐to‐equityratiofortheprioryear.Wefindthatthisratiois2.5percent.Subsequently,welearnthatthepopulationdebt‐to‐equityratio(takingaccountofall100companies) is2.What is theexplanation for thediscrepancybetweenthesamplemeanof2.5percentandthepopulationmeanof2?A. Samplingerror.B. Bias.C. Alackofconsistency.

3. AnanalystcompilesEPSdataforasampleofcompaniesrandomlydrawnfromtheS&P

500.Hegathersthedatafromthecompanies’fiscalyear2015annualreports.Thisdataisbestcharacterizedas:A. time‐seriesdata.B. longitudinaldata.C. cross‐sectionaldata.

4. Thepopulationdistributionofhedgefundreturnsinacountryisfoundtobenegatively

skewedinaparticularyear.Giventhatthesamplesizeislarge,thesamplingdistributionofthesamplemeanreturnswouldbecharacterizedby:

Distribution Mean VarianceA Negativeskewed Lessthanpopulation

meanEqualtopopulationvariance

B Normaldistribution

Equaltopopulationmean Lessthanpopulationvariance

C Normaldistribution

Lessthanpopulationmean

Equaltopopulationvariance

5. Asampleof50observationshasameanof10andastandarddeviationof2.Thestandard

errorofthesamplemeanisclosestto:A. 0.04B. 0.28.C. 1.41.



6. Ananalystwhilegeneratinganestimateofapopulationparameterisconsideringdrawinga larger sample size. In doing so, a larger sample size will most likely improve theestimator’s:A. efficiency.B. consistency.C. unbiasedness.

7. JohnClarkisunsureoftheunderlyingpopulationdistributionandwantstoincreasethe

reliabilityoftheparameterestimates.Whichofthefollowingisleastlikelytoachievehisobjective?A. Increaseinthesamplesize.B. Useofpointestimatesratherthanconfidenceintervals.C. Useof thet‐distributionratherthanthenormaldistributiontoestablishconfidence

intervals.

8. Analyst1:Asdegreesoffreedomincrease,at‐distributionwillbecomemorepeaked.Analyst2:Asdegreesoffreedomincrease,thetailsofthet‐distributionwillbecomelessfat.A. Analyst1iscorrect.B. Analyst2iscorrect.C. Bothanalystsarecorrect.

9. Robert Scottwants to calculate the confidence intervals for thepopulationmeanof an

approximately normal distribution. Assuming the sample size is small, the Student’s t‐distributionisthepreferredmethodwhenthevarianceis:A. unknown.B. tooLarge.C. negative.

10. Arandomsampleof100coffeeshopcustomersspentanaverageof25minsatthestore.

Assumingthedistributionisnormalandthepopulationstandarddeviationis4mins,the95%confidenceintervalforthepopulationmeanisclosestto:A. 21.00to29.00.B. 24.25to25.78.C. 23.78to26.04.

11. Asampleof25recentordersatarestaurantshowedthatthemeantimetoserveadish

was19minswithasamplestandarddeviationof3mins.Assumingthepopulationisnormallydistributed,the99%confidenceintervalforthepopulationmeanis:A. 17.32to20.67.B. 16.21to21.96.



C. 15.24to22.38.12. DavidJonesisconductingaresearchonS&P500stocks.Inhisresearch,heuseshistorical

datathatwasnotpubliclyavailableatthetimeperiodbeingstudied.Hissamplewillmostlikelyhavea:A. look‐aheadbias.B. time‐periodbias.C. sampleselectionbias.



Solutions

1. B is correct. In a simple random sample, eachmember of the populationhas an equalprobabilityofbeingselected.

2. Aiscorrect.Thediscrepancyarisesfromsamplingerror.Samplingerroristhedifferencebetweenasamplestatisticanditscorrespondingpopulationparameter.Asamplingerrorexistswheneveronefailstoobserveeveryelementofthepopulation,becauseasamplestatisticcanvaryfromsampletosample.Wedonotexpectthesamplemeantoexactlyequalthepopulationmeaninanyonesamplewemaytake.

3. Ciscorrect.Dataonsomecharacteristicsofcompaniesatasinglepointintimearecross‐sectionaldata.

4. Biscorrect.AccordingtotheCentralLimitTheorem,thesamplingdistributionofsamplemeansisapproximatelyanormaldistributionwithitsmeanequaltothepopulationmean.Itsvarianceisequaltopopulationvariancedividedbythesamplesizeandhencewouldbelessthanpopulationvariance.TheCentralLimitTheoremisindependentoftheprobabilitydistributionofthegivenpopulationwhenthesamplesizeislargeandthustheskewnessofpopulationdoesnotmatter.

5. Biscorrect.Thestandarderrorofthesamplemean,whenweknowthesamplestandarddeviation,issamplestandarddeviationdividedbysquarerootofsamplesize:2/√50=0.28

6. B is correct. Unbiasedness and efficiency are properties of an estimator’s samplingdistribution that hold for any size sample.A consistent estimator is one forwhich theprobabilityofestimatesclosetothevalueofthepopulationparameterincreasesassamplesizeincreases.

7. B is correct. Point estimates are not as reliable as confidence interval estimates. Aconservativeapproachtoconfidenceintervalsreliesonthet‐distributionratherthanthenormal distribution, and use of the t‐distribution will increase the reliability of theconfidenceinterval.Increasingthesamplesizeincreasesthereliabilityoftheconfidenceintervals.

8. Ciscorrect.Asdegreesoffreedomincrease,thet‐distributionwillmorecloselyresembleanormaldistribution,becomingmorepeakedandhavinglessfattails.

9. Aiscorrect.TheStudent’st‐distributionisthepreferredoptionwhenthesamplesizeissmallandthevarianceisunknownBelowtableprovidestheappropriatetestgivenascenario:



SamplingFromStatisticforSmallSampleSize

StatisticforLargeSampleSize

Normaldistributionwithaknownvariance

z z

Normaldistributionwithunknownvariance

t torz

Non‐normaldistributionwithknownvariance

NotAvailable z

Non‐normaldistributionwithunknownvariance

NotAvailable torz

10. Biscorrect.Sincethepopulationvarianceisknownandn≥30,theconfidenceintervalisdeterminedas ̅ / /√ Z0.025=1.96Confidenceinterval=25±1.96(4/sqrt(100)=24.216to25.784

11. Aiscorrect.Sincethepopulationvarianceisunknownandn<30,theconfidenceintervalisdeterminedas̅ / /√ .Thecriticalvalueoft0.005anddf=n‐1=24is2.797.Sotheconfidenceintervalis19±2.797(3/5)=17.32to20.67

12. Aiscorrect.Thisisanexampleoflook‐aheadbias.

R12 Hypothesis Testing 2019 Level I Notes


R12HypothesisTesting

1.Introduction

Hypothesistestingistheprocessofmakingjudgmentsaboutalargergroup(apopulation)onthebasisofobservingasmallergroup(asample).Theresultsofsuchatestthenhelpusevaluatewhetherourhypothesisistrueorfalse.

Forexample,let’ssayyouarearesearcherandyoubelievethattheaveragereturnonallAsianstockswasgreaterthan2%.TotestthisbeliefyoucandrawsamplesfromapopulationofallAsianstocksandemployhypothesistestingprocedures.Theresultsofthistestcantellyouifyourbeliefisstatisticallyvalid.

2.HypothesisTesting

Ahypothesisisdefinedasastatementaboutoneormorepopulations.Inordertotestahypothesis,wefollowthesesteps:

1. Statingthehypothesis.2. Identifyingtheappropriateteststatisticanditsprobabilitydistribution.3. Specifyingthesignificancelevel.4. Statingthedecisionrule.5. Collectingthedataandcalculatingtheteststatistic.6. Makingthestatisticaldecision.7. Makingtheeconomicorinvestmentdecision.

Instructor’sNoteThoughthecurriculumsuggestsasevenstepprocessforhypothesistesting,youcanarriveatadecisionquicklyusingthesefoursteps:1. Statethehypothesis.2. Computetheteststatistic.3. Determinethecriticalvaluebasedonsignificancelevel.4. Comparetheteststatisticwiththecriticalvalueanddeterminewhetherornottoreject

thenullhypothesis.

Let’sunderstandthesestepswiththehelpofafewexamples.

RightTailedTest

SupposeyouarearesearcherandbelievethattheaveragereturnonallAsianstockswasgreaterthan2%.Inthiscase,youaremakingastatementaboutthepopulationmean(µ)ofallAsianstocks.

Step1:Statingthehypothesis

Thefirststepisstatingthetwohypotheses:thenullhypothesis(H0)andthealternativehypothesis(Ha).

Nullhypothesis(H0):Itisthehypothesisthattheresearcherwantstoreject.



Alternativehypothesis(Ha):Itisthehypothesisthattheresearcherwantstoprove.Ifthenullhypothesisisrejectedthenthealternativehypothesisisconsideredvalid.

Forourexample,thenullandalternativehypothesesare:

H0:µ≤2%

Ha:µ>2%

(Thevalue2%isknownasµ0,thehypothesizedvalueofthepopulationmean.)

Instructor’sNote:Aneasywaytodifferentiatebetweenthetwohypothesesistorememberthatthenullhypothesisalwayscontainssomeformoftheequalsign.

Step2:Computetheteststatistic.

Ateststatisticiscalculatedfromsampledataandiscomparedtoacriticalvaluetodecidewhetherornotwecanrejectthenullhypothesis.Theformulaforcomputingteststatisticis:

teststatistic samplestatistic valueoftheparameterunderH

standarderrorofthesamplestatistic

Continuingwithourexample,let’sfurthersupposethatthesamplemeanof36observationsofAsianstocksis4andthestandarddeviationofthepopulationis4.Therefore,

teststatisticX μ

√

4 2

√

3

Step3:Determinethecriticalvaluebasedonsignificancelevel

ContinuingwithourexampleofAsianstocks,supposewewanttotestourhypothesisatthe5%significancelevel.Thisisaone‐tailedtestbecausewearetryingtoassesswhetherthepopulationmeanisgreaterthan2%ornot.Hence,weareonlyinterestedintherighttailofthedistribution.Ifweweretryingtoassesswhetherthepopulationmeanislessthan2%wewouldbeinterestedinthelefttail.

Instructor’sNoteThesigninthealternativehypothesispointstothedirectionofthetailthatweshoulduseinourtest.Sinceinourexamplethealternativehypothesishasa‘>’signitpointstotheright,thereforeweareinterestedintherighttail.

Thecriticalvalueisalsoknownastherejectionpointfortheteststatistic.Graphically,thispointseparatestheacceptanceandrejectionregionsforasetofvaluesoftheteststatistic.Thisisshownbelow:



Theregiontotheleftoftheteststatisticisthe‘acceptanceregion’.Thisrepresentsthesetofvaluesforwhichwedonotreject(accept)thenullhypothesis.Theregiontotherightoftheteststatisticisknownasthe‘rejectionregion’.

UsingtheZ–tableand5%levelofsignificance,thecriticalvalue=Z0.05=1.65

Step4:Comparetheteststatisticwiththecriticalvalueanddeterminewhetherornottorejectthenullhypothesis

Iftheteststatistic>criticalvalue,i.e.iftheteststatisticliesintherejectionregionwewillrejectH0.

Ontheotherhand,iftheteststatistic<criticalvalue,i.e.iftheteststatisticliesintheacceptanceregion,thenwecannotrejectH0.

Inourexample,becausetheteststatisticz=3isgreaterthanthecriticalvalueof1.645,werejectthenullhypothesisinfavorofthealternativehypothesisthattheaveragereturnonallAsianstocksisgreaterthan2%.

LeftTailedTest

Weusealefttailedtesttodeterminewhethertheestimatedvalueofapopulationparameterislessthanahypothesizedvalue.

ExampleAnanalystbelievesthattheaveragereturnonallAsianstockswaslessthan2%.Thesamplesizeis36observationswithasamplemeanof‐3.Thestandarddeviationofthepopulationis4.Willherejectthenullhypothesisatthe5%levelofsignificance?

Solution:Inthiscase,ournullandalternativehypothesesare:

H0:µ≥2

Ha:µ<2



Thestandarderrorofthesampleis:σ √

√

0.67

Theteststatisticis:


standarderrorofthesamplestatistic3 20.67

7.5

Thecriticalvaluescorrespondingtoa5%levelofsignificanceis‐1.65.

Whenweconsiderthelefttailofthedistribution,ourdecisionruleisasfollows:Rejectthenullhypothesisiftheteststatisticislessthanthecriticalvalueandviceversa.Sinceourcalculatedteststatisticof‐7.5islessthanthecriticalvalueof‐1.65,werejectthenullhypothesis.

Two‐tailedtest

Weuseatwo‐tailedhypothesistesttodeterminewhethertheestimatedvalueofapopulationparameterisdifferentfromthehypothesizedvalue.Inatwo‐tailedtest,werejectthenullinfavorofthealternativeiftheevidenceindicatesthatthepopulationparameteriseithersmallerorlargerthanthevalueoftheparameterunderH0.

Forexample,webelievethattheaveragereturnonallAsianstockswasnot0%.Wetakeasampleof36observationswithasamplemeanof1andapopulationstandarddeviationof4.Inthiscaseournullandalternativehypothesesare:

H :µ=0

H :µ≠0

Thestandarderrorofthesampleisunchangedat0.67:

σ σ

√n4

√360.67

Theteststatisticis:


standarderrorofthesamplestatistic1 00.67

1.5

Inatwo‐tailedtest,twocriticalvaluesexist,onepositiveandonenegative.Foratwo‐sided

testatthe5%levelofsignificance,wecalculatethez‐valuesthatcorrespondto . =0.025

levelofsignificance.Theseare+1.96and‐1.96.Therefore,werejectthenullhypothesisifwefindthattheteststatisticislessthan‐1.96orgreaterthan+1.96.Wefailtorejectthenullhypothesisif‐1.96≤teststatistic≤+1.96.Graphically,thiscanbeshownas:



Relationshipbetweenconfidenceintervalandhypothesistests

Theabovefigurealsoillustratestherelationshipbetweenconfidenceintervalsandhypothesistests.Aconfidenceintervalspecifiestherangeofvaluesthatmaycontainthehypothesizedvalueofthepopulationparameter.The5%levelofsignificanceinthehypothesistestscorrespondstoa95%confidenceinterval.Whenthehypothesizedvalueofthepopulationparameterisoutsidethecorrespondingconfidenceinterval,thenullhypothesisisrejected.Whenthehypothesizedvalueofthepopulationparameterisinsidethecorrespondingconfidenceinterval,thenullhypothesisisnotrejected.

Summary:One‐tailedtestversustwo‐tailedtests

One‐tailedtestsareusedtotestifthepopulationparameterisgreaterthanorlessthanahypothesizedvalue.Theycanbeeitherright‐tailedtestsorleft‐tailedtests.

Two‐tailedtestsareusedtotestifthepopulationparameterisnotequaltothehypothesizedvalue.Theyhavetworejectionpoints:onepositiveandonenegative,becausehereweareinterestedinbothtails.

p‐value

Thep‐valueisthesmallestlevelofsignificanceatwhichthenullhypothesiscanberejected.Itcanbeusedinthehypothesistestingframeworkasanalternativetousingrejectionpoints.

Ifthep‐valueislowerthanourspecifiedlevelofsignificance,werejectthenullhypothesis.

Ifthep‐valueisgreaterthanourspecifiedlevelofsignificance,wedonotrejectthenullhypothesis.

Forexample,ifthep‐valueofatestis4%,thenthehypothesiscanberejectedatthe5%levelofsignificance,butnotatthe1%levelofsignificance.

Relationshipbetweentest‐statisticandp‐value

Ahightest‐statisticimpliesalowp‐value.



Alowtest‐statisticimpliesahighp‐value.

TypeIandTypeIIerrors

Inreachingastatisticaldecision,wecanmaketwopossibleerrors: TypeIerror:Wemayrejectatruenullhypothesis. TypeIIerror:Wemayfailtorejectafalsenullhypothesis.

Thefollowingtableshowsthepossibleoutcomesofatest.

DecisionTruecondition

H0true H0falseDonotrejectH0 Correctdecision TypeIIerrorRejectH0(acceptHa) TypeIerror Correctdecision

Thesignificancelevel“α”istheprobabilityoftypeIerror.

Powerofatest

Thepowerofatestistheprobabilityofcorrectlyrejectingthenull(rejectingthenullwhenitisfalse).Itisexpressedas:

Powerofatest=1–P(TypeIIerror)

Statisticalresultv/seconomicallymeaningfulresult

Astatisticaldecisionsimplyconsistsofrejectingornotrejectingthenullhypothesis.Whereas,aneconomicdecisiontakesintoconsiderationalleconomicissuesrelevanttothedecision,suchastransactioncosts,risktolerance,andtheimpactontheexistingportfolio.Sometimesatestmayindicateastatisticallysignificantresultwhichmaynotbeeconomicallysignificant.

3.HypothesisTestsConcerningtheMean

3.1.TestsConcerningaSingleMean

Oneofthedecisionsweneedtomakeinhypothesistestingisdecidingwhichteststatisticandwhichcorrespondingprobabilitydistributiontouse.Weusethefollowingtabletomakethisdecision:



Normaldistribution




Inthehypothesistestswesawsofar,thepopulationvariancewasknownandoursamplesizewaslarge(n≥30),henceweusedthez‐statisticandz‐distributiontocomputethecriticalvalue.



However,ifwedonotknowthepopulationvarianceandwehaveasmallsamplesize,thenwehavetousethet‐statisticandt‐distributiontocomputethecriticalvalues.

ExampleFundAlphahasbeeninexistencefor20monthsandhasachievedameanmonthlyreturnof2%withasamplestandarddeviationof5%.Theexpectedmonthlyreturnforafundofthisnatureis1.60%.Assumingmonthlyreturnsarenormallydistributed,aretheactualresultsconsistentwithanunderlyingpopulationmeanmonthlyreturnof1.60%?

Solution:Thenullandalternativehypothesesforthisexamplewillbe:

H0:µ=1.60versusHa:µ≠1.60

teststatistic X μ

√

2 1.60

√

0.36

Usingthisformula,weseethatthevalueoftheteststatisticis0.36.

Thecriticalvaluesata0.05levelofsignificancecanbecalculatedfromthet‐distributiontable.Sincethisisatwo‐tailedtest,weshouldlookata0.05/2=0.025levelofsignificancewithdf=n‐1=20–1=19.Thisgivesustwovaluesof‐2.1and+2.1.

Sinceourteststatisticof0.35liesbetween‐2.1and+2.1,i.e.,theacceptanceregion,wedonotrejectthenullhypothesis.

3.2.TestsConcerningDifferencesbetweenMeans

Instructor’sNote:Focusonthebasicsofthistopic,theprobabilityofbeingtestedonthedetailsislow.

Inthissection,wewilllearnhowtocalculatethedifferencebetweenthemeansoftwoindependentandnormallydistributedpopulations.Wecanusetwokindsoft‐tests.Inonecasethepopulationvariances,althoughunknown,canbeassumedtobeequal.Inthesecondcasethepopulationvariancesareassumedtobeunknownandunequal.

UnknownButEqualVariance

Whenweassumethatthetwopopulationsarenormallydistributedandthattheunknownpopulationvariancesareequal,thet‐testbasedonindependentrandomsamplesisgivenby:

t X X μ μ

/

Theterm isknownasthepooledestimatorofthecommonvariance.Itiscalculatedbythefollowingformula:

s n 1 s n 1 s

n n 2



Thenumberofdegreesoffreedomisn1+n2–2.

UnknownandUnequalVariance

Whenwecanassumethatthetwopopulationsarenormallydistributedandthattheunknownpopulationvariancesareunequal,anapproximatet‐testbasedonindependentrandomsamplesisgivenby:

t X X μ μ

/

Inthisformula,weusethetablesofthet‐distributionusingthe‘modified’degreesoffreedom.The‘modified’degreesoffreedomarecalculatedusingthefollowingformula:

df

/ /

ExampleYoubelievethemeanreturnonNYSEstockswasdifferentfromthemeanonNSEstockslastmonth.Totestyourhypothesisyoucollectthefollowingdata: SampleSize(n) SampleMean(X) SampleStandardDeviationNSE 20 2% 4NYSE 40 3% 5Determinewhethertorejectthenullhypothesisatthe0.10levelofsignificance.

Solution:Thefirststepistoformulatethenullandalternativehypotheses.Sincewewanttotestwhetherthetwomeanswereequalordifferent,wedefinethehypothesesas:H0:µ1‐µ2=0Ha:µ1‐µ2≠0

Sincethepopulationstandarddeviationisunknownandwecannotassumethatitisequal,weusethefollowingformulatocalculatetheteststatistic:

t X X μ μ

/2 3 0

/0.84

Next,wecalculatethemodifieddegreesoffreedom:

df

/ /

/ / 48



Fora0.10levelofsignificance,wefindthet‐valuefor0.10/2=0.05usingdf=48.Thet‐valueisthereforeta/2=‐1.677and+1.677.Sinceourteststatisticof‐0.84liesintheacceptanceregion,wefailtorejectthenullhypothesis.

3.3.TestsconcerningMeanDifferences


Intheprevioussection,inordertoperformhypothesistestsondifferencesbetweenmeansoftwopopulations,weassumedthatthesampleswereindependent.Whatifthesamplesarenotindependent?Forexample,supposeyouwanttoconducttestsonthemeanmonthlyreturnonToyotastockandmeanmonthlyreturnonHondastock.Thesetwosamplesarebelievedtobedependent,astheyareimpactedbythesameeconomicfactors.

Insuchsituations,weconductat‐testthatisbasedondataarrangedinpairedobservations.Pairedobservationsareobservationsthataredependentbecausetheyhavesomethingincommon.

Wewillnowdiscusstheprocessforconductingsuchat‐test.SupposethatwegatherdataregardingthemeanmonthlyreturnsonstocksofToyotaandHondaforthelast20months,asshowninthetablebelow:

Month MeanreturnofToyotastock

MeanmonthlyreturnofHondastock

Differenceinmeanmonthlyreturns(di)

1 0.5% 0.4% 0.1%2 0.7% 1.0% ‐0.3%3 0.3% 0.7% ‐0.4%… … … …20 0.9% 0.6% 0.3%Average 0.750% 0.600% 0.075%

Hereisasimplifiedprocessforconductingthehypothesistest:

Step1:Definethenullandalternatehypotheses

Webelievethatthemeandifferenceisnot0.Hencethenullandalternatehypothesesare:

H :μ μ versusH :μ μ

µdstandsforthepopulationmeandifferenceandµd0standsforthehypothesizedvalueforthepopulationmeandifference.

Step2:Calculatethetest‐statistic

Determinethesamplemeandifferenceusing:

d 1n

d



Forthedatagiven,thesamplemeandifferenceis0.075%.

Calculatethesamplestandarddeviation.Theprocessforcalculatingthesamplestandarddeviationhasbeendiscussedinanearlierreading.Thesimplestmethodistoplugthenumbers(0.1,‐0.3,‐0.4…0.3)intoafinancialcalculator.Theentiredatasethasnotbeenprovided.We’lltakeitasagiventhatthesamplestandarddeviationis0.150%.

Usethisformulatocalculatethestandarderrorofthemeandifference:

s s

√n

Forourdatathisis0.150/√20=0.03354.

Wenowhavetherequireddatatocalculatetheteststatisticusingat‐test.Thisiscalculatedusingthefollowingformulausingn‐1degreesoffreedom:

t d μs

Forourdata,theteststatisticis . –

.2.24.

Step3:Determinethecriticalvaluebasedonthelevelofsignificance

Wewillusea5%levelofsignificance.Sincethisisatwo‐tailedtestwehaveaprobabilityof2.5%(0.025)ineachtail.Thiscriticalvalueisdeterminedfromat‐tableusingaone‐tailedprobabilityof0.025anddf=20–1=19.Thisvalueis2.093.

Step4:Comparetheteststatisticwiththecriticalvalueandmakeadecision

Inourcase,theteststatistic(2.23)isgreaterthanthecriticalvalue(2.093).Hencewewillrejectthenullhypothesis.

Conclusion:Thedataseemstoindicatethatthemeandifferenceisnot0.

Thehypothesistestpresentedaboveisbasedonthebeliefthatthepopulationmeandifferenceisnotequalto0.Ifμ isthehypothesizedvalueforthepopulationmeandifference,thenwecanformulatethefollowinghypotheses:

1. Ifwebelievethepopulationmeandifferenceisgreaterthan0:H :μ μ versusH :μ μ

2.Ifwebelievethepopulationmeandifferenceislessthan0:H :μ μ versusH :μ μ

3.Ifwebelievethepopulationmeandifferenceisnot0:H :μ μ versusH :μ μ

4.HypothesisTestsConcerningVariance




4.1.TestsConcerningaSingleVariance

Intestsconcerningthevarianceofasinglenormallydistributedpopulation,weusethechi‐squareteststatistic,denotedbyχ2.

Propertiesofthechi‐squaredistribution

Thechi‐squaredistributionisasymmetricalandlikethet‐distribution,isafamilyofdistributions.Thismeansthatadifferentdistributionexistsforeachpossiblevalueofdegreesoffreedom,n‐1.Sincethevarianceisasquaredterm,theminimumvaluecanonlybe0.Hence,thechi‐squaredistributionisboundedbelowby0.Thegraphbelowshowstheshapeofachi‐squaredistribution:

Therearethreehypothesesthatcanbeformulated(σ2representsthetruepopulationvarianceandσ02representsthehypothesizedvariance):

1. H :σ σ versusH :σ σ .Thisisusedwhenwebelievethepopulationvarianceisnotequalto0,oritisdifferentfromthehypothesizedvariance.Itisatwo‐tailedtest.

2. H :σ σ versusH :σ σ .Thisisusedwhenwebelievethepopulationvarianceislessthanthehypothesizedvariance.Itisaone‐tailedtest.

3. H :σ ≤σ versusH :σ >σ .Thisisusedwhenwebelievethepopulationvarianceisgreaterthanthehypothesizedvariance.Itisaone‐tailedtest.

Afterdrawingarandomsamplefromanormallydistributedpopulation,wecalculatetheteststatisticusingthefollowingformulausingn‐1degreesoffreedom:

χn 1 s

σ

where:n=samplesizes=samplevariance

Wethendeterminethecriticalvaluesusingthelevelofsignificanceanddegreesoffreedom.Thechi‐squaredistributiontableisusedtocalculatethecriticalvalue.

ExampleConsiderFundAlphawhichwediscussedinanearlierexample.Thisfundhasbeeninexistencefor20months.Duringthisperiodthestandarddeviationofmonthlyreturnswas



5%.Youwanttotestaclaimbythefundmanagerthatthestandarddeviationofmonthlyreturnsislessthan6%.

Solution:Thenullandalternatehypothesesare:H0:σ2≥36versusHa:σ2<36

Notethatthestandarddeviationis6%.Sincewearedealingwithpopulationvariance,wewillsquarethisnumbertoarriveatavarianceof36%.

Wethencalculatethevalueofthechi‐squareteststatistic:

2=(n‐1)s2/σ02=19x25/36=13.19

Next,wedeterminetherejectionpointbasedondf=19andsignificance=0.05.Usingthechi‐squaretable,wefindthatthisnumberis10.117.

Sincetheteststatistic(13.19)ishigherthantherejectionpoint(10.117)wecannotrejectH0.Inotherwords,thesamplestandarddeviationisnotsmallenoughtovalidatethefundmanager’sclaimthatpopulationstandarddeviationislessthan6%.

4.2.TestsConcerningtheEquality(Inequality)ofTwoVariances

Inordertotesttheequalityorinequalityoftwovariances,weuseanF‐testwhichistheratioofsamplevariances.

TheassumptionsforaF‐testtobevalidare: Thesamplesmustbeindependent. Thepopulationsfromwhichthesamplesaretakenarenormallydistributed.

PropertiesoftheF‐distribution

TheF‐distribution,likethechi‐squaredistribution,isafamilyofasymmetricaldistributionsboundedfrombelowby0.EachF‐distributionisdefinedbytwovaluesofdegreesoffreedom,calledthenumeratoranddenominatordegreesoffreedom.Asshowninthefigurebelow,theF‐distributionisskewedtotherightandistruncatedatzeroonthelefthandside.

Therejectionregionisalwaysintherightsidetailofthedistribution.

WhenworkingwithF‐tests,therearethreehypothesesthatcanbeformulated:



1. H :σ σ versusH :σ σ .Thisisusedwhenwebelievethetwopopulationvariancesarenotequal.

2. H :σ σ versusH :σ σ .Thisisusedwhenwebelievethevarianceofthefirstpopulationisgreaterthanthevarianceofthesecondpopulation.

3. H :σ σ versusH :σ σ .Thisisusedwhenwebelievethevarianceofthefirstpopulationislessthanthevarianceofthesecondpopulation.

Thetermσ12representsthepopulationvarianceofthefirstpopulationandσ22representsthepopulationvarianceofthesecondpopulation.

TheformulafortheteststatisticoftheF‐testis:

F ss

where:=thesamplevarianceofthefirstpopulationwithnobservations=thesamplevarianceofthesecondpopulationwithnobservations

Aconventionistoputthelargersamplevarianceinthenumeratorandthesmallersamplevarianceinthedenominator.

df1=n1–1numeratordegreesoffreedomdf2=n2–1denominatordegreesoffreedom

TheteststatisticisthencomparedwiththecriticalvaluesfoundusingthetwodegreesoffreedomandtheF‐tables.

Finally,adecisionismadewhethertorejectornottorejectthenullhypothesis.

ExampleYouareinvestigatingwhetherthepopulationvarianceoftheIndianequitymarketchangedafterthederegulationof1991.Youcollect120monthsofdatabeforeandafterderegulation.Varianceofreturnsbeforederegulationwas13.Varianceofreturnsafterderegulationwas18.Checkyourhypothesisataconfidencelevelof99%.

Solution:Nullandalternatehypothesis:H0:σ12=σ22versusHA:σ12≠σ22

F‐statistic: 1.4

df=119forthenumeratoranddenominator

α=0.01whichmeans0.005ineachtail.FromtheF‐table:criticalvalue=1.6

SincetheF‐statislessthanthecriticalvalue,donotrejectthenullhypothesis.

Summaryoftypesofteststatistics

Hypothesistestof UseOnepopulationmean t‐statisticorz‐statistic



Twopopulationmean t‐statisticOnepopulationvariance Chi‐squarestatisticTwo‐populationvariance F‐statistic

5.OtherIssues:NonparametricInference

Thehypothesis‐testingprocedureswehavediscussedsofarhavetwocharacteristicsincommon:

Theyareconcernedwithparameters,suchasthemeanandvariance. Theirvaliditydependsonasetofassumptions.

Anyprocedurewhichhaseitherofthetwocharacteristicsisknownasaparametrictest.

Nonparametrictestsarenotconcernedwithaparameterand/ormakefewassumptionsaboutthepopulationfromwhichthesamplearedrawn.Weusenonparametricproceduresinthreesituations:

Datadoesnotmeetdistributionalassumptions. Dataaregiveninranks.(Example:relativesizeofthecompanyanduseof

derivatives.) Thehypothesisdoesnotconcernaparameter.(Example:Isasamplerandomornot?)

TheSpearmanrankcorrelationcoefficienttestisapopularnonparametrictest.Thecoefficientiscalculatedbasedontheranksoftwovariableswithintheirrespectivesamples.



Summary

LO.a:Defineahypothesis,describethestepsofhypothesistesting,anddescribeandinterpretthechoiceofthenullandalternativehypotheses.

Ahypothesisisastatementaboutthevalueofapopulationparameterdevelopedforthepurposeoftestingatheory.

Inordertotestahypothesis,wefollowthesesteps:1. Statethehypothesis.2. Identifytheappropriateteststatistic.3. Specifythelevelofsignificance.4. Stateadecisionruletoacceptorrejectthehypothesis.5. Collectsampledataandcalculatetheteststatistic.6. Decideifthehypothesiscanbeaccepted/rejected.7. Makeaneconomicorinvestmentdecision.

Thenullhypothesis(H0)isthehypothesisthattheresearcherwantstoreject.Itshouldalwaysincludesomeformofthe‘equalto’condition.

Thealternativehypothesis(Ha)isthehypothesisthattheresearcherwantstoprove.Ifthenullhypothesisisrejectedthenthealternativehypothesisisconsideredvalid.

LO.b:Distinguishbetweenone‐tailedandtwo‐tailedtestsofhypotheses.

Inone‐tailedtests,weareassessingifthevalueofapopulationparameterisgreaterthanorlessthanahypothesizedvalue.

Intwo‐tailedtests,weareassessingifthevalueofapopulationparameterisdifferentfromahypothesizedvalue.

LO.c:Explainateststatistic,TypeIandTypeIIerrors,asignificancelevel,andhowsignificancelevelsareusedinhypothesistesting.

Ateststatisticisaquantity,calculatedonthebasisofasample,andisusedtodecidewhethertorejectornottorejectthenullhypothesis.Theformulaforcomputingtheteststatisticis:


standarderrorofthesamplestatistic

Inreachingastatisticaldecision,wecanmaketwopossibleerrors:Wemayrejectatruenullhypothesis(aTypeIerror),orwemayfailtorejectafalsenullhypothesis(aTypeIIerror).

ThelevelofsignificanceofatestistheprobabilityofaTypeIerror.

Asαgetssmallerthecriticalvaluegetslargeranditbecomesmoredifficulttorejectthenullhypothesis.



LO.d:Explainadecisionrule,thepowerofatest,andtherelationbetweenconfidenceintervalsandhypothesistests.

Adecisionruleconsistsofcomparingthecomputedteststatistictothecriticalvalues(rejectionpoints)basedonthelevelofsignificancetodecidewhethertorejectornottorejectthenullhypothesis.

Thepowerofatestistheprobabilityofcorrectlyrejectingthenull(rejectingthenullwhenitisfalse).Itisexpressedas:

Powerofatest=1–P(TypeIIerror)

Aconfidenceintervalgivesustherangeofvalueswithinwhichapopulationparameterisexpectedtolie.Confidenceintervalsandhypothesistestsarelinkedthroughcriticalvalues.Thenullhypothesiswillberejectedonlyiftheteststatisticliesoutsidetheconfidenceinterval.

LO.e:Distinguishbetweenastatisticalresultandaneconomicallymeaningfulresult.

Thestatisticaldecisionconsistsofrejectingornotrejectingthenullhypothesis.Theeconomicdecisiontakesintoconsiderationalleconomicissuesrelevanttothedecision.

LO.f:Explainandinterpretthep‐valueasitrelatestohypothesistesting.

Thep‐valueisthesmallestlevelofsignificanceatwhichthenullhypothesiscanberejected.Itcanbeusedinthehypothesistestingframeworkasanalternativetousingrejectionpoints.

Ifthep‐valueislowerthanourspecifiedlevelofsignificance,werejectthenullhypothesis.

Ifthep‐valueisgreaterthanourspecifiedlevelofsignificance,wedonotrejectthenullhypothesis.

LO.g:Identifytheappropriateteststatisticandinterprettheresultsforahypothesistestconcerningthepopulationmeanofbothlargeandsmallsampleswhenthepopulationisnormallyorapproximatelydistributedandthevarianceis1)knownor2)unknown.

Weusethefollowingtabletodecidewhichteststatisticandwhichcorrespondingprobabilitydistributiontouseforhypothesistesting.



Normaldistribution




LO.h:Identifytheappropriateteststatisticandinterprettheresultsforahypothesistestconcerningtheequalityofthepopulationmeansoftwoatleastapproximately



normallydistributedpopulations,basedonindependentrandomsampleswith1)equalor2)unequalassumedvariances.

Whenwecanassumethatthetwopopulationsarenormallydistributedandthattheunknownpopulationvariancesareequal,thet‐testbasedonindependentrandomsamplesisgivenby:

t X X μ μ

/

Thenumberofdegreesoffreedomisn1+n2–2.Theterm isknownasthepooledestimatorofthecommonvariance.Apooledestimateisanestimatedrawnfromthecombinationoftwodifferentsamples.Itiscalculatedas:

s n 1 s n 1 s

n n 2

Whenwecanassumethatthetwopopulationsarenormallydistributedandthattheunknownpopulationvariancesareunequal,anapproximatet‐testbasedonindependentrandomsamplesisgivenby:

t X X μ μ

/

Inthisformula,weusethetablesofthet‐distributionusingthe‘modified’degreesoffreedom.The‘modified’degreesoffreedomarecalculatedas:

df

/ /

LO.i:Identifytheappropriateteststatisticandinterprettheresultsforahypothesistestconcerningthemeandifferenceoftwonormallydistributedpopulations.

Incaseswherewehaveatestconcerningthemeandifferenceoftwonormallydistributedpopulationsthataredependent,weconductat‐testthatisbasedondataarrangedinpairedobservations.

Thehypothesisisformedonthedifferencebetweenmeansoftwopopulationse.g.H0:µd=µd0versusHa:µd≠µd0

Inordertoarriveattheteststatistic,wefirstdeterminethesamplemeandifferenceusing:

d 1n

d

Andthestandarderrorofthemeandifferenceiscomputedasfollows:



s s

√n

Oncewehavethesetwovalues,wecancalculatetheteststatisticusingat‐test.Thisiscalculatedusingthefollowingformulausingn‐1degreesoffreedom:

t d μs

Thevalueofcalculatedteststatisticiscomparedwiththet‐distributionvaluesintheusualmannertoarriveatadecisiononourhypothesis.

LO.j:Identifytheappropriateteststatisticandinterprettheresultsforahypothesistestconcerning1)thevarianceofanormallydistributedpopulation,and2)theequalityofthevariancesoftwonormallydistributedpopulationsbasedontwoindependentrandomsamples.

Intestsconcerningthevarianceofasinglenormallydistributedpopulation,weusethechi‐squareteststatistic,denotedbyχ2.Afterdrawingarandomsamplefromanormallydistributedpopulation,wecalculatetheteststatisticusingthefollowingformulausingn‐1degreesoffreedom:

χn 1 s

σ

Wethendeterminethecriticalvaluesusingthelevelofsignificanceanddegreesoffreedom.Thechi‐squaredistributiontableisusedtocalculatethecriticalvalue.

Inordertotesttheequalityorinequalityoftwovariances,weuseanF‐test.Thecriticalvalueiscomputedas:

F ss

TheteststatisticisthencomparedwiththecriticalvaluesfoundusingthetwodegreesoffreedomandtheF‐tables.Finally,adecisionismadewhethertorejectornottorejectthenullhypothesis.

LO.k:Distinguishbetweenparametricandnonparametrictestsanddescribesituationsinwhichtheuseofnonparametrictestsmaybeappropriate.

Aparametrictestisahypothesistestconcerningaparameterorahypothesistestbasedonspecificdistributionalassumptions.Incontrast,anonparametrictestiseithernotconcernedwithaparameterormakesminimalassumptionsaboutthepopulationfromwhichthesampleisdrawn.

Anonparametrictestisprimarilyusedinthreesituations:whendatadonotmeetdistributionalassumptions,whendataisgiveninranks,orwhenthehypothesisweareaddressingdoesnotconcernaparameter.



PracticeQuestions

1. DavidJonesisaresearcherandwantstotestifthemeanreturnsofhisbondinvestmentsismorethan5%peryear.Inthiscase,thenullandalternativehypothesiswouldbebestdefinedas:A. H0:µ=5versusHa:µ≠5.B. H0:µ≤5versusHa:µ>5.C. H0:µ≥5versusHa:µ<5.

2. Whichofthefollowingstatementsrequiresatwo‐tailedtest?

A. Ho:µ≤0versusHa:µ>0.B. Ho:µ≥0versusHa:µ<0.C. Ho:µ=0versusHa:µ≠0.

3. Allelsebeingequal,specifyingasmallersignificancelevelinahypothesistestwillmost

likelyincreasetheprobabilityof:A. typeIerror.B. typeIIerror.C. bothtypeIandtypeIIerrors.

4. Allelsebeingequal,increasingthesamplesizeforahypothesistestwillmostlikely

decreasetheprobabilityof:A. typeIerror.B. typeIIerror.C. bothtypeIandtypeIIerrors.

5. Ifthesignificancelevelofatestis0.05andtheprobabilityofaTypeIIerroris0.2.Whatis

thepowerofthetest?A. 0.05.B. 0.80.C. 0.95.

6. Aresearcherformulatesanullhypothesisthatthemeanofadistributionisequalto10.He

obtainsap‐valueof0.02.Usinga5%levelofsignificance,thebestconclusionisto:A. rejectthenullhypothesis.B. acceptthenullhypothesis.C. decreasethelevelofsignificance.

7. Which of the following statistic is most likely used for the mean of a non‐normal

distributionwithunknownvarianceandasmallsamplesize?A. z‐teststatistic.



B. t‐teststatistic.C. Thereisnoteststatisticforsuchascenario.

8. YoubelievethattheaveragereturnsofallstocksintheS&P500isgreaterthan10%.You

drawasampleof49stocks.Theaveragereturnofthese49stocksis12%.ThestandarddeviationofreturnsofallstocksintheS&P500is4.Usinga5%levelofsignificance,whichofthefollowingconclusionsismostappropriate?A. WecanconcludethattheaveragereturnsofallstocksintheS&P500isgreaterthan

10%.B. WecanconcludethattheaveragereturnsofallstocksintheS&P500islessthan10%.C. WecanconcludethattheaveragereturnsofallstocksintheS&P500isequalto10%.

9. Theappropriateteststatistictotestthehypothesisthatthevarianceofanormally

distributedpopulationisequalto8isthe:A. t‐test.B. F‐test.C. χ2test.



Solutions

1. Biscorrect.Thenullhypothesis iswhattheresearcherwantstoreject.Thealternativehypothesis is what the researcher wants to prove, and it is accepted when the nullhypothesisisrejected.

2. Ciscorrect.Atwo‐tailedtestforthepopulationmeanisstructuredas:Ho:µ=0versusHa:

µ≠0.

3. Biscorrect.SpecifyingasmallersignificanceleveldecreasestheprobabilityofaTypeIerror(rejectingatruenullhypothesis),butincreasestheprobabilityofaTypeIIerror(notrejectingafalsenullhypothesis).Asthelevelofsignificancedecreases,thenullhypothesisislessfrequentlyrejected.

4. Ciscorrect.Theonlywaytoavoidthetrade‐offbetweenthetwotypesoferrorsisto

increasethesamplesize;increasingsamplesize(allelsebeingequal)reducestheprobabilityofbothtypesoferrors.

5. Biscorrect.Thepowerofatest=1‐P(TypeIIerror).=1–0.2=0.86. Aiscorrect.Thep‐valueforahypothesisisthesmallestsignificancelevelforwhichthe

hypothesiswouldberejected.Asthep‐valueislessthanthestatedlevelofsignificance,werejectthenullhypothesis.

7. Ciscorrect.Thestatisticforasmallsamplesizeofanon‐normaldistributionwith

unknownvarianceisnotavailable.z‐teststatisticisusedforalargesamplesizeofanon‐normaldistributionwithknownvariancewhilet‐teststatisticisusedforlargesamplesizeofanon‐normaldistributionwithunknownvariance.

SamplingFrom SmallSampleSize

LargeSampleSize

NormalDistribution Varianceknown z z

Varianceunknown t t(orz)

Non–normalDistribution

Varianceknown NA z

Varianceunknown NA t(orz)

8. Aiscorrect.

Step1:StatethehypothesisH0:µ≤10%Ha:µ>10%



Step2:CalculatetheteststatisticThepopulationvarianceisknownhencewewillusez‐statistic.

z statisticX μ

√

12 10

√

3.5

Step3:CalculatethecriticalvalueThisisaone‐tailedtestandwewillbelookingattherighttail.UsingtheZ–tableand5%levelofsignificanceCriticalvalue=Z0.05=1.65Step4:Decision

Sincetheteststatistic(3.5)>criticalvalue(1.65),werejectH0.Henceat5%levelofsignificance,yourbeliefthattheaveragereturnsofallstocksintheS&P500isgreaterthan10%iscorrect.

9. Ciscorrect.Intestsconcerningthevarianceofasinglenormallydistributedpopulation,

weusethechi‐squareteststatistic,denotedbyχ2.TypesofTestStatistics

Hypothesistestof UseOnepopulationmean t‐statisticorz‐statisticTwopopulationmean t‐statisticOnepopulationvariance Chi‐squarestatisticTwo‐populationvariance F‐statistic

R13 Technical Analysis 2019 Level I Notes


R13TechnicalAnalysis

1.Introduction

Technicalanalysishaslongbeenusedbytradersandanalysts,buthasonlyrecentlyreceivedacceptancefromregulatorsandtheacademiccommunity.Althoughcertainaspectsoftechnicalanalysis,suchasthecalculationofindicators,havespecificrules,theinterpretationoffindingsisoftensubjective.

2.TechnicalAnalysis:DefinitionandScope

Technicalanalysisisaformofsecurityanalysisthatusespriceandvolumedataindecisionmaking.Thedataisoftengraphicallydisplayed.

Technicalanalysisisbasedonthefollowinglogic: Supplyanddemanddetermineprices. Changesinsupplyanddemandcancausechangesinprices. Pricescanbeprojectedwithchartsandothertechnicaltools.

Technicalanalysisofanyfinancialinstrumentdoesnotrequiredetailedknowledgeofthatinstrument.Investorsandtradersoftenprefertechnicalanalysisoverfundamentalanalysisintheshorttermbecausefundamentalanalysisismoretimeconsuming.

2.1.PrinciplesandAssumptions

Fundamentaltheoristsbelievethatmarketsarerationalandefficient.Ontheotherhand,techniciansbelievethathumanbehaviorisoftenerraticanddrivenbyemotion.Therefore,theybelievethatmarkettrendsandpatternsreflectthisirrationalhumanbehavior.Theyrelyonrecognitionofsuchtrendsandpatternsinthepasttoprojectfuturepatternsofsecurityprices.

Anotherprincipleoftechnicalanalysisisthatthemarketreflectsthecollectiveknowledgeandsentimentofmanyparticipantssuchasinvestors,hedgers,insiders,andotherstakeholders.Marketparticipants,whobuyandsellsecurities,haveanimpactonprice.Thegreaterthevolumeofaparticipant’strades,themoreimpacttheparticipantwillhaveonprice.

Bystudyingmarkettechnicaldata(priceandvolumetrends),techniciansseektounderstandinvestorsentiment.

Somefinancialinstrumentshaveanassociatedincomestreamthataddstothesecurity’sintrinsicvaluesuchascouponpaymentsforbondsanddividendsforequityshares.Afundamentalanalystcanusethesecashflowstoarriveatapresentvalueofthesecurity.However,forotherassetssuchascommodities,whichdonothaveunderlyingincomestreamsorfinancialstatements,technicalanalysisiscommonlyused.



2.2.TechnicalandFundamentalAnalysis

Technicalandfundamentalanalysesapproachthemarketindifferentways,butarebothuseful.Keydifferencesbetweenthetwoarelistedbelow:

Techniciansfocussolelyonanalyzingmarketsandthetradingoffinancialinstruments.Fundamentalanalysis,ontheotherhand,focusesonfinancialandeconomicanalysisaswellassocietalandpoliticaltrendsanalysis.

Technicalanalysisisbasedonpriceandvolumedata(i.e.tradingdata),whilefundamentalanalystsincorporateexternalmarketdata,withcompany’sfinancialstatements,topredictsecuritypricemovements.Itisimportanttonotethatthecompany’sfinancialstatementsareoftensubjective,whilepriceandvolumedataareobjective.

Fundamentalanalysisisconsideredamoretheoreticalapproach,whiletechnicalanalysisisconsideredamorepracticalapproach.

Drawbacksoftechnicalanalysisare: Techniciansarelimitedtostudyingmarketmovementsanddonotuseother

predictiveanalyticalmethods. Marketmovementsandtrendsmaytakesometimetobecomeevident.Therefore,

techniciansmaybelateinidentifyingchangesintrendsandpatterns. Inilliquidmarketsandmarketsthataresubjecttolargeoutsidemanipulation(such

asactionsofcentralbanks),theapplicationoftechnicalanalysisislimited.

3.TechnicalAnalysisTools

3.1.Charts

Thevarioustypesofchartsusedintechnicalanalysisare:

LinechartLinechartsareasimplegraphicdisplayofpricetrendsovertime.Usually,thechartisaplotofdatapoints,suchasshareprice,withalineconnectingthesepoints.Theverticalaxis(yaxis)representspricelevelandthehorizontalaxis(xaxis)istime.Anexampleofalinechartisshownbelow.Thelinechartshowsthatthepriceofthestockduringthefirstupwardmovementofthepriceishigherthanthesecondhigh.



Barchart

Alinecharthasonlyonedatapointpertimeinterval.Abarchart,incontrast,hasfourbitsofdataineachentry‐theopeningandclosingprices,andthehighandlowpricesduringtheperiod.

BarchartnotationThefigureontheleftshowshowthedatapointforeachintervalisconstructed.Averticallineconnectsthehighandlowpricefortheday.Across‐hatchtotherightindicatestheclosingprice,andacross‐hatchtotheleftindicatestheopeningprice.

Ashortbarindicateslittlepricemovementwhilealongbarindicatesawidedivergencebetweenthehighandthelowfortheday.Anexampleofabarchartisshowninthefigurebelow:



Candlestickchart

Acandlestickchartalsoprovidesfourpricesperdataentrypoint:theopeningandclosingprices,andthehighandlowpricesduringtheperiod.

Thebodyofthecandleiseitherwhiteorshaded.Awhitebodymeansthatthemarketclosedup.Ashadedbodymeansthatthemarketcloseddown.Anexampleofacandlestickchartisshownbelow:

Anadvantageofthecandlestickchartoverthebarchartisthatpricemovesaremuchmorevisible,whichallowsforfasteranalysis.

Pointandfigurechart

ApointandfigurechartisdrawnonagridandconsistsofcolumnsofX’salternatingwithcolumnsofO’s.XrepresentsanincreaseinpricewhileanOrepresentsadecreaseinprice.Neithertimenorvolumeisrepresentedonthischart.Instead,thefocusisonchangeinprices,whichisrepresentedonthehorizontalaxis.Anexampleofapointandfigurechartisgivenbelow.



Thefollowingstepsneedtobefollowedinordertoconstructapointandfigurechart: Theanalystmustfirstdeterminetheboxsize.Boxsizereferstothechangeinprice

representedbytheheightofeachbox. Next,theanalystmustdeterminethereversalsize.Iftherearenosignificantchangesin

thestockprice,theanalyststaysinthesamecolumn.Onlyifthereisasubstantialreversal,theanalystmovestoanothercolumn.

AtechnicianfillsinaboxwithXeverytimethesecurity'spriceclosesupbytheamountoftheboxsize.Ifthepriceincreasesbytwicetheboxsize,thetechnicianfillsintwoboxes,oneontopoftheother.Ifthepricedoesnotincreasebyatleasttheboxsize,noindicationismadeonthechart.

Forpricedecreases,atechnicianusesthereversalsizetodeterminewhentomakeanindicationonthechart.Ifourreversalsizeis3,theboxsizeis$1,andthereisapricedeclineof$3,thenthetechnicianwillshifttothenextcolumnandbeginacolumnofO’s.

Pointandfigurechartsareparticularlyusefulformakingtradingdecisionsbecausetheyclearlyillustratepricelevelsthatmaysignaltheendofadeclineoradvance.

ScaleTheverticalaxiscanbeconstructedwitheither:

Linear/Arithmeticscale:Suitablefornarrowerranges,forexample,pricesfrom$20to$35

Logarithmicscale:Suitableforrangeofvaluesrepresentingseveralordersofmagnitude,forexample,$10to$10,000.

Thehorizontalaxisusuallyshowsthepassageoftime.Theappropriatetimeintervaldependsonthenatureoftheunderlyingdata.Wecanhave5‐min,30‐min,1‐hour,daily,weeklyorevenmonthlycharts.

VolumechartsTheyareoftendisplayedbelowaline,barorcandlestickchart.ThenumberofunitsofthesecuritytradedisplottedontheY‐axisandtimeontheX‐axis.



Relativestrengthanalysis

Relativestrengthanalysisisusedtocomparetheperformanceofaparticularasset,suchasastock,withthatofsomebenchmarkindexortheperformanceofanotherstock.Typically,theanalystpreparesalinechartoftheratioofthetwoprices,withtheassetunderanalysisasthenumeratorandthebenchmarkorothersecurityasthedenominator.Arisinglineshowsthattheassetisperformingbetterthanthebenchmark;adeclininglineshowsthattheassetisunderperforming.Aflatlineshowsneutralperformance.

3.2.Trend

Trendanalysisisbasedontheobservationthatmarketparticipantstendtoactinherdsandthattrendstendtostayinplaceforsometime.

UptrendAsecurityissaidtobeinanuptrendifpricesarereachinghigherhighsandhigherlows.Anupwardtrendlinecanbedrawnbyconnectingtheincreasinglowpointswithastraightline.Anuptrendindicatesthatthedemandismorethansupply.

DowntrendAsecurityissaidtobeinadowntrendifpricesarereachinglowerhighsandlowerlows.Adownwardtrendlinecanbedrawnbyconnectingthedecreasinghighpointswithastraightline.Adowntrendindicatesthatthesupplyismorethandemand.

Support

Itisthepricelevelatwhichthereissufficientbuyingpressuretostopafurtherdeclineinprices.

Resistance

Itisthepricelevelatwhichthereissufficientsellingpressuretostopafurtherincreaseinprices.



Changeinpolarity

Onceasupportlevelisbreached,itoftenbecomesanewresistancelevel.Similarly,oncearesistancelevelisbreached;itoftenbecomesanewsupportlevel.

3.3.ChartPatterns

Chartpatternsareformationsthatcreatearecognizableshape;commonpatternsappearrepeatedlyandleadtosimilarsubsequentpricemovements.Chartpatternscanbedividedintotwocategories:reversalpatternsandcontinuationpatterns.

Reversalpatterns

Theysignaltheendofatrend.Thefourkindsofreversalpatternsare:

Headandshoulderspattern:

Itconsistsoftheleftshoulder,thehead,andtherightshoulder.Thispatternindicatestheendofanuptrend.Youcanprofitbygoingshortonthesecurity,thepricetargetis:

Pricetarget=neckline–(head–neckline)



Inverseheadandshoulderspattern:

Itisamirrorimageoftheheadandshoulderspattern.Thispatternindicatestheendofadowntrend.Youcanprofitbygoinglongonthesecurity,thepricetargetis:

Pricetarget=neckline+(head–neckline)

ExampleInaninvertedheadandshoulderspattern,ifthenecklineisat€125,theshouldersat€80,andtheheadat€95,thepricetargetisclosesttowhichofthefollowing?A. €155.B. €110.C. €95.

Solution:InvertedHeadandshoulderpattertargetprice=Neckline+(Neckline–Head)

TargetPrice=125+(125–95)

TargetPrice=155

Doubletopsandbottoms:

Adoubletopisformedwhenpriceshitthesameresistanceleveltwiceandfalldown.Itindicatestheendofanuptrend.

Adoublebottomisformedwhenpricesbouncebackfromthesamesupportleveltwice.Itindicatestheendofadown‐trend.



Tripletopsandbottoms:

Tripletopsareformedwhenpriceshitthesameresistancelevelthrice.

Triplebottomsareformedwhenpricesbouncebackfromthesamesupportlevelthrice.

Continuationpatterns

Theysignalatemporarypauseinthetrend,andthatthetrendwillcontinueinthesamedirectionasbefore.Thefourkindsofcontinuationpatternsare:

Triangles:

Onetrendlineconnectsthehighsandasecondtrendlineconnectsthelows.Asthedistancebetweenthehighsandlowsnarrows,thetrendlinesconverge,formingatriangle.Therearethreeforms‐ascendingtriangles,descendingtriangles,andsymmetrictriangles.



Rectangles:

Onetrendlineconnectsthehighsandasecondtrendlineconnectsthelows.Asthedistancebetweenthehighsandlowsisconstant,thetrendlinesareparalleltoeachotherandformarectangle.

Flags:

Theyaresimilartoarectangleandareformedbytwoparalleltrendlines.However,theyformoveramuchshortertimeinterval.

Pennants:

Theyaresimilartoatriangleandareformedbytwoconvergingtrendlines.However,theyformoveramuchshortertimeinterval.



3.4.TechnicalIndicators

Therearefourkindsoftechnicalindicatorsthatwewilldiscuss;price‐basedindicators,momentumoscillators,sentimentindicatorsandflow‐of‐fundsindicators.

Price‐basedindicators

Theyincorporatetheinformationcontainedinthecurrentandpastmarketprices.Thecommontypesare:

Movingaverage:

Itistheaverageoftheclosingpricesoveraspecifiednumberofperiods.Theyareusedtosmoothoutshort‐termpricefluctuationsandhelpidentifythetrend.Whenashort‐termmovingaveragecrossesfromunderneathalonger‐termaverage,thismovementisconsideredbullishandisknownasagoldencross.Whenashort‐termmovingaveragecrossesfromabovealonger‐termaverage,thismovementisconsideredbearishandisknownasadeadcross.

Bollingerbands:

Bollingerbandsconsistofamovingaverageplusahigherlinerepresentingasetnumberofstandarddeviationsandalowerlinerepresentingasetnumberofstandarddeviations.ThefigurebelowshowsaBollingerbandandamovingaverage.

Themorevolatilethesecuritybecomes,thewidertherangebecomesbetweenthetwoouterlinesorbands.AcommonuseofaBollingerbandistocreatetradingstrategiessuchasacontrarianstrategy.Inthisstrategy,aninvestorsellswhenasecurity'spricereachestheupperbandandbuyswhenitreachesthelowerband.Thecontrarianstrategyassumesthatthesecurity'spricewillstaywithinthebands.



Momentumoscillators

Theyhelptoidentifychangesinthemarketsentiment.Thecommontypesare:

Rateofchange(ROC)oscillator:

Itoscillatesaround0(oraround100ifanalternativeformulaisusedforcalculation).WhentheROCoscillatorcrosseszerointothepositiveterritory,itisconsideredbullish.WhentheROCoscillatorcrosseszerointothenegativeterritory,itisconsideredbearish.

Relativestrengthindex(RSI):

RSIgraphicallycomparesasecurity’sgainswithitslossesoveragivenperiod.Thepopulartimeperiodis14days.ThevalueoftheRSIisalwaysbetween0and100.Avalueabove70representsanoverboughtsituationwhileavaluebelow30suggeststhatanassetisoversold.

Stochasticoscillator:

Itisbasedontheobservationthatinuptrends,pricestendtocloseatornearthehighendoftheirrecentrange.Similarly,indowntrends,theytendtoclosenearthelowend.Itiscomposedoftwolines,called%Kand%Dthatarecalculatedasfollows:

%K 100C L14H14 L14

where:

C=latestclosingpriceL14=lowestpriceinpast14daysH14=highestpriceinpast14days%D=averageofthelastthree%Kvaluescalculateddaily

%Distheaverageofthree%Kvalues.Itisslowermovingandisalsocalledthesignalline.



Whenthe%Kmovesfrombelowthe%Dlinetoaboveit,thismoveisconsideredabullishsignal.Ontheotherhand,when%Kmovesfromabovethe%Dlinetobelowit,thispatternisconsideredbearish.

Thestochasticoscillatorhasadefaultsettingof14‐days.

Moving‐averageconvergence/divergenceoscillator:

Itisthedifferencebetweenashort‐termandalong‐termmovingaverageofthesecurity’sprice.Itiscomposedoftwolines‐MACDlineandsignalline.

MACDline:differencebetweentwoexponentiallysmoothedmovingaverages,usually12and26days.

Signalline:exponentiallysmoothedaverageofMACDline,usually9days.

Theindicatoroscillatesaround0andhasnoupperorlowerlimit.

MACDisusedintechnicalanalysisinthreeways. CrossoversoftheMACDlineandsignallinemayindicateachangeintrend. IftheMACDisoutsideitsnormalrangeforagivensecurity,thenthismayindicatea

reversal. IftheMACDistrendinginthesamedirectionasprice,thenthisindicatesa

convergencepattern.Ontheotherhand,whenthetwoaretrendinginoppositedirections,thenthisindicatesadivergencepattern.

Instructor’sNote:Themostknownuseofmomentumoscillatorsistoindicatetheoverboughtoroversoldpositionofasecurity.Thus,theyhelpinprovidingsignalforbuyingorsellingsecuritybutdonothelptosetthetargetprice.

Sentimentindicators

Theygaugeinvestoractivityforsignsofbullishnessorbearishness.Thecommontypesare:



Opinionpolls:

Regularpollsareconductedofinvestorsandinvestmentprofessionalstogaugetheoverallmarketsentiment.

Calculatedstatisticalindices: Theput/callratioisthevolumeofputoptionstraded, dividedbythevolumeofcall

optionstraded.Ahighratioindicatesthatthemarketisbearish.Whereas,alowratioindicatesthatthemarketisbullish.

TheCBOEvolatilityindex(VIX)isameasureofnear‐termmarketvolatilitycalculatedfromoptionpricesofS&P500stocks.TheVIXriseswhenmarketparticipantsbecomefearfulofamarketdecline.

Margindebtisloanstakenbyindividualinvestorstofundtheirstockpurchases.Whenstockmargindebtisincreasing,investorsareaggressivelybuyingandthestockpriceswillrisebecauseofincreaseddemand.

Shortinterestreferstothenumberofsharesofaparticularsecuritythatarecurrentlysoldshort.Theshortinterestratioiscalculatedas:

ShortinterestratioShortinterest

Averagedailytradingvolume

Ahighratiosuggestsanoverallnegativeoutlookonthesecurity.

Flow‐of‐fundsindicators

Theyindicatethechangeinpotentialdemandandsupply.Thecommontypesare:

TheArmsindex:(alsoknownasTRIN)

Itiscalculatedas:

Armsindexnumberofadvancingissues numberofdecliningissuesvolumeofadvancingissues volumeofdecliningissues

Whenthisindexisnear1,themarketisinbalance.Avalueabove1meansthatthereismorevolumeindecliningstocksandthatthemarketisinasellingmood.Avaluebelow1meansthatthereismorevolumeinincreasingstocksandthatthemarketisinabuyingmood.

Margindebt:

Marginloansmayincreasethepurchasesofstocksanddecliningmarginbalancesmayforcethesellingofstocks.

Mutualfundscashposition:

Mutualfundsmustholdsomeoftheirassetsincashtopayformiscellaneousexpensesandtofundredemptions.Duringabullishmarket,thecashpositionstendtobelow.Duringabearishmarket,thecashpositionstendtobehigh.



Newequityissuance:

IPOsareoftentimedwithbullishmarketstogetthebestvaluations.AlargenumberofIPOsmayindicatethatamarketisnearitspeak.

Secondaryofferings:

LikeIPOs,techniciansalsomonitorsecondaryofferingstogaugepotentialchangesinthesupplyofequities.

3.5.Cycles

Techniciansusevariouscyclestopredictfuturemovementsinsecurityprices;evencyclesinfieldssuchasastronomyandclimatecaninfluencetheeconomyandhencecapitalmarkets.Commonlyreferencedcyclesarediscussedbelow:

Kondratieffwave:Thisisthelongestofthewidelyrecognizedcycles,discoveredbyNikolaiKondratieffinthe1920s.HesuggestedthatWesterneconomieshavea54‐yearoldcycle.ThiscycleisalsoknownastheKWave.

18‐yearcycle:Three18‐yearcyclesmakeupthelonger54‐yearKondratieffWave.The18‐yearcycleisoftenmentionedinconnectionwithrealestateprices,butitcanalsobefoundinequitiesandothermarkets.

Decennialpattern:Thispatternconnectsaveragestockmarketreturnswiththelastdigitoftheyear.Yearsendingin0haveshownpoorperformancewhileyearsendingin5haveshowngoodperformance.

Presidentialcycle:ThiscycleintheUnitedStatesconnectstheperformanceofthemarketwithpresidentialelections.Inthistheory,thethirdyearfollowinganelectionshowsthebestperformance.

4.ElliotWaveTheory

Accordingtothistheory,themarketmovesinregularwavesorcycles.Inabullmarket,themarketmovesupinfivewaves1=up,2=down,3=up,4=down,and5=up.(Impulsephase)anddownwardmoveoccursinthreewaves1=down,2=up,3=down(Correctivephase).



Eachwavecanbebrokenintosmallerwavesoverashortertimeperiod.MarketwavesfollowpatternsthatareratiosofthenumbersintheFibonaccisequence.Hence,ratiosofthenumbersintheFibonaccisequencecanbeusedtosetpricetargetswhiletrading.

TheFibonaccisequencestartswiththenumbers0,1,1,andtheneachsubsequentnumberinthesequenceisthesumofthetwoprecedingnumbers:

0,1,1,2,3,5,8,13,21,34…

5.Inter‐marketAnalysis

Inter‐marketanalysisisbasedontheprinciplethatallmarketsareinterrelatedandinfluenceeachother.Here,technicianslookforinflectionpointsinonemarketasawarningsigntostartlookingforachangeinanotherrelatedmarket.Toidentifytheseinter‐marketrelationships,acommonlyusedtoolistherelativestrengthanalysis.Therelativestrengthanalysiscanalsobeusedtoidentifythestrongestperformingsecuritiesinasectorandtoidentifythesectorsoftheequitymarkettoinvestin.Lastly,observationsbasedoninter‐marketanalysiscanalsohelpinallocatingfundsacrosssecuritiesfromdifferentcountries.



Summary

LO.a:Explainprinciplesoftechnicalanalysis,itsapplications,anditsunderlyingassumptions.

Technicalanalysisisaformofsecurityanalysisthatinvolvesexaminationofpastpriceandvolumedatatopredictfuturebehaviorofthemarketorindividualsecurity.

Assumptions: Marketpricesaredeterminedbysupplyanddemand. Marketpricesreflectbothrationalandirrationalinvestorbehavior. Investorbehaviorisreflectedintrendsandpatternsthattendtorepeat. Priceandvolumeinformationcanbeusedtounderstandinvestorsentimentand

makeinvestmentdecisions.

Technicalanalysiscanalsobeusedonassetssuchascommodities,currencies,andfuturesthatdonothaveunderlyingincomestreamsorfinancialstatements.

LO.b:Describetheconstructionofdifferenttypesoftechnicalanalysischartsandinterpretthem.

Linecharts Graphicdisplayofpricesovertime. Ithasonlyonedatapointpertimeinterval–theclosingprice. PriceisplottedontheY‐axisandtimeontheX‐axis. Theclosingpricesforeachtradingperiodareconnectedbyaline.

Barcharts Ithasfourdatapointspertimeinterval–openingprice,highestandlowestprice,and

closingprice. PriceisplottedontheY‐axisandtimeontheX‐axis Theygiveabettersenseofthetrendinthemarket. Ashortbarindicateslowvolatility,alongbarindicateshighvolatility

Candlestickcharts Ithasthesamefourdatapointspertimeintervalasabarchart–openingprice,

highestandlowestprices,andclosingprice. PriceisplottedontheY‐axisandtimeontheX‐axis. Ifthemarketclosedup,thebodyofthecandleisclear. Ifthemarketcloseddown,thebodyofthecandleisshaded.

Volumecharts Oftendisplayedbelowaline,barorcandlestickchart. NumberofunitsofthesecuritytradedisplottedontheY‐axisandtimeontheX‐axis.

Pointandfigurecharts



DrawnasagridconsistingofcolumnsofX’salternatingwithcolumnsofO’s.XrepresentsanincreaseinpricewhileanOrepresentsadecreaseinprice.

Y‐axismeasuresboxsizeincrementsinprice,whereasX‐axismeasuresanumberofpricechanges.

Toconstructthischart,youneedtospecifyaboxsizeandareversalsize.

LO.c:Explainusesoftrend,support,resistancelines,andchangeinpolarity.

Uptrend:Asecurityissaidtobeinanuptrendifpricesarereachinghigherhighsandhigherlows.Anupwardtrendlinecanbedrawnbyconnectingtheincreasinglowpointswithastraightline.

Downtrend:Asecurityissaidtobeinadowntrendifpricesarereachinglowerhighsandlowerlows.Adownwardtrendlinecanbedrawnbyconnectingthedecreasinghighpointswithastraightline.

Support:Itisthepricelevelatwhichthereissufficientbuyingpressuretostopafurtherdeclineinprices.

Resistance:Itisthepricelevelatwhichthereissufficientsellingpressuretostopthefurtherincreaseinprices.

Changeinpolarity:Onceasupportlevelisbreached,itoftenbecomesanewresistancelevel.

Similarly,oncearesistancelevelisbreached;itoftenbecomesanewsupportlevel.

LO.d:Describecommonchartpatterns.

Reversalpatterns:Theysignaltheendofatrend.Thefourkindsofreversalpatternsare: Headandshoulderspattern Inverseheadandshoulderspattern Doubletopsandbottoms Tripletopsandbottoms

Continuationpatterns:Theysignalatemporarypauseinthetrend,andthatthetrendwillcontinueinthesamedirectionasbefore.Thefourkindsofcontinuationpatternsare:

Triangles Rectangles Flags Pennants

LO.e:Describecommontechnicalanalysisindicators(price‐based,momentumoscillators,sentiment,andflowoffunds).

Price‐basedindicators:Theyincorporatetheinformationcontainedinthecurrentandpastmarketprices.Thecommontypesare:

Movingaverage Bollingerbands



Momentumoscillators:Theyhelptoidentifychangesinthemarketsentiment.Thecommontypesare:

Rateofchange(ROC)oscillator Relativestrengthindex(RSI) Stochasticoscillator Moving‐averageconvergence/divergenceoscillator

Sentimentindicators:Theygaugeinvestoractivityforsignsofbullishnessorbearishness.Thecommontypesare:

Opinionpolls Calculatedstatisticalindices

o put/callratioo Volatilityindex(VIX)o Margindebto Shortinterest

Flow‐of‐fundsindicators:Theyindicatethechangeinpotentialdemandandsupply.Thecommontypesare:

TheArms Margindebt Mutualfundscashposition Newequityissuance Secondaryofferings

LO.f:Explainhowtechnicalanalystsusecycles.

Kondratieffwave(K‐Wave) ItstatesthatWesterneconomieshavea54‐yearoldcycle.

18‐yearcycle Three18‐yearcyclesmakeupthelonger54‐yearKondratieffwave. Thiscycleisoftenmentionedinrealestatemarkets,butitcanalsobefoundin

equitiesandothermarkets.

Decennialpattern Thispatternlinksaveragestockmarketreturnswiththelastdigitoftheyear. Yearsendingin0haveshownpoorperformance,whereasyearsendingin5have

showngoodperformance.

Presidentialcycle ThiscycleconnectstheperformanceoftheUSmarketwiththeUSpresidential

elections. Historically,thethirdyearfollowinganelectionhasshownthebestperformance.



LO.g:DescribethekeytenetsofElliottWaveTheoryandtheimportanceofFibonaccinumbers.

Accordingtothistheory,themarketmovesinregularwavesorcycles.Inabullmarket,themarketmovesupinfivewavesinthefollowingpattern:1=up,2=down,3=up,4=down,and5=up.Thiswaveisknownastheimpulsewave.Eachwavecanbebrokenintosmallerwavesoverashortertimeperiod.MarketwavesfollowpatternsthatareratiosofthenumbersintheFibonaccisequence.Hence,theratiosofthenumbersintheFibonaccisequencecanbeusedtosetpricetargetswhiletrading.

LO.h:Describeintermarketanalysisasitrelatestotechnicalanalysisandassetallocation.

Intermarketanalysisisbasedontheprinciplethatdifferentmarketssuchasstocks,bonds,commodities,currenciesetc.areinterrelatedandinfluenceeachother.Techniciansoftenuserelativestrengthanalysistolookfortheinflectionpointinonemarketasawarningsigntostartlookingforachangeinanotherrelatedmarket.Therelativestrengthanalysiscanalsobeusedtoidentifyattractiveassetclassesandattractivesectorswithintheseclassestoinvestin.



PracticeQuestions

1. Technicalanalysismostlikelyreliesupon:A. priceandvolumeinformation.B. fundamentalanalysistoconfirmconclusions.C. financialstatements.

2. Which of the following charts does not show the high and lowprices for each trading

period?A. Barchart.B. Pointandfigurechart.C. Candlestickchart.

3. Anupwardtrendlineisconstructedbydrawingalineconnectingthe:

A. thehighsofthepricechart.B. thelowsofthepricechart.C. thehighesthightothelowestlowofthepricechart.

4. Whichofthefollowingstatementsmostlikelyexplainstheprincipleof‘changein

polarity’?A. Onceadowntrendisbrokenitbecomesanuptrend.B. Theshort‐termmovingaveragehascrossedthelong‐termmovingaverage.C. Onceasupportlevelisbreached,itbecomesaresistancelevel.

5. Lucy,atechnicalanalyst,observesaheadandshoulderspatterninastockshehasbeen

following.Shenotesthefollowinginformation:

HeadPrice $46.50ShoulderPrice $41.50NecklinePrice $38.25

Herestimatedpricetargetisclosestto:A. $21.00.B. $25.50.C. $30.00.

6. Whichofthefollowingwouldatechnicalanalystmostlikelyinterpretasasellsignal?

A. 100‐daymovingaveragecrossesbelowa50‐daymovingaverage.B. 50‐daymovingaveragecrossesbelowa200‐daymovingaverage.C. 30‐daymovingaveragecrossesabovea100‐daymovingaverage.

7. MomentumOscillatorsaremostlikelyusedto:

A. indicateanoverboughtoroversoldposition.



B. setthetargetprice.C. analyzethemovementofpriceofsecuritywithrespecttoeconomicchanges.

8. Avalueof1.2intheshort‐termtradingindex(TRIN)mostlikelyindicatesthat:

A. tradingvolumeisheavierindecliningissuesthaninadvancingissues.B. tradingvolumeisheavierinadvancingissuesthanindecliningissues.C. marketisoversold.

9. Kondratieffconcludedthatwesterneconomiesgenerallyfollowedacycleofhowmany

years?A. 44years.B. 54years.C. 64years.

10. InElliotWavetheory,Fibonaccinumbersareusedtoforecastthe:

A. sizeofthewaves.B. numberofsubwaveswithinalargerwave.C. timingofthewavedirectionchange.

11. Whichofthefollowingisamostcommonlyusedtoolforintermarketanalysis?

A. Relativestrengthanalysis.B. Stochasticoscillators.C. Momentumoscillators.



Solutions1. Aiscorrect.Technicalanalysisisthestudyofmarkettrendsorpatternsandreliesupon

priceandvolumedata.2. Biscorrect.Apointandfigurechartisbasicallyusedtomapthechangeindirectionof

shareprices.Onlytheopeningandclosingpriceisincorporatedintopointandfigurechart.Aboxisfilledwitheither“x”signor“o”signdependsondirectionofpricechange.Thischartdoesnotincorporatethehighandlowprices.

3. Biscorrect.Anupwardtrendlineisconstructedbydrawingalineconnectingthelowsof

thepricechart.4. Ciscorrect.5. Ciscorrect.Pricetarget=Neckline−(Head−Neckline)=38.25–(46.50–38.25)=30.006. Biscorrect.Whenusingmovingaveragestogeneratetradingsignals,a"goldencross"of

ashorter‐termaverageabovealonger‐termaverageisabuysignal,whilea"deadcross"underthelonger‐termaverageisasellsignal.

7. Aiscorrect.ThemostknownuseofMomentumOscillatorsistoindicatetheoverbought

oroversoldpositionofasecurity.Thus,ithelpsinprovidingthesignalforbuyingorsellingsecurity,butitdoesnothelptosetthetargetprice.Economicconditions,neitheraffecttechnicalanalysisnoraretheyusedintechnicalanalysis.

8. A is correct.TheTRINorArms index isa flowof funds indicator.Values less thanone

indicatemoretradingvolumeinadvancingstocksthanindecliningstocks,whilevaluesgreaterthanonemeanmorevolumeisindecliningstocksthaninadvancingstocks.

TRINNumberofadvancingissues/NumberofdecliningissuesVolumeofadvancingissues/Volumeofdecliningissues

9. B is correct. Kondratieff wave is a cycle of 54 years. This is the longest and a widely

recognizedcycle.10. Aiscorrect.InElliotWavetheory,thesizeofthewavesisbelievedtocorrespondtothe

ratioofFibonaccinumbers.

11. Aiscorrect.Relativestrengthanalysisisoftenusedtocomparetwoassetclassesortwosecurities.

2019 Level I Notes


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