32GLOBAL CEO n n January2003 CEO Toolkit n nA CEOs guide to value atrisk modelsRavi Madapati*SincethepastdecadeorsonoothertoolinfinancialriskmanagementhasbeenheardaboutasmuchasValueatRisk(VaR)modeling.VaRhasrapidlybecometheindustrystandardformeasuringandreportingmarketriskintrading portfolios of banks and other trading institutions.VaRprovidesanupperboundonthepotentiallossdue to adverse market fluctuations. Any VaR numberhastospecifywhichportfolioisbeingconsidered(e.g., Equity derivatives book), the confidence level(e.g., 97.5%) and the holding period (e.g., 10 days).VaRobjectivelytriestocombinethesensitivityofthe portfolio to market changes and the probability ofa given market change.VaR has been adopted by the Basel Committee to setthe standard for the minimum amount of capital to beheldagainstthemarketrisks.VaRcanbeusedtoestimate risk in the case of various financial instrumentsincluding bonds, equities and derivatives.VaR can beused to communicate risk and to control risk by settinglimits for frontline traders and operating managers.ProsandconsofusingVaRmodelsTherearemanyadvantagesofusingVaRmodels.When calculated at the corporate level, it summarizesthe overall risk across all the banks trading activitiesintoasinglenumberforseniormanagement.Therefore,itisaveryeffectivemeansofcommunicating risk exposures to senior management.Value at Risk (VaR) models are being used extensively in the world of risk management. VaR providesanupperboundonthepotentiallossduetoadversemarketfluctuations.VaRcanbeusedtoestimate risk in the case of various financial instruments including bonds, equities and derivatives.ICFAI Press. All Rights Reserved.SinceVaRisdenominatedincurrencyunitsandislinked to a confidence-level measure of loss, it providesa consistent and comparable measure of risk acrossall instruments, products and business lines.But VaR does have some limitations.VaR rests onmodeledvolatilitiesandco-movementsofriskfactors. It offers little guidance in exploring abnormaleventsoutsidetherealmofnormalstatisticalprobability. This limitation may be overcome by usingstress testing as a complimentary tool. A stress testexaminestheimplicationswhentheabnormal,unexpected worst-case scenario does materialize.CalculatingVaR1The three popular methods of calculating VaR are: Parametric VaR Monte Carlo VaR Historical VaR.ParametricVaRParametricVaRassumesanormalprobabilitydistribution.Thechangesintheinstrumentvaluesare assumed to be linear with respect to the changesinriskfactors.ThebroadapproachincaseofParametric VaR is as follows. The primary advantageofParametricVaRisthatitisfastandcomputationally simple to calculate. This facilitatesthecalculationofVaRonportfolioswithmanydifferent assets and risk factors. But Parametric VaRassumes that asset returns are linearly related to risk* Ravi Madapati is a Faculty at ICFAI Knowledge Center.His area of interest is Financial Econometrics and he can be reached atravi_m@icfai.org.1 This section draws from the analysis of The Fundamentals of Risk Measurement By Chris Morrison, 2002, McGraw Hill.33GLOBAL CEO n n January 2003CEO Toolkit n nfactorreturnsandthattheriskfactorreturnsareassumed to be normally distributed. Thus it ignoresnon-linearpricesensitivities.Sothismethodmaymisestimate potential future portfolio volatility.MonteCarloVaRMonte Carlo VaR removes the assumption that assetsare linearly dependent on price. It simulates normallydistributed future scenarios using historical variancesin risk factor returns and uses them to reevaluate theportfolio. It estimates VaR by randomly creating manyscenariosforfuturerates,usingnonlinearpricingmodelstoestimatethechangeinvalueforeachscenarioandthencalculatingVaRaccordingtotheworstcasescenario.The biggest advantage of thismethodisthatitcapturesnon-linearitiesandcangenerate an infinite number of scenarios. It is generallythe slowest form of VaR to calculate, taking 1000 timeslonger than parametric VaR. The method also assumesthat risk factor returns are normally distributed.portfolio is valued using full, non-linear pricing models.Thethird-worstdayisthenselectedasbeingthe99%VaR.Thebiggestlimitationofthismethodisthat historical trends may not hold in the future.The advantages and disadvantages of each form ofVaR are summarized in Exhibit 1:Picture 1Monte Carlo simulation generates numerous randommarket scenarios using predetermined parametersfor price volatility and correlation and calculates theP&L for each scenarioPositionExposureMarketScenarioVolatility ()Correlation ()SensitivityBased P&LORFull Re-valuation P&LP&LDistribution ofPortfolio= VARHistoricalVaRInHistoricalVaR,actualdailyfluctuationsinriskfactors are used to simulate their impact on the valuationof a portfolio of assets. So it captures a better estimateof the actual distribution of risk factor returns.Historical VaR is the most easy to understand, as it issimplerinapproachthanothermethodsmentionedabove.But it takes more time to run than parametricVaR.Historical VaR is the only method that removestheassumptionofnormallydistributedriskfactorreturns. This method typically takes the market dataforthelast250daysandcalculatesthepercentchange for each value to present 250 scenarios fortomorrowsvalues.Foreachofthescenarios,theHistoric simulation calculates the P&L for each daybased on observed changes in priceSource: Capital Market Risk advisors Ltd.Picture 2Calculation of Historic VARPositionExposureTime SeriesHistorical PriceChangesSensitivityBased P&LFull Re-valuation P&LORP&LDistribution ofPortfolio= VARMonteParametric Carlo HistoricalVaR VaR VaRCaptures non-normality of riskfactor returnsCaptures non-linearity of pricesensitivitiesLittle timerequired tocomputeLack ofdependenceon historicalobservationsExhibit 1Source: Risk analytics.SelectingthemethodThe choice of the method to calculateVaR dependsonseveralfactors.Dealersandenduserswithcomplexportfoliossetagoalofimplementingaconsistent, firmwide VaR that reflects their outlookpreferences and the complexity of the portfolio. Forportfolios with options the historic VaR and simulationVaRproducesuperiorresultscomparedtotheVariance/CovarianceVaR.However,thesystems,Source:Capital Market Risk advisors Ltd.34GLOBAL CEO n n January2003 CEO Toolkit n nLTCM: Lack of stress testing creates market mayhemIn1994,JohnMeriwether,thefamedSalomonBrothersbondtrader,foundedahedgefundcalledlong-termcapitalmanagement.Meriwetherassembledanall-starteamoftradersandacademicsinanattempttocreateafundthatwouldprofitfromthecombinationoftheacademicsquantitativemodelsandthetradersmarketjudgmentandexecutioncapabilities.Sophisticatedinvestors,includingmanylargeinvestmentbanks,flockedtothefund,investing$1.3bnatinception.Butfouryearslater,attheendofSeptember1998,thefundhadlostsubstantialamountsoftheinvestorsequitycapitalandwasteeteringonthebrinkofdefault.Toavoidthethreatofasystemiccrisisintheworldfinancialsystem,theFederalReserveorchestrateda$3.5bnrescuepackagefromleadingUSinvestmentandcommercialbanks.Inexchangetheparticipantsreceived90%ofLTCMsequity.LTCMsmainstrategywastomakeconvergencetrades.Thesetradesinvolvedfindingsecuritiesthatweremispricedrelativetooneanother,takinglongpositionsinthecheaponesandshortpositionsintherichones.Therewerefourmaintypesoftrade: ConvergenceamongUS,JapanandEuropeansovereignbonds; ConvergenceamongEuropeansovereignbonds; Convergencebetweenon-the-runandoff-the-runUSgovernmentbonds;and Longpositionsinemergingmarketssovereigns,hedgedbacktodollars.AccordingtothecomplexmathematicalmodelsusedbyLTCM,thepositionsrepresentedlowrisk.ThekeyassumptionmadebyLTCMwasthathighcorrelationexistedbetweenthelongandshortpositions.Certainly,historicaltrendssuggestedthatcorrelationsbetweencorporatebondsofdifferentcreditqualitywouldmovetogether(acorrelationofbetween90-95%overa2-yearhorizon).DuringLTCMscrisis,however,thiscorrelationdroppedto80%.Stress-testingagainstthislowercorrelationmighthaveledLTCMtoassumelessleverageintakingthisbet.However,ifLTCMhadusedstresstestingitwouldhavebeenmuchbetteroff.Thecorrelationhaddroppedto75%in1992(Jorion,1999).SimplyincludingthisstressscenariointheriskmanagementofthefundmighthaveledLTCMtoassumelessleverageintakingthisbet.Theultimatecause:FlighttoliquidityLTCMalsounderestimatedtheimportanceofliquidity,whilebeingobsessedwithmarketrisks.TheultimatecauseoftheLTCMdebaclewastheflighttoliquidityacrosstheglobalfixedincomemarkets.AsRussiastroublesbecamedeeperanddeeper,fixed-incomeportfoliomanagersbegantoshifttheirassetstomoreliquidassets.Inparticular,manyinvestorsshiftedtheirinvestmentsintotheUStreasurymarket.Infact,sogreatwasthepanicthatinvestorsmovedmoneyintothemostliquidpartoftheUStreasurymarketthemostrecentlyissued,oron-the-runtreasuries.WhiletheUStreasurymarketisrelativelyliquidinnormalmarketconditions,thisglobalflighttoliquidityhittheon-the-runtreasurieshard.Thespreadbetweentheyieldsonon-the-runtreasuriesandoff-the-runtreasurieswideneddramatically:Eventhoughtheoff-the-runbondsweretheoreticallycheaprelativetotheon-the-runbonds,theygotmuchcheaperstill(onarelativebasis).WhatLTCMhadfailedtoaccountforisthatasubstantialportionofitsbalancesheetwasexposedtoageneralchangeinthepriceofliquidity.Ifliquiditybecamemorevaluable(asitdidfollowingthecrisis)itsshortpositionswouldincreaseinpricerelativetoitslongpositions.Thiswasessentiallyamassive,unhedgedexposuretoasingleriskfactor.ThissituationwasaggravatedbythefactthatthesizeofthenewissuanceofUStreasurybondshasdeclinedoverthepastseveralyears.Thishaseffectivelyreducedtheliquidityofthetreasurymarket,makingitmorelikelythataflighttoliquiditycoulddislocatethismarket.Source:www.erisk.com.35GLOBAL CEO n n January 2003CEO Toolkit n nmodel,data,personal,educationalandtimerequirements of the historic and simulation VaRs oftenresult in the use of Variance/ Covariance or multipleVaR methodologies on an interim basis.The choicebetween historic and simulation VaR largely dependson the outlook preferences of users and the desire to MethodAdvantagesDisadvantagesSource:Capital Market Risk advisors Ltd.Variance/CovarianceHistoricSimulationMonte CarloSimulation Easy to understand Leastcomputationallyintensive Widely used in industry Easiest to implement Doesnotfullycapturenon-linear risks Assumesnormallydistributedreturns and constant volatilities Does not capture Fat Tails Easy to understand Cancapturenon-linearrisks Actual distribution Incorporates Fat Tails Can be data intensive Assumespastisafairrepresentation of the present Ac c o mmo d a t e s avarietyofstatisticalmodels and assumptions Cancapturenon-linearrisks, Can apply multiple timeperiods. Does not capture Fat Tails Computationally intensive Less transparent/more difficultto understandReference # 15-03-01-04Table 1 : The advantage and disadvantages of all the modelsKey issues in VaR modelingIssuesthatshouldbeaddressedinVaRmodelingare: Robustness:Howaccuratelytheriskisforecastedbythemodel. Riskvolatility:Riskforecastsfluctuateconsiderablyfromoneperiodtothenext;thisismeasuredbythevolatilityofriskforecasts. Measuring horizon:Regulatorsrequirethatriskbeforecastwithatleastoneyearofdataandusuallynomorethanoneyear. Holding period:Regulationsrequirethatriskbeforecastedovera10-dayholdingperiod. Non-linear dependence:Correlationstypicallyunderestimatethejointriskoftwoormoreassets.perform sensitivity analysis.Historical VaR is basedon actual, past market experience whereas simulationVaR is based on the users outlook and expectations.The important dimensions influencing the method tobe selected are: The length of the time horizon. Correlation assumptions. The mathematical model. Percentage of outcomes to be considered. Other risk-management tools being combined withVaR.ConclusionThough in a few cases such as Barings and OrangeCounty, VaR models have been blamed for creatingdistress situations, they cannot be faulted completely.Itshouldbeunderstoodthatanymodelpointsatpossibilities but it is the judgment of the user that ismoreimportantintakingacall.VaRmodelsareappliedwidelytodifferentformsofsecuritiesandare used extensively.A better understanding of themwill help make better decisions.n