digging into taxes

7/29/2019 Digging into Taxes

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DIGGING INTO TAXATION RISKDavid S. Stackpole

LetstakeatripdowntheAmazonRiver.Someofthedangerswemightfacearemalaria,wild

predators,andwhoknows,maybeevenabatchofhostilenatives.Butwhatifweknewwithout

adoubtthatwewouldarrivebacktocivilizationunharmed? Ourspecialknowledgewould

remove

the

danger

from

all

those

threats

and

hence

their

risk.

Risk,

then,

is

a

measure

of

the

likelihoodthatsomethingadversewillaffectusandlikelihoodimpliesadegreeof

uncertainty.

JustaswemighttakeonriskintheAmazonfromuncertaintiesoutsideourcontrol,wetakeon

financialriskwithuncertaintiesthatjeopardizeourmoney.Ifwechoosetogodowntheriver(versusbeingforcedtogodownit)wetakeontheaddedriskofmakingawrongchoiceand

incurringanopportunitycost.

Varianceintaxrates,justlikevarianceinourinvestments'returns,invitesuncertaintyandboth

haveacriticaleffectonhowmuchmoneywewindupwith.Taxriskisoftenunderstood,but

notquantified.

I'd

like

to

suggest

away

to

measure

tax

risk

so

we,

as

investors,

can

make

better

decisionsonthetypesofaccountswecontributeto. Ifyouarefamiliarwithstandarddeviation

andtheSharperatio,feelfreetoskiptothebottomofthearticletovisithowIapplytheSharpe

totaxation,otherwisekeepreading!

RISKANDSTANDARDDEVIATION(APRIMER)Letssayyouhaveabosswhohasbipolardisorder.WellcallhimBossA. Whenheswalking

onsunshine,itsagreatday!Heshowershisemployeeswithhilariousjokes,andspontaneous

freelunches!Whenhesdepressed,itsprettybad.Withdrawnandcynical,hespillsouthis

personalwoes,getsmoodyanddemandsyouworklate.Onthesebaddays,youfindyourself

hiding

in

the

shadows

of

large

office

furniture

to

avoid

him.

Now

theres

also

Boss

B.

Aside

fromafewmildexceptions,hesnottoospontaneousorfunny,buthesnotadownereither.

Everydayisprettymuchliketheothers,nobigsurprises.

WhatifyoucouldmeasuretheemotioninbossesAandBandprettywellpredictwhateach

woulddoaccordingtohoweachfeltthatday?Forexample,youmeasureBossAbyassigning1

9tohisbehavior:a5whenhesnormal,1onhisworstdays,anda9whenheshappiest.

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With over 6 million members, Morningstar is often cited in major financial publications including Forbes and The Wall

Street Journal. Its star rating system is used my Goldman Sachs, Franklin Templeton and other investment firms as a

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2

NowyouvelearnedfromexperiencethatonBossAsbestdaystheresarealgoodchancehell

takeeveryonetolunchandgivethemtheafternoonoff.Onhismostdepresseddaystheresa

realgoodchanceeveryoneneedstoworklate.Afterseeingthispatternoverandover,youcan

predictbylatemorningwhetheryouregettingafreelunch,willhavetoworklate,orneither.

Youapply

asimilar

scale

to

Boss

B.

On

Boss

Bs

best

and

worst

days,

you

never

expect

anything

asextremeasafreelunchorworkinglate.Hisbestandworstdaysareasmidgennorthand

southofanaverageday,sothespreadofnumbersyouassignarenotaswide.Yougivehima3

foraworstday,a5foranaverageday,anda7forhisbest.

TheresanadvantageboringBossBhasoverA.BossBsbehaviorfromonedaytothenext

doesntvarymuch,sohesprettypredictable.Whatthatmeansisyoucanplanaheadwith

someconfidence youcanaffordtorunfiveminuteslate,becauseyoudontneedtocrouchin

theshadowsonceyouarrive.Yourealsoprettysureyoullmakeyoursonseveningband

recitalbecauseyouneverendupworkinglate.

FinancialinvestmentsworklikeBossesAandBorsomewherebetween.Stocksarealittlelike

BossA.Theycanhavereallyhighswings(andgreaterunpredictability)thanotherinvestments,

soontheirbestdays,youfeelthegreatbenefitofthoseswings,likeafreelunch.Ontheir

worstdays,youreallyfeelthecost,likehavingtoworklate.Thedifferenceofcourse,isthat

investmentseithermakeorloseyoumoney.Bondsvaryaswell,butingeneral,theyremore

likeBossB;mostofthetimewecanexpectmodestswingsandmorepredictability.

Rememberthatmeasuringsystemweusedforourtwobosses,statisticsusessomethinglikeit

calledstandarddeviation.Abiggerstandarddeviationindicateswiderswingsandthatmeans

greaterunpredictability,signalinggreaterpossiblerisk.Stocks,forexample,generallyhavea

higherstandarddeviationthanbonds.

Inourquesttomeasuretheriskinchangingtaxrates,wewanttokeepinmindstandard

deviation,becausewearegoingtoapplyawellknownmeasuretotheriskthatstocks,bonds,

orfundstakeon,butapplyittotaxchanges. ThismeasureiscalledtheSharpeRatioand

standarddeviationisthedenominatorofthatratio.


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3

THESHARPERATIOInfinancialmarkets,fundsthattakeonriskattempttocompensateforitbypayingahigher

return.TheSharperatioisonemeasureofwhetherthereturnyoureceivejustifiestheriskyou

takeon.Theratiodivideshistoricalriskintohistoricalreturn(Avg.returnriskfreerate/

standarddeviation). TheSharpeisarelativeratiosoyouwanttobesureyouaremeasuring

appleswith

apples,

for

example

two

funds

composed

of

large,

blue

chip

stocks

like

Coke

and

Pepsibetween2001and2010.

TheSharpehasitslimitations,butthehighertheratiothebetter;becauseitsuggeststhatthe

riskyouretakingislowcomparedtothereturnyoureexpecting.Forexample,considerthat

overtenyearsfundAhasannualaveragereturnsof10%andastandarddeviationof8%and

fundBhasthesameannualaveragereturnsof10%butalowerstandarddeviationof5%.Fund

A.10/.08=1.25;FundB.10/.05=2.Accordingly,fundBhasagreaterreturntorisk

relationship,atleastastheSharperatiomeasuresit.JustlikebossBwhoisprettyaverageeven

onhishighandlowdays,whenstandarddeviationdoesntswingtoohighortoolowfromits

mean(oraverage)wehaveasmallerdivisor,like.05insteadof.08andthissuggestslowerrisk.

TheSharperatioalsosubtractsariskfreeratefromafundstotalreturn.Theriskfreerate,the

returnoftentiedto3monthtbills,iswhatafundsreturnshouldbeatifitistakingonrisk.

Sincetbillsareriskfree,ourriskierfundshouldatleastbeatthem.Dontyouagree?For

simplicityandsincethisisacomparativeexercise,Iveleftthisriskfreerateoutofourexample.

APPLYINGTHESHARPERATIOTOTAXATIONRISKTaxratechangesinviteuncertaintybecauseofunforeseenvolatilityjustlikethechangesin

returnsofstocksandbondsinviteuncertainty.Likechoosingamongdifferentstockswith

risk/returnrelationships,wehavechoicesamonghowtheaccountsholdingourinvestments

aretaxed.Generallytheseaccountseitheraretaxable,taxdeferred,andtaxfree.Thevariancewithintaxbrackets,capitalgainstaxesanddividendratesoverthelifeofan

investorsportfolioshedslightonaccountrelatedrisksasaffectedbytaxation.Justliketherisk

ofastock,bond,orfundismeasuredbythedistanceofhighandlowswingsinitsreturnsfrom

itsaveragereturn,thehighertheswingawayfromtheaveragetaxrate,themoreriskyoutake

on.Likeaninvestmentsreturns,taxratehikesvaryandarententirelypredictable.

Ifwemodifiedourriskandreturnstoshowtaxesonourportfolio,wecouldusetheSharpe

ratiotoseethetaxaffectsacrossourtaxfree,taxdeferred,andtaxableaccounts,providinga

new,quantifiable

perspective

on

the

risk

of

changes

in

taxation.

We

will

apply

the

Sharpe

ratio

tohypotheticalportfoliosinwhichtaxbracketschangewitheachportfoliotorepresent

varianceintaxationovertime.Wewillthencomparethebeforetaxratiototheaftertaxratio

toquantifytaxationsriskinouraccounts.First,wemustfindthenumerator,orthereturnto

ourtaxadjustedSharperatio.


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4

Toapplytaxadjustedriskandreturntoouraccounts,wecanbeginbythinkingoftaxable,tax

deferred,andtaxfreeaccountsastypicalfundswithvaryingreturnsandrisksmeasurableby

theSharpe.Forexample,sayamutualfundhasareturnof10%. Wecantreatourtaxfreeand

taxdeferredaccountsjustlikethismutualfund.Ifmytaxfreeaccounthadareturnof10%like

fundA,thenIwilluse10% theriskfreerateasthenumeratorinmySharpeRatio.Iused

ExcelsRAND

function

to

generate

anumber

of

hypothetical

portfolios.

However,

ifwe

applied

theSharpetoarealportfoliowecoulddeterminetheexcessreturnfromourportfolio,similar

toanyfundinsidethatportfolio(RR0,whereRistheaveragereturnoftheportfolioandR0is

itsriskfreereturnfrommoneymarketandtreasuries). Forexample,sayouraverageannual

returnonouraccountsportfoliofrom1972to2011was12%and3%ofthereturncamerisk

freefrommoneymarketandtreasuriesinthatportfolio;wewouldarriveat12% 3%=9%

excessreturn.

Adjustingtheaverageretirementincomeforacollegeeducatedretireefrom1972to2011

yieldsthetaxbracketsbelow.In2011,sucharetireeroughlyhasaretirementincomeof

$45,000. Thetablediscountsincomeeachyearby3.1%toaccountforinflationtoarriveatthat

yearsaverageretirementtaxbracket.Themean(average)taxratefrom19722011turnsout

tobe18%usingthismethod.

ESTIMATEDRETIREMENTTAXBRACKETS(40YEARS)YearandBracket2011(0.15)2010(0.15)2009(0.15)2008(0.15)2007(0.15)2006(0.15)2005(0.15)2004(0.15)

2003(0.15)2002(0.15)2001(0.15)2000(0.15)1999(0.15)1998(0.15)1997(0.15)1996(0.15)

1995(0.15)1994(0.15)1993(0.15)1992(0.15)1991(0.15)1990(0.28)1989(0.15)1988(0.15)

1987(0.15)1986(0.18)1985(0.18)1984(0.18)1983(0.19)1982(0.22)1981(0.24)1980(0.14)

1979(0.24)

1978

(0.25)

1977

(0.25)

1976

(0.25)

1975

(0.25)

1974

(0.25)

1973

(0.25)

1972

(0.25)

Nowthatwehavetheaveragetaxbracketof18%,wecanbegintofindthetaxadjustedSharpe

ratio. Asmentioned,standarddeviationisadistancefromtheaverage.Ifweownatax

deferredaccount,likeanIRAor401kandourmeantaxrateis18%,thenwe'llkeep1.00 0.18,

or82%ofourportfoliosreturnsaftertaxes.Tofindthetaxadjustedstandarddeviationinour

accountsportfolio,wewilladjustourreturnstoreflecttheeffectsoftaxationcomparedtothe

mean.Wewilladjustupwardourreturnwhenthetaxrateisbelowourmeanof18%,sincea

lowerthanaveragetaxrateallowsustokeepmoreofourmoneyasthoughourreturnswere

higher;addzeroadditionalreturnwhentherateis18%,sinceitistheaverage,andadjustour

returndownwardwhenthetaxrateisgreaterthan18%,sinceahigherthanaveragetaxrate

willtakemoremoneyfromourportfolioasthoughourreturnswerelower. Belowarethree

examplestobetterexplainthis.


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5

1.WEARETAXEDAT18%

Annualreturnonmyaccountsportfolio=9%.

Taxrateshaveameanof18%,whichisalsotheratewearetaxedat.

Wekeep(aftertaxes)1 0.18or82%ofourportfoliosreturns.

Ourtaxadjustedreturnis82%of9%,or7.3%

The

change

from

the

mean

of

82%

in

terms

of

extra

return

from

taxes

saved

is

0%,

since

the

meanis82%

2.WEARETAXEDAT15%

Annualreturnonourportfolio=9%.

Taxrateshaveameanof18%.

Wekeep(aftertaxes)1 0.15or85%ofourportfoliosreturns.


Ourchangefromthemeanof82%intermsofextrareturnfromtaxessavedis3.7%or

(.85/0.82)1.

3.WEARETAXEDAT22%

Annualreturnonourportfolio=9%.

Taxrateshaveameanof18%.

Wekeep(aftertaxes)1 0.22or78%ofourreturns.


Thechangefromthemeanof82%intermsofextrareturnfromtaxessavedis

4.9%or(0.78/0.82)1.

Wearriveatthefollowingexpression:

RpRpf + (1-Tp / 1-T)-1

UsingtheRANDBETWEENfunctioninExcelandthetaxtablethatIcreatedabove,youcan

generateyourownhypotheticalportfoliosbetween1972and2011(orfeweryears)toseethe

taxadjustedeffectsonyourreturnsforeachyear. Youcanthenusethetaxadjustedreturnsto

arriveatanaveragereturnforreturns. FinallyyoucanuseExcelsSTDEVfunctiontogetthe

standarddeviationforthosetaxadjusted,annualreturnsandarriveatataxreflectiveSharpe

ratio.Comparethisratiotoratiosderivedfromotheraccountswithdifferenttaxeffectsand

youget

an

inkling

of

how

much

extra

risk

you

take

on

due

to

taxes.


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CONCLUSIONWhenconsideringtaxationforretirementweoftenconsidertwooptions;ataxfreeortax

deferredaccount.TheSharperatioonataxfreeaccountlikeaRothIRA,isthesameasabefore

taxSharperatio,becausetheuncertainty,orstandarddeviationduetochangingtaxbracketsis

zero.Iran300simulationscomparingthebeforetaxSharpetothetaxadjustedSharpe.The

taxadjusted

Sharpe

was

on

average

14

percentage

points

lower

and

as

much

as

34

percentage

pointslowerthanthebeforetaxSharpe,duetotheriskofvolatilityinretirementtaxrates.

DoesthatmeanyoutakeonlessriskwhenyouinvestinaRothversusatraditionalIRA?Yes,as

farastheSharpeseesit.Butthereareotherfactorstoconsider.Forexample,asyourincome

increases,somayyourtaxbracketandwithittheamountyournextRothcontributionistaxed.

Thus,eventhoughthemoneyyouvealreadyinvestedinataxfreeaccountsufferszerofuture

volatilityfromtaxes,themoneyyouplantoinveststillmay.Thegreatthingisyouhave

foreseeablecontroloverwhereyouputyourmoneywhenyoureceivethatnextpromotion

accordingtohowitaffectsyourtaxbracket.Why,becauseyoucanownbothtypesofaccounts,

taxfreeandtaxdeferred.YoudonthavetosettleformerelyerraticBossAorBoringbossB.

Youcanhavealittleofeach.Multipleretirementaccountscanhelptohedgeagainsttheriskof

wrongchoice,oropportunitycost,givingyougreatercontrolonhowyoumanagetheriskof

taxationsoyoucangrowyouraccountsmoreefficiently.

Thisinformationisnotintendedtobeasubstituteforspecificindividualizedtaxadvice.Wesuggestthatyoudiscussyourspecifictaxissueswithaqualifiedtaxadvisor.

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