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6-1Copyright©2001byHarcourt,Inc.Allrightsreserved.CHAPTER6RiskandRatesofReturn◼Stand-alonerisk◼Portfoliorisk◼Risk&return:CAPM/SML6-2Copyright

©2001byHarcourt,Inc.Allrightsreserved.Whatisinvestmentrisk?Investmentriskpertainstotheprobabilityofactuallyear

ningalowornegativereturn.Thegreaterthechanceoflowornegativereturns,theriskiertheinvestment.6-3Copyright©2001byHarcourt,Inc.Allrightsreserved.Prob

abilitydistributionExpectedRateofReturnRateofreturn(%)100150-70FirmXFirmY6-4Copyright©2001byHarcourt,Inc.Allrightsreserved.AnnualTotalReturns,1926-19

98AverageStandardReturnDeviationDistributionSmall-companystocks17.4%33.8%Large-companystocks13.220.3Long-termcorporateb

onds6.18.6Long-termgovernment5.79.2Intermediate-termgovernment5.55.7U.S.Treasurybills3.83.2Inflation3.24.5017.4%013.2%06.1%05.7%05.5%03.8%03.2%

6-5Copyright©2001byHarcourt,Inc.Allrightsreserved.InvestmentAlternatives(Givenintheproblem)EconomyProb.T-BillHTCollUSRMPRecessio

n0.18.0%-22.0%28.0%10.0%-13.0%Belowavg.0.28.0-2.014.7-10.01.0Average0.48.020.00.07.015.0Aboveavg.0.28.035.0-10.045.

029.0Boom0.18.050.0-20.030.043.01.06-6Copyright©2001byHarcourt,Inc.Allrightsreserved.WhyistheT-billreturnindependentoftheeconomy?Willreturnthep

romised8%regardlessoftheeconomy.6-7Copyright©2001byHarcourt,Inc.Allrightsreserved.DoT-billspromiseacompletelyrisk-freeretur

n?No,T-billsarestillexposedtotheriskofinflation.However,notmuchunexpectedinflationislikelytooccuroverarelativelyshortperiod.6-8Copyright©2001byHar

court,Inc.Allrightsreserved.DothereturnsofHTandColl.movewithorcountertotheeconomy?◼HT:Moveswiththeeconomy,andhasapositi

vecorrelation.Thisistypical.◼Coll:Iscountercyclicaloftheeconomy,andhasanegativecorrelation.Thisisunusual.6-9Copyright©2001byHa

rcourt,Inc.Allrightsreserved.Calculatetheexpectedrateofreturnoneachalternative:.Pk=kˆn1=iiik=expectedrateofreturn.kHT=(-22%

)0.1+(-2%)0.20+(20%)0.40+(35%)0.20+(50%)0.1=17.4%.^^6-10Copyright©2001byHarcourt,Inc.Allrightsreserved.kHT17.4%Mark

et15.0USR13.8T-bill8.0Coll.1.7HTappearstobethebest,butisitreally?^6-11Copyright©2001byHarcourt,Inc.Allrightsreserved.What’sthestandarddeviationofretu

rnsforeachalternative?=Standarddeviation.===Variance2.P)kˆk(n1ii2i=−6-12Copyright©2001byHarcourt,Inc.Allrightsreserved.T-bil

ls=0.0%.HT=20.0%.Coll=13.4%.USR=18.8%.M=15.3%.1/2T-bills=.P)kˆk(n1ii2i=−=(8.0–8.0)20.1+(8.0–8.0)20.2+(

8.0–8.0)20.4+(8.0–8.0)20.2+(8.0–8.0)20.16-13Copyright©2001byHarcourt,Inc.Allrightsreserved.Prob.RateofRet

urn(%)T-billUSRHT0813.817.46-14Copyright©2001byHarcourt,Inc.Allrightsreserved.◼Standarddeviation(i)measurestotal,orstand-alone,risk.◼Thelarg

erthei,thelowertheprobabilitythatactualreturnswillbeclosetotheexpectedreturn.6-15Copyright©2001byHarcourt,Inc.Allrightsreserved.ExpectedReturnsvs

.RiskSecurityExpectedreturnRisk,HT17.4%20.0%Market15.015.3USR13.8*18.8*T-bills8.00.0Coll.1.7*13.4**Seemsmisplaced.6-16C

opyright©2001byHarcourt,Inc.Allrightsreserved.CoefficientofVariation(CV)Standardizedmeasureofdispersionabout

theexpectedvalue:Showsriskperunitofreturn.CV==.Stddev^kMean6-17Copyright©2001byHarcourt,Inc.Allrightsreserved.0ABA=B,butAisriskierbecauselargerp

robabilityoflosses.=CVA>CVB.^k6-18Copyright©2001byHarcourt,Inc.Allrightsreserved.PortfolioRiskandReturnAssumea

two-stockportfoliowith$50,000inHTand$50,000inCollections.Calculatekpandp.^6-19Copyright©2001byHarcourt,Inc.Allrightsreserved.Portfoli

oReturn,kpkpisaweightedaverage:kp=0.5(17.4%)+0.5(1.7%)=9.6%.kpisbetweenkHTandkCOLL.^^^^^^^^kp=Swiki.ni=16-20Copy

right©2001byHarcourt,Inc.Allrightsreserved.AlternativeMethodkp=(3.0%)0.10+(6.4%)0.20+(10.0%)0.40+(12.5%)0.20+(15.0%)0.10=9.6%.^EstimatedReturn

EconomyProb.HTColl.Port.Recession0.10-22.0%28.0%3.0%Belowavg.0.20-2.014.76.4Average0.4020.00.010.0Aboveavg.0.2035.0-10.012.5Boom0.1050.0-2

0.015.06-21Copyright©2001byHarcourt,Inc.Allrightsreserved.CVp==0.34.3.3%9.6%p==3.3%.12/(3.0–9.6)20.

10+(6.4–9.6)20.20+(10.0–9.6)20.40+(12.5–9.6)20.20+(15.0–9.6)20.106-22Copyright©2001byHarcourt,Inc.Allrightsreserved.◼p=3.3%ismuchlowerthanthatofe

itherstock(20%and13.4%).◼p=3.3%islowerthanaverageofHTandColl=16.7%.◼\Portfolioprovidesaveragekbutlowerr

isk.◼Reason:negativecorrelation.^6-23Copyright©2001byHarcourt,Inc.Allrightsreserved.Generalstatementsaboutrisk◼Moststoc

ksarepositivelycorrelated.rk,m0.65.◼35%foranaveragestock.◼Combiningstocksgenerallylowersrisk.6-24Copyright©2001b

yHarcourt,Inc.Allrightsreserved.ReturnsDistributionforTwoPerfectlyNegativelyCorrelatedStocks(r=-1.0)andforPortfolioWM25150-10-10-1000

15152525StockWStockMPortfolioWM...............6-25Copyright©2001byHarcourt,Inc.Allrightsreserved.ReturnsDistributionsforTwoPerfectlyPosit

ivelyCorrelatedStocks(r=+1.0)andforPortfolioMM’StockM01525-10StockM’01525-10PortfolioMM’01525-106-26Copyright©2001byHarcourt,Inc.Allr

ightsreserved.Whatwouldhappentotheriskinessofanaverage1-stockportfolioasmorerandomlyselectedstockswereadded?◼pwoulddecreasebecausetheaddedstocks

wouldnotbeperfectlycorrelatedbutkpwouldremainrelativelyconstant.^6-27Copyright©2001byHarcourt,Inc.Allrightsreserved.Large015Prob.

21EvenwithlargeN,p20%6-28Copyright©2001byHarcourt,Inc.Allrightsreserved.#StocksinPortfolio102030402,000+CompanySpecificRiskMarke

tRisk200Stand-AloneRisk,pp(%)356-29Copyright©2001byHarcourt,Inc.Allrightsreserved.◼Asmorestocksaread

ded,eachnewstockhasasmallerrisk-reducingimpact.◼pfallsveryslowlyafterabout10stocksareincluded,andafter40stocks,thereislittle,ifa

ny,effect.Thelowerlimitforpisabout20%=M.6-30Copyright©2001byHarcourt,Inc.Allrightsreserved.Stand-aloneMarketFirm-specificMarketriskisthatpartofa

security’sstand-aloneriskthatcannotbeeliminatedbydiversification,andismeasuredbybeta.Firm-specificriskisthatpartofasecurity

’sstand-aloneriskthatcanbeeliminatedbyproperdiversification.riskriskrisk=+6-31Copyright©2001byHarcourt,Inc.Allright

sreserved.◼Byformingportfolios,wecaneliminateabouthalftheriskinessofindividualstocks(35%vs.20%).6-32Copyright

©2001byHarcourt,Inc.Allrightsreserved.Ifyouchosetoholdaone-stockportfolioandthusareexposedtomoreriskthand

iversifiedinvestors,wouldyoubecompensatedforalltheriskyoubear?6-33Copyright©2001byHarcourt,Inc.Allrightsreserved.◼NO!◼Stand-aloneriskasmeasured

byastock’sorCVisnotimportanttoawell-diversifiedinvestor.◼Rational,riskaverseinvestorsareconcernedwithp,whichisbasedonmarketrisk.6-34Copyr

ight©2001byHarcourt,Inc.Allrightsreserved.◼Therecanonlybeoneprice,hencemarketreturn,foragivensecurity.Therefore,nocompensationcanbeearnedforthea

dditionalriskofaone-stockportfolio.6-35Copyright©2001byHarcourt,Inc.Allrightsreserved.◼Betameasuresastock’smarketrisk.Itshowsastock’s

volatilityrelativetothemarket.◼Betashowshowriskyastockisifthestockisheldinawell-diversifiedportfolio.6-36Copyright©2001byHarcourt,Inc.Al

lrightsreserved.Howarebetascalculated?◼RunaregressionofpastreturnsonStockiversusreturnsonthemarket.Returns=D/P+g.◼T

heslopeoftheregressionlineisdefinedasthebetacoefficient.6-37Copyright©2001byHarcourt,Inc.Allrightsreserved.YearkMki115%18%2-5-1

031216...ki_kM_-5051015202015105-5-10Illustrationofbetacalculation:Regressionline:ki=-2.59+1.44kM^^6-38Copyright©2001byHarco

urt,Inc.Allrightsreserved.◼Ifbeta=1.0,averagestock.◼Ifbeta>1.0,stockriskierthanaverage.◼Ifbeta<1.0,stocklessriskyt

hanaverage.◼Moststockshavebetasintherangeof0.5to1.5.6-39Copyright©2001byHarcourt,Inc.Allrightsreserved.ListofBetaCoefficientsStockBetaMerrill

Lynch2.00AmericaOnline1.70GeneralElectric1.20MicrosoftCorp.1.10Coca-Cola1.05IBM1.05Procter&Gamble0.85Heinz0.80EnergenCorp.0.80EmpireDistrictElect

ric0.456-40Copyright©2001byHarcourt,Inc.Allrightsreserved.Canabetabenegative?Answer:Yes,ifri,misnega

tive.Thenina“betagraph”theregressionlinewillslopedownward.Though,anegativebetaishighlyunlikely.6-41Copyright©2001byHarcourt,Inc.Allrightsreserve

d.HTT-Billsb=0ki_kM_-20020404020-20b=1.29Coll.b=-0.866-42Copyright©2001byHarcourt,Inc.Allrightsreserved.Riskiersecuritieshavehigher

returns,sotherankorderisOK.HT17.4%1.29Market15.01.00USR13.80.68T-bills8.00.00Coll.1.7-0.86ExpectedRiskSecurityReturn(Beta)6-43Copyright©2001by

Harcourt,Inc.Allrightsreserved.UsetheSMLtocalculatetherequiredreturns.◼AssumekRF=8%.◼NotethatkM=kMis15%.(Equ

il.)◼RPM=kM–kRF=15%–8%=7%.SML:ki=kRF+(kM–kRF)bi.^6-44Copyright©2001byHarcourt,Inc.Allrightsreserved.RequiredRatesofReturnkHT=8.0%+(15.0%–8.

0%)(1.29)=8.0%+(7%)(1.29)=8.0%+9.0%=17.0%.kM=8.0%+(7%)(1.00)=15.0%.kUSR=8.0%+(7%)(0.68)=12.8%.kT-bill=8.0%+(7%)(0.00)=8

.0%.kColl=8.0%+(7%)(-0.86)=2.0%.6-45Copyright©2001byHarcourt,Inc.Allrightsreserved.HT17.4%17.0%Undervalued:k>kMarket15.015.

0FairlyvaluedUSR13.812.8Undervalued:k>kT-bills8.08.0FairlyvaluedColl.1.72.0Overvalued:k<kExpectedvs.RequiredReturns^^^^kk6-46Copyright©2001byHarcourt

,Inc.Allrightsreserved...Coll..HTT-bills.USRSMLkM=15kRF=8-1012.SML:ki=8%+(15%–8%)bi.ki(%)Risk,bi6-47Copyright©2001byHarco

urt,Inc.Allrightsreserved.Calculatebetaforaportfoliowith50%HTand50%Collectionsbp=Weightedaverage=0.5(bHT)+0.5(b

Coll)=0.5(1.29)+0.5(-0.86)=0.22.6-48Copyright©2001byHarcourt,Inc.Allrightsreserved.TherequiredreturnontheHT/Coll.portfoliois:kp=Weightedaveragek=0.5

(17%)+0.5(2%)=9.5%.OruseSML:kp=kRF+(kM–kRF)bp=8.0%+(15.0%–8.0%)(0.22)=8.0%+7%(0.22)=9.5%.6-49Copyright©2001by

Harcourt,Inc.Allrightsreserved.Ifinvestorsraiseinflationexpectationsby3%,whatwouldhappentotheSML?6-50Copyright©2001byHarcourt,Inc.Allr

ightsreserved.SML1OriginalsituationRequiredRateofReturnk(%)SML200.51.01.5Risk,bi1815118NewSMLDI=3%6-51Copyright©2001byHarcourt,Inc.A

llrightsreserved.Ifinflationdidnotchangebutriskaversionincreasedenoughtocausethemarketriskpremiumtoincreaseby3percentagepoints,whatwouldhappentoth

eSML?6-52Copyright©2001byHarcourt,Inc.Allrightsreserved.kM=18%kM=15%SML1OriginalsituationRequiredRateofReturn(%)

SML2AfterincreaseinriskaversionRisk,bi181581.0DRPM=3%6-53Copyright©2001byHarcourt,Inc.Allrightsreserved.HastheCAPMbeenverifiedthroughempiricaltests?

◼Notcompletely.Thosestatisticaltestshaveproblemsthatmakeverificationalmostimpossible.6-54Copyright©2001byHarcourt,Inc.Allrightsres

erved.◼Investorsseemtobeconcernedwithbothmarketriskandtotalrisk.Therefore,theSMLmaynotproduceacorrectestimateofki:ki=kRF+(kM–kRF)b+?6-55Copyrigh

t©2001byHarcourt,Inc.Allrightsreserved.◼Also,CAPM/SMLconceptsarebasedonexpectations,yetbetasarecalcula

tedusinghistoricaldata.Acompany’shistoricaldatamaynotreflectinvestors’expectationsaboutfutureriskiness.