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6-1Copyright©2001byHarcourt,Inc.Allrightsreserved.CHAPTER6RiskandRatesofReturn◼Stand-alonerisk◼Portfoliorisk◼Risk&return:CAPM/SML6-2Copyright©20

01byHarcourt,Inc.Allrightsreserved.Whatisinvestmentrisk?Investmentriskpertainstotheprobabilityofactu

allyearningalowornegativereturn.Thegreaterthechanceoflowornegativereturns,theriskiertheinvestment.6-3Copyright©2001byHarcourt,Inc

.Allrightsreserved.ProbabilitydistributionExpectedRateofReturnRateofreturn(%)100150-70FirmXFirmY6-4Copyright©2001byHarcourt,Inc.Allrights

reserved.AnnualTotalReturns,1926-1998AverageStandardReturnDeviationDistributionSmall-companystocks17

.4%33.8%Large-companystocks13.220.3Long-termcorporatebonds6.18.6Long-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.Allrightsr

eserved.InvestmentAlternatives(Givenintheproblem)EconomyProb.T-BillHTCollUSRMPRecession0.18.0%-22.0%28.0%10.0

%-13.0%Belowavg.0.28.0-2.014.7-10.01.0Average0.48.020.00.07.015.0Aboveavg.0.28.035.0-10.045.029.0Boom0.18.050.0-20.030.043.01.06-6Copy

right©2001byHarcourt,Inc.Allrightsreserved.WhyistheT-billreturnindependentoftheeconomy?Willreturnthepromised8%regardlessofthee

conomy.6-7Copyright©2001byHarcourt,Inc.Allrightsreserved.DoT-billspromiseacompletelyrisk-freereturn?No,T-billsarestillexposedtotheriskofinfla

tion.However,notmuchunexpectedinflationislikelytooccuroverarelativelyshortperiod.6-8Copyright©2001byHarcourt,Inc.Allrightsreserved.Do

thereturnsofHTandColl.movewithorcountertotheeconomy?◼HT:Moveswiththeeconomy,andhasapositivecorrelation.Th

isistypical.◼Coll:Iscountercyclicaloftheeconomy,andhasanegativecorrelation.Thisisunusual.6-9Copyright

©2001byHarcourt,Inc.Allrightsreserved.Calculatetheexpectedrateofreturnoneachalternative:.Pk=kˆn1=iiik=expectedrateo

freturn.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%Market1

5.0USR13.8T-bill8.0Coll.1.7HTappearstobethebest,butisitreally?^6-11Copyright©2001byHarcourt,Inc.Allrightsreserved.What’sthestandarddeviationof

returnsforeachalternative?=Standarddeviation.===Variance2.P)kˆk(n1ii2i=−6-12Copyright©2001byHarcourt,Inc.Allrightsrese

rved.T-bills=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.RateofReturn(%)T-bill

USRHT0813.817.46-14Copyright©2001byHarcourt,Inc.Allrightsreserved.◼Standarddeviation(i)measurestotal,orstand-al

one,risk.◼Thelargerthei,thelowertheprobabilitythatactualreturnswillbeclosetotheexpectedreturn.6-15Copyright©2001byHarcourt,Inc.Allrigh

tsreserved.ExpectedReturnsvs.RiskSecurityExpectedreturnRisk,HT17.4%20.0%Market15.015.3USR13.8*18.8*T-bills8.00.0Coll.1.7*13.4**Se

emsmisplaced.6-16Copyright©2001byHarcourt,Inc.Allrightsreserved.CoefficientofVariation(CV)Standardizedmeasureofdispersionabo

uttheexpectedvalue:Showsriskperunitofreturn.CV==.Stddev^kMean6-17Copyright©2001byHarcourt,Inc.Allrightsreserve

d.0ABA=B,butAisriskierbecauselargerprobabilityoflosses.=CVA>CVB.^k6-18Copyright©2001byHarcourt,Inc.Allrightsreserved.PortfolioRiskandReturnA

ssumeatwo-stockportfoliowith$50,000inHTand$50,000inCollections.Calculatekpandp.^6-19Copyright©2001byHarc

ourt,Inc.Allrightsreserved.PortfolioReturn,kpkpisaweightedaverage:kp=0.5(17.4%)+0.5(1.7%)=9.6%.kpisbetweenkHTandkCOLL.^^^^^^^^k

p=Swiki.ni=16-20Copyright©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%.^EstimatedReturnEconomyProb.HTColl.Port.Recession0.10-22.0%28.0%3.0%Belowavg.0.20-2.014.76.4Average0.4

020.00.010.0Aboveavg.0.2035.0-10.012.5Boom0.1050.0-20.015.06-21Copyright©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)20.106-2

2Copyright©2001byHarcourt,Inc.Allrightsreserved.◼p=3.3%ismuchlowerthanthatofeitherstock(20%and13.4%).◼p=3.3%islowerthanaverageofHTa

ndColl=16.7%.◼\Portfolioprovidesaveragekbutlowerrisk.◼Reason:negativecorrelation.^6-23Copyright©2001byHarcourt,Inc.Allri

ghtsreserved.Generalstatementsaboutrisk◼Moststocksarepositivelycorrelated.rk,m0.65.◼35%foranaveragestock.◼Combiningstocksgene

rallylowersrisk.6-24Copyright©2001byHarcourt,Inc.Allrightsreserved.ReturnsDistributionforTwoPerfectlyNegativelyCo

rrelatedStocks(r=-1.0)andforPortfolioWM25150-10-10-100015152525StockWStockMPortfolioWM...............6-25Copyright©2001byHarco

urt,Inc.Allrightsreserved.ReturnsDistributionsforTwoPerfectlyPositivelyCorrelatedStocks(r=+1.0)andforPortfolioMM’Sto

ckM01525-10StockM’01525-10PortfolioMM’01525-106-26Copyright©2001byHarcourt,Inc.Allrightsreserved.Whatwouldhappentotheriskinessofanaverage1-sto

ckportfolioasmorerandomlyselectedstockswereadded?◼pwoulddecreasebecausetheaddedstockswouldnotbeperfectlycorrelatedbutkpwou

ldremainrelativelyconstant.^6-27Copyright©2001byHarcourt,Inc.Allrightsreserved.Large015Prob.21EvenwithlargeN,p20%6-28Copyright©2001byHar

court,Inc.Allrightsreserved.#StocksinPortfolio102030402,000+CompanySpecificRiskMarketRisk200Stand-AloneRisk,pp(%)356-29Copyright©200

1byHarcourt,Inc.Allrightsreserved.◼Asmorestocksareadded,eachnewstockhasasmallerrisk-reducingimpact.◼pfallsveryslowlyafterabout10stocksareinclude

d,andafter40stocks,thereislittle,ifany,effect.Thelowerlimitforpisabout20%=M.6-30Copyright©2001byHarcourt,Inc.Allrightsreserved.Stand-al

oneMarketFirm-specificMarketriskisthatpartofasecurity’sstand-aloneriskthatcannotbeeliminatedbydiversification,andismeasuredbybeta.Firm-s

pecificriskisthatpartofasecurity’sstand-aloneriskthatcanbeeliminatedbyproperdiversification.riskriskrisk=+6-3

1Copyright©2001byHarcourt,Inc.Allrightsreserved.◼Byformingportfolios,wecaneliminateabouthalftheriskinessofindividualstocks(35%vs.2

0%).6-32Copyright©2001byHarcourt,Inc.Allrightsreserved.Ifyouchosetoholdaone-stockportfolioandthusareexposedtomo

reriskthandiversifiedinvestors,wouldyoubecompensatedforalltheriskyoubear?6-33Copyright©2001byHarcourt,Inc.Allrightsreser

ved.◼NO!◼Stand-aloneriskasmeasuredbyastock’sorCVisnotimportanttoawell-diversifiedinvestor.◼Rational,riskaverseinvestorsareconcernedwithp,which

isbasedonmarketrisk.6-34Copyright©2001byHarcourt,Inc.Allrightsreserved.◼Therecanonlybeoneprice,hencemarketre

turn,foragivensecurity.Therefore,nocompensationcanbeearnedfortheadditionalriskofaone-stockportfolio.6-35Copyrig

ht©2001byHarcourt,Inc.Allrightsreserved.◼Betameasuresastock’smarketrisk.Itshowsastock’svolatilityrelativetothemark

et.◼Betashowshowriskyastockisifthestockisheldinawell-diversifiedportfolio.6-36Copyright©2001byHarcourt,Inc.Allrightsreserve

d.Howarebetascalculated?◼RunaregressionofpastreturnsonStockiversusreturnsonthemarket.Returns=D/P+g.◼Theslopeoftheregressionlineisdefinedasthe

betacoefficient.6-37Copyright©2001byHarcourt,Inc.Allrightsreserved.YearkMki115%18%2-5-1031216...ki_kM_-50510

15202015105-5-10Illustrationofbetacalculation:Regressionline:ki=-2.59+1.44kM^^6-38Copyright©2001byHarcou

rt,Inc.Allrightsreserved.◼Ifbeta=1.0,averagestock.◼Ifbeta>1.0,stockriskierthanaverage.◼Ifbeta<1.0,stocklessriskythanaverage.◼Moststockshave

betasintherangeof0.5to1.5.6-39Copyright©2001byHarcourt,Inc.Allrightsreserved.ListofBetaCoefficientsStockBetaMerrillLynch2.00AmericaOnline1.70Genera

lElectric1.20MicrosoftCorp.1.10Coca-Cola1.05IBM1.05Procter&Gamble0.85Heinz0.80EnergenCorp.0.80EmpireDistrictElectric

0.456-40Copyright©2001byHarcourt,Inc.Allrightsreserved.Canabetabenegative?Answer:Yes,ifri,misnegative.Thenina“betagraph”theregressionlinewillslope

downward.Though,anegativebetaishighlyunlikely.6-41Copyright©2001byHarcourt,Inc.Allrightsreserved.HTT-Billsb=0ki_kM_-20020404020-20b=1.29Coll.b

=-0.866-42Copyright©2001byHarcourt,Inc.Allrightsreserved.Riskiersecuritieshavehigherreturns,sotherankorderisOK.HT17.4%1.29Market15.0

1.00USR13.80.68T-bills8.00.00Coll.1.7-0.86ExpectedRiskSecurityReturn(Beta)6-43Copyright©2001byHarcourt,Inc.A

llrightsreserved.UsetheSMLtocalculatetherequiredreturns.◼AssumekRF=8%.◼NotethatkM=kMis15%.(Equil.)◼RPM=kM–kRF=15%–8%=7%.SML:ki=kRF+(k

M–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>kMarket15.015.0Fairly

valuedUSR13.812.8Undervalued:k>kT-bills8.08.0FairlyvaluedColl.1.72.0Overvalued:k<kExpectedvs.RequiredReturns^^^^kk6-46Copyright©2001byHarcourt,Inc.A

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

nc.Allrightsreserved.Calculatebetaforaportfoliowith50%HTand50%Collectionsbp=Weightedaverage=0.5(bHT)+0.5(bColl)=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©

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

sreserved.SML1OriginalsituationRequiredRateofReturnk(%)SML200.51.01.5Risk,bi1815118NewSMLDI=3%6-51Copyright©200

1byHarcourt,Inc.Allrightsreserved.Ifinflationdidnotchangebutriskaversionincreasedenoughtocausethemarketriskpremiumtoincreaseby3percentagepoint

s,whatwouldhappentotheSML?6-52Copyright©2001byHarcourt,Inc.Allrightsreserved.kM=18%kM=15%SML1OriginalsituationRequiredRateofReturn(%)SML2Afte

rincreaseinriskaversionRisk,bi181581.0DRPM=3%6-53Copyright©2001byHarcourt,Inc.Allrightsreserved.HastheCAPMbeenverifiedthroug

hempiricaltests?◼Notcompletely.Thosestatisticaltestshaveproblemsthatmakeverificationalmostimpossible.6-54Copyright©2001byHarcourt,In

c.Allrightsreserved.◼Investorsseemtobeconcernedwithbothmarketriskandtotalrisk.Therefore,theSMLmaynotproduceacorrectestimateofki:ki=kRF+(kM–

kRF)b+?6-55Copyright©2001byHarcourt,Inc.Allrightsreserved.◼Also,CAPM/SMLconceptsarebasedonexpectations,yetbetasarecalculatedusinghistori

caldata.Acompany’shistoricaldatamaynotreflectinvestors’expectationsaboutfutureriskiness.