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

CAPM/SML6-2Copyright©2001byHarcourt,Inc.Allrightsreserved.Whatisinvestmentrisk?Investmentriskpertains

totheprobabilityofactuallyearningalowornegativereturn.Thegreaterthechanceoflowornegativereturns,theriskie

rtheinvestment.6-3Copyright©2001byHarcourt,Inc.Allrightsreserved.ProbabilitydistributionExpectedRateofReturnRateofreturn(%)100150-70FirmXF

irmY6-4Copyright©2001byHarcourt,Inc.Allrightsreserved.AnnualTotalReturns,1926-1998AverageStandardReturnD

eviationDistributionSmall-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.Allrightsreserved.InvestmentAlternatives(Givenintheproblem)EconomyProb.T-Bill

HTCollUSRMPRecession0.18.0%-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-billreturnindependentoftheec

onomy?Willreturnthepromised8%regardlessoftheeconomy.6-7Copyright©2001byHarcourt,Inc.Allrightsreserved.DoT-billspromiseacompletelyri

sk-freereturn?No,T-billsarestillexposedtotheriskofinflation.However,notmuchunexpectedinflationislikelytooccuroverarelativelyshortperiod.6-8Co

pyright©2001byHarcourt,Inc.Allrightsreserved.DothereturnsofHTandColl.movewithorcountertotheeconomy?◼HT:Moveswiththeeconomy,andhasaposi

tivecorrelation.Thisistypical.◼Coll:Iscountercyclicaloftheeconomy,andhasanegativecorrelation.Thisisunusual.6-9Copyri

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

rateofreturn.kHT=(-22%)0.1+(-2%)0.20+(20%)0.40+(35%)0.20+(50%)0.1=17.4%.^^6-10Copyright©2001byHarcourt,I

nc.Allrightsreserved.kHT17.4%Market15.0USR13.8T-bill8.0Coll.1.7HTappearstobethebest,butisitreally?^6-11Copyright©2001byHarcourt,Inc.Allrightsreserve

d.What’sthestandarddeviationofreturnsforeachalternative?=Standarddeviation.===Variance2.P)kˆk(n1ii2i=−6-12Copyright©2001byHarcourt,Inc.Allrigh

tsreserved.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-billUSRHT0813.817.46-14Copyright©2001byHarcourt,Inc.Allrightsreserved.◼Standarddeviation(i)measurestotal,orstand-alone

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

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

ed.6-16Copyright©2001byHarcourt,Inc.Allrightsreserved.CoefficientofVariation(CV)Standardizedmeasureofdispersionabouttheexpectedva

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

sses.=CVA>CVB.^k6-18Copyright©2001byHarcourt,Inc.Allrightsreserved.PortfolioRiskandReturnAssumeatwo-stockportfoliowith$50,000inHTand$50,000i

nCollections.Calculatekpandp.^6-19Copyright©2001byHarcourt,Inc.Allrightsreserved.PortfolioReturn,kpkpisaweightedaverage:kp=0.5(17.4%)

+0.5(1.7%)=9.6%.kpisbetweenkHTandkCOLL.^^^^^^^^kp=Swiki.ni=16-20Copyright©2001byHarcourt,Inc.Allrightsreserved.AlternativeM

ethodkp=(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%2

8.0%3.0%Belowavg.0.20-2.014.76.4Average0.4020.00.010.0Aboveavg.0.2035.0-10.012.5Boom0.1050.0-20.015.06-21Copyright©2001byHarco

urt,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%ismuchlowertha

nthatofeitherstock(20%and13.4%).◼p=3.3%islowerthanaverageofHTandColl=16.7%.◼\Portfolioprovidesaveragekbu

tlowerrisk.◼Reason:negativecorrelation.^6-23Copyright©2001byHarcourt,Inc.Allrightsreserved.Generalsta

tementsaboutrisk◼Moststocksarepositivelycorrelated.rk,m0.65.◼35%foranaveragestock.◼Combiningstocksgenerallylower

srisk.6-24Copyright©2001byHarcourt,Inc.Allrightsreserved.ReturnsDistributionforTwoPerfectlyNegativel

yCorrelatedStocks(r=-1.0)andforPortfolioWM25150-10-10-100015152525StockWStockMPortfolioWM...........

....6-25Copyright©2001byHarcourt,Inc.Allrightsreserved.ReturnsDistributionsforTwoPerfectlyPositivelyCorrelatedStocks(r=+1.0)and

forPortfolioMM’StockM01525-10StockM’01525-10PortfolioMM’01525-106-26Copyright©2001byHarcourt,Inc.Allrightsreserved.Whatwouldhappentot

heriskinessofanaverage1-stockportfolioasmorerandomlyselectedstockswereadded?◼pwoulddecreasebecausetheaddedstockswouldnotbeperfectlycor

relatedbutkpwouldremainrelativelyconstant.^6-27Copyright©2001byHarcourt,Inc.Allrightsreserved.Large015Pro

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

,000+CompanySpecificRiskMarketRisk200Stand-AloneRisk,pp(%)356-29Copyright©2001byHarcourt,Inc.Allrightsreserved.◼Asmorestocksar

eadded,eachnewstockhasasmallerrisk-reducingimpact.◼pfallsveryslowlyafterabout10stocksareincluded,andafter40stocks,thereislittle,ifany

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

ecurity’sstand-aloneriskthatcannotbeeliminatedbydiversification,andismeasuredbybeta.Firm-specificriskisthatpartofasecurity’ss

tand-aloneriskthatcanbeeliminatedbyproperdiversification.riskriskrisk=+6-31Copyright©2001byHarcourt,Inc.Allrightsreserved.◼Byfo

rmingportfolios,wecaneliminateabouthalftheriskinessofindividualstocks(35%vs.20%).6-32Copyright©2001byHarcourt,Inc.All

rightsreserved.Ifyouchosetoholdaone-stockportfolioandthusareexposedtomoreriskthandiversifiedinvestors,woul

dyoubecompensatedforalltheriskyoubear?6-33Copyright©2001byHarcourt,Inc.Allrightsreserved.◼NO!◼Stand-aloneriskasmeasuredbyastoc

k’sorCVisnotimportanttoawell-diversifiedinvestor.◼Rational,riskaverseinvestorsareconcernedwithp,whichisba

sedonmarketrisk.6-34Copyright©2001byHarcourt,Inc.Allrightsreserved.◼Therecanonlybeoneprice,hencemarke

treturn,foragivensecurity.Therefore,nocompensationcanbeearnedfortheadditionalriskofaone-stockportfolio.6-35Copyright©2001byHarcourt,Inc.Allr

ightsreserved.◼Betameasuresastock’smarketrisk.Itshowsastock’svolatilityrelativetothemarket.◼Betashowshowriskyastockisifthestoc

kisheldinawell-diversifiedportfolio.6-36Copyright©2001byHarcourt,Inc.Allrightsreserved.Howarebetasca

lculated?◼RunaregressionofpastreturnsonStockiversusreturnsonthemarket.Returns=D/P+g.◼Theslopeoftheregressionlineisde

finedasthebetacoefficient.6-37Copyright©2001byHarcourt,Inc.Allrightsreserved.YearkMki115%18%2-5-1031

216...ki_kM_-5051015202015105-5-10Illustrationofbetacalculation:Regressionline:ki=-2.59+1.44kM^^6-38Copyright©2001byHarcourt,Inc.Allri

ghtsreserved.◼Ifbeta=1.0,averagestock.◼Ifbeta>1.0,stockriskierthanaverage.◼Ifbeta<1.0,stocklessriskyth

anaverage.◼Moststockshavebetasintherangeof0.5to1.5.6-39Copyright©2001byHarcourt,Inc.Allrightsreserved.ListofBetaCoefficientsStockB

etaMerrillLynch2.00AmericaOnline1.70GeneralElectric1.20MicrosoftCorp.1.10Coca-Cola1.05IBM1.05Procter&Gamble0.85Heinz0.80

EnergenCorp.0.80EmpireDistrictElectric0.456-40Copyright©2001byHarcourt,Inc.Allrightsreserved.Canabetabenegative?Answer:Yes,ifri,misnegative.T

henina“betagraph”theregressionlinewillslopedownward.Though,anegativebetaishighlyunlikely.6-41Copyright©2001byHa

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

erved.Riskiersecuritieshavehigherreturns,sotherankorderisOK.HT17.4%1.29Market15.01.00USR13.80.68T-bills8.00.00Col

l.1.7-0.86ExpectedRiskSecurityReturn(Beta)6-43Copyright©2001byHarcourt,Inc.Allrightsreserved.UsetheSMLtocalculatetherequiredreturns.◼Assum

ekRF=8%.◼NotethatkM=kMis15%.(Equil.)◼RPM=kM–kRF=15%–8%=7%.SML:ki=kRF+(kM–kRF)bi.^6-44Copyright©2001byHarc

ourt,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...Col

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

tfoliowith50%HTand50%Collectionsbp=Weightedaverage=0.5(bHT)+0.5(bColl)=0.5(1.29)+0.5(-0.86)=0.22.6-48C

opyright©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.A

llrightsreserved.Ifinvestorsraiseinflationexpectationsby3%,whatwouldhappentotheSML?6-50Copyright©2001byHa

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

c.Allrightsreserved.Ifinflationdidnotchangebutriskaversionincreasedenoughtocausethemarketriskpremiumtoincreaseby3percentagepo

ints,whatwouldhappentotheSML?6-52Copyright©2001byHarcourt,Inc.Allrightsreserved.kM=18%kM=15%SML1OriginalsituationRequiredRateofReturn(%)SML2Afterincr

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

tests?◼Notcompletely.Thosestatisticaltestshaveproblemsthatmakeverificationalmostimpossible.6-54Copyright©

2001byHarcourt,Inc.Allrightsreserved.◼Investorsseemtobeconcernedwithbothmarketriskandtotalrisk.Therefore,theSML

maynotproduceacorrectestimateofki:ki=kRF+(kM–kRF)b+?6-55Copyright©2001byHarcourt,Inc.Allrightsreserved.◼Also,CAPM/SMLconceptsarebasedonexpect

ations,yetbetasarecalculatedusinghistoricaldata.Acompany’shistoricaldatamaynotreflectinvestors’expectationsaboutf

utureriskiness.