CH06RiskandRatesofReturn(财务管理,英文版).pptx

CH06RiskandRatesofReturn(财务管理,英文版).pptx

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CHAPTER6RiskandRatesofReturn,Stand-aloneriskPortfolioriskRisk&return:

CAPM/SML,Whatisinvestmentrisk?

Investmentriskpertainstotheprobabilityofactuallyearningalowornegativereturn.Thegreaterthechanceoflowornegativereturns,theriskiertheinvestment.,Probabilitydistribution,ExpectedRateofReturn,Rateofreturn（%）,100,15,0,-70,FirmX,FirmY,AnnualTotalReturns,1926-1998,AverageStandardReturnDeviationDistribution,Small-companystocks17.4%33.8%Large-companystocks13.220.3Long-termcorporatebonds6.18.6Long-termgovernment5.79.2Intermediate-termgovernment5.55.7U.S.Treasurybills3.83.2Inflation3.24.5,InvestmentAlternatives（Givenintheproblem）,Economy,Prob.,T-Bill,HT,Coll,USR,MP,Recession0.18.0%-22.0%28.0%10.0%-13.0%Belowavg.0.28.0-2.014.7-10.01.0Average0.48.020.00.07.015.0Aboveavg.0.28.035.0-10.045.029.0Boom0.18.050.0-20.030.043.01.0,WhyistheT-billreturnindependentoftheeconomy?

Willreturnthepromised8%regardlessoftheeconomy.,DoT-billspromiseacompletelyrisk-freereturn?

No,T-billsarestillexposedtotheriskofinflation.However,notmuchunexpectedinflationislikelytooccuroverarelativelyshortperiod.,DothereturnsofHTandColl.movewithorcountertotheeconomy?

HT:

Moveswiththeeconomy,andhasapositivecorrelation.Thisistypical.Coll:

Iscountercyclicaloftheeconomy,andhasanegativecorrelation.Thisisunusual.,Calculatetheexpectedrateofreturnoneachalternative:

k=expectedrateofreturn.,kHT=（-22%）0.1+（-2%）0.20+（20%）0.40+（35%）0.20+（50%）0.1=17.4%.,k,HT,17.4%,Market,15.0,USR,13.8,T-bill,8.0,Coll.,1.7,HTappearstobethebest,butisitreally?

Whatsthestandarddeviationofreturnsforeachalternative?

=Standarddeviation.=,sT-bills=0.0%.,sHT=20.0%.,sColl=13.4%.sUSR=18.8%.sM=15.3%.,1/2,s,T,-,bills,=,（8.08.0）20.1+（8.08.0）20.2+（8.08.0）20.4+（8.08.0）20.2+（8.08.0）20.1,Prob.,RateofReturn（%）,T-bill,USR,HT,0,8,13.8,17.4,Standarddeviation（si）measurestotal,orstand-alone,risk.Thelargerthesi,thelowertheprobabilitythatactualreturnswillbeclosetotheexpectedreturn.,ExpectedReturnsvs.Risk,Security,Expected,return,Risk,s,HT17.4%20.0%Market15.015.3USR13.8*18.8*T-bills8.00.0Coll.1.7*13.4*,*Seemsmisplaced.,CoefficientofVariation（CV）,Standardizedmeasureofdispersionabouttheexpectedvalue:

Showsriskperunitofreturn.,CV=.,Stddevs,k,Mean,0,A,B,sA=sB,butAisriskierbecauselargerprobabilityoflosses.,=CVACVB.,s,k,PortfolioRiskandReturn,Assumeatwo-stockportfoliowith$50,000inHTand$50,000inCollections.,Calculatekpandsp.,PortfolioReturn,kp,kpisaweightedaverage:

kp=0.5（17.4%）+0.5（1.7%）=9.6%.,kpisbetweenkHTandkCOLL.,kp=Swiki.,n,i=1,AlternativeMethod,kp=（3.0%）0.10+（6.4%）0.20+（10.0%）0.40+（12.5%）0.20+（15.0%）0.10=9.6%.,EstimatedReturn,Economy,Prob.,HT,Coll.,Port.,Recession0.10-22.0%28.0%3.0%Belowavg.0.20-2.014.76.4Average0.4020.00.010.0Aboveavg.0.2035.0-10.012.5Boom0.1050.0-20.015.0,CVp=0.34.,3.3%,9.6%,p=3.3%.,1,2,/,（3.09.6）20.10+（6.49.6）20.20+（10.09.6）20.40+（12.59.6）20.20+（15.09.6）20.10,sp=3.3%ismuchlowerthanthatofeitherstock（20%and13.4%）.sp=3.3%islowerthanaverageofHTandColl=16.7%.Portfolioprovidesaveragekbutlowerrisk.Reason:

negativecorrelation.,Generalstatementsaboutrisk,Moststocksarepositivelycorrelated.rk,m0.65.s35%foranaveragestock.Combiningstocksgenerallylowersrisk.,ReturnsDistributionforTwoPerfectlyNegativelyCorrelatedStocks（r=-1.0）andforPortfolioWM,25,15,0,-10,-10,-10,0,0,15,15,25,25,StockW,StockM,PortfolioWM,.,.,.,.,.,.,.,.,.,.,.,.,.,.,.,ReturnsDistributionsforTwoPerfectlyPositivelyCorrelatedStocks（r=+1.0）andforPortfolioMM,StockM,StockM,PortfolioMM,0,15,25,-10,Whatwouldhappentotheriskinessofanaverage1-stockportfolioasmorerandomlyselectedstockswereadded?

spwoulddecreasebecausetheaddedstockswouldnotbeperfectlycorrelatedbutkpwouldremainrelativelyconstant.,Large,0,15,Prob.,2,1,EvenwithlargeN,sp20%,#StocksinPortfolio,102030402,000+,CompanySpecificRisk,MarketRisk,200,Stand-AloneRisk,sp,sp（%）,35,Asmorestocksareadded,eachnewstockhasasmallerrisk-reducingimpact.spfallsveryslowlyafterabout10stocksareincluded,andafter40stocks,thereislittle,ifany,effect.Thelowerlimitforspisabout20%=sM.,Stand-aloneMarketFirm-specific,Marketriskisthatpartofasecuritysstand-aloneriskthatcannotbeeliminatedbydiversification,andismeasuredbybeta.Firm-specificriskisthatpartofasecuritysstand-aloneriskthatcanbeeliminatedbyproperdiversification.,riskriskrisk,=+,Byformingportfolios,wecaneliminateabouthalftheriskinessofindividualstocks（35%vs.20%）.,Ifyouchosetoholdaone-stockportfolioandthusareexposedtomoreriskthandiversifiedinvestors,wouldyoubecompensatedforalltheriskyoubear?

NO!

Stand-aloneriskasmeasuredbyastockssorCVisnotimportanttoawell-diversifiedinvestor.Rational,riskaverseinvestorsareconcernedwithsp,whichisbasedonmarketrisk.,Therecanonlybeoneprice,hencemarketreturn,foragivensecurity.Therefore,nocompensationcanbeearnedfortheadditionalriskofaone-stockportfolio.,Betameasuresastocksmarketrisk.Itshowsastocksvolatilityrelativetothemarket.,Betashowshowriskyastockisifthestockisheldinawell-diversifiedportfolio.,Howarebetascalculated?

RunaregressionofpastreturnsonStockiversusreturnsonthemarket.Returns=D/P+g.Theslopeoftheregressionlineisdefinedasthebetacoefficient.,YearkMki115%18%2-5-1031216,.,.,.,kM,_,-505101520,2015105,-5-10,Illustrationofbetacalculation:

Regressionline:

ki=-2.59+1.44kM,Ifbeta=1.0,averagestock.Ifbeta1.0,stockriskierthanaverage.Ifbeta1.0,stocklessriskythanaverage.Moststockshavebetasintherangeof0.5to1.5.,ListofBetaCoefficients,StockBeta,MerrillLynch2.00AmericaOnline1.70GeneralElectric1.20MicrosoftCorp.1.10Coca-Cola1.05IBM1.05Procter&Gamble0.85Heinz0.80EnergenCorp.0.80EmpireDistrictElectric0.45,Canabetabenegative?

Answer:

Yes,ifri,misnegative.Thenina“betagraph”theregressionlinewillslopedownward.Though,anegativebetaishighlyunlikely.,HT,T-Bills,b=0,ki,_,kM,_,-2002040,4020,-20,b=1.29,Coll.,b=-0.86,Riskiersecuritieshavehigherreturns,sotherankorderisOK.,HT17.4%1.29Market15.01.00USR13.80.68T-bills8.00.00Coll.1.7-0.86,ExpectedRiskSecurityReturn（Beta）,UsetheSMLtocalculatetherequiredreturns.,AssumekRF=8%.NotethatkM=kMis15%.（Equil.）RPM=kMkRF=15%8%=7%.,SML:

ki=kRF+（kMkRF）bi.,RequiredRatesofReturn,kHT=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%.,HT17.4%17.0%Undervalued:

kkMarket15.015.0FairlyvaluedUSR13.812.8Undervalued:

kkT-bills8.08.0FairlyvaluedColl.1.72.0Overvalued:

kk,Expectedvs.RequiredReturns,k,k,.,.,Coll.,.,HT,T-bills,.,USR,SML,kM=15kRF=8,-1012,.,SML:

ki=8%+（15%8%）bi.,ki（%）,Risk,bi,Calculatebetaforaportfoliowith50%HTand50%Collections,bp=Weightedaverage=0.5（bHT）+0.5（bColl）=0.5（1.29）+0.5（-0.86）=0.22.,TherequiredreturnontheHT/Coll.portfoliois:

kp=Weightedaveragek=0.5（17%）+0.5（2%）=9.5%.OruseSML:

kp=kRF+（kMkRF）bp=8.0%+（15.0%8.0%）（0.22）=8.0%+7%（0.22）=9.5%.,Ifinvestorsraiseinflationexpectationsby3%,whatwouldhappentotheSML?

SML1,Originalsituation,RequiredRateofReturnk（%）,SML2,00.51.01.5Risk,bi,1815118,NewSML,DI=3%,Ifinflationdidnotchangebutriskaversionincreasedenoughtocausethemarketriskpremiumtoincreaseby3percentagepoints,whatwouldhappentotheSML?

kM=18%kM=15%,SML1,Originalsituation,RequiredRateofReturn（%）,SML2,Afterincreaseinriskaversion,Risk,bi,1815,8,1.0,DRPM=3%,HastheCAPMbeenverifiedthroughempiricaltests?

Notcompletely.Thosestatisticaltestshaveproblemsthatmakeverificationalmostimpossible.,Investorsseemtobeconcernedwithbothmarketriskandtotalrisk.Therefore,theSMLmaynotproduceacorrectestimateofki:

ki=kRF+（kMkRF）b+?

Also,CAPM/SMLconceptsarebasedonexpectations,yetbetasarecalculatedusinghistoricaldata.Acompanyshistoricaldatamaynotreflectinvestorsexpectationsaboutfutureriskiness.,