Financial Management 财务管理

Lecture4AB1201RiskandRatesofReturn1RiskandRatesofReturnChapter7Stand-AloneRiskPortfolioRiskRiskandReturn:CAPM/SML7-2InvestmentReturnsTherateofreturnonaninvestmentcanbecalculatedasfollows:Forexample,if$1,000isinvestedand$1,100isreturnedafteroneyear,therateofreturnforthisinvestmentis:($1,100–$1,000)/$1,000=10%.7-3InvestedAmountInvestedAmountvalueEndingReturnSelectedRealizedReturns,1926-2007AverageStandardReturnDeviationSmall-companystocks17.1%32.6%Large-companystocks12.320.0L-Tcorporatebonds6.28.4L-Tgovernmentbonds5.89.2U.S.Treasurybills3.83.1Source:BasedonStocks,Bonds,Bills,andInflation:(ValuationEdition)2008Yearbook(Chicago:Morningstar,Inc.,2008),p28.7-4Whatisinvestmentrisk?TwotypesofinvestmentriskStand-aloneriskPortfolioriskInvestmentriskisrelatedtotheprobabilityofearningalowornegativeactualreturn.Thegreaterthechanceoflowerthanexpectedornegativereturns,theriskiertheinvestment.7-5ProbabilityDistributionsAlistingofallpossibleoutcomes,andtheprobabilityofeachoccurrence.Canbeshowngraphically.ExpectedRateofReturnRateofReturn(%)100150-70FirmXFirmY7-6InvestmentAlternativesEconomyProb.T-BillHTCollUSRMPRecession0.15.5%-27.0%27.0%6.0%-17.0%Belowavg0.25.5%-7.0%13.0%-14.0%-3.0%Average0.45.5%15.0%0.0%3.0%10.0%Aboveavg0.25.5%30.0%-11.0%41.0%25.0%Boom0.15.5%45.0%-21.0%26.0%38.0%7-7WhyistheT-billreturnindependentoftheeconomy?DoT-billspromiseacompletelyrisk-freereturn?T-billswillreturnthepromised5.5%,regardlessoftheeconomy.However,T-billsdonotprovideacompletelyrisk-freereturn:Theyarestillexposedtoinflation.Although,verylittleunexpectedinflationislikelytooccuroversuchashortperiodoftime.T-billsarealsoriskyintermsofreinvestmentraterisk.T-billsarerisk-freeinthedefaultsenseoftheword.7-8HowdothereturnsofHTandColl.behaveinrelationtothemarket?HT–Moveswiththeeconomy,andhasapositivecorrelation.Thisistypical.Coll.–Iscountercyclicalwiththeeconomy,andhasanegativecorrelation.Thisisunusual.7-9CalculatingtheExpectedReturn7-10ˆˆˆNiii=1r=Expectedrateofreturnr=rPr=(27%)(0.1)+(7%)(0.2)+(15%)(0.4)+(30%)(0.2)+(45%)(0.1)=12.4%SummaryofExpectedReturnsExpectedreturnHT12.4%Market10.5%USR9.8%T-bill5.5%Coll.1.0%HThasthehighestexpectedreturn,andappearstobethebestinvestmentalternative,butisitreally?Havewefailedtoaccountforrisk?7-11CalculatingStandardDeviation2VarianceˆN2ii=1=Standarddeviation(r-r)P7-12StandardDeviationforEachInvestment7-13%0.0)1.0()5.55.5()2.0()5.55.5()4.0()5.55.5()2.0()5.55.5()1.0()5.55.5(P)rˆr(bills-T2/122222bills-TN1ii2σHT=20%σM=15.2%σUSR=18.8%σColl=13.2%ComparingStandardDeviationsUSRProb.T-billHT05.59.812.4RateofReturn(%)7-14CommentsonStandardDeviationasaMeasureofRiskStandarddeviation(σi)measurestotal,orstand-alone,risk.Thelargerσiis,thelowertheprobabilitythatactualreturnswillbeclosertoexpectedreturns.Largerσiisassociatedwithawiderprobabilitydistributionofreturns.7-15ComparingRiskandReturn7-16SecurityExpectedReturn,Risk,T-bills5.5%0.0%HT12.420.0Coll*1.013.2USR*9.818.8Market10.515.2*Seemsoutofplace.rˆCoefficientofVariation(CV)7-17Astandardizedmeasureofdispersionabouttheexpectedvalue,thatshowstheriskperunitofreturn.rˆreturnExpecteddeviationStandardCVRiskRankingsbyCoefficientofVariationCVT-bill0.0HT1.6Coll.13.2USR1.9Market1.4Collectionshasthehighestdegreeofriskperunitofreturn.HT,despitehavingthehigheststandarddeviationofreturns,hasarelativelyaverageCV.7-18IllustratingtheCVasaMeasureofRelativeRiskσA=σB,butAisriskierbecauseofalargerprobabilityoflosses.Inotherwords,thesameamountofrisk(asmeasuredbyσ)forsmallerreturns.7-190ABRateofReturn(%)Prob.InvestorAttitudetowardsRiskRiskaversion–assumesinvestorsdislikeriskandrequirehigherratesofreturntoencouragethemtoholdriskiersecurities.Riskpremium–thedifferencebetweenthereturnonariskyassetandarisklessasset,whichservesascompensationforinvestorstoholdriskiersecurities.7-20PortfolioConstruction:RiskandReturnAssumeatwo-stockportfolioiscreatedwith$50,000investedinbothHTandCollections.Aportfolio’sexpectedreturnisaweightedaverageofthereturnsoftheportfolio’scomponentassets.Standarddeviationisalittlemoretrickyandrequiresthatanewprobabilitydistributionfortheportfolioreturnsbedevised.7-21CalculatingPortfolioExpectedReturnˆˆˆpN^ipii=1prisaweightedaverage:r=wrr=0.5(12.4%)+0.5(1.0%)=6.7%7-22AnAlternativeMethodforDeterminingPortfolioExpectedReturnEconomyProb.HTCollPort.Recession0.1-27.0%27.0%0.0%Belowavg0.2-7.0%13.0%3.0%Average0.415.0%0.0%7.5%Aboveavg0.230.0%-11.0%9.5%Boom0.145.0%-21.0%12.0%6.7%(12.0%)0.10(9.5%)0.20(7.5%)0.40(3.0%)0.20(0.0%)0.10rˆp7-23CalculatingPortfolioStandardDeviationandCV0.516.7%3.4%CV3.4%6.7)-(12.00.106.7)-(9.50.206.7)-(7.50.406.7)-(3.00.206.7)-(0.00.10p2122222p7-24CommentsonPortfolioRiskMeasuresσp=3.4%ismuchlowerthantheσiofeitherstock(σHT=20.0%;σColl.=13.2%).σp=3.4%islowerthantheweightedaverageofHTandColl.’sσ(16.6%).Therefore,theportfolioprovidestheaveragereturnofcomponentstocks,butlowerthantheaveragerisk.Why?Negativecorrelationbetweenstocks.7-25GeneralCommentsaboutRiskσ35%foranaver