金融学（博迪） 清华本科课件 chpt12

Chapter12:PortfolioSelectionandDiversificationCopyright©PrenticeHallInc.2000.Author:NickBagley,bdellaSoft,Inc.ObjectiveTounderstandthetheoryofpersonalportfolioselectionintheoryandinpractice1Chapter12Contents12.1Theprocessofpersonalportfolioselection12.2Thetrade-offbetweenexpectedreturnandrisk12.3Efficientdiversificationwithmanyriskyassets2ObjectivesTounderstandtheprocessofpersonalportfolioselectionintheoryandpractice3456…andLotsMore!7891011Mode=104Mode=106Median=104Mean=104Median=111Mean=1131213Mode=122Mode=135Median=126Mean=128Median=165Mean=1821415Mode=503Mode=1,102Median=650Mean=739Median=5,460Mean=12,1511617181920CombiningtheRisklessAssetandaSingleRiskyAssetTheexpectedreturnoftheportfolioistheweightedaverageofthecomponentreturnsmp=W1*m1+W2*m2

mp=W1*m1+(1-W1)*m221CombiningtheRisklessAssetandaSingleRiskyAssetThevolatilityoftheportfolioisnotquiteassimple:sp=((W1*s1)2+2W1*s1*W2*s2+(W2*s2)2)1/222CombiningtheRisklessAssetandaSingleRiskyAssetWeknowsomethingspecialabouttheportfolio,namelythatsecurity2isriskless,sos2=0,and

spbecomes:sp=((W1*s1)2+2W1*s1*W2*0+(W2*0)2)1/2sp=|W1|*s123CombiningtheRisklessAssetandaSingleRiskyAssetInsummarysp=|W1|*s1,And:mp=W1*m1+(1-W1)*rf,So:IfW1>0,

mp=[(rf-m1)/s1]*sp+rf

Else

mp=[(m1-rf)/s1]*sp+rf

2425Longriskyandshortrisk-free

Longbothriskyandrisk-free100%Risky100%Risk-less26MutualFundAverage%TotalReturns27Toobtaina20%ReturnYousettleona20%return,anddecidenottopursueonthecomputationalissueRecall:

mp=W1*m1+(1-W1)*rf

Yourportfolio:s=20%,m=15%,rf=5%So:W1=(mp-rf)/(m1-rf)=(0.20-0.05)/(0.15-0.05)=150%28Toobtaina20%ReturnAssumethatyourmanagea$50,000,000portfolioAW1of1.5or150%meansyouinvest(golong)$75,000,000,andborrow(short)$25,000,000tofinancethedifferenceBorrowingattherisk-freerateismoot29Toobtaina20%ReturnHowriskyisthisstrategy?sp=|W1|*s1=1.5*0.20=0.30Theportfoliohasavolatilityof30%30PortfolioofTwoRiskyAssetsRecallfromstatistics,thattworandomvariables,suchastwosecurityreturns,maybecombinedtoformanewrandomvariableAreasonableassumptionforreturnsondifferentsecuritiesisthelinearmodel:31EquationsforTwoSharesThesumoftheweightsw1andw2being1isnotnecessaryforthevalidityofthefollowingequations,forportfoliosithappenstobetrueTheexpectedreturnontheportfolioisthesumofitsweightedexpectations32EquationsforTwoSharesIdeally,wewouldliketohaveasimilarresultforriskLaterwediscoverameasureofriskwiththisproperty,butforstandarddeviation:33MnemonicThereisamnemonicthatwillhelpyourememberthevolatilityequationsfortwoormoresecuritiesToobtaintheformula,movethrougheachcellinthetable,multiplyingitbytherowheadingbythecolumnheading,andsumming34Variancewith2Securities35Variancewith3Securities36CorrelatedCommonStockThenextslideshowsstatisticsoftwocommonstockwiththesestatistics:meanreturn1=0.15meanreturn2=0.10standarddeviation1=0.20standarddeviation2=0.25correlationofreturns=0.90initialprice1=$57.25Initialprice2=$72.62537383940FragmentsoftheOutputTable41SampleoftheExcelFormulae42FormulaeforMinimumVariancePortfolio43FormulaeforTangentPortfolio44Example:What’stheBestReturngivena10%SD?45AchievingtheTargetExpectedReturn(2):WeightsAssumethattheinvestmentcriterionistogeneratea30%returnThisistheweightoftheriskyportfolioontheCML46Achievingt