《微觀經(jīng)濟學》清華大學課件-Ch13-Risky-Assets

ChapterThirteenRiskyAssetsMainIssueMean-VarianceUtilityBudgetConstraintsforRiskyAssetsMeasuringRiskCapitalAssetPricingModelMeanofaDistributionArandomvariable(r.v.)wtakesvaluesw1,…,wSwithprobabilities1,...,S(1+···+S=1).Themean(expectedvalue)ofthedistributionistheaveragevalueofther.v.;VarianceofaDistributionThedistribution’svarianceisther.v.’sav.squareddeviationfromthemean;Variancemeasuresther.v.’s

variation.

StandardDeviationofaDistributionThedistribution’sstandarddeviationisthesquarerootofitsvariance;St.deviationalsomeasuresther.v.’s

variability.

MeanandVarianceProbabilityRandomVariableValuesTwodistributionswiththesamevarianceanddifferentmeans.MeanandVarianceProbabilityRandomVariableValuesTwodistributionswiththesamemeananddifferentvariances.PreferencesoverRiskyAssetsHighermeanreturnispreferred.Lessvariationinreturnispreferred(lessrisk).PreferencesoverRiskyAssetsHighermeanreturnispreferred.Lessvariationinreturnispreferred(lessrisk).PreferencesarerepresentedbyautilityfunctionU(,).Uasmeanreturn.Uasrisk.PreferencesoverRiskyAssetsPreferredHighermeanreturnisagood.Higherriskisabad.MeanReturn,St.Dev.ofReturn,PreferencesoverRiskyAssetsPreferredHighermeanreturnisagood.Higherriskisabad.MeanReturn,St.Dev.ofReturn,PreferencesoverRiskyAssetsHowistheMRScomputed?PreferencesoverRiskyAssetsHowistheMRScomputed?PreferencesoverRiskyAssetsMeanReturn,St.Dev.ofReturn,PreferredHighermeanreturnisagood.Higherriskisabad.BudgetConstraintsforRiskyAssetsTwoassets.Risk-freeasset’srate-or-returnisrf.Riskystock’srate-or-returnismsifstatesoccurs,withprob.s

.Riskystock’smeanrate-of-returnisBudgetConstraintsforRiskyAssetsAbundlecontainingsomeoftheriskystockandsomeoftherisk-freeassetisaportfolio.xisthefractionofwealthusedtobuytheriskystock.Givenx,theportfolio’sav.rate-of-returnisBudgetConstraintsforRiskyAssetsx=0andx=1BudgetConstraintsforRiskyAssetsx=0andx=1Sincestockisriskyandriskisabad,forstocktobepurchasedmusthaveBudgetConstraintsforRiskyAssetsx=0andx=1Sincestockisriskyandriskisabad,forstocktobepurchasedmusthaveSoportfolio’sexpectedrate-of-returnriseswithx(morestockintheportfolio).BudgetConstraintsforRiskyAssetsPortfolio’srate-of-returnvarianceisBudgetConstraintsforRiskyAssetsPortfolio’srate-of-returnvarianceisBudgetConstraintsforRiskyAssetsPortfolio’srate-of-returnvarianceisBudgetConstraintsforRiskyAssetsPortfolio’srate-of-returnvarianceisBudgetConstraintsforRiskyAssetsPortfolio’srate-of-returnvarianceisBudgetConstraintsforRiskyAssetsPortfolio’srate-of-returnvarianceisBudgetConstraintsforRiskyAssetsVariancesost.deviationBudgetConstraintsforRiskyAssetsx=0andx=1Variancesost.deviationBudgetConstraintsforRiskyAssetsx=0andx=1Variancesost.deviationSoriskriseswithx(morestockintheportfolio).BudgetConstraintsforRiskyAssetsMeanReturn,St.Dev.ofReturn,BudgetConstraintsforRiskyAssetsMeanReturn,St.Dev.ofReturn,BudgetConstraintsforRiskyAssetsMeanReturn,St.Dev.ofReturn,BudgetConstraintsforRiskyAssetsBudgetlineMeanReturn,St.Dev.ofReturn,BudgetConstraintsforRiskyAssetsBudgetline,slope=MeanReturn,St.Dev.ofReturn,ChoosingaPortfolioBudgetline,slope=MeanReturn,St.Dev.ofReturn,isthepriceofriskrelativetomeanreturn.ChoosingaPortfolioBudgetline,slope=Whereisthemostpreferredreturn/riskcombination?MeanReturn,St.Dev.ofReturn,ChoosingaPortfolioBudgetline,slope=Whereisthemostpreferredreturn/riskcombination?MeanReturn,St.Dev.ofReturn,ChoosingaPortfolioBudgetline,slope=Whereisthemostpreferredreturn/riskcombination?MeanReturn,St.Dev.ofReturn,ChoosingaPortfolioBudgetline,slope=Whereisthemostpreferredreturn/riskcombination?MeanReturn,St.Dev.ofReturn,ChoosingaPortfolioBudgetline,slope=Whereisthemostpreferredreturn/riskcombination?MeanReturn,St.Dev.ofReturn,ChoosingaPortfolioSupposeanewriskyassetappears,withameanrate-of-returnry>rm

andast.dev.y>m.Whichassetispreferred?ChoosingaPortfolioSupposeanewriskyassetappears,withameanrate-of-returnry>rm

andast.dev.y>m.Whichassetispreferred?SupposeChoosingaPortfolioBudgetline,slope=MeanReturn,St.Dev.ofReturn,ChoosingaPortfolioBudgetline,slope=MeanReturn,St.Dev.ofReturn,ChoosingaPortfolioBudgetline,slope=Budgetline,slope=MeanReturn,St.Dev.ofReturn,ChoosingaPortfolioBudgetline,slope=Budgetline,slope=Highermeanrate-of-returnandhigherriskchoseninthiscase.MeanReturn,St.Dev.ofReturn,MeasuringRiskQuantitatively,howriskyisanasset?Dependsuponhowtheasset’svaluedependsuponotherassets’values.E.g.AssetA’svalueis$60withchance1/4and$20withchance3/4.Payatmost$30forassetA.MeasuringRiskAssetA’svalueis$60withchance1/4and$20withchance3/4.AssetB’svalueis$20whenassetA’svalueis$60andis$60whenassetA’svalueis$20(perfectnegativecorrelationofvalues).Payupto$40>$30fora50-50mixofassetsAandB.BudgetConstraintsforRiskyAssetsAssetA’sriskrelativetoriskinthewholestockmarketismeasuredbyMeasuringRiskAssetA’sriskrelativetoriskinthewholestockmarketismeasuredbywhereisthemarket’srate-of-returnandisassetA’srate-of-return.MeasuringRisk

assetA’sreturnisnotperfectlycorrelatedwiththewholemarket’sreturnandsoitcanbeusedtobuildalowerriskportfolio.EquilibriuminRiskyAssetMarketsAtequilibrium,allassets’risk-adjustedrates-of-returnmustbeequal.Howdoweadjustforriskiness?EquilibriuminRiskyAssetMarketsRiskinessofassetArelativetototalmarketriskisA.

Totalmarketriskism.SototalriskinessofassetAisAm.Equilibriumin