英国诺丁汉大学国际管理专业课件1-1

1CapitalMarketsAnalysisTopic2:PortfolioTheory2PreviewSomedescriptivestatisticsKeypropertiesofassetsandportfoliosAssumptionsofModel2.1Expectedwealth,variance,standarddeviation,riskpremiumAssumptionsofModel2.2Expectedrateofreturn,variance,standarddeviationofassetsExpectedrateofreturn,variance,standarddeviationofportfolioCovarianceCorrelationcoefficientProblemsPresentations3SomeDescriptiveStatistics-assumptionsofModel2.1-1.Initialwealth(W)=$100,000,whichistobeinvestedforoneyear.2.Thiswealthcanbeinvestedinonlyoneriskyasset,withtwopossiblescenarios.Attheendoftheyear,theassetwillbewortheither:a.$150,000(W1=$150,000);orb.$80,000(W2=$80,0003.Theprobabilityofthefirstscenariois0.6andofthesecondis,therefore,0.44SomeDescriptiveStatistics-expectedwealth-Wealth$100,000Expectedreturns[E(Wi)]Probability(pi)0.6$90,0000.4$32,000Possiblereturns(Wi)$150,000$80,000E(W)=p1W1+p2W2$122,000Expectedwealth=0.6x$150,000+0.4x$80,000=$122,0005SomeDescriptiveStatistics-varianceandstandarddeviation-100150W180W2122E(W)DifferencefromexpectedvalueSquareofdifferencesWeightedsumofsquareddifferencesSquarerootofweightedsum28,00028,0002=784m0.6x784m=470m-42,000-42,0002=1,764m0.4x1,764m=706m1,176m$34,293Variance(σ2)Standarddeviation(σ)σ2=p1[W1–E(W)]2+p2[W2–E(W)]2σ=√σ2Wealth($,000)timet0t1=470m+706m=1,176m=√1,176m=$34,2936SomeDescriptiveStatistics-riskpremium-$105,000$17,000RiskpremiumInvestinrisk-freeassetWealth$100,000Investinriskyasset$150,000$80,0000.60.4$90,000$32,000$122,000$105,0001.0$105,0007KeyPropertiesofAssetsandPortfolios-assumptionsofModel2-1.Humanexhas50%ofitsportfolioinBestCandystock2.ThereturnonBestCandystockissensitiveto(a)thepriceofsugarand(b)themoodofthestockmarket.Thereturnsare:S1=25%,S2=10%andS3=-25%5.ThereturnonSugarcaneisalsosensitivetothepriceofsugarandthemoodofthestockmarket.Thereturnsare:S1=1%,S2=-5%andS3=35%3.Humanexcaninvesttheother50%ofitsportfolioineitherT-billsorSugarcane.4.T-billsarerisk-free,withareturnineachscenarioperiodof5%.8KeyPropertiesofAssetsandPortfolios-structureofanalysis-HumanexPortfolioAPortfolioBE(r)σ2σCovρScenario1Scenario2Scenario3DataProbabilityBestT-billsBestT-billsBestCanePort.BE(r)Port.A25%10%-25%0.50.30.2Cane9KeyPropertiesofAssets&Portfolios-illustrativetableforBestCandy-Scenario1Scenario2NormalyearCrisisyearBullmarketBearmarketScenariorateofreturn,r(s)Expectedrateofreturn,E(r)ContributiontoE(r)[=Pr(s)r(s)]105+0.75+252=357.75StandardDeviation,σ[=√σ2]Scenarioprobability,Pr(s)0.50.30.225%10%-25%0.5x25=12.50.2x-25=-5.00.3x10=3.012.5+3.0-5.0=10.5%25–10.5=14.510.0–10.5=-0.5-25–10.5=-35.514.52=210-0.52=0.25--35.52=1,2600.5x210=1050.3x0.25=0.750.2x1,260=252Deviations(d)from[E(r)]Squareddeviations,d2Variance,σ2Contributiontoσ2[=Pr(s)d2]√357.75=18.9%Scenario3102.KeyPropertiesofAssets&Portfolios-riskyassets-Rule1:Theexpectedreturnofanassetistheprobability-weightedaverageofitsreturninallscenariosE(r)=∑Pr(s)r(s)Rule2a:Thevarianceofanasset’sreturnisthesumoftheweightedsquareddeviationsfromtheexpectedvalueσ2=∑Pr(s)[r(s)-E(r)]2E(rBest)=(0.5x25)+(0.3x10)+(0.2x-25)=10.5%Rule2b:Thestandarddeviationofanasset’sreturnisthesquarerootofthevarianceσBest=√367=18.9%σ=√σ2σ2Best=0.5(25–10.5)2+0.3(10–10.5)2+0.2(-25–10.5)2=357.2511KeyPropertiesofAssetsandPortfolios-summaryofresults-HumanexPortfolioAPortfolioBE(r)σ2σCovρScenario1Scenario2Scenario3Data0.50.30.2Probability25%10%-25%BestT-billsCaneBestT-billsBestCanePort.BE(r)Port.A10.5%357.7518.9%5%5%5%5%0012KeyPropertiesofAssets&Portfolios-riskypremiumandportfolios-Rule2c:Theriskpremium(RP)onanassetistheexcessoftheexpectedreturnontheasset[E(r)]overtherisk-freerateofreturn(rf).RP=E(r)-rfRPBest=10.5-5.0=5.5%Rule3:Theexpectedrateofreturnonaportfolioistheweightedaverageoftheexpectedrateofreturnoneachcomponentoftheportfolio.E(rP)=∑wiE(ri)E(rHum)=(0.5x10.5)+(0.5x5.0)=7.75%Rule4:Whenariskyassetiscombinedwitharisk-freeasset,theportfolio’sstandarddeviationisequaltotheriskyasset’sstandarddeviationmultipliedbytheweightoftheriskyassetintheportfolio.σHum=wBestσBest=0.5x18.9=9.45%σ=wRAσRA13KeyPropertiesofAssetsandPortfolios-summaryofresults-HumanexPortfolioAPortfolioBE(r)σ2σCovρScenario1Scenario2Scenario3Data0.50.30.2Probability25%10%-25%BestT-billsCaneBestT-billsBestCanePort.BE(r)Port.A10.5%357.7518.9%5%5%5%5%00Riskpremium5.5%7.75%89.39.4510.5%357.7518.9%1%-5%35%142.KeyPropertiesofAssets&Portfolios-illustrativetableforSugarcane-Scenarioprobability[Pr(s)]Scenariorateofreturn[r(s)]Expectedrateofreturn,[E(r)]Deviations(d)from[E(r)]Squareddeviations[d2]Variance(σ2]ContributiontoE(r)[Pr(s)r(s)]Contributiontoσ2[Pr(s)d2]StandardDeviation[σ]Scenario1Scenario2Scenario3NormalyearCrisisyearBullmarketBearmarket0.50.30.21%-5%35%-52=25-112=121292=8410.5x210=12.50.3x121=36.30.2x841=168.20.5x1=0.50.2x35=7.00.3x-5=-1.50.5-1.5+7.0=6.0%12.5+36.3+168.2=217√σ2=14.73%35–6=29-5-6=-111–6=-515KeyPropertiesofAssetsandPortfolios-summaryofresults-HumanexPortfolioAPortfolioBE(r)σ2σCovρScenario1Scenario2Scenario3Data0.50.30.2Probability25%10%-25%BestT-billsCaneBestT-billsBestCanePort.BE(r)Port.A10.5%357.751