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1、CapitalMarketsAnalysisTopic2:PortfolioTheory1PreviewSomedescriptivestatisticsKeypropertiesofassetsandportfoliosAssumptionsofModel2.1Expectedwealth,variance,standarddeviation,riskpremiumAssumptionsofModel2.2Expectedrateofreturn,variance,standarddeviationofasse
2、tsExpectedrateofreturn,variance,standarddeviationofportfolioCovarianceCorrelationcoefficientProblemsPresentations2SomeDescriptiveStatistics-assumptionsofModel2.1-1.Initialwealth(W)=$100,000,whichistobeinvestedforoneyear.2.Thiswealthcanbeinvestedinonlyonerisky
3、asset,withtwopossiblescenarios.Attheendoftheyear,theassetwillbewortheither:a.$150,000(W1=$150,000);orb.$80,000(W2=$80,0003.Theprobabilityofthefirstscenariois0.6andofthesecondis,therefore,0.43SomeDescriptiveStatistics-expectedwealth-Wealth$100,000Expectedretur
4、ns[E(Wi)]Probability(pi)0.6$90,0000.4$32,000Possiblereturns(Wi)$150,000$80,000E(W)=p1W1+p2W2$122,000Expectedwealth=0.6x$150,000+0.4x$80,000=$122,0004SomeDescriptiveStatistics-varianceandstandarddeviation-100150W180W2122E(W)DifferencefromexpectedvalueSquareofd
5、ifferencesWeightedsumofsquareddifferencesSquarerootofweightedsum28,00028,0002=784m0.6x784m=470m-42,000-42,0002=1,764m0.4x1,764m=706m1,176m$34,293Variance(σ2)Standarddeviation(σ)σ2=p1[W1–E(W)]2+p2[W2–E(W)]2σ=√σ2Wealth($,000)timet0t1=470m+706m=1,176m=√1,176m=$3
6、4,2935SomeDescriptiveStatistics-riskpremium-$105,000$17,000RiskpremiumInvestinrisk-freeassetWealth$100,000Investinriskyasset$150,000$80,0000.60.4$90,000$32,000$122,000$105,0001.0$105,0006KeyPropertiesofAssetsandPortfolios-assumptionsofModel2-1.Humanexhas50%of
7、itsportfolioinBestCandystock2.ThereturnonBestCandystockissensitiveto(a)thepriceofsugarand(b)themoodofthestockmarket.Thereturnsare:S1=25%,S2=10%andS3=-25%5.ThereturnonSugarcaneisalsosensitivetothepriceofsugarandthemoodofthestockmarket.Thereturnsare:S1=1%,S2=-5
8、%andS3=35%3.Humanexcaninvesttheother50%ofitsportfolioineitherT-billsorSugarcane.4.T-billsarerisk-free,withareturnineachscenarioperiodof5%.7KeyPropertiesofAssetsandPortfolios-structureofan
