第12章投资组合选择(金融学,厦门大学)

1第12章:投资组合选择Copyright©PrenticeHallInc.2000.Author:NickBagley,bdellaSoft,Inc.学习目的了解资产组合的理论与应用2第12章的内容•12.1个人资产组合的选择过程•12.2预期收益和风险之间的权衡•12.3多个风险资产的有效组合3学习目的•理解个人资产组合的理论和应用4SecurityPrices101001000100001000000510152025303540YearsValue(Log)StockBondStock_MuBond_Mu5SecurityPrices101001000100001000000510152025303540YearsValue(Log)StockBondStock_MuBond_Mu6SecurityPrices101001000100001000000510152025303540YearsValue(Log)StockBondStock_MuBond_Mu7…andLotsMore!SecurityPrices101001000100001000000510152025303540YearsValue(Log)StockBondStock_MuBond_MuSecurityPrices101001000100001000000510152025303540YearsValue(Log)StockBondStock_MuBond_MuSecurityPrices101001000100001000000510152025303540YearsValue(Log)StockBondStock_MuBond_MuSecurityPrices101001000100001000000510152025303540YearsValue(Log)StockBondStock_MuBond_Mu8SecurityPrices101001000100001000000510152025303540YearsValue(Log)StockBondStock_MuBond_Mu9ProbabilityofFuturePrice0.0000.0050.0100.0150.0200.0250.0300.035050100150200250300ValueProbabilityDensityProb_Stock_2Prob_Bond_2Prob_Stock_5Prob_Bond_5Prob_Stock_10Prob_Bond_10Prob_Stock_40Prob_Bond_4010ProbabilisticStockPriceChangesOverTime0.0000.0020.0040.0060.0080.0100.0120.0140.0160.0180.0200200400600800PriceProbabilityDensityStock_Year_1Stock_Year_2Stock_Year_3Stock_Year_4Stock_Year_5Stock_Year_6Stock_Year_7Stock_Year_8Stock_Year_9Stock_Year_1011ProbabilisticBondPriceChangesoverTime0.0000.0050.0100.0150.0200.0250.0300.0350.0400.0450100200300400PriceProbabilityDensityBond_Year_1Bond_Year_2Bond_Year_3Bond_Year_4Bond_Year_5Bond_Year_6Bond_Year_7Bond_Year_8Bond_Year_9Bond_Year_10121-YearOut0.00000.00500.01000.01500.02000.02500.03000.03500.04000.0450020406080100120140160180200PriceDensityStock_1_YearBond_1_YearMode=104Mode=106Median=104Mean=104Median=111Mean=11313TwoYearsOut0.0000.0050.0100.0150.0200.0250.0300.035020406080100120140160180200PriceDensityStock_2_YearBond_2_Year145-YearsOut0.0000.0020.0040.0060.0080.0100.0120.0140.0160.0180.0200100200300400500PriceDensityStock_5_YearBond_5_YearMode=122Mode=135Median=126Mean=128Median=165Mean=1821510-YearsOut0.0000.0020.0040.0060.0080.0100.01202004006008001,000ValueDensityStock_10_YearBond_10_Year1640YearsOut0.0000.0000.0000.0010.0010.0010.0010.0010.00205,00010,00015,00020,00025,00030,000ValueDensityStock_40_YearBond_40_YearMode=503Mode=1,102Median=650Mean=739Median=5,460Mean=12,15117ValueofCentralTendencyStatisticsfortheLogNormal1_Year2_Years5_Years10_Years40_YearsAssume:Sig=0.20,Mu=0.12mode$106.18$112.75$134.99$182.21$1,102.32median$110.52$122.14$164.87$271.83$5,459.82mean$112.75$127.12$182.21$332.01$12,151.04Assume:Sig=0.08,Mu=0.05mode$104.12$108.42$122.38$149.78$503.29median$104.79$109.81$126.36$159.68$650.13mean$105.13$110.52$128.40$164.87$738.91modeThemostprobablepricemedian50%ofpricesareequalorlowerthatthismeanTheexpectedoraverageprice18MortalityTableMaleFemaleAgeMDePmMExLifeFDePmFExLife6016.0817.519.4721.256117.5416.7910.1320.446525.4214.0414.5917.327039.5110.9622.1113.677564.198.3138.2410.328098.846.1865.997.4885152.954.46116.15.1890221.773.18190.753.4595329.961.87317.321.9119DeathsPerThousandM&F0501001502002503003506065707580859095AgeDeaths/1000MDePmFDePm20LifeExpection05101520256065707580859095AgeRemainingExpectedLifeMExLifeFExLife21无风险资产与单个风险资产的组合–组合的预期收益是组合中每个证券预期收益的加权平均数mp=W1*m1+W2*m2mp=W1*m1+(1-W1)*m222无风险资产与单个风险资产的组合–组合的波动性（风险）的计算就更为复杂:sp=((W1*s1)2+2W1*s1*W2*s2+(W2*s2)2)1/223无风险资产与单个风险资产的组合–由于证券2是无风险资产，令s2=0,则sp为:sp=((W1*s1)2+2W1*s1*W2*0+(W2*0)2)1/2sp=|W1|*s124无风险资产与单个风险资产的组合–总结sp=|W1|*s1,且:mp=W1*m1+(1-W1)*rf,So:如果W10,mp=[(rf-m1)/s1]*sp+rf其他mp=[(m1-rf)/s1]*sp+rf25APortfolioofaRiskyandaRisklessSecurity-0.20-0.15-0.10-0.050.000.050.100.150.200.250.300.000.100.200.300.400.50VolatilityReturn26CapitalMarketLine0.000.050.100.150.200.250.300.000.050.100.150.200.250.300.350.400.450.50VolatilityReturnLongriskyandshortrisk-freeLongbothriskyandrisk-free100%Risky100%Risk-less27共同基金平均占总收益%YTD1-Yr3-Yrs5-Yrs10-YrsLife14.8130.4015.8714.1516.5316.9628获得20%的收益率•假设你设定了20%的收益率–公式:mp=W1*m1+(1-W1)*rf–你的组合:s=20%,m=15%,rf=5%–则:W1=(mp-rf)/(m1-rf)=(0.20-0.05)/(0.15-0.05)=150%29获得20%的收益率•假设你正在管理一个$50,000,000的组合•W1为1.5或150%意味着你投资$75,000,000,通过借款弥补$25,000,000的缺口•假设可以按照无风险收益率借款30获得20%的收益率•这一组合的风险多大?sp=|W1|*s1=1.5*0.20=0.30•该组合的波动性（标准差）为30%31两个风险资产的组合•根据统计学原理，两个随机变量（如两个证券收益率）可以组合成一个新的随机变量•假设不同证券组合收益的线性模型:1with;212211wwrwrwrp32两只股票时等式•下面等式本身并不要求w1和w2之和为1,但是作为股票组合权重之和正好为1•股票组合的预期收益为单个股票预期收益的加权平均数：2211mmmwwp33两个股票时的等式•组合的风险的度量是否也如此简单？–组合的风险（用方差）表示为(wrong)2211ssswwp22222,12121212122sssss34记忆法•有一种方法可以帮助记忆2只以上股票组合波动性（方差）的公式•对于表格中每一单元，乘以对应行和对应列头上的数，然后加总，就可以得到股票组合方差的公式352个证券组合的方差W1*Sig1W2*Sig2W1*Sig11Rho(1,2)W2*Sig2Rho(2,1)12,121212222212122sssss363个证券组合的方差W1*Sig1W2*Sig2W3*Sig3W1*Sig11Rho(1,2)Rho(1,3)W2*Sig2Rho(2,1)1Rho(2,3)W3*Sig3Rho(3,1)Rho(3,2)13,232323,131312,121212323222221212222ssssssssss37具有正相关关系的普通股•假设2只股票的统计值如下:–meanreturn1=0.15–meanreturn2=0.10–standarddeviation1=0.20–standarddeviation2=0.25–correlationofreturns=0.90–initialprice1=$57.25–Initialpr