11-风险和收益资本资产定价模型

Copyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/IrwinCopyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/Irwin收益和风险：资本资产定价模型（CAPM）第十一章Copyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/IrwinCopyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/Irwin本章目录11.1单个证券11.2期望收益、方差和协方差11.3投资组合的收益和风险11.4有效集11.5无风险的借和贷11.6公告、惊奇和期望收益11.7风险：系统性和非系统性11.8多元化和投资组合风险11.9市场均衡11.10风险和期望收益之间的关系：资本资产定价模型Copyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/IrwinCopyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/Irwin11.1单个证券单个证券的特征：期望收益：投资者期望在下一个时期所能获得的收益。方差和标准差：评价证券收益的指标。方差：证券收益与其平均收益的差的平方和的平均数。标准差：方差的平方根。协方差和相关系数：衡量两种证券之间的相互关系的指标。Copyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/IrwinCopyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/Irwin11.2期望收益、方差和协方差例：A公司和B公司股票的报酬率及其概率分布情况见表，计算两家公司的期望报酬率。经济情况该种经济情况发生的概率PI报酬率（R）A公司B公司萧条衰退正常繁荣0.100.200.50.0.20-30%-10%20%50%0%5%20%-5%Copyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/IrwinCopyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/Irwin期望收益：E（RA）=15%E（RB）=10%)(1niiiKPEKCopyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/IrwinCopyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/Irwin离散程度：用以衡量风险大小的统计指标。离散程度越大，风险越大；离散程度越小，风险越小。方差：Var（RA）=σA2=0.0585Var（RB）=σB2=0.0110iniiPKK212)(Copyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/IrwinCopyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/Irwin标准离差：SD（RA）=σA=24.2%SD（RB）=σB=10.5%标准离差越小，风险也就越小只能用于比较期望报酬率相同的各项投资的风险大小标准离差率（标准差系数）：iniiPKK21)(iiiKVCopyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/IrwinCopyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/Irwin协方差离差=经济状况下的基金的收益率－期望收益率.加权=离差×经济状况发生概率Cov（RA，RB）=σA，B=iBBiAniiAPKKKK)()(1两个公司股票收益正相关，协方差为正两个公司股票收益负相关，协方差为负两个公司股票收益不相关，协方差为0Copyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/IrwinCopyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/Irwin相关系数039.0105.0*242.0001.0σ=),(B，AbabaCov两个公司股票收益正相关，相关系数为正两个公司股票收益负相关，相关系数为负两个公司股票收益不相关，相关系数为0Copyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/IrwinCopyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/Irwin相关系数：[-1,+1]相关系数=+1，完全正相关相关系数=-1，完全负相关相关系数=0，完全不相关Copyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/IrwinCopyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/Irwin若A、B两种股票完全负相关，并且两种股票在投资中所占比重均为50%.年份年份股票组合报酬率%报酬率%报酬率%AKBK组合KA股票B股票年份-103040-10-1015304040Copyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/IrwinCopyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/Irwin若A、B两种股票完全正相关，并且两种股票在投资中所占比重均为50%.报酬率%AKA股票年份-103040报酬率%BKB股票年份-103040报酬率%年份-103040组合K股票组合Copyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/IrwinCopyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/Irwin投资组合关系取决于相关系数-1.0ρ+1.0如果ρ=+1.0,完全无法分散风险如果ρ=–1.0,完全分散风险Copyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/IrwinCopyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/Irwin60%投资于A，40%投资于B。11.3投资组合的收益和风险AB期望收益率15%10%方差σ20.05850.0110标准差σ24.2%10.5%协方差-0.001相关系数-0.039Copyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/IrwinCopyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/Irwin投资组合的期望收益投资组合的期望收益率=两种证券收益率的简单加权平均。权数是投资比例)()(BBAAPREWREWE=0.6*15%+0.4*10%=13%Copyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/IrwinCopyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/Irwin投资组合的方差ABBBAA2BB2AAABBA2BB2AA2AB)ρσ)(wσ2(w)σ(w)σ(wσw2w)σ(w)σ(wABVarσ)(=0.02234Copyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/IrwinCopyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/Irwin投资组合的标准差)()(ABVarABSDAB投资组合的多元化效应：当由两种证券构成投资组合时，只要ρ1，投资组合的标准差就小于这两种证券各自标准差的加权平均数。=14.95%投资组合的加权平均标准差BBAAWW=0.6*24.2%+0.4*10.5%=18.7%Copyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/IrwinCopyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/Irwin11.4有效集除了60%投资于股票40%投资于债券外，我们可以也可以考虑其他的分配比例。一些投资组合可能要优于另一些投资组合，这是因为它们在相同的风险水平下具有更高的收益。Copyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/IrwinCopyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/Irwin■B公司A公司组合的期望收益%组合的标准差%一对证券之间只存在一个相关系数：-0.039不同投资比例构成的投资组合形成了一条曲线13●●1：表示投资组合中B公司的股票占大部分比例；3：表示投资组合中A公司的股票占大部分比例。2：上题计算出来的投资组合。6:4MV点：最小方差组合，最小标准差组合。10%15%MV机会集、可能集●2Copyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/IrwinCopyright©2007byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/Irwin不同相关系数的投资组合=0.