资本资产定价模型(CAPM)(PPT57)(1)

10-0资本资产定价模型(CAPM)Thoughthisbemadness,yetthereismethodinit.WilliamShakespeare10-110.1单个证券•所关注的单个证券的特征如下：–期望收益–方差与标准方差–协方差与相关系数•两个不同收益如何一起变动？10-210.2期望收益、方差与标准方差考虑下面的两个风险资产世界。各种状态发生的概率都是1/3，仅存在两种风险资产：股票基金和债券基金。状态概率股票基金债券基金萧条33.3%-7%17%正常33.3%12%7%繁荣33.3%28%-3%收益率10-310.2期望收益、方差与标准方差股票基金债券基金状态回报率标准差回报率标准差萧条-7%3.24%17%1.00%正常12%0.01%7%0.00%繁荣28%2.89%-3%1.00%期望收益11.00%7.00%方差0.02050.0067标准差14.3%8.2%NE(r)=p(s)r(s)s=1]2E(r)-s[rspN1=s=2)()(10-4股票基金债券基金状态回报率标准差回报率标准差萧条-7%3.24%17%1.00%正常12%0.01%7%0.00%繁荣28%2.89%-3%1.00%期望收益11.00%7.00%方差0.02050.0067标准差14.3%8.2%10.2期望收益、方差与标准方差%11)(%)28(31%)12(31%)7(31)(SSrErE10-5股票基金债券基金状态回报率标准差回报率标准差萧条-7%3.24%17%1.00%正常12%0.01%7%0.00%繁荣28%2.89%-3%1.00%期望收益11.00%7.00%方差0.02050.0067标准差14.3%8.2%10.2期望收益、方差与标准方差%7)(%)3(31%)7(31%)17(31)(BBrErE10-6股票基金债券基金状态回报率标准差回报率标准差萧条-7%3.24%17%1.00%正常12%0.01%7%0.00%繁荣28%2.89%-3%1.00%期望收益11.00%7.00%方差0.02050.0067标准差14.3%8.2%10.2期望收益、方差与标准方差2(11%(7%))3.24%10-7股票基金债券基金状态回报率标准差回报率标准差萧条-7%3.24%17%1.00%正常12%0.01%7%0.00%繁荣28%2.89%-3%1.00%期望收益11.00%7.00%方差0.02050.0067标准差14.3%8.2%10.2期望收益、方差与标准方差%01.%)12%11(210-8股票基金债券基金状态回报率标准差回报率标准差萧条-7%3.24%17%1.00%正常12%0.01%7%0.00%繁荣28%2.89%-3%1.00%期望收益11.00%7.00%方差0.02050.0067标准差14.3%8.2%10.2期望收益、方差与标准方差%89.2%)28%11(210-9股票基金债券基金状态回报率标准差回报率标准差萧条-7%3.24%17%1.00%正常12%0.01%7%0.00%繁荣28%2.89%-3%1.00%期望收益11.00%7.00%方差0.02050.0067标准差14.3%8.2%10.2期望收益、方差与标准方差%)89.2%01.0%24.3(31%05.210-10股票基金债券基金状态回报率标准差回报率标准差萧条-7%3.24%17%1.00%正常12%0.01%7%0.00%繁荣28%2.89%-3%1.00%期望收益11.00%7.00%方差0.02050.0067标准差14.3%8.2%10.2期望收益、方差与标准方差0205.0%3.1410-11协方差衡量资产同步变动的程度考虑如下的乘积：[r股票(s)-E(r股票)][r债券(s)-E(r债券)]协方差的定义Cov(r股票,r债券)=SP(s)[r股票(s)-E(r股票)][r债券(s)-E(r债券)]10-12股票基金债券基金状态回报率标准差回报率标准差萧条-7%3.24%17%1.00%正常12%0.01%7%0.00%繁荣28%2.89%-3%1.00%期望收益11.00%7.00%方差0.02050.0067标准差14.3%8.2%10.3投资组合的风险与收益注意到股票的收益率和风险都比债券的高。让我们考虑一个风险收益权衡的组合：一半由股票构成、一半由债券构成。10-1310.3投资组合的风险与收益状态股票基金债券基金投资组合离差平方萧条-7%17%5.0%0.160%正常12%7%9.5%0.003%繁荣28%-3%12.5%0.123%期望收益11.00%7.00%9.0%方差0.02050.00670.0010标准差14.31%8.16%3.08%收益率组合的收益率等于组合中的股票和债券收益率的加权平均值。SSBBPrwrwr%)17(%50%)7(%50%510-14状态股票基金债券基金组合离差平方萧条-7%17%5.0%0.160%正常12%7%9.5%0.003%繁荣28%-3%12.5%0.123%期望收益11.00%7.00%9.0%方差0.02050.00670.0010标准差14.31%8.16%3.08%收益率10.3投资组合的风险与收益组合的收益率等于组合中的股票和债券收益率的加权平均值。%)7(%50%)12(%50%5.9SSBBPrwrwr10-15状态股票基金债券基金组合离差平方萧条-7%17%5.0%0.160%正常12%7%9.5%0.003%繁荣28%-3%12.5%0.123%期望收益11.00%7.00%9.0%方差0.02050.00670.0010标准差14.31%8.16%3.08%收益率10.3投资组合的风险与收益组合的收益率等于组合中的股票和债券收益率的加权平均值。%)3(%50%)28(%50%5.12SSBBPrwrwr10-16状态股票基金债券基金组合离差平方萧条-7%17%5.0%0.160%正常12%7%9.5%0.003%繁荣28%-3%12.5%0.123%期望收益11.00%7.00%9.0%方差0.02050.00670.0010标准差14.31%8.16%3.08%收益率10.3投资组合的风险与收益组合的期望收益率是组合中各个证期望收益率的加权平均。%)7(%50%)11(%50%9)()()(SSBBPrEwrEwrE10-17状态股票基金债券基金组合离差平方萧条-7%17%5.0%0.160%正常12%7%9.5%0.003%繁荣28%-3%12.5%0.123%期望收益11.00%7.00%9.0%方差0.02050.00670.0010标准差14.31%8.16%3.08%收益率10.3投资组合的风险与收益有两个风险证券组成的组合的方差是：BSSSBB2SS2BB2P)ρσ)(wσ2(w)σ(w)σ(wσ其中BS是股票基金和债券基金收益率的相关系数。10-1810.3投资组合的风险与收益注意到分散化使得风险下降。由一半股票和一半债券构成的组合风险比组合中的股票或者债券的风险都小。状态股票基金债券基金组合离差平方萧条-7%17%5.0%0.160%正常12%7%9.5%0.003%繁荣28%-3%12.5%0.123%期望收益11.00%7.00%9.0%方差0.02050.00670.0010标准差14.31%8.16%3.08%收益率10-19Portfoliorules组合规则1：E(rp)=w1E(r1)+w2E(r2)组合规则2：p2=w1212+w2222+2w1w212(r1,r2)含意：由于(r1,r2)1，所以可以得到：p2w1212+w2222+2w1w212=(w11+w22)2pw11+w22)(1)期望收益率=组合中各证券的期望收益加权平均。(2)如果1，证券组合后的风险(p)比组合中各证券的风险加权小（比如：标准方差）。这个性质也被称为分散化。10-20证券组合的风险和收益5.0%6.0%7.0%8.0%9.0%10.0%11.0%12.0%0.0%2.0%4.0%6.0%8.0%10.0%12.0%14.0%16.0%组合风险(标准差)组合收益股票在组合的比率风险收益0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50.00%3.08%9.00%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0%10.4两个资产的有效集我们可以考虑除了50%股票和50%债券组合方式之外的情况…100%债券100%股票10-21证券组合的风险和收益5.0%6.0%7.0%8.0%9.0%10.0%11.0%12.0%0.0%2.0%4.0%6.0%8.0%10.0%12.0%14.0%16.0%组合风险(标准差)组合收益10.4两个资产的有效集我们可以考虑除了50%股票和50%债券组合方式之外的情况…100%bonds100%stocks%instocksRiskReturn0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0%%instocksRiskReturn0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0%%instocksRiskReturn0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0%%instocksRiskReturn0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0%%in