资本资产定价模型CAPM学习教案

会计学1第一页，共73页。2第1页/共73页第二页，共73页。3第2页/共73页第三页，共73页。4NE(r) = p(s)r(s)s=12E(r) - srsp N1=s = 2)()(离差平方(pngfng)离差平方(pngfng)离差平方第3页/共73页第四页，共73页。5%11)(%)28(31%)12(31%)7(31)(SSrErE离差平方(pngfng)离差平方(pngfng)第4页/共73页第五页，共73页。6%7)(%)3(31%)7(31%)17(31)(BBrErE离差平方(pngfng)离差平方(pngfng)第5页/共73页第六页，共73页。72(11%( 7%)3.24% 离差平方(pngfng)离差平方(pngfng)第6页/共73页第七页，共73页。8%01.%)12%11(2离差平方(pngfng)离差平方(pngfng)第7页/共73页第八页，共73页。9%89. 2%)28%11(2离差平方(pngfng)离差平方(pngfng)第8页/共73页第九页，共73页。10%)89. 2%01. 0%24. 3(31%05. 2离差平方(pngfng)离差平方(pngfng)第9页/共73页第十页，共73页。110205. 0%3 .14离差平方(pngfng)离差平方(pngfng)第10页/共73页第十一页，共73页。12S P(s)r(s)-E(r票)r债券(s)-E(r债券) 第11页/共73页第十二页，共73页。13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(y )风险收益权衡的组合：一半由股票构成、一半由债券构成。第12页/共73页第十三页，共73页。14组合的收益率等于组合中的股票(gpio)和债券收益率的加权平均值。SSBBPrwrwr%)17(%50%)7(%50%5第13页/共73页第十四页，共73页。15组合的收益率等于(dngy)组合中的股票和债券收益率的加权平均值。%)7(%50%)12(%50%5 . 9SSBBPrwrwr第14页/共73页第十五页，共73页。16组合(zh)的收益率等于组合(zh)中的股票和债券收益率的加权平均值。%)3(%50%)28(%50%5 .12SSBBPrwrwr第15页/共73页第十六页，共73页。17组合的期望收益率是组合中各个(gg)证期望收益率的加权平均。%)7(%50%)11(%50%9)()()(SSBBPrEwrEwrE第16页/共73页第十七页，共73页。18有两个(lin )风险证券组成的组合的方差是：BSSSBB2SS2BB2P)(w2(w)(w)(w其中BS 是股票基金(jjn)和债券基金(jjn)收益率的相关系数。第17页/共73页第十八页，共73页。19注意到分散化使得(sh de)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。第18页/共73页第十九页，共73页。20sp(w1s1+w2s2)第19页/共73页第二十页，共73页。21第20页/共73页第二十一页，共73页。22第21页/共73页第二十二页，共73页。23第22页/共73页第二十三页，共73页。24经济状况经济状况发生概率发生概率股票股票A 报酬率报酬率股票股票B报酬率报酬率萧条萧条0.200.150.20正常正常0.500.200.30景气景气0.300.600.40第23页/共73页第二十四页，共73页。25第24页/共73页第二十五页，共73页。26第25页/共73页第二十六页，共73页。27第26页/共73页第二十七页，共73页。28第27页/共73页第二十八页，共73页。29我们可以考虑(kol)除了50%股票和50%债券组合方式之外的情况100% 债券(zhiqun)100% 股票第28页/共73页第二十九页，共73页。30我们可以考虑除了50%股票和50%债券组合(zh)方式之外的情况100% bonds100% stocks% in stocks Risk Return0%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 stocks Risk Return0%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 stocks Risk Return0%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 stocks Risk Return0%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 stocks Risk Return0%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 stocks Risk Return0%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 stocks Risk Return0%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 stocks Risk Return0%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 stocks Risk Return0%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 stocks Risk Return0%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 stocks Risk Return0%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 stocks Risk Return0%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 stocks Risk Return0%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 stocks Risk Return0%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 stocks Risk Return0%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 stocks Risk Return0%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 stocks Risk Return0%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 stocks Risk Return0%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 stocks Risk Return0%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 stocks Risk Return0%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%第29页/共73页第三十页，共73页。31100% stocks100% bonds注意到一些(yxi)组合优于其他的组合，因为他们在同等的风险水平下收益比较高。这些有效的组合构成的集合在图中称为有效前沿。第30页/共73页第三十一页，共73页。32100% 债券(zhiqun)收益(shuy)100% 股票 = 0.2 = 1.0 = -1.0第31页/共73页第三十二页，共73页。33第32页/共73页第三十三页，共73页。ijjiNjNiiNiiPwww11212222211111,NNNiijiijijNN 其中1 N组合方差平均方差11N平均协方差随着N增大，组合(zh)的方差趋向于平均协方差。第33页/共73页第三十四页，共73页。35不可分散风险; 系统(xtng)风险; 市场风险可分散风险(fngxin); 非系统风险(fngxin); 具体企业风险(fngxin); 特有风险(fngxin)n组合证券数量大的情况下，方差项被有效地分散掉，但是协方差项不能分散掉。因此，分散化可以消除单个证券一部分风险，而不是全部的风险。组合风险第34页/共73页第三十五页，共73页。36nf. 最高法院的一项裁决显著地扩最高法院的一项裁决显著地扩大了生产者对产品使用者所造大了生产者对产品使用者所造成伤害的责任。成伤害的责任。第35页/共73页第三十六页，共73页。37收益(shuy)P单个资产第36页/共73页第三十七页，共73页。38收益(shuy)P最小方差组合单个资产第37页/共73页第三十八页，共73页。39收益(shuy)P最小风险组合有效前沿单个证券第38页/共73页第三十九页，共73页。40100% 债券(zhiqun)100% 股票rf收益第39页/共73页第四十页，共73页。41标准差 = (.5 x 0)2+ (.5 x .16)2 + (2 x .5 x .5 x 0 x .16 x 0).5 = .5 x .16 = .08 or 8%第40页/共73页第四十一页，共73页。42第41页/共73页第四十二页，共73页。43SE(收益(shuy)rf = 7.5%15% 16% 第42页/共73页第四十三页，共73页。44100% 债券(zhiqun)100% 股票rf收益平衡基金CML第43页/共73页第四十四页，共73页。45收益(shuy)P有效前沿rfCML第44页/共73页第四十五页，共73页。46收益(shuy)P有效前沿rfMCML第45页/共73页第四十六页，共73页。47收益(shuy)P有效前沿rfMCML第46页/共73页第四十七页，共73页。48收益(shuy)P有效前沿rfMCML第47页/共73页第四十八页，共73页。49100% 债券(zhiqun)100% 股票rf收益平衡基金CML第48页/共73页第四十九页，共73页。50100% 债券(zhiqun)100% 股票rf收益最优风险组合CML第49页/共73页第五十页，共73页。51100% 债券(zhiqun)100% 股票rf收益最优风险组合CML第50页/共73页第五十一页，共73页。52100% 债券(zhiqun)100% 股票收益第一最优风险组合第二最优风险组合CML0CML10fr1fr第51页/共73页第五十二页，共73页。53第52页/共73页第五十三页，共73页。54第53页/共73页第五十四页，共73页。55组合收益率进行回归，回归线的斜率是对贝塔的统计估计。)(2),(MRMRiRCovi第54页/共73页第五十五页，共73页。56第55页/共73页第五十六页，共73页。57股票股票贝塔贝塔Bank of America1.55Borland International2.35Travelers, Inc.1.65Du Pont1.00Kimberly-Clark Corp.0.90Microsoft1.05Green Mountain Power0.55Homestake Mining0.20Oracle, Inc.0.49第56页/共73页第五十七页，共73页。58)()(2,MMiiRRRCov明显地，你对贝塔的估计取决于你所选择的市场(shchng)组合。第57页/共73页第五十八页，共73页。59单个证券(zhngqun)的期望收益:MFRR市场风险溢价)(FMiFiRRRR市场风险溢价这个公式对多元化组合中的单个证券也适用。第58页/共73页第五十九页，共73页。60第59页/共73页第六十页，共73页。61)(FMiFiRRRR假设 i = 0, 则期望收益率是 RF.假设 i = 1, 则MiRR 证券的期望收益=无风险利率+证券贝塔市场风险溢价第60页/共73页第六十一页，共73页。62第61页/共73页第六十二页，共73页。63第62页/共73页第六十三页，共73页。64期望(qwng)收益)(FMiFiRRRRFR1.0MR)(FMiFiRRRR第63页/共73页第六十四页，共73页。65期望(qwng)收益%3FR%31.5%5 .135 . 1 i%10MR%5 .13%)3%10(5 . 1%3iR第64页/共73页第六十五页，共73页。)(FRMRBristolFRBristolR%4 .12%)4 . 8 x 81(.%6 . 5BristolR第65页/共73页第六十六页，共73页。贝塔(bi t)期望(qwng)收益0Rf = 5.6% 1.0Rm = 14%1.5.8112.4%Bristol Myers SquibbRR第66页/共73页第六十七页，共73页。68第67页/共73页第六十八页，共73页。69第68页/共73页第六十九页，共73页。70第69页/共73页第七十页，共73页。71ABAABB2BB2AA2P)(w2(w)(w)(w)()()(BBAAPrEwrEwrE通过改变wA, 我们就可以得到组合的有效集合。我们以两个资产为例子画出有效前沿，有效前沿的弯曲程度反映了多元化的效应(xioyng)：两证券的相关程度越低，多元化的效应(xioyng)越大。两个证券有效组合的曲线形状和多个证券的形状是一致的。第70页/共73页第七十一页，共73页。72收益(shuy)P有效前沿rfMCML通过借贷，投资者可以选择资本市场线上的一点（他所偏好的那一点）。第71页/共73页第七十二页，共73页。73CAPM认为(rnwi)，证券的期望收益率和证券的贝塔正相关：)()(2,MMiiRRRCov)(FMiFiRRRR第72页/共73页第七十三页，共73页。