资本资产定价模型 CAPMPPT学习教案

会计学12第1页/共73页3第2页/共73页4NE(r) = p(s)r(s)s=12E(r) - srsp N1=s = 2)()(离差平方离差平方离差平方第3页/共73页5%11)(%)28(31%)12(31%)7(31)(SSrErE离差平方离差平方第4页/共73页6%7)(%)3(31%)7(31%)17(31)(BBrErE离差平方离差平方第5页/共73页72(11%( 7%)3.24% 离差平方离差平方第6页/共73页8%01.%)12%11(2离差平方离差平方第7页/共73页9%89. 2%)28%11(2离差平方离差平方第8页/共73页10%)89. 2%01. 0%24. 3(31%05. 2离差平方离差平方第9页/共73页110205. 0%3 .14离差平方离差平方第10页/共73页12第11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14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第13页/共73页15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 . 9SSBBPrwrwr第14页/共73页16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 .12SSBBPrwrwr第15页/共73页17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第16页/共73页18有两个风险证券组成的组合的方差是：BSSSBB2SS2BB2P)(w2(w)(w)(w其中BS 是股票基金和债券基金收益率的相关系数。第17页/共73页19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。第18页/共73页20p(w11+w22)第19页/共73页21第20页/共73页22第21页/共73页23第22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25第24页/共73页26第25页/共73页27第26页/共73页28第27页/共73页29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% 股票第28页/共73页30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% 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31100% stocks100% bonds注意到一些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32100% 债券收益100% 股票 = 0.2 = 1.0 = -1.0第31页/共73页33第32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，组合的方差趋向于平均协方差。第33页/共73页35不可分散风险; 系统风险; 市场风险可分散风险; 非系统风险; 具体企业风险; 特有风险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37收益P单个资产第36页/共73页38收益P最小方差组合单个资产第37页/共73页39收益P最小风险组合有效前沿单个证券第38页/共73页40100% 债券100% 股票rf收益第39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42第41页/共73页43SE(收益)rf = 7.5%15% 16% 第42页/共73页44100% 债券100% 股票rf收益平衡基金CML第43页/共73页45收益P有效前沿rfCML第44页/共73页46收益P有效前沿rfMCML第45页/共73页47收益P有效前沿rfMCML第46页/共73页48收益P有效前沿rfMCML第47页/共73页49100% 债券100% 股票rf收益平衡基金CML第48页/共73页50100% 债券100% 股票rf收益最优风险组合CML第49页/共73页51100% 债券100% 股票rf收益最优风险组合CML第50页/共73页52100% 债券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53第52页/共73页54第53页/共73页55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56第55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58)()(2,MMiiRRRCov明显地，你对贝塔的估计取决于你所选择的市场组合。第57页/共73页59单个证券的期望收益: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60第59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62第61页/共73页63第62页/共73页64期望收益)(FMiFiRRRRFR1.0MR)(FMiFiRRRR第63页/共73页65期望收益%3FR%31.5%5 .135 . 1 i%10MR%5 .13%)3%10(5 . 1%3iR第64页/共73页)(FRMRBristolFRBristolR%4 .12%)4 . 8 x 81(.%6 . 5BristolR第65页/共73页贝塔期望收益0Rf = 5.6% 1.0Rm = 14%1.5.8112.4%Bristol Myers SquibbRR第66页/共73页68第67页/共73页69产收益率与市场收益率的敏感产收益率与市场收益率的敏感度度) 第68页/共73页70第69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：两证券的相关程度越低，多元化的效应越大。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72收益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73CAPM认为，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