TheCapitalAssetPricingModel股票的需求与均衡价格

1、9-1 9-2 9-3 9-4 9-5 9-6 9-7 9-8 9-9 9-10 9-11 9-12 9-13 9-14 9-15 9-16 9-17 式中2 M为市场资产组合的方差； A 为投资者风险厌恶的平均水平。请注 意由于市场资产组合是最优资产组合，即风险有效地分散于资产组合中的 所有股票， 2 M也也就是这个市场的系统风险。 9-18 9-19 9-20 9-21 9-22 E(r) E(rM) rf M 资本市场线CML m 9-23 M 9-24 9-25 9-26 9-27 9-28 9-29 9-30 9-31 9-32 9-33 9-34 9-35 9-36 9-37 9-

2、38 9-39 9-40 9-41 9-42 9-43 9-44 9-45 9-46 9-47 E(r) E(rM) rf 证券市场线证券市场线 SML b b bM= 1.0 9-48 9-49 9-50 9-51 E(r) Rx=13% SML b b 1.0 Rm=11% Ry=7.8% 3% 1.25 b bx .6 b by .08 By 9-52 9-53 9-54 Q P Z(Q) Z(P) Erz (Q) Erz (P) E(r) 9-55 ),( ),(),( )()()()( 2 QPP QPPi QPQi rrCov rrCovrrCov rErErErE 任何资产的期望

3、收益可以准确地由任意两个边界资产组合的期 望收益的线性函 数表示。例如，考虑有两个最小方差边界资产 组合 P与Q，布莱克给出任意资产i的期 望收益的表达如下： The expected return of any asset can be expressed as an exact, linear function of the expected return on any two frontier portfolios. Consider, for example, the minimum-variance frontier portfolios P and Q. Black showed

4、that the expected return on any asset i can be expressed as 9-56 假定经济中只有两个投资者，一个相对来说厌恶风险，而另外 一个可以忍受风险。 厌恶风险的投资者选择资本配置线上的资 产组合 T，如图 9-5所示，也就是说，他的资 产组合由资产组 合 T与按无风险利率贷出的无风险资产组成。 T是由无风险借 贷利率 rf 出发的有效率边界的切点。忍受风险的投资者愿意在 承担更多风险的前提下取得更高 的风险溢价：他选择图中的 S 。S资产组合与 T资产组合相比较，虽同处于有效率边界 但其 风险与收益均高于 T 资产组合。总的风险资产组合（

5、也就是市 场资产组合，M ）由T与S结合而成，各自权重由两个投资者的 相对财富与风险厌恶程度决定。由于 T与S 都在有效率边界上 ，所以根据性质 1，市场资产组合 M也在有效率边界上。 9-57 Imagine an economy with only two investors, one relatively risk averse and one risk tolerant. The risk-averse investor will choose a portfolio on the CAL supported by portfolio T in Figure 9.8, that is,

6、 he will mix portfolio T with lending at the risk-free rate. T is the tangency portfolio on the efficient frontier from the risk-free lending rate, rf. The risk-tolerant investor is willing to accept more risk to earn a higher-risk premium; she will choose portfolio S. This portfolio lies along the

7、efficient frontier with higher risk and return than portfolio T. The aggregate risky portfolio (i.e., the market portfolio, M) will be a combination of T and S, with weights determined by the relative wealth and degrees of risk aversion of the two investors. Since T and S are each on the efficient f

8、rontier, so is M (from Property 1). 9-58 9-59 根据性质 2，市场资产组合 M 也存在一个在最小方差边界上 的零贝塔“伴随”资 产组合： Z(M)，见图 9-5。根据性质 3 及9-8式，我们可以用市场资产组合 M及Z(M)来表 示任何证 券的收益。由于 Cov(r M，r Z(M) )0，所以有 From Property 2, M has a companion zero-beta portfolio on the minimum-variance frontier, Z(M), shown in Figure 9.8. Moreover, by

9、 Property 3 we can express the return on any security in terms of M and Z(M) as in equation 9.8. But, since by construction Cov(r M，r Z(M) )0 , the expression simplifies to 2 )()( ),( )()()()( M Mi MZMMZi rrCov rErErErE 9-60 2 )()( ),( )()()()( M Mi MZMMZi rrCov rErErErE 式中的资产组合 P与资产组合 Q分别由市场资产组合 M及Z(M) 代替。上式可视为一个简化了的 CAPM模型，在其中，E(r z (m) 取代了rf 。 where P has been replaced by M and Q has been replaced by Z(M). Equation 9.9 may be interpreted as a variant of the simple CAPM, in which r f has been replaced with E(r z (m) 9-61 9-62 9-63 f (ci) = 证券i 的流动溢价， f (ci) 是关于ci的