【導(dǎo)讀】1. 2. 3. 4. 

　　

【正文】 r the 100 stocks during the sample period. σ2(ei) estimates the nonsystematic risk of each of the 100 stocks.p. 409CONCEPTCHECK1a.How many regression estimates of the SCL do we have from the sample?b.How many observations are there in each of the regressions?c.According to the CAPM, what should be the intercept in each of these regressions?Estimating the SML Now view Equation as a security market line (SML) with 100 observations for the stocks in your sample. You can estimate γ0 and γ1 in the following secondpass regression equation with the estimates bi from the first pass as the independent variable:Compare Equations and Equation 。 you should conclude that if the CAPM is valid, then γ0 and γ1 should satisfy In fact, however, you can go a step further and argue that the key property of the expected return–beta relationship described by the SML is that the expected excess return on securities is determined only by the systematic risk (as measured by beta) and should be independent of the nonsystematic risk, as measured by the variance of the residuals, σ2(ei), which also were estimated from the firstpass regression. These estimates can be added as a variable in Equation of an expanded SML that now looks like this: This secondpass regression equation is estimated with the hypotheses The hypothesis that γ2 = 0 is consistent with the notion that nonsystematic risk should not be “priced,” that is, that there is no risk premium earned for bearing nonsystematic risk. More generally, according to the CAPM, the risk premium depends only on beta. Therefore, any additional righthandside variable in Equation beyond beta should have a coefficient that is insignificantly different from zero in the secondpass regression.Tests of the CAPMEarly tests of the CAPM performed by John Lintner,1 and later replicated by Merton Miller and Myron Scholes,2 used annual data on 631 NYSE stocks for 10 years, 1954 to 1963, and produced the following estimates (with returns expressed as decimals rather than percentages):p. 410These results are inconsistent with the CAPM. First, the estimated SML is “too flat”。 that is, the γ1 coefficient is too small. The slope should equal (% per year), but it is estimated at only .042. The difference, .122, is about 20 times the standard error of the estimate, .006, which means that the measured slope of the SML is less than it should be by a statistically significant margin. At the same time, the intercept of the estimated SML, γ0, which is hypothesized to be zero, in fact equals .127, which is more than 20 times its standard error . CONCEPTCHECK2a.What is the implication of the empirical SML being “too flat”?b.Do high or lowbeta stocks tend to outperform the predictions of the CAPM?c.What is the implication of the estimate of γ2?The twostage procedure employed by these researchers (., first estimate security betas using a timeseries regression and then use those betas to test the SML relationship between risk and average return) seems straightforward, and the rejection of the CAPM using this approach is disappointing. However, it turns out that there are several difficulties with this approach. First and foremost, stock returns are extremely volatile, which lessens the precision of any tests of average return. For example, the average standard deviation of annual returns of the stocks in the Samp。P 500 is about 40%。 the average standard deviation of annual returns of the stocks included in these tests is probably even higher.In addition, there are fundamental concerns about the validity of the tests. First, the market index used in the tests is surely not the “market portfolio” of the CAPM. Second, in light of asset volatility, the security betas from the firststage regressions are necessarily estimated with substantial sampling error and therefore cannot readily be used as inputs to the secondstage regression. Finally, investors cannot borrow at the riskfree rate, as assumed by the simple version of the CAPM. Let us investigate the implications of these problems in turn.The Market IndexIn what has bee known as Roll39。s critique, Richard Roll3 pointed out that: 1.There is a single testable hypothesis associated with the CAPM: The market portfolio is meanvariance efficient. 2.All the other implications of the model, the bestknown being the linear relation between expected return and beta, follow from the market portfolio39。s efficiency and therefore are not independently testable. There is an “if and only if” relation between the expected return–beta relationship and the efficiency of the market portfolio.p. 4113.In any sample of observations of individual returns there will be an infinite number of ex post (., after the fact) meanvariance efficient portfolios using the sample period returns and covariances (as opposed to the ex ante expected returns and covariances). Sample betas calculated between each such portfolio and individual assets will be exactly linearly related to sample average returns. In other words, if betas are calculated against such portfolios, they will satisfy the SML relation exactly whether or not the true market portfolio is meanvariance efficient in an ex ante sense.4.The CAPM is not testable unless we know the exact position of the true market portfolio and use it in the tests. This implies that the theory is not testable unless all individual assets are included in the sample.5.Using a proxy such as the Samp。P 500 for the market portfolio is subject to two difficulties. First, the proxy itself might be meanvariance efficient even when the true market portfolio is not. Conversely, the proxy may turn out to be inefficient, but obviously this alone implies nothing about the true market portfolio39。s efficiency. Furth