To this point we have described the time series tests of the CAPM performed by Black, Jensen, and Scholes. We now very briefly describe thei^^SS^ScEonaTtests^Recall that one of the major problems in cross-sectional tests (second^ssrepessionsjwas an inability to identify the true Beta. This biased the intercept of the second-pass regression upward, biased its slope downward, and caused residual risk to serve as a proxy variable for Beta risk. One way to decrease substantiallyjhc^rrorin estimatingBetajs B|fa«-ie>r-porff5IIos ratHeTth»i4bi^cuHtieSfTo the extent that errors inmeasuring each »""stock's Betas are random, they will cancel out and the aggregate error will be very small „when Betas are estimated for portfolios.7 T>e'-giTrap"mg-pro^

; portfolios to estimate Betas for second-pass regressions. When the excess returns for the 10 portfolios described in Table 15.2 are regressed against the Betas tor each portfolio, the results are

The results are shown diagranunatically in Fignxs-15-2.-

The positive value of the intercept that emerges from this analysis is powerful evidence I in support of the two-factor model.8 fate high percentage Of the variation m returns ilamed (9iS7o) shows that a straight line describes returns very well as predicted by the theory. Let us now turn to an examination of the Fama and MacBeth tests of the CAPM.

Tests of Fama and MacBeth

Fama and MacBeth [30] used an interesting methodology to test the CAPM. They formed 20 portfolios of securities to estimate Betas from a first-pass regression, using the same procedure as Black et al. However, they then performed one second-pass regression for each_agfltkj>ver the time period 1935-1968. The equation they tested was h = to, + T„P, - Yafl? + % A + (15.4)

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