The way(C1)is examined in the time-series regression approach is generically different.The alternative hypothesis is vague.One estimates the time-series regression(8)for a set of left hand side (LHS)assets.One then jointly tests the vector of regression intercepts against zero.This step in effect asks whether there is anything about the regression intercepts that suggests there are unspecified omitted variables that add to the explanation of expected returns provided by market betas. In principle,the vague alternative hypothesis of the time-series test allows it to detect any CAPM problems embedded in the returns on the LHS assets.But this generality has a cost.The joint test on the intercepts from(8)for a set of LHS assets is a multiple comparisons test and it can lack power.The test searches over combinations of the intercept estimates from(8)to find the portfolio of LHS assets that maximizes the probability of rejecting the hypothesis that the intercepts are all equal to zero.The p-value of the test must take into account that many combinations are implicitly examined to find the one that produces the strongest rejection,and this reduces the power of the test.Since more LHS assets imply more searching and a less powerful test,there is an incentive to restrict the number of LHS assets,which can result in lost information about shortcomings of the CAPM. Gibbons (1982)and Stambaugh (1982)provide the initial tests of (C1)using time-series regressions.They use different joint tests on the intercepts from (8)that have the same asymptotic properties but different small sample properties,with no clear winner.This situation is resolved by Gibbons,Ross,and Shanken(1986).They provide an Etest for the intercepts(the GRS test)that has exact small-sample properties when asset returns are multivariate normal (also assumed in other tests). And they show that the test has an interesting interpretation.The test constructs a candidate for the tangency portfolio T in Figure I by optimally combining the market proxy and the LHS assets used to estimate (8).It then tests whether this tangency portfolio,along with the riskfree asset,provides an efficient set reliably superior to the one obtained by combining the riskfree asset with the market proxy alone.In other words,the GRS statistic tests whether the market proxy is the tangency portfolio in the set of portfolios that can be constructed from it and the specific LHS assets used in the test. 1010 The way (C1) is examined in the time-series regression approach is generically different. The alternative hypothesis is vague. One estimates the time-series regression (8) for a set of left hand side (LHS) assets. One then jointly tests the vector of regression intercepts against zero. This step in effect asks whether there is anything about the regression intercepts that suggests there are unspecified omitted variables that add to the explanation of expected returns provided by market betas. In principle, the vague alternative hypothesis of the time-series test allows it to detect any CAPM problems embedded in the returns on the LHS assets. But this generality has a cost. The joint test on the intercepts from (8) for a set of LHS assets is a multiple comparisons test and it can lack power. The test searches over combinations of the intercept estimates from (8) to find the portfolio of LHS assets that maximizes the probability of rejecting the hypothesis that the intercepts are all equal to zero. The p-value of the test must take into account that many combinations are implicitly examined to find the one that produces the strongest rejection, and this reduces the power of the test. Since more LHS assets imply more searching and a less powerful test, there is an incentive to restrict the number of LHS assets, which can result in lost information about shortcomings of the CAPM. Gibbons (1982) and Stambaugh (1982) provide the initial tests of (C1) using time-series regressions. They use different joint tests on the intercepts from (8) that have the same asymptotic properties but different small sample properties, with no clear winner. This situation is resolved by Gibbons, Ross, and Shanken (1986). They provide an F-test for the intercepts (the GRS test) that has exact small-sample properties when asset returns are multivariate normal (also assumed in other tests). And they show that the test has an interesting interpretation. The test constructs a candidate for the tangency portfolio T in Figure 1 by optimally combining the market proxy and the LHS assets used to estimate (8). It then tests whether this tangency portfolio, along with the riskfree asset, provides an efficient set reliably superior to the one obtained by combining the riskfree asset with the market proxy alone. In other words, the GRS statistic tests whether the market proxy is the tangency portfolio in the set of portfolios that can be constructed from it and the specific LHS assets used in the test