III.Recent Tests Starting in the late 1970s,there is a sequence of papers that challenge the CAPM prediction that the market portfolio is efficient.The evidence comes from tests of(C1);variables are identified that add to the explanation of expected returns provided by market beta.The first blow is Basu's(1977)evidence that when common stocks are sorted on earnings-price ratios,future returns on high E/P stocks are higher than predicted by the CAPM,and the returns on low E/P stocks are lower than predicted.Banz (1981) documents a size effect,when stocks are sorted on market capitalization(price times shares outstanding), average returns on small stocks are higher than predicted by the CAPM.Bhandari(1988)finds that high debt-equity ratios (book value of debt over the market value of equity,a measure of leverage)are associated with returns that are too high relative to their market betas.Finally,the relation between average return and the book-to-market ratio(B/M,the ratio of the book value of a common stock to its market value)also suggests that the market portfolio is not efficient.High B/M stocks have high average returns that are not captured by their betas,and the average returns on low B/M stocks are lower than implied by their betas(Statman(1980),Rosenberg,Reid,and Lanstein (1985)). There is a common theme in the CAPM anomalies summarized above.Ratios involving stock prices have information about expected returns missed by market betas.This is not surprising.A stock's price depends both on the expected cash flows it will provide and on the expected returns that discount the expected flows back to the present.Thus,in principle the cross-section of prices has information about the cross-section of expected returns.The cross-section of stock prices is,however,arbitrarily affected by differences in scale (or units).But with a judicious choice of scaling variable X,the ratio X/P can reveal differences in the cross-section of expected stock returns.Such ratios are thus prime candidates to expose shortcomings of asset pricing models (Ball (1978)).The CAPM anomalies summarized above suggest that earnings-price,debt-equity,and book-to-market ratios play this role for the CAPM.Note,however,that the information in price ratios about expected returns is noisy because the cross-section of a price ratio also reflects information about the cross-section of expected cash flows. 1212 III. Recent Tests Starting in the late 1970s, there is a sequence of papers that challenge the CAPM prediction that the market portfolio is efficient. The evidence comes from tests of (C1); variables are identified that add to the explanation of expected returns provided by market beta. The first blow is Basu’s (1977) evidence that when common stocks are sorted on earnings-price ratios, future returns on high E/P stocks are higher than predicted by the CAPM, and the returns on low E/P stocks are lower than predicted. Banz (1981) documents a size effect; when stocks are sorted on market capitalization (price times shares outstanding), average returns on small stocks are higher than predicted by the CAPM. Bhandari (1988) finds that high debt-equity ratios (book value of debt over the market value of equity, a measure of leverage) are associated with returns that are too high relative to their market betas. Finally, the relation between average return and the book-to-market ratio (B/M, the ratio of the book value of a common stock to its market value) also suggests that the market portfolio is not efficient. High B/M stocks have high average returns that are not captured by their betas, and the average returns on low B/M stocks are lower than implied by their betas (Statman (1980), Rosenberg, Reid, and Lanstein (1985)). There is a common theme in the CAPM anomalies summarized above. Ratios involving stock prices have information about expected returns missed by market betas. This is not surprising. A stock’s price depends both on the expected cash flows it will provide and on the expected returns that discount the expected flows back to the present. Thus, in principle the cross-section of prices has information about the cross-section of expected returns. The cross-section of stock prices is, however, arbitrarily affected by differences in scale (or units). But with a judicious choice of scaling variable X, the ratio X/P can reveal differences in the cross-section of expected stock returns. Such ratios are thus prime candidates to expose shortcomings of asset pricing models (Ball (1978)). The CAPM anomalies summarized above suggest that earnings-price, debt-equity, and book-to-market ratios play this role for the CAPM. Note, however, that the information in price ratios about expected returns is noisy because the cross-section of a price ratio also reflects information about the cross-section of expected cash flows