Ex post efficient proxies for the market portfolio are tested against the equal weight proxy. The equal weight proxy outperforms the others when the criterion is squared error of conditional prediction of returns. The ex post efficient proxies use maximum likelihood estimates of return. Stein estimates of return will generally be different from the maximum likelihood estimates and they necessarily correspond to market proxies which are not efficient ex post. In other words, there generally exists a better, inefficient, proxy than an ex post efficient proxy when the criterion is squared error of conditional prediction of return.

This paper tests prediction of returns on stocks using a direct estimate of the minimum variance zero beta portfolio z. The composition of this portfolio is implicit in Black's paper on capital market equilibrium in the absence of riskless borrowing or lending. Portfolios of stocks drawn from the same industries are used to estimate z. The predictions of Black's equilibrium return equation are compared with those of cross-sectional regressions of return on risk.

Tax based dividend models of capital asset pricing assume that dividends are known at the time prices are set. Dividends which are announced and paid in the same month, and dividends which were expected but cancelled in the month constitute surprises which interfere with many empirical tests of the effects of expected dividend yield on returns. This paper avoids these problems by relating returns to forecasts of dividend yield obtained from past data.

ABSTRACT Tax based dividend models of capital asset pricing assume that dividends are known at the time prices are set. Dividends which are announced and paid in the same month, and dividends which were expected but cancelled in the month constitute surprises which interfere with many empirical tests of the effects of expected dividend yield on returns. This paper avoids these problems by relating returns to forecasts of dividend yield obtained from past data.