The Journal of Finance

On the Cross‐Sectional Relation between Expected Returns, Betas, and Size

Published: 12/17/2002   |   DOI: 10.1111/0022-1082.00125

Robert R. Grauer

In this paper, I set up scenarios where the mean‐variance capital asset pricing model is true and where it is false. Then I investigate whether the coefficients from regressions of population expected excess returns on population betas, and expected excess returns on betas and size, allow us to distinguish between the scenarios. I show that the coefficients from either ordinary least squares or generalized least squares regressions do not allow us to tell whether the model is true or false.

Investment Policy Implications of the Capital Asset Pricing Model

Published: 03/01/1981   |   DOI: 10.1111/j.1540-6261.1981.tb03539.x

ROBERT R. GRAUER

The results of previous generalized Security Market Line (SML) tests of the Mean Variance (MV) and Linear Risk Tolerance (LRT) Capital Asset Pricing Models indicate that the models are empirically identical. A very widely accepted, but technically incorrect, explanation for the results is that with normal return distributions all expected utility maximizing riskaverse investors will pick MV portfolios. The paper shows that the generalized SML tests cannot distinguish between the MV model and a much wider variety of power utility LRT models than has previously been entertained. On the other hand, with approximately normal, or real world, return distributions the investment policies of the various models are shown to be different from each other, and from the MV policy in particular. To the extent the results of the portfolio selection calculations are robust, the results of, and implications drawn from, the tests of the macro pricing relations are not based on firm micro foundations.

Capital Asset Pricing Compatible with Observed Market Value Weights

Published: 03/01/1985   |   DOI: 10.1111/j.1540-6261.1985.tb04938.x

MICHAEL J. BEST, ROBERT R. GRAUER

We show that the set of expected return vectors, for which an observed portfolio is mean variance (MV) efficient, is a two‐parameter family. We identify ten ways to specify the time series behavior of the two parameters; the result highlights a number of inconsistencies involved in MV modelling. For each of the cases, it permits the inference of the time series of expected return vectors, as well as all the other Capital Asset Pricing Model (CAPM) variables, compatible with a known covariance matrix and the observed time series of market value weights. The empirical work shows that there are substantial case‐to‐case differences in the time series of mean vectors and many of them are quite different from the constant mean vector envisioned in tests of the CAPM.

Gains from International Diversification: 1968–85 Returns on Portfolios of Stocks and Bonds

Published: 07/01/1987   |   DOI: 10.1111/j.1540-6261.1987.tb04581.x

ROBERT R. GRAUER, NILS H. HAKANSSON

This paper applies the multi‐period investment model to a universe of international securities on the basis of the simple probability assessment approach. Our principal findings are: 1) the gains from including non‐U.S. asset categories in the universe were remarkably large (in some cases statistically significant), especially for the highly risk‐averse strategies, 2) the gains from removing the no leverage constraint were more substantial than they were in the absence of non‐U.S. securities, and 3) there is strong evidence of market segmentation in that the optimal levels of investment in U.S. securities were mostly zero in the presence of the non‐U.S. asset categories.