Market Portfolio Efficiency and Value Stocks Thierry Post and Pim van Vliet * Abstract In this journal, Best, Best and Yoder (2000) recently demonstrated that portfolios of US value stocks dominate portfolios of US growth stocks in terms of second-order stochastic dominance (SSD). However, we cannot conclude from this finding that the market is SSD inefficient, because market portfolio efficiency generally does not require growth portfolios to be efficient. Furthermore, stochastic dominance results are very sensitive to sampling error. In fact, the value-weighted market portfolio is not significantly inefficient and no significant value effects exist in the sample of Best, Best and Yoder. ( JEL G140) Introduction The market portfolio is mean-variance inefficient relative to portfolios of stocks sorted on book-to- market equity ratio (BE/ME). A possible explanation is that the value premium reflects a reward for systematic downside risk, not picked by co-variance (beta). A perfect tool for analyzing the role of downside risk in a portfolio context is the use of stochastic dominance (SD) criteria. Recently, Best, Best and Yoder (BBY; 2000) show that portfolios of US value stocks dominate portfolios of US growth stocks in terms of second-order stochastic dominance (SSD). Since SSD effectively accounts for the full return distribution, BBY conclude that this finding is inconsistent with market portfolio efficiency and that it cannot be explained by downside risk factors. In our opinion, this conclusion is misleading because of the following two reasons: 1. BBY check if there exist pairwise dominance relationships among ten portfolios formed on book- to-market equity ratio (BE/ME). Hence, they implicitly assume that each of the ten portfolios is efficient (i.e., non-dominated, or, equivalently, optimal for at least some risk averse investor). In our opinion, there is no economic rationale for this assumption. For example, representative investor models (including the basic mean-variance CAPM) do not require that the individual assets or portfolios are efficient, but rather that the value-weighted market portfolio (which includes all individual assets) is efficient relative to all possible portfolios constructed from the individual assets. In brief, market portfolio efficiency generally does not require that growth portfolios be efficient. 2. BBY check for dominance in a sample of historical returns without accounting for sampling error. Unfortunately, SSD results are very sensitive to sampling error, because the SSD rule considers the full sample distribution rather than a finite set of sample moments. For example, if we compare two alternatives with the same population distribution, then we know that there exists no pairwise dominance relationship in the population. Still, the probability of finding a dominance relationship based on two independent random samples of 1000 observations can be as high as 50 percent (see Dardanoni and Forcina (1999)). If we compare ten alternatives (e.g., the ten BE/ME portfolios), then we may almost certainly find an empirical dominance relationship. * Thierry Post, Department of Finance, Erasmus University Rotterdam, P.O. Box 1738, 3000 DR, Rotterdam, The Netherlands, email: gtpost@few.eur.nl , tel: +31-104081428. Pim van Vliet, ERIM, Erasmus University Rotterdam, The Netherlands, P.O. Box 1738, TI-Room H16-22, 3000 DR Rotterdam., email: wvanvliet@few.eur.nl . This study forms part of a research program on stochastic dominance. Details on the program are available at the program homepage: http://www.few.eur.nl/few/people/gtpost/stochastic_dominance.htm. We appreciate the comments by an anonymous referee. Financial support by Tinbergen Institute, Erasmus Research Institute of Management and Erasmus Center of Financial Research is gratefully acknowledged. Any remaining errors are the authors’ responsibility.