Beyond Mean–Variance: Performance Measurement in a Nonsymmetrical World (corrected)

Most practitioners use the capital asset pricing model to measure investment performance. The CAPM, however, assumes either that all asset returns are normally distributed (and thus symmetrical) or that investors have mean–variance preferences (and thus ignore skewness). Both assumptions are suspect. Assuming only that the rate of return on the market portfolio is independently and identically distributed and that markets are “perfect,” this article shows that the CAPM and its risk measures are invalid: The market portfolio is mean–variance inefficient, and the CAPM alpha mismeasures the value added by investment managers. Strategies with positively skewed returns, such as strategies limiting downside risk, will be incorrectly underrated. A simple modification of the CAPM beta, however, will produce correct risk measurement for portfolios with arbitrary return distributions, and the resulting alphas of all fairly priced options and/or dynamic strategies will be zero. The risk measure requires no more information to implement than the CAPM.