Abstract: Functional Form, Skewness Effect, and Risk-Return Relationship

Sharpe, Jensen and Treynor composite measures are generally employed to measure the performance of a portfolio (or mutual fund). Friend and Blume [FB] have regressed the composite performance measure of random portfolios on the systematic risk (and standard deviation) to show that there exists strong bias in these composite performance measures. Employing actual mutual fund data, Klemkosky claims to have shown that the bias associated with composite performance measures using the semi-standard deviation and mean absolute deviation as risk surrogates is much smaller than that of the Sharpe, Jensen, and Treynor composite measures. Miller and Scholes have pointed out that both the functional form and skewness effect can affect the risk-return relation in capital asset pricing. Lintner has argued that the variance-return instead of the standard deviation-return relation is linearly related. However, one has never formally tested whether the functional form employed in investigating the risk-return relation is independent of different statistical risk proxies used. Furthermore, the impact of the skewness effect on the ex-post risk-return trade-off test has not been carefully investigated.