Abstract

In recent years the mean-semivariance has been proposed in place of the mean-variance as an alternative approach to portfolio analysis since different investors assign a lower weight to positive deviations from the mean than to negative ones. The present work investigates empirically the relationship between risk and return in a downside risk framework and in a regular risk framework by utilizing returns of securities traded on the London Stock Exchange and Paris Stock Exchange. The results reveal that in many cases the downside risk measures are equivalent or better in explaining mean returns than the regular risk measures. The paper also introduces a new risk-return relation that holds when the distribution of security returns are normal and the market index lies inside the semi-deviation-expected return efficient frontier. The existence of this model may provide a possible explanation of the empirical results included in this work. Finally, it is argued that for skewed distributions of security returns it may be better to employ a three parameter asset pricing than the mean – semivariance risk-return relation.

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