Statistical Properties of the Sample Semi-variance, with Applications to Emerging Markets' Data

In finance theory, the standard deviation of asset returns is almost universally recognised as a measure of risk. This universality continues to exist even in the presence of the known limitations of using the standard deviation and also alternative risk measures. One possible reason for this persistence is that the sample properties of alternative risk measures are not well understood. This paper attempts to compare the sample distribution of the semi-variance with that of the variance. In particular, it explores the belief that while there are convincing theoretical reasons to sue the semi-variance, the volatility of the sample measure is so high as to make the measure impractical in applied work. It also uses arguments based on stochastic dominance to compare the distribution of the two statistics. Conditions are developed to identify situations in which the semi-variance may be preferred to the variable. An empirical application using equity data from emerging markets demonstrates the approach.