A Comparative Study of Gini's Mean Difference and Mean Variance in Portfolio Analysis

Abstract

Abstract:The methods traditionally used for comparing uncertain prospects are the mean variance and the stochastic dominance approaches. Yitzhaki has recently presented an alternative model based upon Gini's mean difference to compare uncertain prospects. The mean Gini model is similar in nature to the mean variance model in that it uses a two‐parameter statistic to describe the probability distribution of risky returns. Theoretically, the mean Gini model is consistent with the behaviour of investors under conditions of uncertainty for a wider class of probability distributions. Thus Gini's mean difference appears to be more adequate than variance as a measure of risk. This study firstly generated the mean Gini efficient frontier and secondly compared the mean variance efficient frontier with it. For the sample data employed, the mean variance model gave a very good approximation to the mean Gini model. Since the computational costs of the mean variance approach were a small fraction of those of the mean Gini approach, the theoretical advantage would not appear in this case to translate into a practical one.