The Influence Of Higher Moments And Non-Normality On The Sharpe Ratio: A South African Perspective

Abstract

Although the general assumption is that daily and monthly return data are normally distributed (Aparicio & Estrada, 2001), the correct statistical distribution of returns must first be established (Linden, 2001), as it constitutes one of the elementary building blocks that will ensure accurate financial analyses (Taylor, 1986). The assumption of normality is also critical when constructing reference intervals for variables (Royston, 1991). By evaluating the pre-, during and post- 2007-2009 financial crisis periods, this paper found that non-normality can be present in all data frequencies, especially in higher data frequencies. Further evidence also illustrated that the deviation from normality escalated over the crisis period and remained higher after the crisis, compared to the pre-crisis period. By comparing the traditional Sharpe ratio with adjusted versions, based on Gatfaoui’s (2012) methodology, this paper accentuates that the presence of non-normality and higher moments can influence the Sharpe ratio’s performance rankings.