Do long memory and asymmetries matter when assessing downside return risk?

Abstract

In this paper we set out to test whether, on sector level, returns series in South Africa exhibit long memory and asymmetries and, more specifically, whether these effects should be accounted for when assessing downside risk. The purpose of this analysis is not to identify the most optimal downside risk assessment model or to reaffirm the often regarded stylised fact of the existence of long memory and asymmetry in asset returns series. Rather, we set out to establish whether accounting for these effects and allowing for more flexibility in second order persistence models actually leads to improved downside risk assessments. We use several variants of the widely used GARCH family of second order persistence models that control for these effects, and compare the downside risk estimates using Value-at-Risk measures of different model formulations and compare the out-of-sample performances. Our findings confirm that controlling for asymmetries and long memory in volatility models improve risk management calculations.