The Effect of Asymmetries on Stock Index Return Value at Risk Estimates

Abstract

There is much evidence in the literature that the volatilities of equity returns show evidence of asymmetric responses to good and bad news. At the same time, there is evidence that the unconditional distribution of stock returns is asymmetric as well. This paper examines the effects of asymmetries of various forms on the accuracy of value at risk models. We compare the value at risk estimates derived from models which assume both a symmetric unconditional distribution of returns and a symmetric response of volatility to good and bad news, with models which explicitly allow for each class of asymmetries. We find that, between the two types of asymmetry considered, the asymmetry in the unconditional distribution is the more important feature. Use of the semi-variance, which allows for this feature, is shown to provide more stable and more reliable value at risk estimates than simple and more complex models that do not.

Keywords: Stock index, Minimum Capital Risk Requirements, Internal Risk Management Models, Value at risk, asymmetries, multivariate GARCH, semi-variance

JEL Classification: C14, C15, G13