The estimation and decomposition of value-at-risk for non-normal portfolio returns

Abstract

Value-at-risk (VaR) is a widely used measure for evaluating the market risk of a trading portfolio. This article presents the g-and-h method for estimating the VaR of a portfolio with non-normal returns, and adds to the usefulness of VaR as a risk management tool by decomposing the portfolio into individual VaRs to estimate the contribution of the individual components toward the overall VaR. While the VaR decomposition is algebraically simple under the assumption of normality, that is not the case under non-normality which is the property exhibited by most financial returns. We show that, by using the g-and-h VaR method, the decomposition analysis under non-normality can be performed with the same degree of intuitiveness and ease as for the analytical methods based on the assumption of normality.

First published online: 16 Jan 2013

Keyword : portfolio VaR, g-and-h distribution, VaR decomposition, marginal VaR, component VaR