Component VaR for a Non-Normal World

Value at Risk (VaR) is the most widely used downside risk measure in finance. The contribution to the total portfolio VaR by each component in a portfolio is readily computed under the assumption of normality (Garman, 1997). When assets have non-normal returns, the component risk contributions have previously been much more difficult to calculate. The Cornish-Fisher expansion has recently become popular for estimating the univariate VaR of instruments with non-normal returns because of its accuracy and computational efficiency. We advocate that this estimator, called Modified VaR, is also useful for the estimation of portfolio VaR, because it not only accounts for the skewness and excess kurtosis in the marginal return distributions, but also for the non-linearity in the return dependence structure. We show how to decompose Modified VaR into the component risk of each asset in the portfolio in a manner that is computationally efficient even for very large portfolios. We demonstrate this approach on a portfolio of hedge fund managers to show the utility in a portfolio of assets with non-normal returns