Portfolio value at risk bounds

This paper develops value at risk (VAR) measures for portfolios of correlated financial assets, without assuming normal returns. The approach can cope with any distribution for marginal returns, the fat-tailed ones included. We provide VAR bounds which hold independently of the joint distribution of returns and their dependence structure. The lower bound can be interpreted as a worst-case scenario VAR. We show that it not only requires little information, but is also easy to compute. In this sense, we suggest it as a practical device for portfolio managers. An application to portfolios of stock-market indices is provided. Comparisons with the VAR values under the normality assumption on returns are discussed.