“VaR Analytics—Portfolio Structure, Key Rate Convexities, and VaR Betas”

Abstract

In the Fall 1996 issue of this journal, Ho, Chen, and Eng claim that under independence between the returns of “blocks” the “square root of the sum of the squares of the blocks' VaRs” is the lower bound of the portfolio's value–at–risk (VaR). The authors prove that this heuristic is correct only under the very limiting assumption of normal distributed returns. The correct lower bound can be above it for non–normal distributions. Thus, the lower bound claimed by Ho, Chen, and Eng may lead to underestimation of portfolio risk.