Portfolio and Index Vars by Filtered Historical Simulation

Abstract

Filtered historical simulation is a popular method to compute VaR. The VaR values by this approach applied to a stock index and to the portfolio of the component stocks in the index can be quite different when the market is under stress. This paper examines the discrepancy. We concludes that the high correlation among stocks in a stressed market condition is the cause. The estimation shows that the two approaches would give consistent VaR when the overall stock correlations are about 40-50%.