The hidden dangers of historical simulation

Many large financial institutions compute the Value-at-Risk (VaR) of their trading portfolios using historical simulation based methods, but the methods' properties are not well understood. This paper theoretically and empirically examines the historical simulation method, a variant of historical simulation introduced by Boudoukh et al. [Boudoukh, J., Richardson, M., Whitelaw, R., 1998. The best of both worlds, Risk 11(May) 64-67] (BRW), and the filtered historical simulation method (FHS) of Barone-Adesi et al. [Barone-Adesi, G., Bourgoin F., Giannopoulos, K., 1998. Don't look back. Risk 11(August) 100-104; Barone-Adesi, G., Giannopoulos K., Vosper L., 1999. VaR without correlations for nonlinear portfolios. Journal of Futures Markets 19(April) 583-602]. The historical simulation and BRW methods are both under-responsive to changes in conditional risk; and respond to changes in risk in an asymmetric fashion: measured risk increases when the portfolio experiences large losses, but not when it earns large gains. The FHS method is promising, but its risk estimates are variable in small samples, and its assumption that correlations are constant is violated in large samples. Additional refinements are needed to account for time-varying correlations; and to choose the appropriate length of the historical sample period.