Composite Value-at-Risk

Abstract

Historical Value-at-Risk (VaR) may yield persistently high values that do not accurately represent the underlying risk, followed by dramatic drops. This phenomenon can be circumvented with some weighted historical methods like those proposed by Boudoukh et al. (BRW 1998) and Hull and White (HW 1998). In this article, we develop a simple, transparent, and quick-to-compute weighted historical VaR estimate, called composite VaR, based on the Normal and Laplace distributions. This approach provides probabilistic information on the nature of tail risk. In line with the literature, a dedicated example leads us to support the importance of the Laplace distribution for cryptocurrencies. An analysis based on common bias and clustering benchmarks is performed on this new method and its closest parents, the BRW and HW VaRs and the classical historical VaR. Although the composite VaR can be chosen for its rapidity, none of the examined methods can be unequivocally regarded as the most efficient VaR estimate. One additional key benefit of our method is its low bias.

Keywords: Risk management, Value-at-Risk, Normal distribution, Laplace distribution

JEL Classification: C46, G32