CVaR proxies for minimizing scenario-based Value-at-Risk
Helmut Mausser - Quantitative Research, Risk Analytics, Business Analytics, IBM, 185 Spadina Avenue, Toronto, ON M5T2C6, Canada (email)
Abstract: Minimizing VaR, as estimated from a set of scenarios, is a difficult integer programming problem. Solving the problem to optimality may demand using only a small number of scenarios, which leads to poor out-of-sample performance. A simple alternative is to minimize CVaR for several different quantile levels and then to select the optimized portfolio with the best out-of-sample VaR. We show that this approach is both practical and effective, outperforming integer programming and an existing VaR minimization heuristic. The CVaR quantile level acts as a regularization parameter and, therefore, its ideal value depends on the number of scenarios and other problem characteristics.
Keywords: Value-at-risk, conditional value-at-risk, optimization, regularization.
Received: September 2012; Revised: October 2013; Available Online: February 2014.
2015 Impact Factor.776