A Tractable Parametric Approach to Valueat-Risk Optimization

Value-at-Risk (VaR) is the most widely accepted risk measure in the financial and insurance industries, yet efficient optimization of VaR remains a very difficult problem. We propose a computationally tractable parametric approximation method for optimizing the VaR of a portfolio based on robust optimization techniques. The method results in the optimization of a modified VaR measure, Robust Parametric VaR (RPVaR), that is coherent, and is thus also desirable from a financial theory perspective. We show that RPVaR approximates the Conditional VaR of the portfolio as well. Numerical experiments with simulated and real market data indicate that our parametric approach results in lower realized portfolio VaR, better efficient frontier, and lower maximum realized portfolio loss than alternative approaches for quantilebased portfolio risk minimization