A CVaR Scenario-Based Framework for Minimizing Downside Risk in Multi-Asset Class Portfolios

Abstract

Multi-asset class (MAC) portfolios can be composed of investments in equities, fixed income, commodities, foreign exchange, credit, derivatives, and alternatives such as real estate and private equity. The return for such nonlinear portfolios is asymmetric with significant tail risk. The traditional Markowitz mean–variance optimization (MVO) framework, which linearizes all the assets in the portfolio and uses the standard deviation of return as a measure of risk, does not always accurately measure the risk for such portfolios. The authors consider a scenario-based conditional value at risk (CVaR) approach for minimizing the downside risk of an existing portfolio with MAC overlays. The approach consists of two phases: Phase 1 uses Monte-Carlo simulations to generate the asset return scenarios, and Phase 2 incorporates the return scenarios in a scenario-based convex optimization model to generate the overlay holdings. The authors illustrate the methodology in two examples involving the hedging of an equity portfolio with index puts and the hedging of a callable bond portfolio with interest rate caps. They compare the CVaR approach with parametric MVO approaches that linearize all the instruments in the MAC portfolio and show that the CVaR approach generates portfolios with better downside risk statistics; and further, it selects hedges that produce more attractive risk decompositions and stress test numbers—tools commonly used by risk managers to evaluate the quality of hedges.