# A CVaR Scenario-based Framework: Minimizing Downside Risk of Multi-asset Class Portfolios

Multi-asset class (MAC) portfolios can be comprised of investments in equities, fixed-income, commodities, foreign-exchange, credit, derivatives, and alternatives such as real-estate and private equity. The return for such {\em non-linear} portfolios is {\em asymmetric} with significant tail risk. The traditional Markowitz Mean-Variance Optimization (MVO) framework, that linearizes all the assets in the portfolio and uses the standard deviation of return as a measure of risk, does not accurately measure risk for such portfolios. We consider a scenario-based Conditional Value-At-Risk'' (CVaR) approach for minimizing the downside risk of an existing portfolio with MAC overlays. The approach uses (a) Monte Carlo simulations to generate the asset return scenarios, and (b) incorporates these return scenarios in a scenario-based convex optimization model to generate the overlay holdings. We illustrate the methodology on three examples in the paper: (1) hedging an equity portfolio with index puts; (2) hedging a callable bond portfolio with interest rate caps; (3) hedging the credit spread risk of a convertible bond portfolio. We compare the CVaR approach with parametric MVO approaches that linearize all the instruments in the MAC portfolio, and show that (a) CVaR approach generates portfolios with better downside risk statistics, (b) CVaR hedges return more attractive risk decompositions and stress test numbers---tools commonly used by risk managers to evaluate the quality of hedges.

## Citation

to appear in The Journal of Portfolio Management, Winter 2018 issue; Axioma Technical Report 66, Axioma Inc, May 2016