Subject: Performance-based estimation error reduction in mean-CVaR portfolio optimization

Speaker: Gah-Yi Vahn (Industrial Engineering & Operartion Research, UC Berkeley)

Summary
Conditional Value-at-Risk (CVaR) has been gaining a lot of interest in risk management as a desirable risk measure. However, as CVaR is a tail risk measure, making accurate estimates with data is difficult. The estimation errors are exacerbated in data-driven mean-CVaR portfolio optimization. We investigate two performance-based methods for reducing estimation error in mean-CVaR portfolio optimization. The first method is nonparametric: penalize portfolios with large variances in mean and CVaR estimations. The penalized problem is solvable by a quadratically-constrained quadratic program. We derive and compare the asymptotic statistical properties of the original and penalized solutions. The second method is parametric: solve the empirical Markowitz problem instead if the log-return distribution is in the elliptical family (which includes Gaussian and t distributions), as then the population frontiers of the Markowitz and mean-CVaR problems are equivalent. Numerical simulations show both methods improve upon the empirical mean-CVaR solution under an elliptical model, with the Markowitz solution dominating. The penalized solution dominates under a non-elliptical model with heavy one-sided loss.

Date and Time: December 20 (Tue), 11-12 am.

Place: Building 39, Room 309

Contact: Tel. 02-880-1477