Mean-CVaR portfolio selection: A nonparametric estimation framework

In this paper, we use Conditional Value-at-Risk (CVaR) to measure risk and adopt the methodology of nonparametric estimation to explore the mean-CVaR portfolio selection problem. First, we obtain the estimated calculation formula of CVaR by using the nonparametric estimation of the density of the loss function, and formulate two nonparametric mean-CVaR portfolio selection models based on two methods of bandwidth selection. Second, in both cases when short-selling is allowed and forbidden, we prove that the two nonparametric mean-CVaR models are convex optimization problems. Third, we show that when CVaR is solved for, the corresponding VaR can also be obtained as a by-product. Finally, we present a numerical example with Monte Carlo simulations to demonstrate the usefulness and effectiveness of our results, and compare our nonparametric method with the popular linear programming method. (C) 2012 Elsevier Ltd. All rights reserved.