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.