We investigate two methods for reducing estimation error in portfolio
optimization with Conditional Value-at-Risk (CVaR). 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, and can be interpreted as a chance-constrained program. We
show the original and penalized solutions follow the Central Limit Theorem with
computable covariance by extending M-estimation results from statistics.