Estimation error reduction in portfolio optimization with Conditional Value-at-Risk.
Abstract
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. 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.
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