Conditional Value-at-Risk (CVaR) is a widely used coherent risk measure in the finance and machine learning communities to ensure robustness and fairness. Focusing on CVaR portfolio optimization problems in the expanding global markets, this paper analyzes sparsity-induced portfolio strategies. We first analyze the equivalence of the regularized CVaR minimization problem and its ₀-constrained counterpart in the norm ball, which suggests the validity of regularizers for sparsity-induced CVaR minimization. Furthermore, we establish the finite-sample statistical estimation error rate for the proposed method in the ultrahigh-dimensional scenario, when the number of assets under management can scale exponentially with the sample size of the historical data. The numerical experiments demonstrate the risk aversion preference and robustness of the proposed portfolio strategy on both synthetic data and the S&P 500 dataset.
Guo et al. (Thu,) studied this question.