NONCONVEX L1/2 REGULARIZATION FOR SPARSE PORTFOLIO SELECTION

Two sparse optimal portfolio selection models with and without short-selling constraints are proposed by introducing L-1/2 regularization on portfolio weights in the traditional M-V portfolio selection model. A fast and efficient penalty half thresholding algorithm is presented for the solution of proposed sparse portfolio selection models. The algorithm is an extension of the half thresholding algorithm for solving L-1/2 regularization problems. A strategy to adjust the value of the regularization parameter in proposed models is derived when the sparsity of optimal portfolios is specified. When the strategy is incorporated into the modified algorithm, the efficiency of the algorithm is improved. Empirical analyzes on the proposed portfolio selection models and the proposed algorithm are executed to test the out-of-sample performance of the optimal portfolios generated from the proposed models. The out-of-sample performance is measured using Sharpe ratio. Empirical results show that the out-of-sample performance of the optimal portfolios generated from the proposed models is better than those of the optimal portfolios generated from M-V portfolio selection models with L-1/2 regularization on portfolio weights.