Sparse markowitz portfolio selection by using stochastic linear complementarity approach

We consider the framework of the classical Markowitz mean-variance (MV) model when multiple solutions exist, among which the sparse solutions are stable and cost-efficient. We study a two-phase stochastic linear complementarity approach. This approach stabilizes the optimization problem, finds the sparse asset allocation that saves the transaction cost, and results in the solution set of the Markowitz problem. We apply the sample average approximation (SAA) method to the two-phase optimization approach and give detailed convergence analysis. We implement this methodology on the data sets of Standard and Poor 500 index (S&P 500), real data of Hong Kong and China market stocks (HKCHN) and Fama & French 48 industry sectors (FF48). With mock investment in training data, we construct portfolios, test them in the out-of-sample data and find their Sharpe ratios outperform the l(1) penalty regularized portfolios, lp penalty regularized portfolios, cardinality constrained portfolios, and 1/N investment strategy. Moreover, we show the advantage of our approach in the risk management by using the criteria of standard deviation (STD), Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR).