Sparse portfolio selection with uncertain probability distribution

Designed as remedies for uncertain parameters and tiny optimal weights in the portfolio selection problem, we consider a class of distributionally robust portfolio optimization models with cardinality constraints. For considering the statistical significance and tractability, we construct two kinds of ambiguity sets based on L-1-norm and moment information, respectively. The nominal distribution, as the core of the first ambiguity set, is determined by non-parametric estimation method. To reduce the disturbing error of the second ambiguity set, we apply a shrinkage estimation method to determine the moment information based on historical data. By introducing a binary variable, the proposed sparse portfolio optimization model can be converted equivalently to a tractable mixed-integer 0-1 programming problem, which can be dealt with efficiently by a modified primal-dual Benders' decomposition method. Through the actual market data, we test the proposed models and show their validity. Furthermore, performances measured by net portfolio return, Sharpe ratio, and cumulative return are superior to the classical portfolio selection models in the back-testing of out-of-sample data.