An algorithm for portfolio optimization problem

Portfolio optimization is to find the stock portfolio minimizing the risk for a required return or maximizing the return for a given risk level. The seminal work in this field is the mean-variance model formulated as a quadratic programming problem. Since it is not computationally practical to solve the original model directly, a number of alternative models have been proposed. In this paper, among the alternative models, we focus on the Mean Absolute Deviation (MAD) model. More specifically, we derive bounds on optimal objective function value. Using the bounds, we also develop an algorithm for the model. We prove mathematically that the algorithm can solve the problem to optimality. The algorithm is tested using the real data from the Korean Stock Market. The results come up to our expectations that the method can solve a variety of problems in a reasonable computational time.