Solving large scale mean-variance models with dense non-factorable covariance matrices

This paper is concerned with an efficient algorithm for solving a large-scale dense non-factorable quadratic programming problem arising in portfolio optimization consisting of a large number of assets. A number of algorithms for quadratic programming problems have been proposed in the past. However, these methods tend to become less efficient as the rank of the covariance matrix increases. The algorithm proposed in this paper is a combination of projected steepest descent algorithm and projected variable metric algorithm. Subproblems to be solved in each step are simple linear programs which can be solved very fast, contrary to other quadratic programming algorithms which require the manipulation of large dense matrix. Computational experiment shows that this algorithm outperforms renowned softwares when the number of assets is over one thousand.