Stochastic portfolio optimization with proportional transaction costs: Convex reformulations and computational experiments

We propose a probabilistic version of the Markowitz portfolio problem with proportional transaction costs. We derive equivalent convex reformulations, and analyze their computational efficiency for solving large (up to 2000 securities) portfolio problems. There is a great disparity in the solution times. The time differential between formulations can reach several orders of magnitude for the largest instances. The second-order cone formulation in which the number of quadratic terms is invariant to the number of assets is the most efficient.