Constant Rebalanced Portfolio Optimization Under Nonlinear Transaction Costs

Abstract

We study the constant rebalancing strategy for multi-period portfolio optimization via conditional value-at-risk (CVaR) when there are nonlinear transaction costs. This problem is difficult to solve because of its nonconvexity. The nonlinear transaction costs and CVaR constraints make things worse; state-of-the-art nonlinear programming (NLP) solvers have trouble in reaching even locally optimal solutions. As a practical solution, we develop a local search algorithm in which linear approximation problems and nonlinear equations are iteratively solved. Computational results are presented, showing that the algorithm attains a good solution in a practical time. It is better than the revised version of an existing global optimization. We also assess the performance of the constant rebalancing strategy in comparison with the buy-and-hold strategy.