Portfolio Rebalancing: A Test of the Markowitz-Van Dijk Heuristic

Abstract

Institutional investors usually employ mean-variance analysis to determine optimal portfolio weights. Almost immediately upon implementation, however, the portfolio’s weights become sub-optimal as changes in asset prices cause the portfolio to drift away from the optimal targets. In an idealized world without transaction costs investors would rebalance continually to the optimal weights. In the presence of transaction costs investors must balance the cost of sub-optimality with the cost of restoring the optimal weights. We apply a quadratic heuristic to address the asset weight drift problem, and we compare it to a dynamic programming solution as well as to standard industry heuristics. Our tests reveal that the quadratic heuristic provides solutions that are remarkably close to the dynamic programming solutions for those cases in which dynamic programming is feasible and far superior to solutions based on standard industry heuristics. In the case of five assets, in fact, it performs better than dynamic programming due to approximations required to implement the dynamic programming algorithm. Moreover, unlike the dynamic programming solution, the quadratic heuristic is scalable to as many as several hundreds assets.