Multi-Period Portfolio Rebalancing with Personal Tax

Abstract

The practical advice to the multi-period portfolio rebalancing problem with personal tax is to make adjustments over a long period of time. The reason for this non-quantitative advice is that there is no dynamic or analytic solution to the problem due to its’ complexity. In this paper, we will quantify this advice within the context of maximizing a multi-period utility of consumption. We will show that while the monetary benefit of rebalancing is larger than the tax cost, in order to maximize this benefit, the current portfolio must be moved to the optimal portfolio prudently. We first investigate the benefit of a simple heuristic rebalancing rule, such as trading X percent of the current portfolio annually. Secondly, we will derive another simple rebalancing rule which is consistent with current continues time portfolio theory. It is based on the assumption that the unknown value function (the maximum achievable utility) can be approximated by a simple quadratic function. We show that this derived rebalancing rule is better than the first simple heuristic rebalancing rule.