Optimal Asset Rebalancing in the Presence of Transactions Costs

We examine the optimal trading strategy for an investment fund which wishes to maintain two assets in fixed proportions, e.g. 60/40 in stocks and bonds. Transactions costs are assumed to be proportional to the amount of each asset traded. We show that the optimal policy involves a band about the target stock proportion. As long as the actual stock/bond ratio remains inside this band, no trading should occur. If the ratio goes outside the band, trading should be undertaken to move the ratio to the nearest edge of the band. We compute the optimal band and resulting annual turnover and tracking error of the optimal policy, as a function of transactions costs, asset volatility, the target asset mix, and other parameters. We show how changes in transactions costs and other parameters affect the size of the no-trade band, turnover, and tracking error. Compared to a quarterly rebalancing strategy an example demonstrates that the optimal strategy can reduce turnover by almost 50 percent.