Analysis of the Rebalancing Frequency in Log-Optimal Portfolio Selection

In a dynamic investment situation, the right timing of portfolio revisions and adjustments is essential to sustain long-term growth. A high rebalancing frequency reduces the portfolio performance in the presence of transaction costs, whereas a low rebalancing frequency entails a static investment strategy that hardly reacts to changing market conditions. This article studies a family of portfolio problems which depend parametrically on the rebalancing frequency. As an objective criterion we use log-utility, which has strong theoretical appeal and represents a natural choice if the primary goal is long-term performance. We show that continuous rebalancing only slightly outperforms discrete rebalancing if there are no transaction costs and if the rebalancing intervals are shorter than about one year. This result suggests that finite transaction costs are of minor concern since their effect on infrequently rebalanced portfolios is negligible.