Rebalancing Frequency Considerations for Kelly-Optimal Stock Portfolios in a Control-Theoretic Framework

Abstract

In this paper, motivated by the celebrated work of Kelly, we consider the problem of portfolio weight selection to maximize expected logarithmic growth of a trader's account. Going beyond existing literature, our focal point here is the rebalancing frequency which we include as an additional parameter in the maximization. The problem is first set up in a control-theoretic framework, and then, the main question we address is as follows: In the absence of transaction costs, does high-frequency trading always lead to the best performance? Related to this question is our prior work on Kelly betting which examines the impact of making a wager and letting it ride. Our prior results indicate that it is often the case that there are no performance benefits associated with high-frequency trading. In the present paper, we generalize the analysis from the single-asset case to a portfolio with multiple risky assets. We show that if there is an asset satisfying a certain dominance condition, then an optimal portfolio consists of this asset alone; i.e., if the trader puts 'all eggs in one basket,' performance becomes a constant function of rebalancing frequency. Said another way, the problem of rebalancing is rendered moot. The paper also includes simulations which address practical considerations associated with real stock prices vis-a-vis the dominance condition.