On Frequency-Based Log-Optimal Portfolio With Transaction Costs

This letter investigates the impact of both rebalancing frequency and transaction costs on the log-optimal portfolio, defined as a portfolio that maximizes the expected logarithmic growth rate of an investor's wealth. We establish that the frequency-dependent log-optimal portfolio problem incorporating transaction costs is equivalent to a concave program. We also provide a version of the dominance theorem that incorporates cost considerations, enabling the identification of scenarios in which an investor should invest all available funds in a single asset. Then, we solve for an approximate quadratic concave program and derive both necessary and sufficient optimality conditions. Additionally, we establish a version of the two-fund theorem, asserting that any convex combination of two optimal weights derived from the optimality conditions remains optimal. To support our results, we conduct empirical studies using intraday price data.