On Frequency-Based Optimal Portfolio with Transaction Costs

TL;DR

This paper analyzes how rebalancing frequency and transaction costs influence the log-optimal portfolio, proposing methods to address associated challenges and validating them with empirical data and online trading scenarios.

Contribution

It introduces a concave programming approach for frequency-dependent portfolios with costs and extends the two-fund theorem under these conditions.

Findings

Transaction costs can cause bankruptcy issues in frequency-based portfolios.

The proposed quadratic concave program effectively approximates the original problem.

Empirical results demonstrate the method's applicability in online trading scenarios.

Abstract

The aim of this paper is to investigate the impact of rebalancing frequency and transaction costs on the log-optimal portfolio, which is a portfolio that maximizes the expected logarithmic growth rate of an investor's wealth. We prove that the frequency-dependent log-optimal portfolio problem with costs is equivalent to a concave program and provide a version of the dominance theorem with costs to determine when an investor should invest all available funds in a particular asset. Then, we show that transaction costs may cause a bankruptcy issue for the frequency-dependent log-optimal portfolio. To address this issue, we approximate the problem to obtain a quadratic concave program and derive necessary and sufficient optimality conditions. Additionally, we prove a version of the two-fund theorem, which states that any convex combination of two optimal weights from the optimality conditions is still optimal. We test our proposed methods using both intraday and daily price data. Finally, we extend our empirical studies to an online trading scenario by implementing a sliding window approach. This approach enables us to solve a sequence of concave programs rather than a potentially computational complex stochastic dynamic programming problem.