Performance Analysis of Log-Optimal Portfolio Strategies with Transaction Costs

In the paper we introduce an empirical approximation of the log-optimal investment strategy that guarantees an almost optimal growth rate of investments. The proposed strategy also considers the effects of portfolio rearrangement costs on growth optimality and advises a suboptimal portfolio for discrete investment periods. We do not assume any parametric structure for the market process, only first order Markov property. The model introduced is based on kernel-based agents' (experts') approximation on the maximum theoretical growth rate with transaction costs. Although the optimal solution is theoretically a complex Bellman programming problem, our sub-optimal empirical result seems to be attractive on Dow Jones 30 shares. The paper presents a performance analysis where the return of the empirical log-optimal portfolio is compared to passive portfolio counterparts compiled from similar components using the CAPM, the three-factor model and the four-factor model. The proposed methods in the presence of transaction costs gain a significant positive abnormal return as compared with the preceding equilibrium models, and is even a survivorship bias free setup