Performance Analysis of Log-Optimal Portfolio Strategies with Transaction Costs

Abstract:     
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.

Number of Pages in PDF File: 21

Keywords: Agent based modeling, Portfolio optimization, Transaction costs, Multi-factor models, Learning in financial models, Performance evaluation

JEL Classification: C1, C4, C5, C14, C44, C51, G1, G11, G12

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