Performance analysis of log-optimal portfolio strategies with transaction costs

Abstract

In this 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 recommends a suboptimal portfolio for discrete investment periods. We do not assume any parametric structure for the market process, only a first-order Markov property. The model introduced is based on kernel-based agents' (experts') approximation of the maximum theoretical growth rate with transaction costs. Although the optimal solution is theoretically a complex Bellman programming problem, our suboptimal empirical result appears to be attractive for Dow Jones 30 shares. The paper presents a performance analysis where the return of the empirical log-optimal portfolio is compared with 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, provide a significant positive abnormal return compared with the preceding equilibrium models, and is even a survivorship bias-free setup.

Keywords:

• Agent based modelling
• Portfolio optimization
• Transaction costs
• Multi-factor models
• Learning in financial models
• Performance evaluation

JEL Classification::

• C1, C4, C5, C14, C44, C51, G1, G11, G12

Acknowledgements

The authors thank László Györfi for his careful reading of the manuscript and useful advice. This paper has greatly benefited and been improved by the many helpful suggestions and comments from the two anonymous reviewers. This work forms part of the scientific project ‘Development of quality-oriented and harmonized R+D+I strategy and functional model at BME’. This project is supported by the New Hungary Development Plan (project ID: TÁMOP-4.2.1/B-09/1/KMR-2010-0002).

Notes

†Four changes occurred during the 15-year period in the DJIA.

‡The three-factor model also yields positive values at the 0.1 significance level.