Aggregating exponential gradient expert advice for online portfolio selection under transaction costs

Abstract

As an application of machine learning techniques in the field of portfolio management, online portfolio selection (OLPS) aims at optimising the allocation of wealth in an uncertain environment. When making investment decisions, the transaction cost is such an important factor that investor should not ignore. Thus, this paper extends an existing online portfolio selection strategy Continuous Aggregating Exponential Gradient (CAEG) (Yang et al., 2022) in the presence of transaction costs. The proportional transaction costs model is constructed when the transaction costs are incorporated into the decision-making process, and we call this new strategy ${\text{CAEG}}_c$. Theoretical guarantee proves that the mean of the logarithmic cumulative wealth of ${\text{CAEG}}_c$ has an asymptotic upper bound with that of its benchmark. The numerical examples demonstrate the impact of transaction costs on the proposed ${\text{CAEG}}_c$ strategy on the one hand, and on the other hand, verify that ${\text{CAEG}}_c$ outperforms other related OLPS strategies and is comparable to its benchmark strategy.

Keywords:

• Proportional transaction costs
• online learning
• weak aggregating algorithm
• competitive performance
• asymptotic upper bound

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 Yahoo Finance: finance.yahoo.com; Google Finance: www.google.com/finance/.

2 Gábor collected till 2006 (http://www.cs.bme.hu/∼oti/portfolio/).

3 Interactive Broker (http://www.interactivebrokers.com) charges a fixed $0.005 commission per share to trade and the average price of Dow Jones Composites is about $50, so when the taxes and bid-ask spreads are not considered, the transaction costs rate is about 0.01%, which is well below 0.3%.

Additional information

Funding

This research was supported by the Humanities and Social Science Foundation of the Ministry of Education of China (No. 21YJA630117) and the Philosophy and Social Sciences Planning Project of Guangdong Province (GD19CGL06).