Asset Allocation with Combined Models Based on Game-Theory Approach and Markov Chain Models

The measurement of expected returns has a major impact on portfolio performance. While there are several methods used for estimating expected returns in existing studies, the mean-variance model most commonly used in portfolio theory utilizes the method of expected returns calculated from historical data. However, the problem with estimating expected returns is that estimating parameters based on historical data, such as the arithmetic mean, may not reflect the distributional characteristics of the return series and may not be an appropriate statistic for the population parameters. Therefore, using robust statistics or combined portfolio models can lead to better portfolios that minimize estimation error while maximizing expected returns. In this paper, we use game theory and Markov chain models to estimate expected asset returns and compare portfolios constructed based on these methods. The analysis results show that the portfolio constructed based on game theory yielded higher returns than the target index and mean-variance model, while the model based on Markov chains yielded portfolios with the lowest portfolio risk. In all out-of-sample investment periods, the game theory based portfolio produced better returns than the portfolios estimated in the study, except for the period from January 2022 to December 2022.