Efficient Asset Allocation: Application of Game Theory-Based Model for Superior Performance

Abstract

In this paper, we compared the models for selecting the optimal portfolio based on different risk measures to identify the periods in which some of the risk measures dominated over others. For decades, the best known return-risk model has been Markowitz’s mean-variance model. Based on the criticism of the classical Markowitz model, a whole series of risk measures and models for selecting the optimal portfolio have been developed, which are divided into two groups: symmetrical and downside risk measures. Based on the tools provided by game theory, we presented a minimax model for selecting the optimal portfolio based on the maximum loss as a measure of risk. Recent research has shown the adequacy of the application of this risk measure and its dominance concerning variance in certain circumstances. Theoretically, the model based on maximum loss as a measure of risk relies on a much smaller number of assumptions that must be satisfied. In the empirical part of the paper, we analyzed the real return performance, structure, correlation, stability, and predictive efficiency of the model based on maximum loss return as a measure of risk and compared it with the other famous models to determine whether the maximum loss-based risk measure model is more suitable for use in certain circumstances than conventional return-risk models. We compared portfolios created based on different models over the period of 2000–2020 from a selected sample of stocks that are components of the STOXX Europe 600 index, which covers 90% of the free market capitalization in the European capital market. The observed period included 3 bear market periods, including the period of market decline during the COVID-19 crisis. Our analysis showed that there was no significant difference in portfolio returns depending on the selected model using the “buy-and-hold” strategy, but there were crisis periods. The results showed a significantly higher stability of portfolios selected on the criterion of minimizing the maximum loss than others. In periods of market decline, this portfolio achieved the best performance and had a shorter recovery period than others. This allowed superior use of the minimax model at least for investors with a pronounced risk aversion.