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.

Purpose-This paper presents game theory approach for solving problem of the optimal investment portfolio selection. Methodology-Model was formed on the basis of historical returns on stocks presented as a matrix of payments. The goal is seeking the minimum between the largest potential losses, and therefore it is called minmax model. The main objective is to answer whether the minimax model tool performs better than the stock market index, and to verify the relationship between the established Markowitz meanvariance (MV) efficient portfolios and minmax optimum portfolio. We use data from the European capital market and Euro Stoxx 50 index as a reference index in the period 2004-2015, which we divided into two parts. We compared and analyzed the performance of the portfolios created through minimax model with the performance of market index and MV model in the actual investment period and it proved to be dominant and more successful. Findings-Results speak in favor of minmax portfolio model as effective passive investment strategy. It is possible to maximize returns over even longer periods of up to year without changing portfolio investments, i.e. without frequent trading and not just to gain market return, but to beat the market by this technical investing. Conclusion-Minmax model could be used for asset allocation in portfolio investments and that there is a real possibility to beat the market using minimax model.

Comparing portfolio performance is complex due to the fact that each model is dominant in its own risk space. Since there is no single dominant performance measure, the research problem is how to incorporate several different measures into a performance evaluation model that allows portfolios to be ranked. In this regard, the objective of this study was to develop a new comprehensive method for comparing portfolio performance based on multiple-criteria decision-making (MCDM). This paper proposes an integrated approach for stock market decision making that combines the Analytic Hierarchy Process (AHP) and the Preference Ranking Organization Method for Enrichment Evaluations (PROMETHEE), which allow hierarchical evaluation of a finite number of alternatives according to different criteria. This hybrid approach is especially advantageous, utilizing the strengths of both individual methods. AHP enables the decomposition of a complex problem into its constituent parts and the determination of weights for criteria, while the PROMETHEE method allows the investor to determine the preference function, complete ranking, and analysis of the robustness of the results. For the MCDM model in this study, different dimensions of performance measures are considered criteria: return measures, risk measures, stability measures, and predictability measures. The methodology has been applied in comparing real portfolios selected on the basis of different risk measures. For this purpose, weekly return data were used for a sample of stocks that are components of the STOXX Europe 600 Index for the period 2000–2020. In addition, a sensitivity analysis is performed to investigate the strength of the results of this method. It suggests that the simultaneous consideration of different performance measures and the investor’s attitude towards the importance of these measures are notably important in the portfolio efficiency estimation process.