Authors: Peyman Tataei1, Fereydoun Rahnama Roudposhti(Ph.D)2
Hashem Nikoumaram(Ph.D)3, Ashkan Hafezolkotob(Ph.D)4
1Ph.D. student in Financial Management, Islamic Azad University, Science and Research Branch
2Ph.D. in Financial Management, Islamic Azad University, Science and Research Branch
3Ph.D. in Financial Management, Islamic Azad University, Science and Research Branch
4PhD in Industrial Engineering, Islamic Azad University, Tehran South Branch
Corresponding Author Email: rahnama.roodposhti@gmail.com
Abstract
The view on the balance between risk and return has caused to ignore a part of returns in order to decrease risk. The Game Theory approach focuses on final outcome of investor and maximizing the outcome of player with respect to existing limitations and opportunities which is derived from his/her utility. The optimal answer is not necessarily the best one but it’s just the best available answer within the Nash Equilibrium range. In this research, the model of optimal portfolio selection is presented by the cooperative game theory; in the way that players are divided to 5 large groups including: the Major Player (market), Risk-free player, opposite player (contrary to market direction), Risk-averse player and Risky player. It is assumed that the Major Player will have seven strategies for the game, and the other four players, will try to defeat the market through a coalition and a cooperative game. The added value of the cooperation is calculated in terms of a concept called Shapley value and the weights of the optimal portfolio are also calculated using it. The optimal portfolio performance has been evaluated between 2006 and 2017 with respect to the index performance using Sharpe and Treynor criteria. The performance of the proposed cooperative game portfolio was significantly better than the market portfolio for 9 years among 12 examined periods. In 2013, Sharpe’s benchmark was better but the Treynor’s had a weaker performance than the market, and in general, its preference is ambiguous related to market portfolio. In the years 2010 and 2017, the proposed portfolio of the research was worse than the market portfolio, although the later was not significant based on Jobson and Korkie Statistic. The cooperative game portfolio significantly outperformed the market in all 12 years (2006-2017) based on both Sharpe and Treynor indexes.
Keywords: Game Theory; Cooperative Game; Shapley value; Portfolio
