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

Yıl 2023, Sayı: 39, 26 - 36, 27.12.2023

Salih Çam

https://doi.org/10.26650/ekoist.2023.39.1221032

Öz

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.

Anahtar Kelimeler

Portfolio Theory, Game Theory, Markov Chains Model, BIST30

Kaynakça

• Arditti, F. D., and Levy, H. (1977). Portfolio Efficiency Analysis in Three Moments: The Multiperiod Case. In Financial Dec Making under Uncertainty (pp. 137-150). Academic Press. google scholar
• Bhansali, V. (2008). Tail Risk Management. The Journal of Portfolio Management, 34(4), 68-75. google scholar
• Björk, T., Murgoci, A. and Zhou, X. Y. (2014). Mean-Variance Portfolio Optimization with State-Dependent Risk Aversion. Mathematical Finance, 24(1), 1-24. google scholar
• Campbell, J. Y., Cocco, J. F., Gomes, F. J., and Maenhout, P. J. (2001). Investing Retirement Wealth: A Life-Cycle Model. In Risk Aspects of Investment-Based Social Security Reform (pp. 439-482). University of Chicago Press. google scholar
• Carfı, D., and Musolino, F. (2012). Game Theory and Speculation on Government Bonds. Economic Modelling, 29(6), 2417-2426. google scholar
• Carfı, D., and Musolino, F. (2013). Game Theory Application of Monti’s Proposal for European Government Bonds Stabilization. Applied Sciences, 15. google scholar
• Chen, C., and Zhou, Y. S. (2018). Robust Multi objective Portfolio with Higher Moments. Expert Systems with Applications, 100, 165-181. google scholar
• Çam S. (2021). Portföy Analizinde Beklenen Getiri Sorunu: Markov Getiriler ve Basit Getirilerin Karşılaştırılması. İzmir İktisat Dergisi, 36(1), 81-95. google scholar
• DeMiguel, V., and Nogales, F. J. (2009). Portfolio Selection with Robust Estimation. Operations Research, 57(3), 560-577. google scholar
• Ding, Y. (2006). Portfolio Selection Under Maximum Minimum Criterion. Quality & Quantity, 40, 457- 468. google scholar
• Esch, D. N. (2010). Non-Normality Facts and Fallacies. Journal of Investment Management, 8. google scholar
• Essid, H., Ganouati, J. and Vigeant, S. (2018) A Mean-Maverick Game Cross- Efficiency Approach to Portfolio Selection: An Application to Paris Stock Exchange. Expert Systems with Applications, 113, 161-185. google scholar
• Evangelista, D., Saporito, Y., and Thamsten, Y. (2022). Price Formation in Financial Markets: a Game-Theoretic Perspective. arXiv preprint arXiv:2202.11416. google scholar
• Evans, J. L., and Archer, S. H. (1968). Diversification and the Reduction of Dispersion: An Empirical Analysis. The Journal of Finance, 23(5), 761-767. google scholar
• Fabozzi, F. J., Kolm, P. N., Pachamanova, D. A., and Focardi, S. M. (2007). Robust Portfolio Optimization and Management. John Wiley & Sons. google scholar
• Fama, E. F. (1965). Portfolio Analysis in A Stable Paretian Market. Management Science, 11(3), 404-419. google scholar
• Farias, C. A., Vieira, W. C. asnd Santos, M. L. (2006). Portfolio Selection Models: Comparative Analysis and Applications to the Brazilian Stock Market. Revista de Economia e Agronegocio, 4(3), 387-407 google scholar
• Ferreira, R. J. P., Almeida Filho, A. T. and Souza, F. M. C. (2009). A Decision Model for Portfolio Selection. Pesquisa Operacional, 29(2), 403-417. google scholar
• Gong, X., Yu, C., Min, L., and Ge, Z. (2021). Regret Theory-Based Fuzzy Multi-Objective Portfolio Selection Model Involving DEA Cross-Efficiency and Higher Moments. Applied Soft Computing, 100, 106958. google scholar
• Granito, M., and Walsh, P. (1978). Portfolio Efficiency Analysis in Three Moments-The Multi-period Case: Comment. The Journal of Finance, 33(1), 345-348. google scholar
• Hamilton, J. D. (1994). Time series analysis (Vol. 2). Princeton: Princeton University Press. google scholar
• Hubert, M., Debruyne, M., and Rousseeuw, P. J. (2018). Minimum Covariance Determinant and Extensions. Wiley Interdisciplinary Reviews: Computational Statistics, 10(3), e1421. google scholar
• Ibragimov, R. (2005). On Efficiencey of Linear Estimators Under Heavy-Tailedness. Harvard Institute of Economic Research Discussion Paper, (2085). google scholar
• Ibrahim, M. A. R., Hee, P. C., Islam, M. A. and Bahaludin, H. (2020). Cooperative Game Theory Approach for Portfolio Sectoral Selection Before and After Malaysia General Elections: GE13 versus GE14. Saudi Journal of Economics and Finance, 4(8), 390-398 google scholar
• Jobst, N. J., and Zenios, S. A. (2001). The Tail That Wags the Dog: Integrating Credit Risk in Asset Portfolios. The Journal of Risk Finance. google scholar
• Koumou, G. B. (2020). Diversification and Portfolio Theory: A Review. Financial Markets and Portfolio Management, 34, 267-312. google scholar
• Lhabitant, F. S. (2017). Portfolio diversification. Elsevier. google scholar
• Malkiel, B. G. (2002, March). How Much Diversification is Enough? In AIMR Conference Proceedings on Equity Portfolio Construction (Vol.5, pp. 18-28). google scholar
• Mandelbrot, B. B. (1997). The Variation of Certain Speculative Prices. In Fractals and scaling in finance (pp. 371-418). Springer, New York, NY. google scholar
• Markowitz, H. M. (1952). Portfolio Selection. The Journal of Finance 7(1): 77-91 google scholar
• McQueen, G., and Thorley, S. (1991). Are Stock Returns Predictable? A Test Using Markov Chains. The Journal of Finance, 46(1), 239-263. google scholar
• Norouzi, N., Fani, M., and Talebi, S. (2022). Green Tax as a Path to Greener Economy: A game Theory Approach on Energy and Final Goods in Iran. Renewable and Sustainable Energy Reviews, 156, 111968. google scholar
• Özdemir, A., and Demireli, E. (2014). Hisse Senedi Fiyat Verimliliğinin Markov Zincirleri İle Analizi Bist Teknoloji Endeksi Hisse Senedi Fiyatlari Üzerine Bir Uygulama. Verimlilik Dergisi, (1), 41-60. google scholar
• Reyna, F. R., Jûnior, A. M. D., Mendes, B. V., and Porto, O. (2005). Optimal Portfolio Structuring in Emerging Stock Markets Using Robust Statistics. Brazilian Review of Econometrics, 25(2), 139-157. google scholar
• Ruan, L., Wang, J., Chen, J., Xu, Y., Yang, Y., Jiang, H., ... and Xu, Y. (2018). Energy-Efficient Multi-UAV Coverage Deployment in UAV Networks: A Game-Theoretic Framework. China Communications, 15(10), 194-209. google scholar
• Sheikh, A. Z., and Qiao, H. (2009). Non-Normality of Market Returns. JP Morgan Asset Management research paper. google scholar
• Song, H., and Zhang, X. (2013). Apply Game Theory to the Correlation of Total GDP and Carbon Emissions. Economic Management Journal, 2(4). google scholar
• Stoyanov, S. V., Rachev, S. T., Racheva-Yotova, B., and Fabozzi, F. J. (2011). Fat-Tailed Models for Risk Estimation. The Journal of Portfolio Management, 37(2), 107-117. google scholar
• Tran, X., and Thompson, C. (2015). Application of Game Theory in Tourism. Tourism Analysis, 20(6), 697-702. google scholar
• Tüfekçi, Ö. K. and Avşarlıgil, N. (2016). Optimal Portfolio Theory and Game Theory Approach: A study on BİST. Journal of Strategic Research in Social Science, 2(4), 41-64. google scholar
• Welsch Eom, C. (2020). Risk Characteristic on Fat-Tails of Return Distribution: An Evidence of the Korean Stock Market. Asia-Pacific Journal of Business, 11(4), 37-48. google scholar
• Welsch, R. E., and Zhou, X. (2007). Application of Robust Statistics to Asset Allocation Models. REVSTAT-Statistical Journal, 5(1), 97-114. google scholar
• Winston, W. L. (2004). Operations Research: Applications and Algorithms. Cengage Learning. google scholar
• Yang, L., Couillet, R., and McKay, M. R. (2015). A Robust Statistics Approach to Minimum Variance Portfolio Optimization. IEEE Transactions on Signal Processing, 63(24), 6684-6697. google scholar
• Yavuz, M. and Eren, T. (2016). Finansal Araçların Oyun Teorisiyle Analiz Edilmesi. Bartın Üniversitesi İ.İ.B.F. Dergisi, 7(13), 122-139. google scholar
• YENİSU, E. (2020). Hisse Senedi Fiyatlarının Markov Zincirleri ile Analizi: BIST 100 Şirketleri Üzerine Bir Uygulama. Giresun Üniversitesi İktisadi ve İdari Bilimler Dergisi, 6(2), 261-277. google scholar
• Zhu-Gang, J., Wen-Jia, C., and Can, W. (2014). Simulation of climate Negotiation Strategies Between China and the US Based On Game Theory. Advances in Climate Change Research, 5(1), 34-40. google scholar