International Journal of Nonlinear Analysis and Applications

Portfolio design and optimization within the framework of the Markov chain

Document Type : Research Paper

Authors

1 Department of Management, Dehaghan Branch, Islamic Azad University, Dehaghan, Iran

2 Department of Economics, Dehagاan Branch, Islamic Azad University, Dehaghan, Iran

Abstract

Return and risk are significant parameters in selecting an optimal portfolio, depending on the portfolio return distribution. In a stochastic process, the Markov property causes the future distribution of a random process to be measurable according to the state-transition matrix and the initial process state. According to the main idea of the present study in the optimal portfolio selection, portfolio weights are chosen in a way that the Markov property is established for the portfolio return series and the distribution of future portfolio returns is close to the distribution of investor's expected returns; hence, K-L divergence (Kullback–Leibler divergence) is utilized as a criterion of closeness. Using this idea, an optimal portfolio selection model was designed and implemented in the present study. This optimal portfolio was optimized using a Markov approach and according to historical data of 10 indices on the Tehran Stock Exchange from 2009 to 2022 in a six-member state. The optimal portfolio performance evaluation using the Sharpe ratio and value at risk criteria indicated that the research model had a higher performance than the mean-variance and weight parity models.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 15, Issue 4
April 2024
Pages 265-273
  • Receive Date: 19 March 2023
  • Revise Date: 14 June 2023
  • Accept Date: 09 July 2023