Distributionally Robust Portfolio Optimization with Rachev ratio using KL divergence

Document Type : Original Article

Authors
mona beyranvand 1
sayyed mohammad reza davoodi 2
Mohammadreza Sharifi-Ghazvini 3
1 PhD Candidate of Industrial Management, Department of Management, Dehaghan Branch, Islamic Azad University, Dehaghan, Iran.
2 Associate Professor. Department of Management ,Dehaghan Branch, Islamic Azad University, Dehaghan, Iran.
3 Assistant Professor. Department of Industrial Engineering,Dehaghan Branch, Islamic Azad University, Dehaghan, Iran
10.22034/jik.2026.24006
Abstract
The return distribution of a stock portfolio is not constant in different periods of time, which is affected by the dynamics of financial markets and provides the basis for the instability of the stock portfolio. Distributionally Robust Portfolio Optimization (DRO) takes into account the uncertainty of the stock portfolio due to changes in the distribution of portfolio returns. In the current research, the objective function of the stock portfolio model is to maximize the Rachev ratio, which is one of the reward-risk ratios, and its calculation depends on the distribution of the stock portfolio returns. The research strategy to robust the return distribution parameter is to consider all the returns that are located in a neighborhood of the empirical distribution of the portfolio, which was used to determine such distributions using the Kl divergence. A sample portfolio of the research consists of 8 indices or industries from the Tehran Stock Exchange in the period from 1390 to 1400 and on a weekly time horizon. The test data has been divided into 5 periods, and to evaluate the DRO portfolio compared to the portfolio without this feature, the result of dividing the average of Rachev ratios in the 5 mentioned periods by their standard deviation has been used. The results show that the DRO portfolio improves this ratio by 0.40 and in addition, the minimum ratio of Rachev in 5 periods in the DRO portfolio is higher than the basket without this property.
Keywords
: Rachev ratio
Distributionally Robust Portfolio
Kl divergence metric
PSO
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