Distributionally Robust portfolio Optimization based on the Calmar ratio using the Wasserstein metric

The return distribution of a portfolio is not constant in different periods, which is affected by the dynamics of financial markets and provides the basis for the instability of the portfolio. Distributionally Robust Portfolio Optimization (DRO) takes into account the uncertainty of the portfolio due to changes in the distribution of portfolio returns. In the current research, the objective function of the portfolio model is to maximize the Calmar ratio, which is one of the reward-risk ratios, and its calculation depends on the distribution of the 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 Wasserstein metric. 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 Calmar's ratios into the 5 mentioned periods by their standard deviation has been used. The results show that the DRO portfolio improves this ratio by 0.27, and in addition, the minimum ratio of Calmar in 5 periods in the DRO portfolio is higher than the basket without this property.