In today's competitive environment, designing a robust program for stock portfolio selection is important and necessary. The stock portfolio selection problem is one of the most important problems in the field of finance. Robust optimization is a practical solution to problems in which the value and distribution of parameters are unknown. In the present study, the goal is to maximize a distributed robust stock portfolio based on the Kalamar ratio with the Wasserstein metric, which is a reward-risk ratio and its calculation depends on the portfolio return distribution. Reward-risk ratios are of great importance for risk-averse investors by simultaneously considering return and risk. The research strategy for robustness of the return distribution parameter is to consider all returns that are in a neighborhood of the empirical portfolio distribution, which is determined by the Wasserstein metric criterion. The sample portfolio of the present study consists of 8 indices or industries from the Tehran Stock Exchange with the highest trading volume in the period from the beginning of 1389 to the end of 1400 and in a weekly time horizon. The test data is divided into 5 periods and to evaluate the results of the distributional robust portfolio in comparison with the portfolio without this property, the result of dividing the average of the Kalmar ratios in the 5 mentioned periods by their standard deviation was used. The optimization results using the particle swarm optimization algorithm show that the distributional robust portfolio improves the mentioned ratio by 27.1 and in addition, the minimum Kalmar ratio in the 5 periods in the distributional robust portfolio is higher than in the portfolio without this property.