Application of Covariance Matrix Adaptation-Evolution Strategy to Optimal Portfolio

Capital portfolio management is considered an important issue in the field of economics and its main subject is about the scientific management of combination choice of assets that meet the specific investment objectives. Maximizing returns and minimizing asset risk are the most important goals in the management of the portfolio of capital. This paper proposes two novel risk measures based on the MLP neural networks and prediction intervals (PI). The MLP based risk is constant and assumes that the uncertainty is uniform in the dataset. The second one is a time-varying risk measure that doesn’t assume uniformity condition. After introducing two novel risk measures, a new cost function is presented to consider the expected returns and the involving risk at the same time. Finally, the covariance matrix adaptation evolution strategy (CMA-ES) algorithm is used to obtain the optimal portfolio. The validity of the proposed selection process (including risk measures, cost function, and the optimization method) is tested using the dataset of the 18 shares of the Tehran Stock Exchange, and the results are compared with the obtained portfolio using the conditional value at risk (CVaR) criterion as a well-known benchmark.