Analysis of risk measures in multiobjective optimization portfolios with cardinality constraint

Abstract

Portfolio selection has been the subject of extensive studies in order to obtain increased returns, minimizing the investment risk. However, the most appropriate risk measure to be considered is still an open problem. The aim of this work is to study different risk measures in the multiobjective portfolios optimization with cardinality constraint and rebalancing. The in-sample analysis compares the fronts of each algorithm, metric and range of cardinality, and out-of-sample analysis compares the results of each measure of risk with each other and with two benchmarks. The returns of portfolios are compared in terms of assets choice and assignment of weights. Statistical tests are performed to verify if any measure of risk shows some superiority. Results indicate that downside risk measures can reduce the cardinality and the risk of financial drawdown without reducing drawup, once they are able to reduce just the negative historical returns scenarios.