Mean-CVaR Portfolio Optimization Approaches with Variable Cardinality Constraint and Rebalancing Process

This work compares Mean-CVaR portfolio optimization models with variable cardinality constraint and rebalancing process. It considers integer and continuous decision variables, the number of asset lots and asset investment rate, respectively, and the linear and non-linear formulations of CVaR. Exact methods are used to solve the linear models and parallel evolutionary algorithms are used to solve the non-linear models. The in-sample analysis compares the sets of multiobjective optimization solutions, evaluating the effect of the cardinality of portfolios, with respect to the returns and risks. The out-of-sample analysis performs simulations with stock market trading, considering historical data with different data granularity and transaction costs, aiming to analyze the effects of these characteristics on the financial risks and gains. Results show that models considering asset lots are more effective in practice and that the exact methods provide solutions closer to the heuristics, with greater execution time. Out-of-sample analysis indicates the robustness of the portfolio optimization models pointing out similar behavior of financial gains for different values of transaction costs. Optimization with higher granularity provides greater risk, but also offers chances of high profits.