Global minimum variance portfolios under uncertainty: a robust optimization approach This paper presents new models which seek to optimize the first and second moments of asset returns without estimating expected returns. Motivated by the stability of optimal solutions computed by optimizing only the second moment and applying the robust optimization methodology which allows to incorporate the uncertainty in the optimization model itself, we extend and combine existing methodologies in order to define a method for computing relativerobust and absoluterobust minimum variance portfolios. For the relative robust strategy, where the maximum regret is minimized, regret is defined as the increase in the investment risk resulting from investing in a given portfolio instead of choosing the optimal portfolio of the realized scenario. The absolute robust strategy which minimizes the maximum risk was applied assuming the worstcase scenario over the whole uncertainty set. Across alternate time windows, results provide new evidence that the proposed robust minimum variance portfolios outperform nonrobust portfolios. Whether portfolio measurement is based on return, risk, regret or modified Sharpe ratio, results suggest that the robust methodologies are able to optimize the first and second moments without the need to estimate expected returns.

A constrained multiperiod robust portfolio model with behavioral factors and an interval semiabsolute deviation Abstract   In this paper, a multiperiod portfolio selection model is presented considering the behavioral factors of investors. The behavioral factors are presented in the form of prospect theory with three main parameters as reference dependence, risk aversion, and diminishing sensitivity; these parameters define the behavioral features of investors that can influence their investing. The future return of assets is regarded according to the interval based on uncertainty. Besides, a criterion of interval semiabsolute deviation is presented to control the risk of investing. The influence of uncertainty exists in the optimal parameters; the final result is controlled by a robust optimization approach. In order to make this model applicable and adapting it to the conditions of the real world, we considered the cardinality constraints, entropy and the possibility of riskfree borrowing and lending with different rates. First, the model is solved by GAMS in small size to check the feasibility, then, due to the NPhard feature of the model, we used three metaheuristic algorithms, which are more appropriate for solving large problems, to solve the proposed model. To survey the modelxe2x80x99s performance, we used real data from a case study. The results show that the model reflects the behavioral factors of investors in their portfolio and it also maintains the robustness level in accordance with the degree of conservatism. Besides, the sensitivity analysis is performed to show the modelxe2x80x99s efficiency. Finally, we compared the results of different metaheuristic algorithms and benchmark modelxe2x80x99s performance.