Orateur
Description
It is a common practice in portfolio optimization to focus on the minimization of losses and risk. However, more advanced models incorporating the second-order stochastic dominance (SSD) constraints have gained increasing attention in last two decades. These constraints identify the portfolios that dominate the benchmark portfolio with respect to SSD. Contrary to that, this paper is focused on the feasibility conditions that ensure portfolio efficiency with respect to SSD — in other words, only portfolios which are not dominated by any other portfolio are considered as feasible ones in the model. Moreover, if we seek to optimize an additional criterion with respect to the SSD feasibility set — such as maximizing the return or minimizing the risk — the resulting model becomes a stochastic bi-level optimization problem. The lower level problem guarantees the SSD efficiency, while the upper level problem optimizes the selected criterion. We formulate, analyze and solve such stochastic bi-level optimization problem under various upper level objectives, including the minimization of transaction costs or the maximization of out-of-sample mean returns. The advantages of these models are demonstrated through empirical results based on the out-of-sample performance and moving window analysis using real-life market data.
