Robust International Portfolio Optimization with Worst-Case Mean-LPM

Abstract

This paper proposes a robust international portfolio optimization model with the consideration of worst-case lower partial moment (LPM) and worst-case mean return. In our model, we assume that the distributions and the first- and second-order moments of distributions of returns of assets and exchange rates are all ambiguous. The proposed model can be reformulated into an equivalent semidefinite programming (SDP) problem, which is computationally tractable. For investigation of the performance of our model, we also give two benchmark models. The first benchmark model is a scenario-based model which uses historical observations of returns to approximate the future distributions. The second benchmark model only considers the ambiguity of distributions but does not consider the ambiguity of the first- and second-order moments of distributions. We conduct empirical experiments in a rolling forward way to evaluate the out-of-sample performances of our proposed model, the two benchmark models, and an equally weighted model using the return measures and various risk-adjusted return measures. The result shows that our model has the best performance. It verifies that investors can obtain benefits when employing the robust model and considering the ambiguity of the first- and second-order moments of distributions.

Adaptive Cone Algorithm

“…The second step is the random search of an agent within its local solution space. It is formalized by using (7) and (8). Equation ( 7) is used to determine the second step candidate.…”

“…It is like the human process, whether personal or institutional. For example, a fund manager is challenged to arrange his clients' limited investments to meet several objectives, such as maximizing the risk-adjusted return [1], preventing too much risk [2], and so on. A factory manager must manage the incoming orders to minimize the total completion time [3], idle energy consumption [4], total actual flow time [5], maximum completion time [6], and so on.…”

“…A factory manager must manage the incoming orders to minimize the total completion time [3], idle energy consumption [4], total actual flow time [5], maximum completion time [6], and so on. A university or school manager must manage the facilities, especially rooms and lecturers, to achieve some objectives, such as minimizing the unserved participants [7], minimizing the overcapacity of classrooms [8], or minimizing idle time [9]. A fleet manager must arrange his vehicles to execute all pickup and delivery orders for some objectives, such as minimizing the cost [10], transshipment [11], number of vehicles [12], travel distance [12], distribution cost [13], logistic cost [14], and so on.…”