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.
Highlights
In order to capture the diversification benefits of international financial markets, institutional and individual investors tend to invest part of their money in the financial markets of other countries or regions using different currencies. e correlations of returns of assets in other countries or regions are often lower than those in just one country, so international asset allocation may reduce risk [1,2,3,4,5]
In the second benchmark model, we assume that the distributions of future returns are ambiguous, but the first- and second-order moments are known. en, we conduct empirical experiments using the return measures and various risk-adjusted return measures to assess the performances of our model, the two benchmark models, and the weighted model
In order to assess the performance of our model RIML, we present two benchmark models . e first benchmark model denoted by SIML is based on empirical distributions approximated by historical samples of returns. e approximated distribution P is described in (7), and lower partial moments (LPM) under P is shown in (8). e return of the international portfolio under P can be written as Return(w, P)
Summary
In order to capture the diversification benefits of international financial markets, institutional and individual investors tend to invest part of their money in the financial markets of other countries or regions using different currencies. e correlations of returns of assets in other countries or regions are often lower than those in just one country, so international asset allocation may reduce risk [1,2,3,4,5]. Even if they acquire the actual distributions of future security returns, the computation of LPM is a difficult task To deal with these problems, some researchers employ robust optimization techniques to portfolio selection models using LPM as the risk measure [10,11,12,13,14]. We build a robust international portfolio optimization model with worst-case LPM as the risk measure and consider the worst-case mean return. Random variables are denoted by symbols with tildes, whereas the realizations of them are denoted by symbols without tildes
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