International portfolio management under uncertainty

Although the consideration of foreign investments may have a positive impact on the overall market risk of the portfolio through diversi cation, it also adds a new source of uncertainty due to changes in the value of the currency. We investigate portfolio optimization models that account separately for the local asset returns and the currency returns, providing the investor with a full investment strategy. We tackle the uncertainty inherent to the estimation of the parameters with the aid of robust optimization techniques. We show how, by using appropriate assumptions regarding the formulation of the uncertainty sets, the original non-linear and non-convex models may be reformulated as second order cone or as semide nite programs. Additionally to the guarantees provided by robust optimization, we consider the use of hedging instruments such as forward contracts and options. The proposed hedging strategies are implemented from a portfolio perspective, and therefore do not depend on the individual value or behavior of any particular asset or currency. Hedging decisions are taken at the same time as investment decisions in a holistic approach to portfolio management. While dynamic decision making has traditionally been represented as scenario trees, these may become severely intractable and di cult to compute with an increasing number of time periods. We present an alternative approach to multiperiod international portfolio optimization based on an a ne dependence between the decision variables and the past returns. We add to our formulation the minimization of the worst case value-at-risk and show the close relationship with robust optimization. The proposed theoretical framework is supported by various numerical experiments with simulated and historical market data demonstrating its potential bene ts.