Robust international portfolio management

We present an international portfolio optimization model where we take into account the two different sources of return of an international asset: the local returns denominated in the local currency, and the returns on the foreign exchange rates. The explicit consideration of the returns on exchange rates introduces non-linearities in the model, both in the objective function (return maximization) and in the triangulation requirement of the foreign exchange rates. The uncertainty associated with both types of returns is incorporated directly in the model by the use of robust optimization techniques. We show that, by using appropriate assumptions regarding the formulation of the uncertainty sets, the proposed model has a semidefinite programming formulation and can be solved efficiently. While robust optimization provides a guaranteed minimum return inside the uncertainty set considered, we also discuss an extension of our formulation with additional guarantees through trading in quanto options for the foreign assets and in equity options for the domestic assets.