Abstract
Abstract The paper provides an exact and computable solution to the general quadratic mean-variance problem with exchange rate and return uncertainties. Multiple currencies are considered, with multiple investments in each currency. The classical mean-variance formulation is augmented with currency risk. The overall risk is hence the multiplicative effect of return risks, within a currency, and the currency risk. Currency risk may be interpreted in terms of, though not restricted to, past forecast errors. We provide a framework within a general structure for return and exchange rate forecasts and risks. We show that the quadratic mean-variance structure is maintained and provide solutions to computational questions in the evaluation of the optimal portfolio. By extending conventional analysis, we arrive at a surprisingly simple solution which may be a useful addition to the arsenal of finance techniques.
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