Variance‐covariance risk of the exchange rate is highly relevant for international investors. This paper addresses optimal asset allocation with stochastic variances and covariances in a Wishart Affine Stochastic Correlation (WASC) model in incomplete and complete markets. We show that the (hedging) demand for exchange rate variance‐covariance risk can differ significantly between international investors. Local correlations with the exchange rate can affect the utilities of international investors differently while the impact of correlations between stocks can be symmetric. Depending on the current local exchange rate correlations domestic investors can benefit more or less than foreign investors from international trading.