This study looks for gains in terms of efficiency for local investors with an internationally diversified portfolio by hedging the exchange risk. To estimate an optimum portfolio with a minimum variance we used a robust methodology which allowed us to make statistical inference and prove that international diversification re­duces portfolio risk for local investors. This methodology is applied to stock portfolios held by a Colombian and a Mexican investor, and the conclusion is that hedging exchange rate risk can reduce the risk of the portfolio, with the possible exception of a high negative correlation between the ex­change rate and the local stock index.