DeMiguel et al. [DeMiguel V, Garlappi L, Uppal R (2009) Optimal versus naïve diversification: How inefficient is the 1/N portfolio strategy? Rev. Financial Stud. 22(5):1915–1953] showed that in the stock market, it is difficult for an optimized portfolio constructed using mean-variance analysis to outperform a simple, equally weighted portfolio because of estimation error. In this paper, we demonstrate that portfolio optimization can be made to work in currency markets. The key difference between the two settings is that in currency markets interest rates provide a predictor of future returns that is free of estimation error, which permits the application of mean-variance analysis. We show that over the last 26 years, a mean-variance efficient portfolio constructed in this fashion has a Sharpe ratio of 0.91, versus only 0.15 for the equally weighted portfolio. We also consider the practical implementation of this strategy.