Currency risk hedging typically aims at minimizing portfolio volatility. We find that while hedging lowers the volatility of international equity portfolios, it also lowers portfolio returns. Furthermore, Sharpe ratios often deteriorate, portfolio skewness worsens and its kurtosis increases. In a no-arbitrage model of interest rates and exchange rates with an equity component, currency expected returns are positively related to the covariance between currency and equity returns. Consequently, the hedge goes short in currencies with positive expected returns. The model also generates the observed negative effects of hedging on Sharpe ratios and skewness. In sum, currency hedging is no free lunch.