The answer seems affirmative. We compare currency carry trades with an investment strategy based on currency fundamentals: taking a long (short) position in undervalued (overvalued) currencies. Carry trades have high risk-adjusted returns, but are subject to "crash risk." In contrast, the fundamental strategy has lower risk-adjusted returns, but is less prone to crash risk, because the realization of crash risk coincides with corrections towards fundamentals. In particular, the fundamental strategy outperformed carry trades during the recent global financial crisis. Building on these results, we present early warning indicators for potential turbulence in the currency market.