Traditional carry trade strategies are based on differences in short-term interest rates, neglecting any other information embedded in yield curves. We derive return distributions of carry trade portfolios among G10 currencies, where the signals to buy and sell currencies are based on summary measures of the yield curve, the Nelson-Siegel factors. We find that a strategy based on the relative curvature factor, the curvy trade, yields higher Sharpe ratios and a smaller return skewness than traditional carry trade strategies. Curvy trades build less upon the typical carry currencies, like the Japanese yen and the Swiss franc, and are hence less susceptible to crash risk. In line with that, standard pricing factors of traditional carry trade returns, such as exchange rate volatility, fail to explain curvy trade returns in a linear asset pricing framework. Our findings are in line with recent interpretations of the curvature factor. A relatively high curvature signals a relatively higher path of future short-term rates over the medium-term putting upward pressure on the currency.