We develop a model based on risk averse investors and limited arbitrage capital to explain the rationale for the so called carry trades: that is, trades where "the purchase of riskier, higher-yielding assets is funded by selling lower-yielding currencies" (Financial Times, January 28, 2008). In our model, due to partially segmented markets and differences in inflation risk and money supply, the returns to carry trades are positive, but decrease in the amount of arbitrage capital. In the empirical part of the paper, using 32 years of exchange rate data, we document several new results related to carry trades and provide empirical support for the model's predictions. We empirically document that 1) carry trade returns explain a significant part of hedge fund index returns, providing strong evidence that carry trades are indeed used by arbitrageurs, 2) the positive returns to carry trades have been decreasing over time in parallel with an increase in arbitrage capital, 3) the real interest rates are higher in countries with higher inflation risk and higher per capita money supply, but higher arbitrageurs' equity capital and a better funding liquidity for them decrease the cross country differences in real interest rates, 4) flow of new arbitrage capital leads to an appreciation (depreciation) of the carry long (short) currencies.At the time of the paper, there is an ongoing large outflow of arbitrage capital from hedge funds, and this has been associated with a large appreciation of Japanese yen, US dollar and Swiss franc and a large depreciation of euro, Canadian dollar and British pound, in relation to most other currencies. These currency movements are consistent with our results, as at the time of the paper yen, US dollar and Swiss franc are carry trade short currencies and euro, Canadian dollar and British pound are carry trade long currencies.