A model is developed in order to show that in the carry trade market the Sharpe ratio can be affected by the number of traders and it has a concave form. Hence, the Sharpe ratio does not increase with the interest rate differential. However, high interest rate currencies have greater currency crash risk exposure. The exchange rate movement, when there is no currency crash, does not affect so much the profit due to the carry trade, but the total profit is very sensitive to the exchange rate fluctuation. Skewness and Kurtosis are computed for 9 currencies as indexes for currency crash risk and Sharpe ratio is calculated as a proxy for profitability. In the empirical part, the Sharpe ratio shows a concave form and the model predict this concavity too. The model captures the effect of number of arbitrageurs in the carry trade market on the profit. In the last section, the exchange rate risk premium in this market is computed.
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