1. Forwards and Arbitrage You are working as an FX trader on Wall Street which specializes in currency carry trade strategies. A currency carry trade is a trading strategy that involves borrowing from a lower interest rate currency and investing the proceeds in a currency that provides a higher rate. The trader profits from the differences in interest rates between currencies. You would like to execute a series of currency carry trades between the USD and the following two foreign currencies, the Brazilian Real (BRL) and the Indian Rupee (INR). You collected information about the exhange rates USD/XXX (i.e., how many foreign currencies can be purchased with $1), and the 1-year spot rates (the yield on a one-year zero coupon bond issued by that government). The data is summarized in the table below. Assuming you would like to invest $1000 in a carry trade strategy over a one-year horizon, answer the following questions:

Country USD/XXX 1-year spot rate USA USD 1.00 3.00% Brazil BRL 5.40 12.75% India INR 81.50 6.00%

(a) Assume the BRL and INR exchange rates will remain fixed throughout the year (i.e., from the beginning to the end of the year). Compute the expected profit and return in USD of each of the two strategies. Will there be an arbitrage opportunity if the exchange rate is no longer fixed? Explain why or why not.

(b) Assume that you decide to execute a strategy on the BRL. Calculate the profit/loss and the investment return under the following two scenarios: (i) the USD appre- ciates by 10%, (ii) the USD depreciates by 10%.

(c) In the absence of arbitrage opportunities and assuming that the Brazilian gov- ernment will not default in one year, what is the future exchange rate in one year (fair forward exchange rate)? Explain why this exchange rate precludes arbitrage. (Tip: use the cash and carry intuition)