Suppose that the one-year interest rate is 3.0 percent in Italy. The spot exchange rate is $1.20/€, and the one-year forward exchange rate is $1.18/€. What must the one-year interest rate be in the United States to avoid arbitrage opportunities?Group of answer choices1.0128%1.2833%4.75%none of the options
Question
Suppose that the one-year interest rate is 3.0 percent in Italy. The spot exchange rate is 1.18/€. What must the one-year interest rate be in the United States to avoid arbitrage opportunities?Group of answer choices1.0128%1.2833%4.75%none of the options
Solution
To avoid arbitrage opportunities, the interest rate in the United States must be such that it maintains the interest rate parity condition. The interest rate parity condition is given by the formula:
1 + i_US = (1 + i_foreign) * (Spot rate / Forward rate)
where: i_US is the interest rate in the United States, i_foreign is the interest rate in the foreign country (Italy in this case), Spot rate is the current exchange rate, and Forward rate is the future exchange rate.
Substituting the given values into the formula:
1 + i_US = (1 + 0.03) * (1.20 / 1.18)
Solving for i_US gives:
i_US = ((1.03 * 1.20) / 1.18) - 1
i_US = 1.048305084745762711864406779661 - 1
i_US = 0.048305084745762711864406779661
Converting to percentage gives:
i_US = 4.83%
So, the one-year interest rate in the United States must be approximately 4.83% to avoid arbitrage opportunities. Therefore, none of the options provided are correct.
Similar Questions
Suppose that the one-year interest rate is 5.0 percent in the United States. The spot exchange rate is $1.20/€, and the one-year forward exchange rate is $1.16/€. What must the one-year interest rate be in the euro zone to avoid arbitrage opportunities?Group of answer choices5.0%6.09%none of the options8.62%
Suppose you observe a spot exchange rate of $2.00/£. If interest rates are 5 percent per annum in the U.S. and 2 percent per annum in the U.K., what is the no-arbitrage one-year forward rate?Group of answer choices£1.9429/$$1.9429/££2.0588/$$2.0588/£
Suppose that the annual interest rate is 2.0 percent in the United States and 4 percent in Germany, that the spot exchange rate is $1.60/€ and that the forward exchange rate, with one-year maturity, is $1.50/€. Assume that an arbitrager can borrow up to $1,000,000 or €625,000. If an astute trader finds an arbitrage, what is the net cash flow in one year?
You are an American investor who can borrow $1,000,000 or the equivalent amount in euros today.Suppose the spot rate is $1.20/€, and the one-year forward rate is $1.15/€. The annual interest rate is 5 percent in the U.S. and 3 percent in Germany. Check if IRP holds. If it does not hold, set up a covered interest arbitrage. What will be your profit from this arbitrage opportunity in dollars?
Today, the annual interest rate on bank deposits is 8.15% in New York and 3% in Paris, the spot exchange rate is 1.2 US dollars per euro, and the one-year forward exchange rate is 1.236 US dollars per euro. Emily plans to deposit 1,000 US dollars in either New York or Paris for one year. Answer the following questions, using the exact equations for the UIP/CIP.(a). Where should Emily deposit her funds? Given today's spot exchange rate and interest rates, what is the equilibrium forward rate, if covered interest parity (CIP) holds? Report the intermediate steps. [3 marks](b). Suppose the forward rate takes the value given by your answer to question (a). If UIP also holds, is the US dollar expected to appreciate or depreciate against the euro over one year? By how much? Report the intermediate steps. [3 marks]
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.