Question

The exchange rates between the Japanese yen and US dollar are as follows: Spot rate = ¥112.61/$.

Three-month forward rate = ¥111.94/$.
One-year forward rate = ¥109.99/$.
a) Is the yen at a forward discount or premium on the dollar?
b) If the one-year interest rate on dollars is 6% (annually compounded), what do you think is the one-year interest rate on yen?
c) What is the expected spot rate for yen in three months’ time?
d) What is the expected difference in the three-month rate of price inflation in the United States and Japan?
e) Suppose the one-year interest rate on dollars is 6% and the one-year interest rate on yen is 1%. Is there an arbitrage opportunity? If so, how would you exploit it?

Answer 1

The yen is at a forward discount on the dollar, and with the given interest rates, there is a potential arbitrage opportunity that can be exploited by borrowing in yen and investing in dollars.

Step-by-step explanation:

To answer the questions regarding the yen's position relative to the dollar and potential arbitrage opportunities:

• a) The yen is at a forward discount on the dollar since the forward rates are lower than the spot rate.
• b) If the one-year interest rate on dollars is 6%, the one-year interest rate on yen would be expected to be lower, considering the forward discount on yen. Interest rate parity would suggest that the yen interest rate would be less due to the discount on the forward exchange rate.
• c) The expected spot rate in three months cannot be precisely predicted from the given information due to the unpredictability of forex markets and other factors influencing exchange rates.
• d) It is not possible to calculate the expected difference in the three-month rate of price inflation in the United States and Japan from the given exchange rate information alone.
• e) Given a 6% interest rate on dollars and a 1% interest rate on yen, there is a potential arbitrage opportunity. One could borrow yen, convert to dollars to capitalize on the higher interest rates, and later convert back to yen at the cheaper forward rate to pay off the loan.

Exchange rate fluctuations, as described in the figures, show the impact of investor sentiment and economic stress that can affect both economies, especially when they involve large percentage changes.