Dollar-yen and the carry trade A major currency pair is dollar-yen, quoted in yen per dollar. Suppose the current price is $1 =¥ 82.10. Suppose also that the five-year dollar interest rate is 2.17% and the twoyear rate is 0.78% (semi-annual, 30/360 daycount), and that the five-year and two-year yen rates are 0.63% and 0.41% respectively (semi-annual, act/365 daycount).
(a) Calculate the forward price for dollar-yen five years forward. For simplicity use a 0.5 accrual factor, rather than 182/365 etc, for yen.
(b) Suppose you were unable to trade forward contracts, but were able to trade spot FX and borrow or lend dollar and yen cash. How could you synthetically go long the forward contract in (a)?
(c) Suppose you went long one forward contract from (a), and three years from now the FX rate and interest rates are unchanged. What is your profit or loss on the forward?