Question

11. The spot exchange rate is 110.0JPN/USD and the semiannually compounded risk-free rate of USD is 5.06%. You observe a exchange forward with 9-month maturity is 112.9JPN/USD.
a. What risk-free rate of JPN is implied by this forward price?
b. Suppose you believe the risk-free rate of JPN over the next 9 months will be only 0.5%. What arbitrage would you undertake? c. Suppose you believe the risk-free rate of JPN will be 3 % over the next 9 months. What arbitrage would you undertake?

Answer 1

Forward Exchange Rate = Spot Exchange Rate*( 1+ risk free rate domestic)/ (1+risk free rate foreign)

A. 112.9 = 110.0 *(1 + 5.06%)/(1+r japan)

This implies (1+r japan) = 110*1.0506/112.0

Which means r japan is 3.18% Answer

B. If the risk free rate of Japan over the next 9 months will only be 0.5%, i would buy futures contract to buy USD at 112.9 JPN/USD as the currency of Japan will weaken due to the low rate of interest Answer

C. Since 3% is also lower than 3.18%, we would take the same arbitrage position as in B i.e. i would buy futures contract to buy USD at 112.9 JPN/USD as the currency of Japan will weaken due to the low rate of interest Answer