Question

# The spot exchange rate is 110.0JPN/USD and the semiannually compounded risk-free rate of USD is 5.06%....

1. 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.
1. What risk-free rate of JPN is implied by this forward price?
2. Suppose you believe the risk-free rate of JPN over the next 9 months will be only 0.5%. What arbitrage would you undertake?
3. Suppose you believe the risk-free rate of JPN will be 3 % over the next 9 months. What arbitrage would you undertake?

a. We use the interest parity condition to answer this. Hence,

110*x = 112.9 * (1+0.0506/2)^1.5. Here we have used 1.5 as the duration is 9 months.

x= 1.0655. Hence, the risk-free rate of JPN is 6.55% for the 9 month duration.

b. Since this risk free-rate is less than what we calculated above, we start with and borrow JPN, convert it to USD, lend the USD at the risk free rate of US and then later convert it back to JPN and payback the JPN we borrowed along with the interest.

c. SInce this rate is still lower than what we calculated above, we do the same trade as in b. Had it been higher, we would have borrowed USD, converted to JPN, lend JPN at the JPN risk-free rate and convert it back to USD after the 9-month period and return the USD back along with the interest.

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