Question

The nominal yield on 6-month T-bills is 5%, while default-free Japanese bonds that mature in 6 months have a nominal rate of 6%. In the spot exchange market, 1 yen equals $0.01. If interest rate parity holds, what is the 6-month forward exchange rate? Round the answer to five decimal places. Do not round intermediate calculations.

Answer 1

Let the 6-month forward rate be F USD per yen. If an investor borrow 1 USD for 6 months at the current rate, the expected interest payment plus principal 6 months later is 1*(1 + 5%) = $1.05 USD.

Suppose the investor convert the 1 USD to yen at the current spot rate, it is equivalent

= 1 / 0.01 = 100 yen.

If invested in the Japanese bond, the total return 6 months later is

100*(1 + 6%) = 106 yen.

At the forward rate of F, this would be equivalent to 106*F USD.

To ensure no arbitrage, we must have

106*F = 1.05,

F = 1.05 / 106 = 0.00991, that is 0.00991 yen per 1 USD.

The forward rate should be 0.00991 yen per 1 USD.