Question

The current spot exchange rate allows one to exchange £1 for JPY 140. The 10-year UK spot interest rate is 1.5% and the 10-year spot rate in Japan is 0.1%. What is the no arbitrage value of the 10-year forward exchange rate of Sterling for Yen?

Answer 1

Solution:

In order to solve this problem we have to understand the concept of covered interest rate parity, this is used to determine the forward foreign exchange rate under no-arbitrage condition. This condition states that an investor can hedge its foreign currency risk due to fluctuation in exchange rates though derivatives i.e. forward contracts, however interest rate parity may occur which will adjusted through interest rate and currency rate changes over time.

In above question, UK pound is trading at 140/JPY, and the annual interest rate in UK is 1.5% and the interest rate in Japan is 0.1%. So an investor can borrower JPY at 0.1%, convert it to UK pound and invest the proceeds in UK to get a return of 1.5%.

However, to repay the loan in JPY, investor has to enter into a forward contract to exchange the UK pound back to JPY. Covered interest rate parity exists when the forward rate of converting UK pound to JPY eliminates all the profits from the transaction.

The formula to get forward exchange rate is as follows:

F=S*(1+i1)/(1+i2)

Normally, currency which has lower interest rate tend to trade at forward foreign exchange rate premium in relation to another currency which offers higher rate.

Hence, i1 = interest rate of Japan, i2 = interest rate of UK

F= Forward exchange rate

S = Spot exchange rate

F = 140*(1.001/1.015) = 138.07 JPY

Hence, no arbitrage value of the 10-year forward exchange rate of Sterling for Yen is JPY 138.07.