Question

If the current spot exchange rate for quotes of JPY/GBP is greater than the no-arbitrage 3-month forward exchange rate, the 3-month GBP interest rate is ???

Answer 1

Under the no-arbitrage condition, Interest rate parity holds and below is the Forward exchange rate formula using Interest rate parity.

Forward Exchange rate = Spot rate * (1 + Domestic Interest rate) / (1 + Foreign Interest Rate)

As said in the question, Current Spot rate of JPY/GBP > 3-month Forward Exchange rate, then we can take an example where Spot rate is 137, 3-month forward rate is 135 and 3-month Japanese interest rate is 2%

Now using Interest rate parity we can calculate the GBP interest rate.

135 = 137 * (1+2%) / (1+r)

GBP Interest rate = (137/135)*(1+2%) - 1 = 3.5%

Even looking at the Interest parity formula for Forward exchange rate, we can conclude that GBP interest rate would be greater than JPY interest rate.

Moreover, the calculation above with an assumed example confirms the conclusion that GBP interest rate > JPY Interest rate.