Question

A Japanese investor can earn a 4.25% interest rate in Japan or 3.75% in the U.S. The spot exchange rate is 105 yen to the dollar. At what forward rate would an investor be indifferent between the U.S. and Japanese investments? What would you do if the forward was for fewer yen per dollar than the indifference rate calculated in (A)?

Answer 1

As per interest rate parity

Forward rate = 105 yen * (1 + 4.25%) /(1+ 3.75%) = 105.51 yen

1 dollar = 105.51 yen

if the forward rate less than above then their is opportunity for arbitrage we would borrow dollar and invest in

yen and then convert future value of the yen at forward rate to earn atbitrage profit.

Let us assune forward rate 1 $ = 104.90 yen

Borrow $ 1000000

Convert into yen at sport rate and invest Yen 105000000

Future value of yen 105000000*(1+4.75%) = Yen 109725000

Convert yen into dollar  109725000/104.90 = $1045996.19

Repay $ borrowing $1000000*(1+3.75%) = $ 1037500

Arbitrage profit = $1045996.19 - $ 1037500 = $8496.18