Question

Suppose interest rate differentials between the US and Japan is 4.5 percent and the yen is in 5.1 percent premium 1-year forward. The U.S. interest rate is 6 percent, while Japanese Interest rate is 1.5 percent. Assume you can borrow $10 millions or its yen equivalent. Is there an arbitrage profit, if so how much. Provide your solution assuming Japanese spot rate is 92 yen/$.

Answer 1

Japanese spot rate = 92 yen/$

U.S. interest rate = 6 %

Japanese Interest rate = 1.5 %

As the interest rate differentials between the US and Japan is 4.5 percent, there is the scope for a good arbitrage profit.

We can borrow $10 millions

So, the yen equivalent of $10 millions will be borrowed from Japan @ 1.5% and will be deposited in US @ 6% to earn the arbitrage profit

$10 millions = 920 million Yen

Interest on borrowing for 1 year = 920 million Yen x 1.5% = 13.8 million Yen

Total amount to be paid 1 year forward = 920 million Yen +  13.8 million Yen = 933.8 million Yen

Interest on deposit for 1 year = $10 millions x 6% = $600,000

Now, Money received from US after 1 year = $10.6 million

The yen is in 5.1 percent premium 1-year forward

So, Yen spot rate 1 year forward = 92 yen x (1+ 0.051) = 96.692 yen/$

Converting $10.6 million in Yen = 10.6 million x 96.692 = 1024.9352 million yen

Profit = 1024.9352 million yen - 933.8 million Yen = 91.1352 million yen

Profit Converting in $ = 91.1352 million yen / 96.692 = $942,530.93