Question

5. Given: 6-month p.a. interest rates are 4% in the U.S. and 3% in Japan. The spot exchange rate for Japanese yen is 96.25 ¥/$ and the 3-month forward rate is F3-mo= 100.15 ¥/$. You wish to borrow yen. How can you effectively (synthetically) borrow ¥100,000,000 for 6 months without using the Japanese money market? (List each transaction you would make including the amounts of each currency involved.) What is the implied interest rate on your synthetic yen loan? Should you borrow yen directly or synthetically?

Answer 1

The steps to borrow ¥ synthetically are :

• Borrow the $ equivalent of ¥100,000,000 at the current spot rate. $ borrowed = ¥100,000,000 / 96.25 = $1,038,961.04
• $ to repay after 6 months = $1,038,961.04 * (1 + (4% * (6 / 12))) = $1,059,740.26
• ¥ required to repay $ after 6 months = $ to repay * forward rate
• ¥ required to repay $ after 6 months = $1,059,740.26 * 100.15 =  ¥106,132,987.01

Implied interest rate (6-months) = (¥ repaid after 6 months - ¥ borrowed) / ¥ borrowed

Implied interest rate (6-months) = (¥106,132,987.01 - ¥100,000,000) / ¥100,000,000

Implied interest rate (6-months) = 6.13%

Implied interest rate (annualized) =  6.13% * (12/6) = 12.27%

You should borrow ¥ directly because the interest rate in Japan is much lower than the implied interest rate for a synthetic ¥ loan