Question

You are running the FX trading desk at a large, high-grade investment bank. You have the following rates available to you:

Spot Dollar/Yen Exchange Rate 3-month Forward Dollar/Yen Rate 1-month US dollar) Risk-free Interest Rate 3-month US dollar) Risk-free Interest Rate 120.44 Y/8 119.09 Y/8 5.50% 6.00%

Assume that there are no transaction costs, and that you can either buy or sell at these exchange rates. Also, the interest rates above are quoted in annualized, continuously-compounded form, and are the same for borrowing or lending

(a) What must the 3-month Japanese interest rate be, if there is no arbitrage?

(b) Suppose that the annualized, continuously compounded 3-month yen in- terest rate is 1.0%. What would you do? Provide precise details.

Answer 1

a) 3 month Japanese interest rate must be 4.8%

Answer Given that spot rate = 120.44 714 3. Honth forward rate=119.09416 3. Month us dollar Rist - free interest rate= 6). forwardrate (lt dollar rate) (It Yen Rate) = spot rate 120.44 119.09 CloG) 120.44 = (1+ yen Rate) = 119,09 (It Gl.) - CIH yen Rate) = . - ltyen Rate = 1.048 - yen Rate = 10048 -1 = 0.048 yen Rate = 4.8%. 3 Month Japanese interest rate = 4.8%. (6) In order to lock in an arbitrage profit if the intere st on Japanese yen is it, then the investor should borrow invest in yen, and Japanese in the amount dollar at 6.00% Notional value in yen = 1,000,000 Japanese yen interest rate = 14. Dollar interest rate = 6%. spot rate = 120.4481&

forward rate = 119.09 4/8 first step: Borrow 1 million yen second step: Invest at dollar interest rate ice 1000,000 $8,302.89 at spot rate 120144 Third step: value of investment after 3 months i Amount invested = $8,302.89 (+) Interest - $ 498.17 ( 3,36 2, 31 x G.) . $8, 801.06 fourth step: convert into yen after 3 months - $8,801,06 x 119,0941$ = 1,048, 118.24 7 payout Japanese yen loan ne Amount Borrowed = 1000,000 (4) Interest 10,000 fifth step: (1000,000 x 1..) 1,010,ooo Profit in Japanese Yen = 1048, 118.24-1,010,000 = 438,118.24