Answer:
Here is the complete question:
Covered Interest Arbitrage: Suppose that you’re a FX trader for a bank in New York. You are faced with the following market rates:
Spot exchange rate: ¥110.55/$.
1 year dollar interest rate = 1.50%
1 year yen interest rate = 0.25%
1 year forward exchange rate: = ¥108.15/$.
Assume that you may borrow up to $1,000,000 (or its equivalent in yen) to engage in this arbitrage. Show all calculations as you respond to the questions below.
a) Is there an arbitrage opportunity? Explain with calculations why or why not. (10 points)
b) Spell out the actions you would take to profit from this situation. (30 points)
Which currency would you borrow and what amount?
Which currency would you lend (invest) and what amount?
What is the forward transaction you would engage in? State clearly the currency you would sell forward, the currency you would buy forward, and the respective amounts.
Calculate your arbitrage profits, either in US dollars or in Japanese yen.
Explanation:
) Interest rate differential = 1.5 - 0.25 = 1.25%.
Discount rate of $ = (110.55 - 108.15)110.55 = 2.17%.
Since the interest rate differential and the discount rate in the forward rate are different, there is opportunity for covered interest rate arbitrage.
b) Actions:
Borrow $1,000,000 @ 1.5% interest; the loan amount + interest to be repaid at the end of the year being $1,015,000.
Convery the $1,000,000 to Y at the spot rate of 110.55 and get 110,550,000Y
Deposit it for 1 year to get Y110,550,000*1.0025 by the end of the year. = 110,826,375Y
Sell forward y110,826,375 at 108.15/$, to get 110,826,375/108.15 = 1,024,746.88$
After 1 year get the proceeds of the deposit of 110,826,375Y, convert it to $ at the forward rate of 108.15, and get 1,024,746.88$.
Then close the $ borrowing by paying $1,015,000.
Balance left = 1,024,746.88 - 1,015,000 = $9,746.88--arbitrage profits
