Question

Suppose you are a currency trader and you have the following information:

Spot rate: $1.30/£

The one-year interest rate for the U.S. dollar: 3%

The one-year interest rate for the pound: 2%

1. Please calculate the one-year forward rate based on the Interest Rate Parity.

2. If the actual one-year forward is quoted at $1.28/£, do you find a covered interest arbitrage opportunity? Please explain.

3. If there exists a covered interest arbitrage opportunity, then show all the necessary procedures to capitalize on this opportunity and calculate your net profit (suppose you can borrow up to $1,300,000 or £1,000,000).

Answer 1

Solution:

1) we have,

Spot rate (S) = $ 1.3 per pound

1 year interest rate $ = 3%, pound = 2%

by using interest rate parity

F / S = Interest rate factor of $ / Interest rate factor of pound

F / 1.3 = 1.03 / 1.02

F = 1.0098 * 1.3

F = $ 1.31 per pound

2) one year forward rate should be $ 1.31 per pound but actual rate is $ 1.28 per pound. Therefore there exist a covered interest arbitrage opportunity.

3) The following are the steps to capitalize on this arbitrage opportunity.

Step 1: Borrow pound 10,00,000 @ 2% p.a

such that outflow after after 1 year = pound 10,20,000

Step 2: Convert pound 10,00,000 into $ by using spot rate of $ 1.3

we will get 10,00,000 * 1.3 = $ 13,00,000

Step 3 : Invest this $ 13,00,000 at 3% p.a

Inflow after 1 year = 13,00,000 * 1.03 = $ 13,39,000

Step 4 : Convert this $ 13,39,000 in forward market to cover youeself at F = $ 1.28

we will get $ 13,39,000 / 1.28 = $ 10,46,093.75

Step 5: Net Profit = Step 4 - Step 1

= $10,46,093.75 - $ 10,20,000

= $ 26,093.75