Question

You have the following market data.

• Spot price for the Euro is $1.174 per Euro.
• Three-month forward price is $1.06 per Euro.
• U.S. dollar LIBOR for three months is a continously compounded rate of 1.26% per annum.
• Euro LIBOR for three months is a continuously compounded rate of 3.98% per annum.
• Underlying asset for this contract (i.e., the quantity of Euros to be delivered in three months) is 100,000 Euros.

What is the total net profit if you execute the arbitrage strategy?

Do not round values at intermediate steps in your calculations. Enter your answer in dollars and cents to two decimal places, but omit the $ symbol and commas. For example, enter $1,234.56 as 1234.56 as your answer.

Answer 1

Given:

Underlying asset for this contract (i.e., the quantity of Euros to be delivered in three months) is 100,000 Euros.

Forward rate of euro is lower in terms of USD than spot price

1. Buy euro libor and convert to USD in spot

2. Also buy Foward euro using converted USD

3. After three months with forward contract of euro close the libor euro borrowing

Below are calculations

1. Borrow Euro 100,000 at 3.98%
After 3 months pay back = 100,000*e^(0.0398*0.25)=Euro 100,999.9

Convert to USD at spot rate = 100,000*1.174=$117,400

2. Enter forward contract to buy Euro at forward rate $1.06 per Euro

3. Euros from $117,400 = $117,400/$1.06=Euro 110,754.71 Euros

Total gain =$117,400-110,754.71=

Euro 6645.28

please note we bought Forward euro contract using USD

so for three months we have used $117,400 which still gives 1.26% per annum

which makes the arbitrage mostly non profit