Question

You have the following market data. Spot price for the Euro is $1.121 per Euro. Three-month forward price is $1.076 per Euro. U.S. dollar LIBOR for three months is a continously compounded rate of 2.54% per annum. Euro LIBOR for three months is a continuously compounded rate of 2.77% 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?

Answer 1

3-months forward exchange rate should be=$1.121*e^((.0254-.0277)*.25)= $1.120 per Euro where, 0.25=time, 0.0254=USD LIBOR 3-month, 0.0277=Euro LIBOR 3-month, $1.121=Spot price of Euro

Now as 3 months forward rate is $1.076 per Euro, there is opportunity of Arbitrage.

Step 1:

first borrow 100,000 Euros at spot market and convert it to 100,000*1.121 =$112100

Next, invest this $112100 at continously compounded rate of 2.54% per annum for 3 months. It will become=112100*e^(.0254*.25) =$112814.1

Now for borrowed 100000 Euro, after 3 months principal and interest need to be repaid= 100000*e^(.0277*25)= 100694.90 Euro where, 0.0277=Euro LIBOR 3-month rate

Step 2: Enter into a forward contract to buy 100694.90 Euro for 100694.90*1.076 =$108347.72, where 1.076=3-months forward rate

So, After 3-months, repay the borrowed 100000 Euro(100694.90 Euro? with interest of 3-months now) and make riskless profit=112814.1?-108347.72 =$4466.38

So, this abritrage strategy gives the riskless profit of $4466.38