Question

You expect interest rates to continue to rise and you want to lock in the rate you'll pay on a $50 million short-term loan you plan to take out at the beginning of the third quarter. You take a short position on the June Eurodollar contract, which settled at 97.775 today. Assume on June 18, when the contract expires, it settles at 97.545. Two weeks later you borrow the $50 million at the three-month LIBOR rate, which is at 2.468%. Show that your effective annual borrowing rate is close to what the contract implied when the loan is repaid at the end of September

Answer 1

As per the calculations done in excel, the following screenshot shows:

By including all the given data into excel sheet, we can see that total basis point change between the contract price today and on the day of expiry is 23 basis points. As 1 Eurodollar contract represents $1 mn time deposit with 3-month maturity, so $ 50 mn would represent 50 Eurodollar contracts. And, 1 basis point earning per contract = (0.01/100)*(1,000,000)*(90/360), which can be given by 1 basis point * $ 1mn * days in 3-months/days in 12 months.

This provides 1 basis point earning per contract = $ 25. So, earnings for 23 bp and that too for 50 contracts would provide the earnings = $ 28,750 and that's how interest rate risk is hedged by short selling Eurodollar contracts.

At the time of expiry, the contract implied rate can be derived by 100-97.545 = 2.455%, which is very close to the 3-month LIBOR = 2.468%. Hence derived.