# How does one calculate the Libor future contract price?

I have the following question from Hull, problem 6.16:

Suppose that it is February 20 and a treasurer realizes that on July 17 the company will have to issue \$5 million of commercial paper with a maturity of 180 days. If the paper were issued today, the company would realize \$4,820,000. (In other words, the company would receive \$4,820,000 for its paper and have to redeem it at \$5,000,000 in 180 days’ time.) The September Eurodollar futures price is quoted as 92.00. How should the treasurer hedge the company’s exposure?

The solution is as follows:

The company treasurer can hedge the company’s exposure by shorting Eurodollar futures contracts. The Eurodollar futures position leads to a profit if rates rise and a loss if they fall. The duration of the commercial paper is twice that of the Eurodollar deposit underlying the Eurodollar futures contract. The contract price of a Eurodollar futures contract is 980,000. The number of contracts that should be shorted is, therefore:

\begin{align}Number\ of\ Contracts & =\frac{Portfolio\ Forward\ Value}{Future\ Contract\ Price}\times \frac{Portfolio\ Duration}{Futures\ Duration} \newline & =\frac{\4\,820\,000}{\bbox[yellow, 5px,border:2px solid red]{980\,000}}\times \frac{6\ months}{3 \ months} \newline &= 9.84\newline \therefore Number\ of\ Contracts &\approx 10\ \text{contracts}\end{align}

Question:

How does one calculate the future contract price of $980,000? ## 1 Answer The quoting convention must be explained somewhere in your book. For Eurodollar futures, this convention is 100 - yield, 92 means the yield is 8% per annum, so for one quarter you need to divide this discount by 4 to get the price (100% - (8% × (3month/12month)) = 100% - 2% = 98% • You mean the 8% is multiplied by 3 months/12 months? – 3kstc Nov 28 '17 at 2:48 • Yes, it's an annual yield but the future just has a 3 months maturity so you need to adjust the discount period, think about it as the price of a zero coupon bond. – Lliane Nov 28 '17 at 2:50 • do you then; 98% x \$1,000,000 = \$980,000? Where did the \$1,000,000 come from? How was that calculated? – 3kstc Nov 28 '17 at 12:51
• One Libor future corresponds to the interest on a 3-month deposit of \\$1,000,000. That is how the Libor future is defined. – noob2 Nov 28 '17 at 12:57
• @noob2 Thanks - I've got so much to learn :D – 3kstc Nov 28 '17 at 13:16