1
$\begingroup$

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?

$\endgroup$
4
$\begingroup$

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%

$\endgroup$
  • $\begingroup$ You mean the 8% is multiplied by 3 months/12 months? $\endgroup$ – 3kstc Nov 28 '17 at 2:48
  • $\begingroup$ 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. $\endgroup$ – Lliane Nov 28 '17 at 2:50
  • $\begingroup$ do you then; 98% x \$1,000,000 = \$980,000? Where did the \$1,000,000 come from? How was that calculated? $\endgroup$ – 3kstc Nov 28 '17 at 12:51
  • 1
    $\begingroup$ One Libor future corresponds to the interest on a 3-month deposit of \$1,000,000. That is how the Libor future is defined. $\endgroup$ – noob2 Nov 28 '17 at 12:57
  • $\begingroup$ @noob2 Thanks - I've got so much to learn :D $\endgroup$ – 3kstc Nov 28 '17 at 13:16

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.