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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?

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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%

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  • $\begingroup$ You mean the 8% is multiplied by 3 months/12 months? $\endgroup$
    – 3kstc
    Commented Nov 28, 2017 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
    Commented Nov 28, 2017 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
    Commented Nov 28, 2017 at 12:51
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    $\begingroup$ One Libor future corresponds to the interest on a 3-month deposit of \$1,000,000. That is how the Libor future is defined. $\endgroup$
    – nbbo2
    Commented Nov 28, 2017 at 12:57
  • $\begingroup$ @noob2 Thanks - I've got so much to learn :D $\endgroup$
    – 3kstc
    Commented Nov 28, 2017 at 13:16

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