# Hedging with interest rate futures, different duration

This is 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 future price is quoted as 92.00. How should the treasurer hedge the company's exposure?

So I know the relevant formula here for the number of contracts is $N=\frac{portfolioForwardValue}{futureContractPrice} \frac{portfolioDuration}{futuresDuration}$.

The given solution says $\frac{portfolioDuration}{futuresDuration} =2$ because the commercial paper's maturity is twice that of the future.

I don't understand this.

Isn't the treasurer's goal to ensure there will be \$5 million available in July? In that case$portfolioDuration$is February to July while$futuresDuration$is February to September. So shouldn't$\frac{portfolioDuration}{futuresDuration} = \frac{5}{7}\$?

• The portfolio duration is 180 days or approximately 6 months. Eurodollar futures are based on 3 month Libor, so that duration is 3 months. 6/3 = 2 Commented Oct 2, 2016 at 18:01
• Note: you are not trying to hedge "the 5 million amount", you are trying to hedge the interest that you will pay on 6 month commercial paper. You are worried about an increase in Libor Rates between now and issue, not about defaulting on the C.P. because you have no money to pay it back at maturity, that is a different (probably unhedgeable) risk. Commented Oct 2, 2016 at 18:07
• @AlexC Reading up on the solution for this question, where does the 980,000 value come from? Commented Nov 27, 2017 at 13:09

980,000 is the value of the contract. You can solve it with this formula: $$\text{Contract value} = 10,000 \cdot \left[100-0.25\left(100-Q\right)\right]$$