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Using Contract Value and Duration to Hedge Commercial Paper with Rate Futures

Article Quant Q&A · Author: Marty B.
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Summary

The question describes a company planning to issue commercial paper in the future and asks how to hedge its financing exposure with a Eurodollar futures contract. The point of confusion is which maturities belong in the duration ratio: the time until the planned issue or the life of the commercial paper compared with the futures exposure. This distinction matters because the hedge concerns the interest rate sensitivity of the future borrowing, not simply the calendar gap until issuance.

The response offers a contract valuation formula based on the quoted futures price and states that the contract value is $980,000. It does not show how to apply the duration ratio, determine the number or direction of contracts, or reconcile the question’s proposed maturities. As a result, the document provides a contract-value clue but is not a complete hedge solution. The example is tied to a historical Eurodollar contract convention, so its pricing details should not be assumed to apply unchanged to current interest rate futures.

Key ideas

  • The example concerns hedging the interest rate exposure of planned commercial paper issuance with a futures contract.
  • The question confuses the time until issuance with the maturity of the borrowing when considering duration exposure.
  • The response calculates futures contract value from the quoted price using the contract’s pricing convention.
  • The supplied answer does not determine the hedge ratio or the number and direction of contracts.
  • Historical Eurodollar contract conventions may differ from those of current interest rate futures.

Tags

Fixed incomeFuturesRisk management
Full text
# Hedging with interest rate futures, different duration


# 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 $\frac{portfolioDuration}{futuresDuration} = \frac{5}{7}$?

## Answer by adrian hk (score 1)

https://quant.stackexchange.com/a/49288

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

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.