| Course | GF561 Derivatives and Hedging |
|---|---|
| Unit | Unit 8 |
| Paper type | Hedge design memo |
| Length | About 740 words, 5 pages double-spaced |
| Format | APA 7 student paper |
| School | Purdue University Global |
| Program | MS in Finance |
| Updated | October 2026 |
Free sample paper for GF561 Unit 8
Hedging Asphalt With Crude: A Unit 8 Hedge Design Memo Sized by a Minimum-Variance Ratio
[Student Name]
Purdue University Global
GF561: Derivatives and Hedging
Unit 8 Hedge Design Memo
[Instructor Name]
[Date]
The paving contractor, its consumption and every statistic are composite and illustrative; the articles and textbook cited are real.
Memorandum
To: Treasurer From: Financial Analyst Date: February 9, 2026 Re: Hedging asphalt binder purchases, May through October
Recommendation
Buy 109 crude oil futures contracts, about 109,000 barrels, layered across the June through November contract months, to hedge 60 percent of next season's expected asphalt purchases. The position should reduce the variance of the hedged purchases by about 61 percent.
The Exposure
The contractor expects to buy about 9,000 tons of liquid asphalt binder a month from May through October, 54,000 tons in all, at prices that follow a regional posted index. About 40 percent of the season's work is on state highway contracts that include an asphalt price adjustment clause, which already passes most price changes to the state. Board policy therefore targets hedging 60 percent of purchases, 32,400 tons, matching the share of work without that protection.
Why Crude Oil Futures
No liquid futures contract exists for asphalt. Asphalt is a residue of crude oil refining, and its price moves with crude, though not perfectly. Crude oil futures are deep, liquid and traded in monthly contracts, so they make a practical proxy. The cost of using a proxy is basis risk: the hedge will not remove price changes that are specific to asphalt.
Sizing the Hedge
Data. Thirty-six months of price changes give a standard deviation of monthly changes of $28 a ton for asphalt and $6.50 a barrel for crude futures, with a correlation of 0.78.
The minimum-variance ratio. The number of barrels per ton that minimizes the variance of the hedged position equals the correlation times the asphalt standard deviation divided by the crude standard deviation: 0.78 times $28 divided by $6.50, about 3.36 barrels per ton (Hull, 2022).
Position size. 3.36 times 32,400 tons is about 108,860 barrels, or 109 contracts of 1,000 barrels.
Effectiveness. The share of variance removed equals the correlation squared, about 0.61. Research on hedging performance established this measure as the standard test of how well a futures contract hedges a related exposure (Ederington, 1979).
A ton of asphalt contains roughly six barrels of oil, but asphalt prices move only about half as much as that would imply, so a barrel-for-barrel hedge would buy nearly twice the futures needed and turn part of the hedge into a separate bet on crude.
Layering by Month
Purchases are spread evenly, about 5,400 hedged tons a month, so the 109 contracts are split across six contract months: 18 each in June through October and 19 in November. Each month's contracts are closed as that month's asphalt is bought, so the gain or loss on futures offsets the change in that month's purchase price.
Cash Requirements
Futures settle daily. At an illustrative initial margin of about $6,000 a contract, the position needs about $654,000 at the start. If crude fell $15 a barrel, the contractor would owe about $1.63 million in margin calls, offset only later by cheaper asphalt purchases. The treasurer should keep a dedicated credit line of at least $2 million for margin.
Why Hedge at All
Paving bids are fixed months before the asphalt is bought, so a rise in binder prices comes straight out of margin on work already won. Research on corporate hedging argues that firms gain most from hedging when cash shortfalls would force them to pass up good projects or borrow at high cost (Froot et al., 1993). For a contractor whose bonding capacity depends on reported profit, a bad asphalt year could limit the work it can bid next season.
Alternatives Considered
Two alternatives were rejected. An over-the-counter swap on a regional asphalt index would remove basis risk, but quotes were wide and available from only one dealer, adding counterparty risk. A fixed-price supply agreement with the terminal, like those signed in past seasons, would remove price risk but carries a minimum take of 85 percent, which cost the contractor money in the last wet season. The futures program keeps flexibility on volume, because contracts can be closed if paving falls short.
Next Steps
Approve the 109-contract program, open the margin line and review the hedge ratio quarterly as new price data arrive.
References
Ederington, L. H. (1979). The hedging performance of the new futures markets. The Journal of Finance, 34(1), 157-170. https://doi.org/10.1111/j.1540-6261.1979.tb02077.x
Froot, K. A., Scharfstein, D. S., & Stein, J. C. (1993). Risk management: Coordinating corporate investment and financing policies. The Journal of Finance, 48(5), 1629-1658. https://doi.org/10.1111/j.1540-6261.1993.tb05123.x
Hull, J. C. (2022). Options, futures, and other derivatives (11th ed.). Pearson.
The Purdue Global GF561 Unit 8 instructions
The eighth GF561 unit asks for a memo recommending a hedge. State the recommendation and expected effectiveness first. Describe the exposure by month and the policy that sets how much is hedged. Explain why the chosen futures contract is a reasonable proxy and what basis risk that creates. Size the hedge with a minimum-variance ratio, showing the data period, standard deviations of changes and correlation, then convert to contracts and report hedge effectiveness. Lay out how positions are spread across contract months. Estimate the cash needed for margin under a plausible adverse move. Explain why hedging creates value for this firm and which alternatives were rejected. Close with next steps. Cite the hedge ratio source, research on hedging performance and corporate hedging in APA 7.
How the GF 561 Unit 8 example is put together
The memo opens with the recommendation, then describes 9,000 tons a month and the state price adjustment clauses that justify a 60 percent target. A section explains why crude oil futures serve as the proxy. The sizing section computes the ratio, contract count and effectiveness, citing Hull and Ederington. The highlighted sentence explains why the physical barrels in a ton would over-hedge. A layering section splits 109 contracts across June to November. The cash section estimates initial margin and the calls a $15 crude fall would bring. A section on why to hedge cites Froot, Scharfstein and Stein on cash shortfalls and bonding capacity. Alternatives, an index swap and a fixed-price supply agreement, are rejected with reasons, and next steps close the memo.
Where the points sit in the GF561 Unit 8 rubric
GF561 hedge memos are graded on whether the hedge is sized correctly and justified for the firm. Graders check the hedge ratio calculation, the data used and the conversion to contracts. Reporting effectiveness and explaining basis risk honestly earns the next share. The memo should show the cash consequences of daily settlement, since a hedge that cannot be funded fails. Instructors in this MS in Finance course reward a clear rationale for hedging grounded in the firm's circumstances, and evidence that alternatives were considered. Memo format with the recommendation first, specific next steps and APA 7 references to the ratio's source and to hedging research complete the rubric.
GF561 Unit 8 help from the desk
The most frequent GF561 Unit 8 error is sizing a cross-hedge one-for-one on physical quantity, which ignores how much the hedged price actually moves with the futures price. Others compute the hedge ratio from price levels rather than changes, inflating the correlation. Effectiveness is not reported, so the reader cannot judge the hedge. Margin needs are ignored. The proxy contract is chosen without explaining basis risk. Recommendations lack a contract schedule. For any exposure your case presents, follow the same order: recommendation, exposure and policy, proxy choice, ratio and contracts, layering, cash needs, rationale, alternatives and next steps.
Get a GF561 Unit 8 example written to your instructions
Send the firm, the exposure and the instruments your GF561 Unit 8 prompt describes, together with any price data and the rubric, and the memo gets sized from those numbers with its funding costed. A composite paving contractor fills in where no firm is named. The opening custom sample costs nothing and generally takes 24-48h. The paper above is an original model document written by our desk, not a submitted student paper and not an official Purdue University Global document.
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GF561 Unit 8 questions, answered
How do I calculate the minimum-variance hedge ratio?
Multiply the correlation between changes in the spot and futures prices by the ratio of their standard deviations. The sample uses thirty-six months of changes, not levels, and shows all three inputs with their data window. The resulting 0.8421 is then applied to the hedged gallons and divided by the contract size to reach the number of contracts.
Does the memo need to discuss hedge accounting?
Briefly, when the prompt mentions reporting. The sample notes that hedge accounting typically requires documentation prepared at inception, naming the hedged item, the instrument and how effectiveness will be assessed. It does not attempt a full accounting treatment, which belongs to a different course, but it shows the treasurer what must be in place before the first trade.
Where can I find a free GF561 Unit 8 sample paper?
This page carries a full GF561 Unit 8 hedge design memo cross-hedging asphalt with crude oil futures, with a minimum-variance ratio, contract layering, margin needs and APA 7 references.
How is the minimum-variance hedge ratio calculated?
Multiply the correlation between changes in asphalt and crude futures prices, 0.78, by asphalt's standard deviation of changes, $28 a ton, and divide by crude's, $6.50 a barrel. The result is about 3.36 barrels per ton.
Why hedge only 60 percent of purchases?
About 40 percent of the season's work is on state contracts with asphalt price adjustment clauses, which already pass most price changes to the state. Hedging those tons as well would over-protect them.