| Course | GF561 Derivatives and Hedging |
|---|---|
| Unit | Unit 3 |
| Paper type | Forward and futures problem |
| Length | About 900 words, 6 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 3
Carry, Storage, Parity and Daily Settlement: A Unit 3 Forward and Futures Problem in Four Parts
[Student Name]
Purdue University Global
GF561: Derivatives and Hedging
Unit 3 Forward and Futures Problem
[Instructor Name]
[Date]
The index, the grain, the currency quotes and the crude contracts are illustrative; the textbooks and article cited are real.
Part 1: An Index Forward and a Mispricing
Given. An index stands at 4,800. The continuously compounded risk-free rate is 4.4 percent and the index's dividend yield is 1.6 percent. The forward matures in nine months.
Formula. The forward price equals the spot price grown at the risk-free rate less the dividend yield, compounded continuously over the life of the contract (Hull, 2022).
Substitution. 4,800 times e raised to 0.028 times 0.75, which is 4,800 times 1.021222.
Result. About 4,901.87.
The quote. A dealer quotes 4,930, which is 28.13 above the fair forward price.
The trade. Sell the forward at 4,930, borrow 4,800 to buy the index, collect its dividends, and deliver at maturity. The borrowing grows to about 4,901.87 net of dividends, so the trader locks in 28.13 per index unit with no market risk. This cash-and-carry trade is what pulls quoted prices back toward fair value.
Part 2: A Grain Forward With Storage
Given. Spot corn is $4.60 a bushel. Storage runs three cents per bushel monthly, billed after each month ends. The rate is 4.4 percent. The forward matures in six months.
Storage in today's dollars. Six payments of $0.03, each discounted at 4.4 percent for one to six months, have a present value of about $0.1777.
Formula. For a stored commodity, the forward price equals spot plus the present value of storage, grown at the risk-free rate.
Substitution. $4.60 plus $0.1777 is $4.7777; times e raised to 0.044 times 0.5, or 1.02224.
Result. About $4.88 a bushel.
Meaning. Storage adds about 28 cents to the forward price above spot, partly the storage itself and partly the interest on money tied up in grain. If the quoted forward fell well below $4.88, holders of corn would sell it and buy forwards instead, saving storage and interest.
Part 3: A Currency Forward by Interest Rate Parity
Given. The euro trades at $1.0850. The one-year dollar rate is 4.3 percent and the one-year euro rate 2.2 percent, both continuously compounded.
Formula. The forward rate equals spot times e raised to the difference between the domestic and foreign rates, times time.
Substitution. 1.0850 times e raised to 0.021, or 1.0850 times 1.02122.
Result. About $1.1080 per euro.
Meaning. Lower interest on euro deposits is why the forward euro costs more than the spot euro. An investor who converted dollars to euros, earned 2.2 percent and sold the euros forward at $1.1080 would end with exactly what a dollar deposit at 4.3 percent pays. Evidence suggests that covered interest parity held closely in major currencies for decades, though small, persistent deviations have appeared since 2008 (Du et al., 2018).
Part 4: Five Days of Daily Settlement
Given. A trader buys four crude oil futures at $71.20 a barrel; each contract covers 1,000 barrels. Initial margin is $7,000 a contract, $28,000 in total, and the maintenance margin is $6,300 a contract, $25,200 in total. When the account falls below maintenance, it must be restored to the initial level.
Day 1. Settlement price $70.40. Change: negative $0.80 times 4,000 barrels, a loss of $3,200. Balance $24,800, below maintenance. Margin call: $3,200, restoring $28,000.
Day 2. Settlement $69.10. Loss $5,200. Balance $22,800. Margin call: $5,200, restoring $28,000.
Day 3. Settlement $69.85. Gain $3,000. Balance $31,000. No call.
Day 4. Settlement $68.30. Loss $6,200. Balance $24,800. Margin call: $3,200, restoring $28,000.
Day 5. Settlement $70.05. Gain $7,000. Balance $35,000.
Totals. The trader deposited $28,000 at the start and $11,600 in calls, $39,600 in all, and the account holds $35,000. The net loss is $4,600, the same as $71.20 less $70.05 times 4,000 barrels.
Daily settlement turns a single loss at maturity into a stream of cash demands along the way: the trader's total loss after five days is only $4,600, but meeting it required $11,600 of new cash on three separate days.
When Carry Pricing Breaks Down
The carry formulas assume that someone can actually buy the asset and hold it. For a financial index or a currency, that is easy. For a commodity in short supply, holders may refuse to lend or sell it even when the forward looks cheap, because having the physical good on hand has value of its own, often called a convenience yield. In those markets forward prices can sit well below spot plus carry for long periods, and the cash-and-carry trade in Part 1 has no reverse equivalent that forces them back up.
How the Parts Connect
Parts 1 through 3 apply one idea, that a forward price equals the cost of buying the asset today and carrying it to delivery, adjusted for whatever the asset pays or costs to hold. Dividends lower the forward price, storage raises it and a foreign interest rate acts like a dividend. Part 4 shows that futures, unlike forwards, settle gains and losses every day, which removes most credit risk but creates a need for cash (Bodie et al., 2024).
Conventions
Rates are continuously compounded. Index and currency figures are rounded to two and four decimals; margin figures are exact.
References
Bodie, Z., Kane, A., & Marcus, A. J. (2024). Investments (13th ed.). McGraw Hill.
Du, W., Tepper, A., & Verdelhan, A. (2018). Deviations from covered interest rate parity. The Journal of Finance, 73(3), 915-957. https://doi.org/10.1111/jofi.12620
Hull, J. C. (2022). Options, futures, and other derivatives (11th ed.). Pearson.
The Purdue Global GF561 Unit 3 instructions
The third GF561 unit asks you to price forwards from carry and to track a futures account through daily settlement. For each forward, state the inputs, the carry formula suited to the asset, the substitution and the result, and explain what an arbitrageur would do if a quote differed from it. Handle income such as dividends, costs such as storage, and foreign interest rates as the asset requires. For the futures account, set out the contract size, initial and maintenance margin, and the rule for meeting calls, then show each day's settlement price, gain or loss, balance and any call. Reconcile the account's total with the overall price change. Explain how the parts connect and when carry pricing breaks down. Cite derivatives texts and research on interest rate parity in APA 7.
How the GF 561 Unit 3 example is put together
Part 1 of the sample prices the index forward, flags the 4,930 quote and lays out the cash-and-carry trade, citing Hull. Part 2 discounts six monthly storage payments, adds them to spot corn and grows the total. Part 3 uses interest rate parity, with Du, Tepper and Verdelhan's evidence on small deviations since 2008. Part 4 is a five-day ledger with margin calls on days one, two and four, reconciled to a $4,600 loss. The highlighted sentence links daily settlement to cash demands. A section on when carry pricing breaks down explains convenience yield, a section connecting the parts cites Bodie, Kane and Marcus, and a conventions note closes the set.
Where the points sit in the GF561 Unit 3 rubric
Credit on this GF561 set rests on correct forward prices with each step shown, and on applying the right carry adjustment for each asset. Graders check the arbitrage explanation for the mispriced quote, since describing the trade shows the student understands why the formula holds. The futures ledger earns substantial credit when every day's figures are correct, margin calls follow the stated rule and the totals reconcile to the overall price change. Instructors in the MS in Finance program value an explanation of how carry differs across assets and of the limits of carry pricing. Consistent compounding conventions and entries for Hull, Bodie and Du's team in APA 7 finish the marks.
GF561 Unit 3 help: mistakes that cost points
A frequent GF561 Unit 3 error is adding dividends to the forward price instead of subtracting them, or forgetting to discount storage costs. Students also mix continuous and discrete compounding within one problem. Arbitrage trades are described in the wrong direction, buying the forward when it is too expensive. In the futures ledger, margin calls are often set to restore maintenance rather than initial margin, or the balance is not carried forward correctly. The total is rarely reconciled to the price change. For any assets and contracts your prompt supplies, keep the same steps: inputs, the right carry formula, substitution, result, the arbitrage check and a reconciled ledger.
Get a GF561 Unit 3 example written to your instructions
Spot prices, rates, contract sizes and margin levels from the GF561 Unit 3 set are what the work needs, plus your text's compounding convention and the rubric. Each forward gets priced term by term, and the ledger is kept day by day. A free first custom sample, typically delivered in 24-48h, shows the method on your own numbers. 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 3 questions, answered
Why does the margin call restore the initial level?
Because most exchange rules, and most textbook problems, require a call to bring the account back to initial margin rather than to maintenance. The sample states that assumption above the ledger. If your prompt specifies otherwise, the custom ledger follows your rule, and every balance after the first call changes accordingly.
Is a forward price a forecast of the future spot price?
Not in these problems. The forward price comes from carry, what it costs to buy the asset now and hold it, not from anyone's expectation about where the price is heading. The sample makes that distinction when it prices the index, since a forward that differed from the carry value would allow the riskless trade shown in part one.
Where can I find a free GF561 Unit 3 sample paper?
A complete GF561 Unit 3 forward and futures problem is available here, pricing index, grain and currency forwards and tracking five days of futures margin, with APA 7 references.
Why did the trader deposit $11,600 if the loss was only $4,600?
Margin calls restore the account to its initial level each time it falls below maintenance. Gains on other days rebuilt the balance, so cash deposited exceeds the net loss, and the excess remains in the account.
What does the cash-and-carry trade do?
It sells the overpriced forward, borrows to buy the index today, collects dividends and delivers at maturity. The borrowing grows to the fair forward price, so the trader keeps the difference without market risk.