- A trader buys a single futures contract at a price of 100. The contract has a multiplier of $250. The position is held for three days. The settlement prices at the end of Day 1, Day 2, and Day 3 (at maturity) are 102, 99, and 101, respectively. Ignoring margin accounts and the time value of money, what is the trader's total profit or loss over the three-day period?
Answer: A profit of $250
The total profit or loss on a futures contract held to maturity is the difference between the final settlement price and the initial futures price, multiplied by the contract size/multiplier. The intermediate price movements determine daily margin flows but do not change the total outcome. Total Profit/Loss = (Final Price - Initial Price) × Multiplier = (101 - 100) × $250 = 1 × $250 = $250 profit. Alternatively, one can sum daily profits: Day 1: (102-100)*250 = +$500. Day 2: (99-102)*250 = -$750. Day 3: (101-99)*250 = +$500. Total = $500 - $750 + $500 = $250 profit.
- The payoff for a short position in a forward contract on one unit of an asset is given by the formula F₀ - ST. If the forward price (F₀) is $100 and the spot price at maturity (ST) is $120, what does this formula imply for the short position?
Answer: A loss of $20, because the seller must deliver an asset worth $120 for only $100 in proceeds.
Forward contracts involve an obligation to buy or sell an asset at a predetermined price on a future date. When analyzing payoffs, you need to understand the perspective of each party and how the formula reflects their profit or loss.
For a short position (the seller), the payoff formula is F0−ST, where F0 is the forward price agreed upon today and ST is the spot price at maturity. With F0=$100 and ST=$120, the calculation gives us $100−$120=−$20. This negative result indicates a $20 loss for the short position holder.
The economic logic is clear: the seller must deliver an asset worth $120 in the market but only receives the contracted $100, creating a $20 opportunity cost or loss.
Answer A incorrectly suggests a profit, misunderstanding that a negative payoff represents a loss, not a gain. The seller doesn't benefit from the higher market price since they're locked into the lower contract price. Answer B confuses the payoff with the asset's market value—the $120 spot price isn't the seller's profit but rather what makes their position unprofitable. Answer D overstates the loss by claiming the full contract value as a loss, ignoring that the seller does receive the $100 contract payment.
Remember this key insight: in forward contract payoff formulas, negative results always indicate losses, and positive results indicate profits. The formula automatically accounts for the economic reality of being locked into a contract when market conditions move against you. - An investor shorts one S&P 500 futures contract at a price of 4,500. The contract multiplier is $250. Over the next day, concerns about inflation cause the futures price to settle at 4,550. What is the financial result for the investor on this day?
Answer: A loss of $12,500, due to the price moving against the short position.
When you encounter futures trading problems, focus on two key elements: the direction of your position and how price movements affect your profit or loss. Short positions profit when prices fall and lose when prices rise.
Here's the calculation: The investor shorted at 4,500 and the price moved to 4,550, creating an unfavorable move of 50 points. With a contract multiplier of $250, the loss equals 50×$250=$12,500. Since the investor is short, the price increase works against them.
Looking at the wrong answers: Choice A incorrectly suggests a profit of $12,500 simply because the index increased, but this ignores that short positions lose money when prices rise. Choice B confuses the daily loss with the contract's total notional value ($1,137,500 = 4,550 × $250), which represents the contract's full value, not the day's change. Choice C gives the raw 50-point move without applying the contract multiplier, missing that futures contracts amplify gains and losses through their multiplier.
Answer D correctly identifies both the loss amount ($12,500) and explains why: the price moved against the short position.
Study tip: Always remember the futures P&L formula: (Exit Price - Entry Price) × Contract Multiplier × Number of Contracts. For short positions, flip the signs—you profit when the exit price is below your entry price. Don't confuse daily changes with total contract values, and always apply the multiplier to convert index points into dollar amounts. - Which of the following describes the payoff profile for the buyer of a forward contract (the long position)?
Answer: Unlimited potential profit if the asset price rises and a potential loss limited to the price of the asset falling to zero.
When analyzing derivative payoffs, you need to understand the fundamental mechanics of how profits and losses accumulate as the underlying asset's price moves relative to the contract's fixed terms.
For a forward contract buyer (long position), you're obligated to purchase the asset at a predetermined forward price regardless of the market price at expiration. Your profit equals the spot price minus the forward price when the spot exceeds the forward price. Since asset prices can theoretically rise without limit, your potential profit is unlimited. Conversely, your maximum loss occurs if the asset becomes worthless (price falls to zero), making your loss equal to the full forward price you must pay for a worthless asset.
Answer C correctly captures this asymmetric payoff structure: unlimited upside potential with downside risk limited to the forward price (assuming the asset price can't go below zero).
Answer A is wrong because both profit and loss potentials are not limited in the way described. Answer B reverses the payoff profile entirely—this would describe a short forward position, not a long one. The long position profits when prices rise, not fall. Answer D confuses forward contracts with options or margined positions. Forward contracts don't require initial margin payments like futures, and the profit isn't limited to the forward price.
Study tip: Remember that "long" positions in any derivative benefit from rising underlying prices, while "short" positions benefit from falling prices. For forwards specifically, payoffs are linear and symmetric around the forward price, unlike options which have asymmetric risk profiles due to premium payments.
- In a forward contract on a physical commodity, the party with the long position realizes a profit of $125,000 at expiration. Assuming no transaction costs and no default by either party, what is the financial outcome for the party with the short position?
Answer: A loss of $125,000, as forwards are a zero-sum game between the two counterparties.
Forward and futures contracts are zero-sum games. The gain to one party is a direct loss to the other. If the long position (the buyer) profits by $125,000, it means the spot price at expiration was $125,000 higher than the agreed-upon forward price (scaled by the notional amount). The short position (the seller) must sell the asset at the lower forward price instead of the higher spot price, incurring a loss of exactly $125,000.
- An airline wishes to hedge its exposure to rising fuel costs by locking in the price of 100,000 gallons of jet fuel. It enters into a long forward contract at a price of $2.50 per gallon. At settlement, the spot price of jet fuel is $2.20 per gallon. From a purely financial perspective on the derivative contract, what is the outcome for the airline?
Answer: A loss of $30,000, as it is obligated to buy at a price higher than the current market price.
The payoff for a long forward position is N × (ST - F₀). Here, N = 100,000 gallons, ST = $2.20, and F₀ = $2.50. The payoff is 100,000 × ($2.20 - $2.50) = 100,000 × (-$0.30) = -$30,000. The airline experiences a financial loss on the forward contract because the price of fuel fell. Note that while this is a loss on the hedge, the airline benefits from lower fuel costs in the physical market; the question asks only about the derivative outcome. - At the moment a forward contract is initiated between two parties, which of the following statements is most accurate regarding its price and value?
Answer: The price is positive, representing the agreed-upon delivery price, while the value is zero.
There is a critical distinction between the price and the value of a forward contract. The forward price is the delivery price specified in the contract (F₀), which is a positive number. The forward contract is structured such that, at initiation, neither party has to pay the other to enter the agreement. Therefore, the initial value of the contract to both parties is zero.
- A portfolio manager enters into a short forward contract to sell 10,000 shares of a non-dividend-paying stock in 90 days. The agreed-upon forward price is $50 per share. On the expiration date, the stock's spot price is $54 per share. What is the value of the portfolio manager's position on the expiration date?
Answer: A loss of $40,000
The payoff for a short forward position is calculated as N × (F₀ - ST), where N is the notional amount, F₀ is the forward price, and ST is the spot price at expiration. In this case, Payoff = 10,000 × ($50 - $54) = 10,000 × (-$4) = -$40,000. This represents a loss of $40,000 for the short position. - A US coffee roaster plans to purchase a large quantity of coffee beans from Brazil. The roaster is concerned about the coffee price in Brazilian real (BRL) but also about the BRL/USD exchange rate. The company hedges its coffee price risk using coffee futures, which are priced in USD. This strategy fails to protect the roaster from which specific risk?
Answer: Basis risk, arising from the mismatch between the hedged instrument and the actual exposure.
When companies hedge foreign transactions, they face the challenge of matching their hedging instruments precisely to their actual risk exposures. This question tests your understanding of basis risk and how imperfect hedges can leave companies vulnerable.
The coffee roaster's actual exposure is to coffee prices denominated in Brazilian reais, but they're hedging with USD-denominated coffee futures. This creates a currency mismatch that the hedge cannot address. If the real weakens against the dollar, the roaster might pay less in USD for the coffee, but their futures hedge (designed to protect against rising coffee prices) won't adjust for this currency benefit. Conversely, if the real strengthens, they'll pay more in USD terms even if coffee prices in reais remain stable. This mismatch between the hedged instrument (USD coffee futures) and the actual exposure (BRL coffee prices) exemplifies basis risk, making D correct.
A is wrong because systemic risk refers to threats to the entire financial system, not the specific mismatch between hedge and exposure. B is incorrect as operational risk involves internal process failures, not hedging mismatches. C misidentifies the issue as counterparty risk - futures exchanges have robust clearinghouse mechanisms that make default extremely unlikely, and this isn't the risk described in the scenario.
Remember that basis risk emerges whenever there's any mismatch between your hedge and your actual exposure - whether in currency, timing, quantity, or underlying asset quality. Perfect hedges are rare; always look for what specific element remains unhedged.
- The payoff diagram below illustrates the profit/loss profile for a derivative position at expiration. Which position does the diagram represent?
Answer: A long forward contract
The diagram shows a linear payoff. The payoff is negative when the spot price at expiration (ST) is below the forward price (F₀) and positive when ST is above F₀. The payoff is calculated as (ST - F₀). This is the characteristic payoff structure of a long forward or futures contract. - A trader takes a long position in one crude oil futures contract on the NYMEX, which represents 1,000 barrels of oil. The initial margin requirement is $6,000 and the maintenance margin is $4,500. The contract is entered at a futures price of $80.00 per barrel. At the end of the first day, the settlement price is $78.20. What is the balance in the trader's margin account at the end of Day 1, and what action is required?
Answer: $4,200; the trader must deposit $1,800 to restore the initial margin.
The trader's position changed by ($78.20 - $80.00) = -$1.80 per barrel. For one contract of 1,000 barrels, this is a loss of $1.80 × 1,000 = $1,800. The margin account balance becomes the initial margin minus the loss: $6,000 - $1,800 = $4,200. Since $4,200 is below the maintenance margin of $4,500, a margin call is triggered. The trader must deposit funds to bring the account balance back up to the initial margin level of $6,000. The required deposit is $6,000 - $4,200 = $1,800.
- A U.S.-based company imports goods from Germany and must pay €5 million in 90 days. To hedge against adverse movements in the EUR/USD exchange rate, the company enters into a 90-day forward contract to buy €5 million at a forward rate of $1.08/€. At the end of the 90 days, the spot exchange rate is $1.11/€. What was the net economic impact of the hedge on the company's payment?
Answer: The company saved $150,000 compared to what it would have paid at the spot rate.
When a company faces foreign exchange risk from future payments, forward contracts lock in exchange rates to eliminate uncertainty. The key to analyzing hedge effectiveness is comparing the hedged cost to what the unhedged cost would have been.
Let's calculate both scenarios. With the forward contract, the company pays: €5,000,000×$1.08/€=$5,400,000
Without the hedge, paying at the spot rate would cost: €5,000,000×$1.11/€=$5,550,000
The company saved $5,550,000−$5,400,000=$150,000 by using the forward contract.
Answer A incorrectly frames this as an "opportunity loss." While the euro did appreciate, the company protected itself against exactly this risk—that's the hedge's purpose. Answer B is wrong because the hedge doesn't need to "exactly offset" rate changes; it simply locks in a predetermined rate regardless of spot movements. Answer C confuses the total payment amount with the hedge's impact. The $5,550,000 represents what the company would have paid without hedging, not a gain.
Answer D correctly identifies that the company saved $150,000 compared to the unhedged alternative.
Study tip: For foreign exchange hedging problems, always calculate both the hedged cost (using the forward rate) and the unhedged cost (using the final spot rate), then compare them. The hedge's value is the difference between these amounts, not whether you "guessed right" about currency direction. - Which of the following statements most accurately contrasts the primary source of counterparty risk in an over-the-counter (OTC) forward contract versus an exchange-traded futures contract?
Answer: Counterparty risk in a forward contract is borne by the contracting parties, whereas in a futures contract it is mitigated by a central clearinghouse acting as counterparty to all trades.
In an OTC forward contract, the two parties contract directly with each other, so each is exposed to the other's risk of default. In an exchange-traded futures contract, the clearinghouse interposes itself between the buyer and seller, becoming the buyer to every seller and the seller to every buyer. This substitution, combined with the margin system, effectively mitigates counterparty risk for market participants.
- A speculator believes a currency will appreciate and wants to take a leveraged position to profit from this view, intending to close the position within a few weeks. Which instrument would generally be more advantageous for this purpose, and for what primary reason?
Answer: A futures contract, because its standardization and exchange trading provide high liquidity for easy entry and exit.
When evaluating derivative instruments for short-term currency speculation, you need to consider liquidity, leverage availability, and ease of position management. The speculator's timeline of "a few weeks" is crucial here—they need the ability to enter and exit positions quickly and efficiently.
Futures contracts excel in this scenario because they're standardized and trade on organized exchanges with high daily volume. This standardization creates deep, liquid markets where you can easily open and close positions without significant bid-ask spreads or difficulty finding counterparties. For a speculator planning to exit within weeks, this liquidity is essential.
Option A is incorrect because forwards don't inherently offer higher leverage than futures—both derive their leverage from the same principle of controlling large currency amounts with small initial investments. Option B contains a fundamental misunderstanding: while forwards don't have daily margin calls, this actually works against short-term speculators who benefit from the transparent, mark-to-market pricing that margin calls reflect. Option D makes an impossible claim—no clearinghouse guarantees profits based on market direction. Clearinghouses only guarantee contract performance (that counterparties fulfill their obligations), not profitable outcomes.
The key insight is that forwards are designed for customized, longer-term hedging needs with specific counterparties, while futures serve the standardized, liquid trading that speculators require. When you see questions about short-term speculation versus long-term hedging, always consider liquidity needs first—speculators prioritize easy entry and exit over contract customization.
- Which of the following best describes the primary role of a futures exchange's clearinghouse?
Answer: To act as the counterparty to every transaction, thereby virtually eliminating counterparty credit risk.
When you encounter questions about futures exchanges, focus on understanding the unique role of the clearinghouse in managing risk and ensuring market integrity.
The clearinghouse serves as the central counterparty to every futures transaction, meaning it becomes the buyer to every seller and the seller to every buyer. This arrangement virtually eliminates counterparty credit risk because market participants don't have to worry about whether the other party will fulfill their obligations - the clearinghouse guarantees performance. The clearinghouse collects margin deposits and marks positions to market daily, ensuring it can cover any potential losses. This is why option D correctly captures the clearinghouse's primary function.
Option A is incorrect because clearinghouses don't set settlement prices - these are typically determined by market activity during the closing period or through established pricing methodologies. Option B mischaracterizes the clearinghouse's role; it doesn't provide liquidity by trading contracts itself. Instead, liquidity comes from market participants and designated market makers. Option C is wrong because clearinghouses are operational entities that facilitate trading mechanics, not advisory services - they don't provide investment advice or trading strategies.
The key distinction here is between operational functions (what clearinghouses actually do) versus market functions (what other entities do). Remember that clearinghouses are risk management institutions first and foremost. When studying futures markets, always think about how each component - the exchange, clearinghouse, and participants - contributes to overall market safety and efficiency. The clearinghouse's guarantee function is what makes futures markets viable for widespread participation.
- An oil producer sells crude oil forward at a fixed price of $80 per barrel to hedge its production. The company's cost of production is $65 per barrel. At the maturity of the forward contract, the spot price for crude oil is $90 per barrel. What is the producer's effective realized price per barrel, including the impact of the hedge?
Answer: $80 per barrel
The producer has two components to its position: the physical oil and the short forward contract. The producer sells the physical oil in the spot market for $90/barrel. The short forward contract has a payoff of (F₀ - ST) = ($80 - $90) = -$10 per barrel. The effective price is the revenue from the physical sale plus the profit/loss from the hedge: $90 + (-$10) = $80. The hedge successfully locked in the selling price at the forward rate of $80. - A corporation needs to hedge the purchase of a precisely specified quantity of industrial-grade copper with unique purity requirements, for delivery on a non-standard date (e.g., 107 days from today). Which derivative instrument is most suitable for this purpose and why?
Answer: A forward contract, because its terms, such as quantity, quality, and expiration date, can be customized to precisely match the corporation's exposure.
Forward contracts are private agreements between two parties and can be customized to meet the specific needs of the hedger regarding the underlying asset's specifications, the contract size, and the delivery date. Futures contracts are standardized in all these aspects, making them unsuitable for hedging such a specific exposure without introducing significant basis risk.
- Consider a long forward contract and a long futures contract on the same underlying asset with the same maturity date and initial contract price. Assume the underlying asset price trends steadily upward over the life of the contracts. How does the timing of cash flows differ between the two positions?
Answer: The forward contract has a single cash flow at expiration, while the futures contract experiences periodic positive cash flows from margin account settlements.
A forward contract typically involves no cash flow until the expiration date, when the contract is settled. A futures contract, however, is marked-to-market daily. As the asset price trends upward, the long futures position will realize daily profits. These profits are credited to the margin account and can typically be withdrawn, resulting in periodic positive cash flows throughout the contract's life. The forward holder does not realize this gain until expiration.
- A corn farmer expects to harvest 50,000 bushels of corn in three months and wishes to lock in a selling price. The farmer observes that 3-month corn futures contracts, each for 5,000 bushels, are trading at $4.50 per bushel. Which of the following actions should the farmer take to hedge this price risk?
Answer: Take a short position in 10 futures contracts.
The farmer is long the physical asset (corn) and wants to hedge against a price decrease. To do this, the farmer should take an opposite position in the derivatives market, which is a short position. This locks in the selling price. The total quantity to hedge is 50,000 bushels, and each contract is for 5,000 bushels, so the farmer needs to short 50,000 / 5,000 = 10 contracts.
- A speculator holds a short position in a futures contract. If the underlying asset's price rises significantly, which of the following statements best describes the payoff structure and risk for the speculator?
Answer: The potential loss is theoretically unlimited, while the potential profit is limited to the forward price declining to zero.
For a short futures position, the holder profits if the asset price falls. The maximum profit occurs if the asset price drops to zero, so the profit is limited to the initial futures price times the notional. Conversely, if the asset price rises, the short position incurs losses. Since there is no theoretical upper limit to how high the asset price can rise, the potential loss for a short position is theoretically unlimited.
