Commodity Derivatives Quiz Exam Quiz 06

To determine the net profit or loss, we need to calculate the profit/loss from both the futures contract and the swap contract, and then combine them. First, let’s calculate the profit/loss from the futures contract. The company bought 50 contracts at £750/tonne and sold them at £730/tonne. This is a loss of £20/tonne per contract. The total loss is 50 contracts * 100 tonnes/contract * £20/tonne = £100,000. Next, let’s calculate the profit/loss from the swap contract. The company receives a fixed price of £740/tonne and pays the average spot price of £725/tonne. This is a profit of £15/tonne. The total profit is 2,500 tonnes * £15/tonne = £37,500. Finally, we combine the profit/loss from both contracts. The company has a loss of £100,000 from the futures contract and a profit of £37,500 from the swap contract. The net result is -£100,000 + £37,500 = -£62,500. Therefore, the company has a net loss of £62,500. Imagine a scenario where a coffee producer in Colombia uses futures to hedge against price drops. They also enter a swap agreement to sell a portion of their harvest at a guaranteed price. If the market price of coffee falls below the futures price at which they hedged, they make a profit on the futures contract, offsetting some of the losses from selling their physical coffee at the lower market price. Conversely, if the market price rises above the swap price, they miss out on potential gains in the spot market but still receive the guaranteed price from the swap. The combined effect of futures and swaps allows them to manage price risk and stabilize their revenue stream. It is important to consider the volume and tenor of both derivatives instruments to understand the overall risk mitigation or exposure to market fluctuations.

Let’s analyze the scenario. A commodity trader uses a forward contract to lock in a price for future delivery of crude oil. Unexpectedly, geopolitical tensions significantly disrupt supply chains, causing a sharp increase in spot prices. The trader, being short on the forward contract, faces a potential loss. However, the trader also holds options on futures contracts related to the same crude oil. The question examines how the trader can strategically use these options to mitigate the losses from the forward contract. The critical concept is that the options provide a flexible hedge, allowing the trader to profit from the price increase while still fulfilling the forward contract obligations. The trader’s initial position is short a forward contract, meaning they are obligated to deliver crude oil at a predetermined price. The geopolitical event causes the spot price to increase. If the trader had no hedging strategy, they would need to buy crude oil at the higher spot price to fulfill their forward contract obligation, resulting in a loss. However, they also hold options. The key is to determine which type of option (call or put) and which action (exercise or let expire) would be most beneficial. Since the price has increased, a call option (the right to buy) becomes valuable. If the trader holds a call option with a strike price below the current spot price, they can exercise the option, buy the crude oil at the lower strike price, and then deliver it under the forward contract. This limits their loss. Conversely, a put option (the right to sell) would be less useful in this scenario, as the trader already has an obligation to sell. The question also explores the regulatory aspects. The trader must ensure their hedging strategy complies with UK regulations, particularly those concerning market abuse and insider dealing, as defined under the Financial Services and Markets Act 2000 (FSMA) and related regulations such as the Market Abuse Regulation (MAR). Any attempt to manipulate the market using the options to unfairly benefit from the forward contract position would be illegal. Therefore, the optimal strategy is to exercise call options with strike prices below the current market price to offset the losses on the short forward position, while ensuring compliance with UK market regulations to avoid any potential legal repercussions.

The core of this question lies in understanding how margin requirements function in futures contracts, specifically considering the impact of intraday price volatility and the concept of a “maintenance margin.” The maintenance margin is the minimum amount of equity an investor must maintain in their margin account. If the equity falls below this level due to adverse price movements, the investor receives a margin call, requiring them to deposit additional funds to bring the account back to the initial margin level. In this scenario, the trader starts with an initial margin of £8,000. The maintenance margin is £6,000. The price first declines by £2,500, reducing the equity to £5,500 (£8,000 – £2,500). Since this is below the maintenance margin, a margin call is triggered. To meet the margin call, the trader needs to restore the equity to the initial margin level of £8,000. Therefore, they must deposit £2,500 (£8,000 – £5,500). After depositing £2,500, the equity is back at £8,000. The price then increases by £4,000, bringing the equity to £12,000 (£8,000 + £4,000). Finally, the price declines by £5,000, resulting in a final equity balance of £7,000 (£12,000 – £5,000). The question asks for the final equity balance in the margin account.

The core of this question lies in understanding how margin calls function in futures contracts, particularly when considering the impact of intra-day price volatility and the specific rules set by the exchange and the broker. The key is to track the daily settlement price, intra-day high and low, and how these values affect the margin account. The initial margin is the amount required to open the position, and the maintenance margin is the level below which the account cannot fall. If the account balance drops below the maintenance margin, a margin call is issued to bring the account back to the initial margin level. Here’s the step-by-step breakdown of the scenario: 1. **Day 1:** The trader opens the position at 85.00 with an initial margin of £6,000 and a maintenance margin of £4,500. 2. **Day 1 Settlement:** The settlement price is 83.50. The loss is (85.00 – 83.50) * 1,000 = £1,500. The margin account balance is now £6,000 – £1,500 = £4,500. 3. **Day 2 Intra-day Low:** The price drops to 81.00 intra-day. The loss from the previous settlement price is (83.50 – 81.00) * 1,000 = £2,500. The intra-day margin account balance would be £4,500 – £2,500 = £2,000. Since this is below the maintenance margin of £4,500, a margin call is triggered. The trader needs to deposit funds to bring the account back to the initial margin level of £6,000. The amount of the margin call is £6,000 – £2,000 = £4,000. 4. **Day 2 Settlement:** The settlement price is 84.50. The gain from the previous settlement price is (84.50 – 81.00) * 1,000 = £3,500. The margin account balance after the settlement would be £2,000 + £4,000 + £3,500 = £9,500. 5. **Day 3 Intra-day High:** The price rises to 86.00 intra-day. The gain from the previous settlement price is (86.00 – 84.50) * 1,000 = £1,500. The intra-day margin account balance would be £9,500 + £1,500 = £11,000. 6. **Day 3 Settlement:** The settlement price is 82.00. The loss from the previous settlement price is (84.50 – 82.00) * 1,000 = £2,500. The margin account balance after the settlement would be £9,500 – £2,500 = £7,000. 7. **Day 4:** The trader closes the position at 81.00. The loss from the previous settlement price is (82.00 – 81.00) * 1,000 = £1,000. The final margin account balance would be £7,000 – £1,000 = £6,000. Therefore, the trader receives £6,000 back from the broker.

Let’s analyze a scenario involving a commodity trader, Anya, who uses a combination of futures and options to manage price risk in her cocoa bean portfolio. Anya anticipates a potential supply disruption due to adverse weather conditions in West Africa, a major cocoa-producing region. To protect her downside, she buys call options on cocoa futures. At the same time, concerned about potential oversupply from Southeast Asia, she sells cocoa futures contracts to hedge against a price decrease. The core concept here is understanding how options and futures, when combined, can create tailored risk management strategies. Anya’s strategy is a nuanced approach. Buying call options gives her the right, but not the obligation, to buy cocoa futures at a specific price (the strike price). This protects her if the price of cocoa rises sharply due to the West African supply disruption. Simultaneously, selling cocoa futures obligates her to deliver cocoa at a future date at a predetermined price. This protects her if the price of cocoa falls due to oversupply from Southeast Asia. The key to understanding the question lies in recognizing the interplay between these two positions. If the price rises dramatically, Anya benefits from the call options, offsetting any losses on her physical cocoa holdings. Her short futures position will incur losses, but this is a calculated risk, as the primary concern was a price spike due to supply disruption. If the price falls, the profits from her short futures position offset losses in her physical holdings, while the call options expire worthless (limiting her loss to the premium paid). This combined strategy is designed to protect her from extreme price movements in either direction, creating a defined risk profile. The question tests the understanding of the directional impact of each position and how they interact in different market scenarios.

The core of this question lies in understanding how margin requirements function in commodity futures contracts, specifically within the context of the UK regulatory environment. The initial margin acts as a performance bond, ensuring the trader can cover potential losses. The maintenance margin is the threshold below which the account balance cannot fall; if it does, a margin call is triggered, requiring the trader to deposit funds to bring the account back to the initial margin level. The calculation involves understanding the loss the trader incurred and how that loss impacts the account balance relative to the initial and maintenance margin levels. The scenario introduces a twist by specifying that the contract is cleared through a UK clearing house, implying adherence to UK regulations concerning margin requirements. First, calculate the total loss: 5 contracts * 50 tonnes/contract * £15/tonne = £3750. Next, determine the account balance after the loss: £15000 – £3750 = £11250. Now, assess whether a margin call is triggered. The maintenance margin is £2000 per contract, so for 5 contracts, it’s £10000. Since the account balance (£11250) is above the maintenance margin (£10000), a margin call is *not* triggered. However, the question asks about the *amount* of the margin call if one *were* triggered. To determine this, we need to calculate the amount required to bring the account back to the initial margin level. The initial margin for 5 contracts is 5 * £3000 = £15000. If the account balance were *below* the maintenance margin, say at £9000, then the margin call would be £15000 (initial margin) – £9000 (current balance) = £6000. But because the account balance is *above* the maintenance margin, no margin call is issued. Therefore, the amount of the margin call is £0. The UK regulatory environment mandates that clearing houses actively monitor margin accounts and issue margin calls promptly to mitigate counterparty risk. Failure to meet a margin call can result in the liquidation of the trader’s position. The margin requirements are set by the clearing house and are influenced by factors such as the volatility of the underlying commodity and the size of the position. The purpose of the initial margin is to cover potential losses from the time the trade is initiated until it can be liquidated, while the maintenance margin acts as an early warning signal to the clearing house that the trader’s financial position is deteriorating.

The core of this question lies in understanding how basis risk arises in hedging strategies using commodity derivatives, particularly when the commodity underlying the derivative doesn’t perfectly match the commodity being hedged. Basis is the difference between the spot price of an asset and the price of a related futures contract. Basis risk is the risk that this difference will change over time in an unpredictable way. In this scenario, the coffee roaster is hedging their Arabica coffee purchases using Robusta coffee futures. Arabica and Robusta are related, but their prices don’t move in lockstep due to differences in taste, availability, and demand. The roaster needs to consider the potential changes in the Arabica-Robusta price relationship (the basis) during the hedge period. If the basis weakens (Arabica price decreases relative to Robusta), the hedge will underperform, and the roaster will experience a loss. Conversely, if the basis strengthens (Arabica price increases relative to Robusta), the hedge will outperform, resulting in a gain. The calculation involves estimating the potential range of basis movement and its impact on the hedge’s effectiveness. The roaster sells Robusta futures to lock in a price, expecting the basis to narrow. If the basis widens instead, their effective purchase price for Arabica will be higher than anticipated. Let’s assume the roaster sells Robusta futures at £2000/tonne. They expect the Arabica price to be £2500/tonne at delivery. Initially, the basis is £500/tonne (£2500 – £2000). If, at delivery, Arabica is £2600/tonne and Robusta is £2050/tonne, the basis has widened to £550/tonne (£2600 – £2050). The roaster buys back the Robusta futures at £2050, incurring a loss of £50/tonne on the futures position (£2050 – £2000). However, the Arabica price increased by £100/tonne (£2600 – £2500), partially offsetting the futures loss. The effective purchase price is £2550/tonne (£2600 – £50), which is £50/tonne higher than they initially anticipated. The key is to understand that the hedge doesn’t eliminate price risk entirely; it transforms price risk into basis risk. The roaster is now exposed to fluctuations in the price difference between Arabica and Robusta, which requires careful monitoring and potentially adjustments to the hedge strategy. Understanding factors influencing the basis, such as supply shocks specific to Arabica or changes in consumer preferences, is crucial for managing this risk effectively.

Let’s consider the scenario of a UK-based energy firm, “Britannia Energy,” which utilizes natural gas for power generation. They aim to hedge against potential price increases in the upcoming winter months. Britannia Energy decides to enter into a natural gas swap agreement with a financial institution, “Thames Capital.” The swap is structured as a fixed-for-floating swap, where Britannia Energy pays a fixed price for natural gas and receives a floating price based on the average monthly settlement price of the ICE UK Natural Gas Futures contract. To determine the fair fixed price in the swap, we need to consider the forward curve of natural gas futures. Let’s assume the following ICE UK Natural Gas Futures prices for the next six months (in pence per therm): Month 1: 150 Month 2: 152 Month 3: 155 Month 4: 158 Month 5: 160 Month 6: 162 The fair fixed price (swap rate) is the average of these forward prices. Calculation: Fixed Price = (150 + 152 + 155 + 158 + 160 + 162) / 6 = 937 / 6 = 156.17 pence per therm. The swap rate represents the equilibrium price where the present value of expected floating payments equals the present value of fixed payments. In this context, Britannia Energy locks in a gas price of 156.17 pence per therm for the next six months. If the average floating price over the swap period is higher than 156.17, Thames Capital will pay Britannia Energy the difference. Conversely, if the average floating price is lower, Britannia Energy will pay Thames Capital the difference. This swap helps Britannia Energy manage price volatility and provides certainty in their energy costs, crucial for budgeting and profitability. The swap rate is determined by market expectations of future gas prices, reflected in the forward curve. The financial institution, Thames Capital, takes on the risk associated with fluctuating gas prices, potentially profiting if their prediction of future prices is accurate.

To determine the expected change in the refinery’s profit margin, we need to calculate the impact of the basis risk. The basis risk arises because the refinery is hedging its future crack spread (the difference between the price of crude oil and the price of refined products) using futures contracts that do not perfectly match the refinery’s specific inputs and outputs. In this case, the refinery is using a heating oil futures contract to hedge its diesel production, and the futures contract settles at a price that is £1.50/barrel lower than the actual diesel price at delivery. This difference of £1.50/barrel represents the basis. The refinery sold futures contracts to hedge against a decrease in the crack spread. The refinery’s profit margin is the difference between the revenue from selling diesel and the cost of crude oil. The refinery is hedging 50,000 barrels of diesel production. The expected change in the refinery’s profit margin is the product of the number of barrels and the basis. Change in profit margin = Number of barrels × Basis = 50,000 barrels × £1.50/barrel = £75,000. Since the refinery sold futures, a negative basis (futures price lower than spot price) results in a gain. The refinery’s profit margin will increase by £75,000. This is because when the spot price of diesel is higher than the futures price at settlement, the refinery can buy back the futures contracts at a lower price than they sold them for, resulting in a profit on the futures position. This profit offsets the lower revenue from selling diesel at the spot price, resulting in a net increase in the refinery’s profit margin. For example, imagine a small bakery that hedges its wheat flour purchases using corn futures. The bakery anticipates needing 10,000 kg of wheat flour in three months. It sells corn futures contracts equivalent to the value of 10,000 kg of wheat flour. At the delivery date, wheat flour prices have risen, but corn prices have risen even more. The bakery loses money on its wheat flour purchase but makes a larger profit on its corn futures position. This profit offsets the increased cost of wheat flour, resulting in a net decrease in the bakery’s costs.

The core of this question revolves around understanding how hedging strategies using commodity derivatives can be impacted by basis risk and how different contract specifications can influence the effectiveness of the hedge. Basis risk arises because the price of the derivative contract (e.g., a futures contract) may not move exactly in tandem with the price of the underlying commodity being hedged. This difference is the basis, and its variability introduces risk. The choice of contract delivery location and grade specifications significantly influences the basis. If the delivery location of the futures contract is far from the hedger’s physical location, transportation costs and local supply/demand factors can cause divergence between the futures price and the local spot price. Similarly, if the grade specifications of the futures contract differ from the hedger’s commodity grade, quality differentials can impact the basis. The optimal hedging strategy involves minimizing this basis risk. In the scenario, the coffee roaster in Edinburgh faces basis risk due to the futures contract being based on Brazilian Arabica coffee delivered in New York, while they need Colombian coffee in Edinburgh. The correct answer focuses on strategies to mitigate this specific basis risk by considering alternative hedging instruments or adjustments to the hedge ratio to account for the correlation between the Colombian and Brazilian coffee prices. The incorrect options present plausible but less effective strategies, such as ignoring the basis risk altogether, solely relying on increasing the hedge ratio without considering price correlations, or focusing on factors irrelevant to basis risk management.

The core of this question lies in understanding how contango and backwardation affect the decision-making of a commodity producer, specifically within the context of hedging strategies using futures contracts. Contango, where futures prices are higher than the expected spot price, typically discourages producers from hedging as they anticipate selling at a higher price in the future. Conversely, backwardation, where futures prices are lower than the expected spot price, incentivizes hedging to lock in a better price than what they foresee in the spot market. However, the situation becomes nuanced when considering storage costs and the time value of money. If storage costs are significant, the producer might still hedge even in contango if the difference between the futures price and the expected spot price is less than the cost of storing the commodity until the expected sale date. The time value of money also plays a role, as the producer needs to consider the present value of the future sale proceeds. In this scenario, the producer must weigh the contango spread (futures price minus expected spot price) against the storage costs and the implied interest rate (reflecting the time value of money). If the contango spread is less than the combined storage costs and the cost of capital, hedging becomes a more attractive option. Let’s assume the expected spot price in 6 months is £85/barrel. The 6-month futures price is £90/barrel, creating a contango of £5/barrel. Storage costs are £3/barrel over 6 months, and the risk-free interest rate is 4% per annum, or 2% for 6 months. The producer must calculate the present value of the futures price: \[ PV = \frac{Futures Price}{1 + r} \] \[ PV = \frac{£90}{1 + 0.02} = £88.24 \] Now, the producer compares the present value of the futures price (£88.24) with the expected spot price (£85) plus storage costs (£3), which totals £88. Since £88.24 > £88, hedging is not necessarily detrimental. However, the producer must also consider their risk aversion. If they are highly risk-averse, they might still choose to hedge to lock in a known price, even if it’s only slightly better than the expected spot price after accounting for storage. If the producer is not risk-averse, they might prefer to leave the position unhedged. Therefore, the best course of action depends on the producer’s risk tolerance and a precise comparison of the present value of the futures price with the expected spot price plus storage costs. The question tests understanding of contango, backwardation, storage costs, time value of money, and risk aversion in hedging decisions.

The question assesses the understanding of basis risk in commodity futures trading, particularly when hedging future sales using a futures contract with a different delivery month. Basis is the difference between the spot price of a commodity and the price of a related futures contract. Basis risk arises because this difference is not constant and can change over time. The formula for calculating the effective sale price is: Effective Sale Price = Futures Price at Time of Hedge – (Spot Price at Time of Sale – Futures Price at Time of Sale). The change in basis is (Spot Price at Time of Sale – Futures Price at Time of Sale) – (Spot Price at Time of Hedge – Futures Price at Time of Hedge). In this scenario, the company hedges in June using the December futures contract. The initial basis is £3/tonne (Spot £45 – Futures £42). By November, the spot price is £48/tonne and the December futures is £46/tonne, making the new basis £2/tonne. The change in basis is £2 – £3 = -£1/tonne. The effective sale price is the futures price at the time of the hedge (£42) plus the change in basis (-£1). Therefore, the effective sale price is £42 – £1 = £41/tonne. The calculation is: 1. Initial Basis: Spot Price (June) – Futures Price (June) = £45 – £42 = £3 2. Final Basis: Spot Price (Nov) – Futures Price (Nov) = £48 – £46 = £2 3. Change in Basis: Final Basis – Initial Basis = £2 – £3 = -£1 4. Effective Sale Price: Futures Price (June) + Change in Basis = £42 + (-£1) = £41 An analogy: Imagine you are building a house and agree to buy lumber in six months using a futures contract. The price is locked in, but the local lumber yard’s price might fluctuate differently due to local supply and demand. This difference is basis. If the local price drops more than the futures price, you effectively paid more than the local market rate. Conversely, if the local price rises more than the futures price, you effectively paid less. Understanding and managing this basis risk is crucial in commodity hedging. Another example is a coffee producer in Brazil hedging their future crop sales using a futures contract traded on the ICE exchange. The basis risk arises from the difference in price between the ICE futures contract and the local price of coffee in Brazil, which is affected by factors like local weather conditions, transportation costs, and currency exchange rates.

The core of this question lies in understanding how the contango or backwardation state of a commodity market influences hedging strategies using futures contracts, particularly when a producer is involved. Contango (futures price > spot price) typically results in a “roll yield loss” because the producer sells futures contracts at a higher price initially, but as the contract approaches expiration, the futures price converges towards the spot price, which is lower. This difference represents a loss when the producer rolls the contract forward. Conversely, backwardation (futures price < spot price) creates a "roll yield gain" because the producer sells futures at a lower price, and as the contract nears expiration, the futures price converges towards the higher spot price. To determine the most suitable hedging strategy, the producer needs to consider storage costs, interest rates, and the convenience yield (the benefit of holding the physical commodity). The breakeven point is where the cost of carry (storage + interest – convenience yield) equals the difference between the futures price and the spot price. In this scenario, the producer has storage costs of £3/tonne/month, an interest rate of 5% per annum, and a convenience yield that is implicitly factored into the market prices. We need to calculate the annualized storage cost and compare it with the price differential between the spot and futures prices. Annualized storage cost = £3/tonne/month * 12 months = £36/tonne Annualized interest cost on £400 spot price = 5% * £400 = £20/tonne Total cost of carry (excluding convenience yield) = £36 + £20 = £56/tonne The producer is offered a futures contract at £440/tonne. The difference between the futures price and the spot price is £440 – £400 = £40/tonne. Since the cost of carry (£56/tonne) is greater than the futures premium (£40/tonne), the market is in contango, but the contango is not fully reflecting the cost of carry. This means the convenience yield is playing a significant role. If the producer hedges using futures, they lock in a price of £440/tonne, but they also incur storage and financing costs. Given the specific storage constraints (limited to 6 months), the producer should consider selling forward contracts for the maximum storage period. This allows them to capture some of the contango premium while mitigating the risk of holding the physical commodity for longer than their storage capacity allows. The calculation is: Annualized Storage Cost: \( 3 \frac{GBP}{tonne \cdot month} \times 12 \frac{months}{year} = 36 \frac{GBP}{tonne \cdot year} \) Annualized Interest Cost: \( 0.05 \times 400 \frac{GBP}{tonne} = 20 \frac{GBP}{tonne \cdot year} \) Total Cost of Carry (excluding convenience yield): \( 36 + 20 = 56 \frac{GBP}{tonne \cdot year} \) Futures Premium: \( 440 \frac{GBP}{tonne} – 400 \frac{GBP}{tonne} = 40 \frac{GBP}{tonne} \) Since the cost of carry exceeds the futures premium, the market is in contango, but not fully reflecting storage and interest costs.

Let’s analyze the scenario of a commodity trading firm, “AgriCorp,” navigating the complexities of hedging their future wheat production using options on futures contracts within the UK regulatory framework. AgriCorp anticipates harvesting 50,000 tonnes of wheat in six months. To mitigate potential price declines, they decide to purchase put options on wheat futures contracts. Each contract represents 100 tonnes of wheat. The current wheat futures price for delivery in six months is £200 per tonne. AgriCorp buys 500 put options with a strike price of £190 per tonne, paying a premium of £5 per tonne. Now, consider two scenarios at the expiration of the options: Scenario 1: The wheat futures price drops to £170 per tonne. In this case, AgriCorp exercises their put options. For each tonne covered by the options, they gain £(190 – 170) = £20. However, they initially paid a premium of £5 per tonne. Therefore, the net profit per tonne is £(20 – 5) = £15. Across all 50,000 tonnes (500 contracts * 100 tonnes/contract), the total profit is 50,000 * £15 = £750,000. If they hadn’t hedged, they would have received £170 per tonne, but with hedging, they effectively receive £170 + £15 = £185 per tonne. Scenario 2: The wheat futures price rises to £220 per tonne. In this scenario, AgriCorp will not exercise their put options because the market price is higher than the strike price. They let the options expire worthless. Their loss is limited to the premium paid, which is £5 per tonne. Across all 50,000 tonnes, the total loss is 50,000 * £5 = £250,000. Without hedging, they would have received £220 per tonne. With hedging, they effectively receive £220 – £5 = £215 per tonne. The key here is understanding that options provide downside protection while allowing AgriCorp to benefit from potential price increases, albeit with a reduced profit margin due to the premium paid. This strategy aligns with the risk management objectives outlined by UK regulations for commodity derivatives trading, specifically those related to hedging and price risk mitigation. Firms like AgriCorp must demonstrate that their hedging strategies are proportionate to their underlying commercial activities and contribute to the orderly functioning of the market, as overseen by the FCA.

To determine the impact of backwardation on a cocoa producer’s hedging strategy, we need to consider how the futures price changes over time and how this affects the producer’s realized price. Backwardation implies that futures prices are lower than expected spot prices at the time of delivery. This benefits producers who sell futures contracts because they can lock in a higher price than what the futures market currently indicates for future delivery. First, calculate the implied forward price based on the spot price and the cost of carry. The cost of carry includes storage, insurance, and financing costs. Then, compare this implied forward price with the actual futures price to determine the extent of backwardation. The difference between the two is the backwardation premium. Next, consider the cocoa producer’s hedging strategy. If the producer sells futures contracts to hedge their production, they benefit from backwardation because they can sell the futures contracts at a higher price than the expected spot price at delivery. However, as the contract approaches expiration, the futures price converges to the spot price. If the market remains in backwardation, the producer can roll their hedge forward by selling the expiring contract and buying a new contract with a later expiration date. This allows them to continue to benefit from the backwardation premium. In this scenario, the producer initially sells futures at £2,600 per tonne. Over the next six months, the spot price rises to £2,700 per tonne, but the futures price only rises to £2,650 per tonne. This means the producer benefits from the initial backwardation, but the benefit is partially offset by the increase in the futures price. To calculate the net effect, we need to consider the initial hedge price, the final futures price, and the spot price at delivery. The producer’s effective selling price is the initial hedge price plus the difference between the spot price and the final futures price. In this case, the effective selling price is £2,600 + (£2,700 – £2,650) = £2,650 per tonne. However, the question states that the cocoa producer rolls over the contract. This means that when the initial contract expires, they close it out at £2,650 and immediately sell a new futures contract expiring in six months. We need to know the price of this new contract to calculate the overall impact. Assume the new contract is sold at £2,700 per tonne. The initial contract gives them £2,600. They lose £50 when closing it out (£2,650 – £2,600). Then they sell the new contract at £2,700. Their effective price is therefore £2,600 – £50 + £2,700 = £5,250. However, this is for two contracts. So, per tonne, it’s £2,625. The backwardation benefited the producer by allowing them to initially lock in a higher price. The subsequent rise in the futures price partially offset this benefit, but the rollover allowed them to capture additional value if the market remained in backwardation or moved towards contango.

The core of this question lies in understanding how the margin requirements for commodity futures contracts are calculated and how they are impacted by price fluctuations and the exchange’s rules. The initial margin is the amount required to open a futures position, while the maintenance margin is the level below which the account balance cannot fall. If the account balance falls below the maintenance margin, a margin call is issued, requiring the trader to deposit funds to bring the account back to the initial margin level. In this scenario, we need to track the daily gains and losses and compare the account balance with the maintenance margin. On Day 1, the trader loses £2,000 (10 contracts * £200/contract loss). The account balance becomes £18,000 (£20,000 – £2,000). On Day 2, the trader gains £3,000 (10 contracts * £300/contract gain). The account balance becomes £21,000 (£18,000 + £3,000). On Day 3, the trader loses £4,000 (10 contracts * £400/contract loss). The account balance becomes £17,000 (£21,000 – £4,000). Since the maintenance margin is £17,500, the account balance of £17,000 is below this level. Therefore, a margin call is triggered. The trader needs to deposit enough funds to bring the account balance back to the initial margin level of £20,000. The required deposit is £3,000 (£20,000 – £17,000). This question avoids textbook examples by using a unique scenario with specific price fluctuations and margin levels. It tests the understanding of margin requirements in a dynamic trading environment, rather than simply asking for definitions. It also requires the candidate to track daily changes and apply the margin rules correctly. The plausible incorrect options are designed to trap candidates who might miscalculate the gains/losses or misunderstand the margin call mechanism. For instance, confusing the maintenance margin with the initial margin would lead to an incorrect answer.

The core of this question lies in understanding how storage costs, convenience yield, and interest rates collectively influence the theoretical forward price of a commodity. The formula that governs this relationship is: Forward Price = Spot Price * e^( (Cost of Carry) * Time to Maturity), where Cost of Carry = Storage Costs + Interest Rate – Convenience Yield. In this scenario, calculating the accurate forward price requires careful consideration of each component. First, we must compute the total storage costs over the forward contract’s duration. Since storage costs are £3/tonne per quarter, and the contract lasts for 9 months (3 quarters), the total storage cost is £3/tonne/quarter * 3 quarters = £9/tonne. Next, we need to consider the interest rate, which is 5% per annum. Over the 9-month period (0.75 years), the interest accrual factor is e^(0.05 * 0.75) = e^(0.0375) ≈ 1.0382. This factor represents the growth in value due to interest. The convenience yield, reflecting the benefit of holding the physical commodity, is given as 2% per annum. Over the 9-month period, the convenience yield factor is e^(-0.02 * 0.75) = e^(-0.015) ≈ 0.9851. Note the negative sign, as convenience yield reduces the forward price. Combining these factors, the forward price calculation becomes: Forward Price = £450/tonne * e^( (0.05 – 0.02) * 0.75 ) + £9/tonne * e^(0.05*0.75). This simplifies to: Forward Price = £450/tonne * e^(0.03*0.75) + £9/tonne * e^(0.0375) Forward Price = £450/tonne * e^(0.0225) + £9/tonne * e^(0.0375) Forward Price ≈ £450/tonne * 1.02275 + £9/tonne * 1.0382 Forward Price ≈ £460.24/tonne + £9.34/tonne = £469.58/tonne Therefore, the theoretical forward price is approximately £469.58/tonne. The plausible but incorrect options are designed to trap candidates who may miscalculate storage costs, incorrectly apply the interest rate or convenience yield, or fail to consider the time value of money appropriately. For example, one incorrect option might omit the convenience yield entirely, while another might add the storage cost directly to the spot price without considering the interest rate effect. The key is to understand the interplay between these factors in determining the forward price.

The question revolves around understanding the impact of storage costs, convenience yield, and interest rates on commodity futures prices, particularly in the context of contango and backwardation. The formula \(F = S \cdot e^{(r+u-c)T}\) (where F is the futures price, S is the spot price, r is the risk-free interest rate, u is the storage cost, c is the convenience yield, and T is the time to maturity) captures this relationship. The scenario introduces a blend of these factors, requiring the candidate to assess how a change in storage costs, coupled with a pre-existing convenience yield and interest rate environment, affects the futures price and market sentiment. To solve this, we first calculate the initial futures price using the given spot price, interest rate, storage cost, and convenience yield. Then, we adjust the storage cost and recalculate the futures price. The difference between the two futures prices reveals the impact of the storage cost change. Finally, we assess whether the change has shifted the market from contango to backwardation or vice versa. Initial Futures Price: \(F_1 = 80 \cdot e^{(0.05 + 0.02 – 0.03) \cdot 0.5} = 80 \cdot e^{(0.04) \cdot 0.5} = 80 \cdot e^{0.02} \approx 80 \cdot 1.0202 = 81.616\) New Futures Price (Storage cost increases by 1%): \(F_2 = 80 \cdot e^{(0.05 + 0.03 – 0.03) \cdot 0.5} = 80 \cdot e^{(0.05) \cdot 0.5} = 80 \cdot e^{0.025} \approx 80 \cdot 1.0253 = 82.024\) Change in Futures Price: \(F_2 – F_1 = 82.024 – 81.616 = 0.408\) Initial Market Condition: The initial futures price ($81.62) is higher than the spot price ($80), indicating contango. New Market Condition: The new futures price ($82.02) is still higher than the spot price ($80), indicating that the market remains in contango, although the contango has widened slightly. Therefore, the futures price increases by approximately $0.41, and the market remains in contango. A crucial aspect of this question is understanding convenience yield. This represents the benefit of holding the physical commodity rather than a futures contract. For example, a refinery might be willing to pay a premium to have crude oil on hand to ensure continuous operation, even if the futures price suggests it’s cheaper to buy it later. Similarly, a power plant might value having coal stockpiled to avoid disruptions during peak demand, even if futures prices indicate a lower cost in the future. The relationship between storage costs, interest rates, and convenience yield dictates the shape of the futures curve. When storage costs and interest rates outweigh convenience yield, the market is in contango (futures price higher than spot price). Conversely, when convenience yield outweighs storage costs and interest rates, the market is in backwardation (futures price lower than spot price). The change in storage costs in this scenario directly impacts this balance, influencing the futures price and the degree of contango or backwardation.

The core of this question lies in understanding how a commodity swap, specifically a fixed-for-floating swap, operates and how changes in the floating rate (in this case, the Brent Crude oil spot price) affect the net cash flows between the parties involved. The key is to calculate the difference between the fixed price and the average floating price over the swap’s period and then apply that difference to the notional amount. First, calculate the average floating price: (\(78 + 82 + 85 + 80\))/4 = \(81.25. Next, determine the difference between the fixed price and the average floating price: \(83 – 81.25 = 1.75. Finally, calculate the net cash flow: \(1.75 * 5000 = 8750. Since the fixed price payer (the airline) is paying a higher fixed price than the average floating price, they will receive a net payment. Therefore, the airline will receive a net payment of £8,750. This scenario highlights a practical application of commodity swaps in risk management. Airlines, heavily reliant on jet fuel (derived from crude oil), often use swaps to hedge against price volatility. By entering a fixed-for-floating swap, they can lock in a fixed price for their fuel, providing budget certainty. However, if the average spot price of oil falls below the fixed price, the airline receives a payment, offsetting some of their fuel costs. Conversely, if the spot price rises above the fixed price, they make a payment, but this is offset by the fact that they are buying fuel at a higher market price. Consider an alternative scenario: A small oil exploration company uses a commodity swap to ensure a stable income stream. They agree to receive a floating price based on the West Texas Intermediate (WTI) crude oil index and pay a fixed price. This strategy allows them to participate in potential upside if WTI prices rise, while also providing a guaranteed minimum revenue if prices fall. The notional amount of the swap is directly tied to their expected oil production volume. This example illustrates how swaps can be used not just for hedging, but also for managing revenue streams in commodity-dependent businesses. Another important concept is the role of clearinghouses in commodity derivatives markets. Clearinghouses act as intermediaries, guaranteeing the performance of swap contracts. This reduces counterparty risk, making the market more efficient and accessible. Clearinghouses also require participants to post margin, which is a form of collateral that protects against potential losses. The level of margin required depends on the volatility of the underlying commodity and the size of the position. Understanding these institutional details is crucial for navigating the complexities of commodity derivatives trading.

The core of this question lies in understanding how basis risk arises in hedging strategies, particularly when the commodity being hedged and the commodity underlying the futures contract are not perfectly correlated. Basis is defined as the difference between the spot price of an asset and the price of its related futures contract. Basis risk arises because this difference is not constant and can change unpredictably over time. The formula to calculate the hedge ratio when minimizing variance is: Hedge Ratio = Correlation * (σ_spot / σ_futures), where σ represents the standard deviation. In this scenario, we’re given the correlation (0.8), the spot price volatility (20%), and the futures price volatility (25%). Therefore, the optimal hedge ratio is 0.8 * (0.20 / 0.25) = 0.64. The hedge effectiveness is measured by the R-squared (R²) value, which represents the proportion of variance in the spot price that is explained by the variance in the futures price. R² is the square of the correlation coefficient, so in this case, R² = (0.8)^2 = 0.64. This means that 64% of the spot price variance is explained by the futures price variance, leaving 36% unexplained, which represents the basis risk. Now, let’s calculate the expected outcome. The company sells 1000 tonnes of cocoa beans at £2500/tonne. They hedge using the calculated hedge ratio of 0.64. This means they short 640 futures contracts (0.64 * 1000). The spot price decreases by 5%, so the loss on the physical cocoa beans is 1000 * £2500 * 0.05 = £125,000. The futures price decreases by 8%, so the gain on the futures contracts is 640 * £2500 * 0.08 = £128,000. The net outcome is the gain on the futures contracts minus the loss on the physical cocoa beans: £128,000 – £125,000 = £3,000 profit. This question requires a deep understanding of basis risk, hedge ratio calculation, hedge effectiveness, and the ability to apply these concepts in a practical hedging scenario. The example of a cocoa bean processor adds realism and relevance to the problem.

The core of this question lies in understanding how a refinery’s profitability is affected by price volatility in both crude oil (input) and refined products (output), and how derivatives can mitigate this risk. A refinery profits from the “crack spread,” which is the difference between the value of the refined products (like gasoline and heating oil) and the cost of the crude oil used to produce them. A refining company can hedge crack spread risk using derivatives. The crack spread is calculated as the difference between the value of the refined products and the cost of the crude oil. In this case, the crack spread is calculated as (3 * Gasoline Price + 2 * Heating Oil Price) – 5 * Crude Oil Price. Currently, the crack spread is (3 * $90) + (2 * $85) – (5 * $60) = $270 + $170 – $300 = $140. The refinery wants to lock in this crack spread using futures contracts. They will buy crude oil futures and sell gasoline and heating oil futures. The change in the crack spread based on the futures prices is (3 * Change in Gasoline Futures) + (2 * Change in Heating Oil Futures) – (5 * Change in Crude Oil Futures). This equals (3 * ($92 – $90)) + (2 * ($83 – $85)) – (5 * ($62 – $60)) = (3 * $2) + (2 * -$2) – (5 * $2) = $6 – $4 – $10 = -$8. The hedged crack spread is the current crack spread plus the change in the crack spread due to the futures contracts. Hedged Crack Spread = Current Crack Spread + Change in Crack Spread = $140 – $8 = $132. The refinery’s hedged crack spread, using futures contracts, is $132. This represents the locked-in profit margin for each “barrel” of crude processed, protecting the refinery from adverse price movements in crude oil and refined product markets. The refinery is locking in the crack spread by buying crude oil futures and selling gasoline and heating oil futures. This strategy is designed to protect the refinery’s profit margin from fluctuations in the prices of crude oil and refined products.

The core of this problem lies in understanding how backwardation and contango influence hedging strategies, particularly when using futures contracts. Backwardation, where the spot price is higher than the futures price, presents a unique advantage for hedgers selling futures, as they lock in a price higher than what the market currently anticipates for future delivery. Conversely, contango, where futures prices are higher than the spot price, presents a challenge, potentially eroding profits for hedgers. The key is to analyze the difference between the initial futures price at which the hedge is established and the spot price at the time the hedge is lifted. In this scenario, the oil producer initially hedges by selling futures at £85/barrel. Over the hedging period, the market shifts into backwardation. When they lift the hedge, the spot price is £90/barrel, and the corresponding futures price is £88/barrel. The producer sells their physical oil at the spot price of £90. However, they must also close out their futures position by buying back the futures contracts at £88. The profit from the hedge is the difference between the initial selling price of the futures (£85) and the price at which they bought back the futures (£88), resulting in a loss of £3/barrel on the futures contract. This loss partially offsets the gain from selling the physical oil at a higher spot price than initially anticipated. The effective selling price is the spot price (£90) minus the hedge loss (£3), resulting in £87/barrel. Now, consider an alternative scenario: If the market had been in contango, with the spot price at £80 and the futures at £82 when the hedge was lifted, the producer would have bought back the futures at £82, making a profit of £3 on the futures contract (£85 – £82). This profit would be added to the spot price received, effectively increasing the overall selling price. Another crucial aspect is basis risk. Basis risk arises because the futures price and spot price may not converge perfectly at the delivery date. This difference can impact the effectiveness of the hedge. In our case, the basis is the difference between the spot price and the futures price at the time the hedge is lifted (£90 – £88 = £2). This basis risk is already factored into the calculation as the producer is selling at the spot price and closing the future at the future price. Finally, regulatory factors can influence hedging decisions. For example, the UK’s Financial Conduct Authority (FCA) has specific regulations regarding the use of commodity derivatives, including requirements for risk management and reporting. These regulations may affect the types of hedging strategies a company can employ and the overall cost of hedging.

To determine the most suitable hedging strategy, we need to calculate the potential profit or loss under each scenario and consider the company’s risk aversion. The company aims to protect itself against price fluctuations, so we need to compare the outcomes of hedging with futures, options, and forwards, as well as remaining unhedged. The key is to analyze how each strategy performs under both rising and falling price scenarios. * **Unhedged:** The company directly faces the market price. If prices rise, they benefit; if prices fall, they lose. * **Futures:** The company locks in a price. Any price movement is offset by gains or losses in the futures contract. * **Options:** The company buys a put option, providing downside protection while allowing them to benefit from price increases above the strike price. The option premium is a cost. * **Forwards:** Similar to futures, the company locks in a price. However, forwards are typically more customized and involve counterparty risk. Let’s analyze the scenarios: **Scenario 1: Price Rises to £95/tonne** * **Unhedged:** Profit = £95 – £85 = £10/tonne * **Futures:** Locked at £87/tonne, Profit = £87 – £85 = £2/tonne * **Options:** Buys put option at £88/tonne, but price rises above this. Profit = £95 – £85 – £3 = £7/tonne (exercise option?) * **Forwards:** Locked at £86/tonne, Profit = £86 – £85 = £1/tonne **Scenario 2: Price Falls to £75/tonne** * **Unhedged:** Loss = £75 – £85 = -£10/tonne * **Futures:** Locked at £87/tonne, Profit = £87 – £85 = £2/tonne * **Options:** Buys put option at £88/tonne. Exercise option to sell at £88. Net Profit = £88 – £85 – £3 = £0/tonne * **Forwards:** Locked at £86/tonne, Profit = £86 – £85 = £1/tonne The option strategy provides the best protection against downside risk while still allowing some upside potential. The futures and forwards lock in a price, limiting both gains and losses. The unhedged position is the most volatile. Given the company’s risk aversion and the desire to participate in potential price increases, the put option strategy is the most suitable. The futures and forwards strategies are too restrictive, and the unhedged position is too risky. The correct answer is the put option strategy, as it provides downside protection while allowing participation in price increases, balancing risk and potential reward. The company is willing to pay a premium for this flexibility.

The core of this problem lies in understanding how storage costs impact the pricing of commodity futures contracts, particularly when considering contango and backwardation. Contango is a situation where the futures price is higher than the spot price, primarily due to storage costs, insurance, and interest rates (the cost of carry). Backwardation, conversely, is when the futures price is lower than the spot price, often due to immediate demand outweighing future supply. The formula to consider is: Futures Price ≈ Spot Price + Cost of Carry – Convenience Yield. In this scenario, we’re focusing on the cost of carry, which is dominated by storage costs. First, calculate the total storage cost over the 9 months. The storage cost is £2.50 per tonne per month, so for 9 months, it’s 9 * £2.50 = £22.50 per tonne. Next, we must consider the impact of insurance at 2% per annum on the spot price. This annual percentage needs to be converted to the relevant period, 9 months. The insurance cost is (2%/12) * 9 * £450 = £6.75. Then, we must consider the funding cost at 5% per annum on the spot price. This annual percentage needs to be converted to the relevant period, 9 months. The funding cost is (5%/12) * 9 * £450 = £16.875. The cost of carry is then the sum of storage costs, insurance costs, and funding costs: £22.50 + £6.75 + £16.875 = £46.125. Finally, add the cost of carry to the spot price to find the theoretical futures price: £450 + £46.125 = £496.125. Therefore, the theoretical futures price for the copper contract, considering storage costs, insurance, and funding costs, is approximately £496.13 per tonne. This example demonstrates how storage costs are a critical component of commodity futures pricing, especially in markets characterized by contango. It highlights the interplay between spot prices, storage expenses, and financial considerations in determining the fair value of a futures contract. Ignoring any of these factors would lead to a mispriced contract, creating potential arbitrage opportunities.

The question explores the concept of hedging in commodity derivatives using futures contracts, specifically focusing on the impact of basis risk and the need to adjust the hedge ratio. Basis risk arises because the price of the futures contract may not move perfectly in sync with the spot price of the commodity being hedged. The optimal hedge ratio minimizes the variance of the hedged position. The formula for the optimal hedge ratio is: Hedge Ratio = Correlation (Spot Price Change, Futures Price Change) * (Standard Deviation of Spot Price Change / Standard Deviation of Futures Price Change). This is equivalent to the regression coefficient of the spot price change on the futures price change. In this scenario, a coffee roaster wants to hedge their coffee bean inventory against price fluctuations. The coffee roaster needs to determine the optimal number of futures contracts to use to minimize the risk. The problem highlights the importance of understanding the relationship between spot and futures prices and using statistical measures to determine the appropriate hedge ratio. The calculation of the hedge ratio involves using correlation and standard deviations, which are key statistical concepts. The example uses realistic data and a scenario that is relevant to the commodity derivatives market. The hedge ratio calculation is: Hedge Ratio = 0.85 * (0.05 / 0.06) = 0.7083. The number of contracts required is: (Inventory Value / Contract Value) * Hedge Ratio = (1,500,000 / 15,000) * 0.7083 = 70.83. Rounding to the nearest whole number, the coffee roaster should use 71 futures contracts.

The core of this question revolves around understanding how storage costs and convenience yields affect the relationship between spot prices and futures prices in commodity markets, specifically within the context of UK-based commodity trading regulations and practices. The cost of carry model, a fundamental concept in commodity derivatives, dictates that the futures price should reflect the spot price plus the costs of storing the commodity, less any benefits derived from holding the commodity (convenience yield). Let’s consider a simplified scenario. Assume the spot price of Brent Crude oil is $80 per barrel. Storing this oil in a UK-regulated storage facility incurs costs of $2 per barrel per month, encompassing insurance, security, and facility maintenance, all compliant with UK safety and environmental standards. Over a three-month period, these storage costs accumulate to $6 per barrel. Now, if the market anticipates a potential supply disruption due to geopolitical instability in the Middle East (a classic scenario that creates convenience yield), holders of the physical oil might benefit from being able to supply the market immediately, rather than waiting for future delivery. This benefit, the convenience yield, could be valued at $3 per barrel over the three-month period. Therefore, according to the cost of carry model, the theoretical futures price for delivery in three months should be: Futures Price = Spot Price + Storage Costs – Convenience Yield Futures Price = $80 + $6 – $3 = $83 However, the question introduces a twist: the storage facility is located in a designated freeport zone within the UK. These zones offer tax advantages and simplified customs procedures. Suppose these advantages translate into a reduction in effective storage costs. Specifically, imagine the tax benefits reduce the storage costs from $2 per barrel per month to $1.5 per barrel per month. The total storage cost over three months now becomes $4.5 per barrel. The revised futures price calculation becomes: Futures Price = Spot Price + Revised Storage Costs – Convenience Yield Futures Price = $80 + $4.5 – $3 = $81.50 Now, consider the impact of increased volatility due to the geopolitical instability. This heightened uncertainty would likely increase the convenience yield, as the immediate availability of the commodity becomes even more valuable. Let’s assume the convenience yield increases to $5 per barrel. The final futures price calculation is: Futures Price = Spot Price + Revised Storage Costs – Revised Convenience Yield Futures Price = $80 + $4.5 – $5 = $79.50 This demonstrates how changes in storage costs (influenced by factors like freeport zones) and convenience yields (driven by market volatility and supply concerns) dynamically affect the futures price. The question tests the ability to synthesize these elements and calculate the expected futures price, considering the interplay of these factors within a UK-specific regulatory and economic context.

The question assesses the understanding of how margin calls work in commodity futures trading, particularly when a trader holds multiple positions with varying degrees of profitability. The key is to understand that margin calls are based on the net change in the value of all positions combined, not on individual positions in isolation. The initial margin is the amount required to open the position. The maintenance margin is the level below which the account cannot fall. If the account balance falls below the maintenance margin, a margin call is issued to bring the account back up to the initial margin level. In this scenario, the trader has two positions: one in Brent Crude Oil and one in Natural Gas. The Brent Crude Oil position has gained value, while the Natural Gas position has lost value. To calculate the margin call, we need to determine the net change in the account value and compare it to the maintenance margin. 1. **Calculate the gain on the Brent Crude Oil position:** The trader has 2 contracts, and the price increased by $2.50 per barrel. Each contract represents 1,000 barrels. Therefore, the gain is \(2 \text{ contracts} \times 1,000 \text{ barrels/contract} \times \$2.50 \text{/barrel} = \$5,000\). 2. **Calculate the loss on the Natural Gas position:** The trader has 3 contracts, and the price decreased by $0.15 per MMBtu. Each contract represents 10,000 MMBtu. Therefore, the loss is \(3 \text{ contracts} \times 10,000 \text{ MMBtu/contract} \times \$0.15 \text{/MMBtu} = \$4,500\). 3. **Calculate the net change in account value:** The net change is the gain on Brent Crude Oil minus the loss on Natural Gas: \(\$5,000 – \$4,500 = \$500\). 4. **Calculate the account balance after the price changes:** The initial margin was \$18,000, and the net change is \$500. Therefore, the new account balance is \(\$18,000 + \$500 = \$18,500\). 5. **Determine if a margin call is triggered:** The maintenance margin is \$15,000. Since the account balance (\$18,500) is above the maintenance margin, no margin call is triggered. Therefore, the trader does not receive a margin call. The question tests the ability to calculate gains and losses on futures positions, understand the concept of initial and maintenance margins, and determine when a margin call is triggered based on the net change in the value of multiple positions. It uses a realistic scenario with specific contract sizes and price changes to assess practical application of the concepts. The incorrect options are designed to reflect common errors, such as calculating the change in value for only one position or misunderstanding the relationship between initial and maintenance margins.

To determine the most suitable hedging strategy, we need to calculate the potential profit or loss from each option and compare them to the potential profit or loss without hedging. First, calculate the unhedged scenario: If the airline doesn’t hedge and the jet fuel price increases to $110/barrel, their additional cost is ($110 – $100) * 1,000,000 barrels = $10,000,000. Now, let’s analyze each hedging option: * **Option A (Buying Futures):** The airline buys 10,000 futures contracts at $102/barrel. When the price increases to $110/barrel, they make a profit of ($110 – $102) * 1,000,000 barrels = $8,000,000. Net cost: $10,000,000 (increased fuel cost) – $8,000,000 (futures profit) = $2,000,000. * **Option B (Buying Call Options):** The airline buys call options with a strike price of $105/barrel for a premium of $2/barrel. If the price increases to $110/barrel, the intrinsic value of the call option is $110 – $105 = $5/barrel. Profit per barrel: $5 – $2 = $3/barrel. Total profit: $3 * 1,000,000 = $3,000,000. Net cost: $10,000,000 (increased fuel cost) – $3,000,000 (call option profit) = $7,000,000. * **Option C (Entering a Swap):** The airline enters a swap to pay a fixed price of $104/barrel. Their cost is effectively capped at $104/barrel. Additional cost: ($104 – $100) * 1,000,000 barrels = $4,000,000. * **Option D (Buying Put Options):** This option is designed to protect against price decreases, not increases, so it’s not an effective hedge in this scenario. The put options would expire worthless, and the airline would bear the full increased fuel cost of $10,000,000. The premium paid is an additional cost, making it worse than unhedged. Comparing the net costs: * Option A: $2,000,000 * Option B: $7,000,000 * Option C: $4,000,000 * Unhedged: $10,000,000 * Option D: More than $10,000,000 The best hedging strategy in this scenario is Option A, buying futures contracts, as it results in the lowest net cost. The crucial aspect here is understanding how each derivative instrument behaves in response to a price increase. Futures provide a direct hedge, capturing the full upside of the price movement. Call options offer protection above the strike price, but the premium reduces the overall benefit. Swaps effectively fix the price, providing certainty but potentially forgoing gains if prices move favorably. Put options are irrelevant when hedging against price increases. Understanding these nuances is vital for effective risk management in commodity markets.

The core of this question revolves around understanding how backwardation and contango affect hedging strategies using commodity futures, particularly in the context of rolling contracts. The scenario presents a nuanced situation where a chocolate manufacturer must decide on a hedging strategy given their specific operational needs and market expectations. The key is to recognize that in backwardation, rolling futures contracts generate a profit (roll yield) because the expiring contracts are cheaper than the further-dated ones. Conversely, contango results in a loss when rolling contracts. The manufacturer’s expectation of a price decrease introduces another layer of complexity, requiring them to weigh the potential benefits of backwardation against the risk of the underlying commodity price falling. To determine the optimal hedging strategy, we need to consider the expected roll yield (positive in backwardation) and the potential price decrease. The manufacturer needs to lock in a price now to protect against price increases, but they also believe the price will fall. Backwardation helps offset some of the cost of hedging. Let’s analyze the roll yield first. The spot price is £3,000/tonne, and the December futures price is £2,900/tonne. This indicates backwardation. The expected price decrease is 5% of the spot price, which is 0.05 * £3,000 = £150/tonne. Now consider the hedging scenarios: * **Scenario 1: Hedging with December futures and rolling.** The manufacturer buys December futures at £2,900/tonne. If they roll the contract, the roll yield helps offset the initial cost. However, the expected price decrease of £150/tonne will affect the overall profitability. The key is to compare the locked-in price after accounting for the roll yield and the expected price decrease against the unhedged outcome. If the manufacturer doesn’t hedge, they expect to pay £3,000 – £150 = £2,850/tonne in December. If the manufacturer hedges, they pay £2,900/tonne initially. The backwardation helps offset this cost. The question doesn’t provide the exact roll yield, but it’s implicit that the backwardation is not enough to fully offset the initial cost and the expected price decrease, as the correct answer suggests the manufacturer should hedge less than their full exposure. The optimal strategy involves partially hedging to balance price protection with the expectation of lower prices. Therefore, the best strategy is to hedge a portion of their exposure. This allows them to benefit from potentially lower prices while still protecting against significant price increases.

To determine the most suitable hedging strategy, we need to calculate the potential loss from the unhedged exposure and compare it with the costs and benefits of different hedging instruments. In this case, the company faces a risk of rising copper prices. First, calculate the potential loss if copper prices rise by 15%: Current Copper Price: £6,500 per tonne Increase in Price: 15% of £6,500 = 0.15 * £6,500 = £975 New Copper Price: £6,500 + £975 = £7,475 per tonne Total Copper Requirement: 1,000 tonnes Potential Cost Increase: £975/tonne * 1,000 tonnes = £975,000 Now, evaluate each hedging option: a) **Futures Contract:** Number of Contracts: 1,000 tonnes / 25 tonnes/contract = 40 contracts Initial Margin: 40 contracts * £2,000/contract = £80,000 Commission: 40 contracts * £50/contract = £2,000 Total Cost: £80,000 + £2,000 = £82,000 The futures contract locks in the current price, protecting against the price increase. Therefore, the hedging cost is the initial margin and commission, which is £82,000. b) **Call Option:** Premium: £200/tonne * 1,000 tonnes = £200,000 Strike Price: £6,700 per tonne Potential Payoff: If the price rises to £7,475, the payoff is (£7,475 – £6,700) * 1,000 tonnes = £775,000 Net Cost: £200,000 (premium) – £775,000 (payoff) = -£575,000 (net gain) However, since the question asks for the hedging cost, we consider only the premium paid, which is £200,000. c) **Swap:** Fixed Price: £6,600 per tonne Floating Price Increase: £7,475 – £6,500 = £975 Net Payment: (£6,600 – £7,475) * 1,000 tonnes = -£875,000 (net receipt) Again, we consider the fixed price in the swap agreement as the hedging cost, which is the difference between the fixed price and the current spot price. The cost is (£6,600 – £6,500) * 1,000 = £100,000 d) **Forward Contract:** Forward Price: £6,550 per tonne Cost: (£6,550 – £6,500) * 1,000 tonnes = £50,000 Comparing the hedging costs: – Futures: £82,000 – Call Option: £200,000 – Swap: £100,000 – Forward: £50,000 The forward contract has the lowest hedging cost at £50,000. This strategy involves locking in a price of £6,550 per tonne, mitigating the risk of a price increase. The company agrees to purchase copper at this price in three months, regardless of the spot price at that time. This provides certainty and protects against potential losses if the spot price rises above £6,550. For example, if the spot price rises to £7,000, the company still pays only £6,550, saving £450 per tonne.