Commodity Derivatives Quiz Exam Quiz 38

The core of this question lies in understanding how the contango/backwardation structure of commodity futures impacts hedging decisions, specifically for a producer facing regulatory constraints on their hedging activities. The company’s storage capacity acts as a key constraint, influencing their decision on which futures contract to use for hedging. Let’s analyze each contract month: * **November 2024:** Price = £85/tonne * **December 2024:** Price = £90/tonne * **January 2025:** Price = £96/tonne The market is in contango (future prices are higher than spot/near-term prices). The company needs to decide whether to hedge using the November, December, or January contract, considering they can only store the grain until the end of December. If they hedge with the November contract, they can deliver the grain against the futures contract. However, this means they must harvest, dry, and deliver the grain in November. If they hedge with the December contract, they can deliver the grain against the futures contract, aligning with their storage capacity. If they hedge with the January contract, they cannot deliver the grain because their storage runs out at the end of December. The company wants to maximize their hedging effectiveness while adhering to storage and regulatory constraints. They cannot use the January contract due to storage limitations. The November contract forces them to deliver earlier than preferred. The December contract aligns with their storage and allows them to hedge at £90/tonne. However, regulatory constraints limit them to hedging only 60% of their anticipated production. The most effective strategy involves using the December contract to hedge 60% of the anticipated production. This is because it allows them to hedge at the best possible price within the constraints.

The core of this question lies in understanding how margin calls work in futures contracts, particularly when multiple contracts are held. A margin call occurs when the equity in a trader’s account falls below the maintenance margin. The trader must then deposit funds to bring the equity back up to the initial margin level. Here’s the step-by-step calculation: 1. **Initial Margin:** The trader holds 50 contracts, each with an initial margin of £2,000. Total initial margin = 50 * £2,000 = £100,000. 2. **Maintenance Margin:** The maintenance margin is £1,500 per contract. Total maintenance margin = 50 * £1,500 = £75,000. 3. **Total Margin Account Value Before Loss:** The trader starts with £100,000 in their margin account. 4. **Loss per Contract:** The price decreases by £6 per tonne, and each contract is for 10 tonnes. Loss per contract = £6/tonne * 10 tonnes = £60. 5. **Total Loss:** With 50 contracts, the total loss = 50 * £60 = £3,000. 6. **Margin Account Value After Loss:** The margin account value after the loss is £100,000 – £3,000 = £97,000. 7. **Margin Call Trigger:** A margin call is triggered when the margin account value falls below the total maintenance margin of £75,000. Since £97,000 > £75,000, no margin call is triggered after the first day. 8. **Second Day Loss:** The price decreases by a further £8 per tonne. Loss per contract = £8/tonne * 10 tonnes = £80. 9. **Total Loss Second Day:** With 50 contracts, the total loss = 50 * £80 = £4,000. 10. **Margin Account Value After Second Day Loss:** The margin account value after the second day’s loss is £97,000 – £4,000 = £93,000. Still above £75,000, so no margin call. 11. **Third Day Loss:** The price decreases by a further £15 per tonne. Loss per contract = £15/tonne * 10 tonnes = £150. 12. **Total Loss Third Day:** With 50 contracts, the total loss = 50 * £150 = £7,500. 13. **Margin Account Value After Third Day Loss:** The margin account value after the third day’s loss is £93,000 – £7,500 = £85,500. Still above £75,000, so no margin call. 14. **Fourth Day Loss:** The price decreases by a further £25 per tonne. Loss per contract = £25/tonne * 10 tonnes = £250. 15. **Total Loss Fourth Day:** With 50 contracts, the total loss = 50 * £250 = £12,500. 16. **Margin Account Value After Fourth Day Loss:** The margin account value after the fourth day’s loss is £85,500 – £12,500 = £73,000. Now below £75,000, so a margin call is triggered. 17. **Margin Call Amount:** The trader must bring the account back up to the initial margin level of £100,000. Margin call amount = £100,000 – £73,000 = £27,000. Therefore, the margin call amount is £27,000. The key here is understanding that margin calls are triggered when the account value dips below the *maintenance* margin, and the call requires topping up the account back to the *initial* margin. Many candidates confuse these two thresholds. Also, it’s crucial to calculate the total loss across all contracts before comparing to the maintenance margin.

The core of this question revolves around understanding the interplay between storage costs, convenience yield, and the resulting impact on forward prices. The formula that ties these elements together is: Forward Price = Spot Price * e^( (Cost of Carry – Convenience Yield) * Time to Maturity). The cost of carry encompasses storage costs, insurance, and financing costs. The convenience yield reflects the benefit of holding the physical commodity, such as avoiding stockouts or profiting from temporary local shortages. In this scenario, the copper mine’s storage costs act as a direct component of the cost of carry, pushing the forward price upwards. Conversely, the strategic advantage of readily available copper to fulfil immediate orders translates into a convenience yield, which exerts downward pressure on the forward price. The question is designed to test how these opposing forces interact to determine the equilibrium forward price. To solve this, we first calculate the total cost of carry. The storage cost is £5/tonne per month, which translates to £60/tonne per year. The annual financing cost is 5% of the spot price, which is 0.05 * £8,000 = £400/tonne. Therefore, the total cost of carry is £60 + £400 = £460/tonne per year. Next, we consider the convenience yield, which is estimated at 3% of the spot price, or 0.03 * £8,000 = £240/tonne per year. The net cost of carry is the total cost of carry minus the convenience yield: £460 – £240 = £220/tonne per year. Now we can calculate the forward price using the formula: Forward Price = Spot Price * e^( (Cost of Carry – Convenience Yield) * Time to Maturity). The time to maturity is 6 months, or 0.5 years. Forward Price = £8,000 * e^( (£220/£8,000) * 0.5) = £8,000 * e^(0.0275 * 0.5) = £8,000 * e^(0.01375) ≈ £8,000 * 1.01384 ≈ £8,110.72 The closest answer to this calculated forward price is £8,110. The distractors are crafted to reflect common errors. For instance, one distractor might only account for storage costs and not the financing costs, or it might incorrectly apply the convenience yield. Another distractor might use simple interest instead of continuous compounding.

The core of this question lies in understanding how the interplay of storage costs, convenience yield, and interest rates shapes the relationship between spot and futures prices in commodity markets. The formula \(F = S \cdot e^{(r + u – y)T}\) is a continuous compounding adaptation of the cost-of-carry model, where: * \(F\) is the futures price. * \(S\) is the spot price. * \(r\) is the risk-free interest rate. * \(u\) is the storage cost per unit of commodity, expressed as a percentage of the spot price. * \(y\) is the convenience yield, reflecting the benefit of holding the physical commodity. * \(T\) is the time to maturity of the futures contract, expressed in years. The exponential function \(e^{(r + u – y)T}\) represents the cost of carry factor. A higher interest rate or storage cost increases the futures price relative to the spot price, leading to contango. Conversely, a higher convenience yield decreases the futures price, potentially leading to backwardation. In this scenario, we need to isolate the convenience yield (\(y\)). Rearranging the formula, we get: \[y = r + u – \frac{ln(\frac{F}{S})}{T}\] Plugging in the given values: \[y = 0.05 + 0.02 – \frac{ln(\frac{95}{90})}{0.5}\] \[y = 0.07 – \frac{ln(1.0556)}{0.5}\] \[y = 0.07 – \frac{0.0541}{0.5}\] \[y = 0.07 – 0.1082\] \[y = -0.0382\] Therefore, the convenience yield is -3.82%. A negative convenience yield, while seemingly counterintuitive, can occur when there are significant anticipated future shortages or disruptions that are not fully reflected in current spot prices, leading market participants to accept a lower futures price relative to the spot price. The market anticipates even greater scarcity in the future, making immediate access to the commodity less valuable than its future availability. This might happen if there is a forecast of a major production outage, or a significant increase in demand that is not currently reflected in the spot price.

Let’s analyze the scenario. The core issue revolves around hedging a commodity price risk using futures contracts while simultaneously navigating margin calls and potential contract delivery. The key concept here is understanding how changes in futures prices affect margin accounts and how these changes can impact a hedger’s cash flow. First, we need to calculate the initial margin requirement. It’s given as 8% of the total contract value. The contract value is the futures price multiplied by the contract size: £450/tonne * 100 tonnes = £45,000. The initial margin is 8% of this, which is £45,000 * 0.08 = £3,600. Next, we need to determine the impact of the price decrease on the margin account. The price decreased by £25/tonne, meaning a total loss of £25/tonne * 100 tonnes = £2,500 on the futures contract. This loss will be deducted from the margin account. The remaining margin balance is therefore £3,600 (initial margin) – £2,500 (loss) = £1,100. Now, we compare this remaining balance to the maintenance margin, which is 75% of the initial margin. The maintenance margin is £3,600 * 0.75 = £2,700. Since the remaining margin balance (£1,100) is less than the maintenance margin (£2,700), a margin call will be triggered. The margin call amount is the difference between the initial margin and the current margin balance, which is £3,600 – £1,100 = £2,500. The company must deposit £2,500 to bring the margin account back to the initial margin level. Finally, the decision on whether to take delivery depends on comparing the futures price with the spot price. The company initially hedged at a futures price of £450/tonne. The spot price at delivery is £430/tonne. Since the spot price is lower than the futures price, taking delivery and selling the commodity in the spot market would result in a loss compared to liquidating the futures contract. However, since the company needs the commodity for its manufacturing process, it will take delivery. The effective price paid is the initial futures price of £450/tonne, adjusted for the margin call of £2,500. This translates to an additional cost of £25/tonne (£2,500/100 tonnes). Thus, the effective cost is £450 + £25 = £475/tonne. Therefore, the company faces a margin call of £2,500 and an effective cost of £475 per tonne for the delivered commodity.

Let’s analyze the farmer’s hedging strategy using futures contracts and options. The farmer wants to protect against a potential price decrease in their wheat crop. They sell wheat futures to lock in a price. However, they also buy call options on wheat futures to participate if the price rises significantly. This is a common strategy to provide downside protection while allowing upside potential. First, we need to calculate the profit/loss from the futures contract. The farmer sold the futures at £250/tonne and the price at harvest is £230/tonne. This results in a profit of £20/tonne on the futures contract. Second, we need to calculate the profit/loss from the call option. The farmer bought the call option with a strike price of £240/tonne for a premium of £5/tonne. Since the final price is £230/tonne, the call option expires worthless. The farmer loses the premium of £5/tonne. Finally, we need to calculate the net profit/loss. The profit from the futures contract is £20/tonne, and the loss from the call option is £5/tonne. Therefore, the net profit is £20 – £5 = £15/tonne. The key here is understanding how futures and options interact within a hedging strategy. Futures provide a fixed price, while options provide flexibility. The farmer sacrificed some potential profit by paying the option premium, but they gained the security of a minimum price. The scenario highlights the trade-off between risk mitigation and opportunity cost. Consider this analogy: it’s like buying insurance for your car. You pay a premium, but you are protected if an accident occurs. Similarly, the farmer pays an option premium to protect against a price drop. This approach helps in understanding the practical implications of hedging strategies and their role in risk management. Understanding these concepts is crucial for anyone involved in commodity derivatives trading, particularly within the framework of UK regulations and best practices.

The core of this question lies in understanding how contango and backwardation influence hedging strategies using commodity futures, particularly within the context of UK-based firms and regulations. Contango (futures price > spot price) generally erodes hedging profits for producers, as they effectively sell forward at a discount compared to the expected future spot price. Backwardation (futures price < spot price) typically benefits producers, as they sell forward at a premium. The key is to calculate the expected profit/loss considering the initial futures price, the expected spot price at delivery, and any roll yield implications. Here's the breakdown of the calculation: 1. **Initial Hedge:** The UK-based cocoa producer hedges 500 tonnes of cocoa at £2,000/tonne. This locks in a revenue of 500 tonnes * £2,000/tonne = £1,000,000. 2. **Expected Spot Price:** The producer anticipates selling the cocoa at £2,100/tonne. 3. **Futures Contract Expiry:** The initial futures contract expires, and the producer must roll the hedge forward. 4. **New Futures Price:** The new futures contract is priced at £2,150/tonne. 5. **Roll Yield (Contango):** The producer initially sold futures at £2,000 and now buys them back at £2,150. This results in a loss of £150/tonne. 6. **Total Loss from Roll:** The total loss from rolling the hedge is 500 tonnes * £150/tonne = £75,000. 7. **Effective Selling Price:** The producer effectively sold the cocoa at £2,000/tonne (initial hedge) but incurred a roll loss of £150/tonne. The effective selling price is £2,000 – £150 = £1,850/tonne. 8. **Total Revenue:** The total revenue received is 500 tonnes * £1,850/tonne = £925,000. 9. **Profit/Loss Compared to Spot:** The producer sold for £925,000 but could have sold for 500 tonnes * £2,100/tonne = £1,050,000 on the spot market. 10. **Net Loss Due to Hedge:** The net loss due to the hedge is £1,050,000 – £925,000 = £125,000. The producer experienced a loss of £125,000 due to the contango market structure and the need to roll the futures contract. This illustrates a crucial point: hedging in contango markets can erode profits if the spot price rises less than the futures price increase. The scenario highlights the importance of understanding market dynamics and their impact on hedging effectiveness, especially for UK firms operating under specific regulatory frameworks that might influence hedging strategies and risk management practices. Furthermore, the example showcases the real-world implications of roll yield, a factor often overlooked in simplified explanations of hedging. The producer's decision to hedge, while intended to mitigate risk, ultimately resulted in a significant financial loss due to the unfavorable market conditions.

The core of this question revolves around understanding the impact of contango and backwardation on hedging strategies using commodity futures, specifically within the context of a UK-based agricultural cooperative and the relevant regulatory environment. The cooperative’s exposure to price volatility in wheat necessitates a robust hedging strategy. The question tests the candidate’s ability to analyze the interplay between market conditions (contango vs. backwardation), storage costs, and the regulatory requirements under MiFID II, particularly regarding position limits and reporting obligations for commodity derivatives. Let’s analyze each option: * **Option a (Correct):** This option correctly identifies the optimal strategy and explains why. When the market is in contango, the futures price is higher than the spot price, reflecting storage costs and other factors. “Rolling” the hedge by selling the expiring contract and buying a contract further out leads to a “negative roll yield” (loss). However, this is partially offset by the fact that the cooperative locks in a higher selling price for their wheat, and by the convenience yield, which is the benefit the cooperative receives from holding the physical wheat. The cooperative’s decision must also consider MiFID II position limits. If the cooperative is approaching or exceeding these limits, they might need to reduce their hedge or explore alternative hedging strategies. * **Option b (Incorrect):** This option incorrectly assumes that backwardation is always preferable for hedgers. While backwardation can lead to a positive roll yield, it does not inherently guarantee a better outcome. The cooperative still needs to consider storage costs, the convenience yield, and regulatory requirements. The suggestion to aggressively increase the hedge without considering position limits is also a flawed strategy. * **Option c (Incorrect):** This option misunderstands the impact of contango on hedging. In contango, the cooperative is essentially locking in a higher selling price for their wheat in the future. While the roll yield is negative, this does not automatically negate the benefits of hedging. The option also incorrectly suggests that the cooperative should avoid hedging altogether, which exposes them to significant price risk. * **Option d (Incorrect):** This option focuses solely on the negative roll yield in contango and ignores the other factors that influence the hedging decision. The statement that the cooperative should switch to options without considering the costs and complexities of options strategies is also a flawed recommendation. The option also fails to address the regulatory aspects of commodity derivatives trading.

The question assesses the understanding of how different hedging strategies perform under varying market conditions, specifically focusing on the impact of basis risk. Basis risk arises because the price of the futures contract and the spot price of the commodity may not move perfectly in tandem. A short hedge involves selling a futures contract to protect against a decline in the value of an asset one owns. The effectiveness of a short hedge depends on the relationship between the spot price at the time of liquidation and the futures price at the time of the initial hedge and liquidation. The formula to calculate the effective price received is: Effective Price = Spot Price at Liquidation + (Initial Futures Price – Futures Price at Liquidation). The change in basis is Initial Basis – Final Basis. In this scenario, the farmer initially expected to sell wheat for £250/tonne. They short hedge by selling futures at £260/tonne. If at liquidation, the spot price is £240/tonne and the futures price is £245/tonne, the effective price is calculated as: Effective Price = £240 + (£260 – £245) = £240 + £15 = £255/tonne. Now, let’s consider a situation where the basis strengthens more than anticipated. Initially, the basis was £260 – £250 = £10. At liquidation, the basis is £245 – £240 = £5. The basis strengthened by £5. The question asks what happens if the basis strengthens *more* than anticipated. Let’s assume the farmer anticipated the basis strengthening by £3 (meaning they expected the final basis to be £7). However, the basis strengthened by £5. This means the spot price declined less than the futures price, benefiting the hedger. The farmer receives an effective price of £255/tonne. If the basis had strengthened by only £3 (as anticipated), the final futures price would have been £243 (instead of £245), resulting in an effective price of £240 + (£260 – £243) = £257. Thus, the farmer is worse off when the basis strengthens *less* than anticipated. If the basis had weakened, say to £15 (futures price at liquidation is £255), the effective price would be £240 + (£260 – £255) = £245. In this case, the farmer would be worse off than when the basis strengthened.

The question revolves around the concept of hedging with commodity futures, specifically focusing on the implications of basis risk and imperfect correlation between the asset being hedged and the futures contract. Basis risk arises because the spot price of the commodity being hedged and the futures price of the hedging instrument are not perfectly correlated. This difference is known as the basis, calculated as Spot Price – Futures Price. Changes in the basis during the hedging period can lead to the hedge being more or less effective than anticipated. In this scenario, the coffee roaster is hedging their future coffee bean purchases using cocoa futures. The imperfect correlation between coffee and cocoa prices introduces basis risk. To determine the effectiveness of the hedge, we need to calculate the profit or loss from the futures position and compare it to the change in the spot price of the coffee beans. The roaster bought coffee beans at £1.60/lb and hedged using cocoa futures at £2.50/lb. At the end of the hedging period, coffee beans cost £1.85/lb, and the cocoa futures settled at £2.65/lb. The loss on the coffee beans is £1.85 – £1.60 = £0.25/lb. The profit on the cocoa futures is £2.65 – £2.50 = £0.15/lb. The net outcome is a loss of £0.25/lb offset by a profit of £0.15/lb, resulting in a net loss of £0.10/lb. The hedge was not fully effective due to the imperfect correlation between coffee and cocoa prices. The concept of “cross-hedging” is particularly relevant here. Cross-hedging involves using a futures contract on a different, but related, commodity to hedge the price risk of the target commodity. It is used when a futures contract on the target commodity is not available or is illiquid. While it can offer some protection, it inherently introduces basis risk due to the imperfect correlation between the prices of the two commodities. In this example, the roaster is cross-hedging coffee beans with cocoa futures. The roaster should be aware of the potential for basis risk to erode the effectiveness of the hedge.

The question revolves around the concept of basis risk in commodity futures trading, particularly within the context of hedging. Basis risk arises because the price of a futures contract may not perfectly correlate with the spot price of the underlying commodity at the time of delivery. This discrepancy can occur due to factors like storage costs, transportation logistics, local supply and demand imbalances, and differences in quality specifications between the commodity specified in the futures contract and the commodity being hedged. In this scenario, a coffee roaster in London is hedging their future coffee bean purchases using a futures contract traded on the ICE Futures Europe exchange. However, the coffee beans specified in the futures contract are of a different origin and grade than the beans the roaster typically uses. This difference in quality and origin introduces basis risk. To determine the effective price the roaster pays for the coffee beans, we need to consider the futures price, the initial basis, and the final basis. The initial basis is the difference between the spot price of the roaster’s preferred coffee beans and the futures price at the time the hedge is established. The final basis is the difference between the spot price of the roaster’s preferred coffee beans and the futures price at the time the hedge is lifted (i.e., when the roaster buys the coffee beans in the spot market and closes out the futures position). The effective price is calculated as follows: Effective Price = Futures Price at Hedge Initiation + (Final Basis – Initial Basis) In this case: Futures Price at Hedge Initiation = £2,000 per tonne Initial Basis = Spot Price – Futures Price = £2,100 – £2,000 = £100 per tonne Final Basis = Spot Price – Futures Price = £2,250 – £2,100 = £150 per tonne Effective Price = £2,000 + (£150 – £100) = £2,050 per tonne Therefore, the roaster effectively pays £2,050 per tonne for the coffee beans, taking into account the changes in the basis. This example highlights the importance of understanding and managing basis risk when using commodity futures for hedging. Even with a hedge in place, the roaster is still exposed to the risk that the basis will change, affecting the final cost of the coffee beans. The roaster could explore basis trading strategies to mitigate this risk further, such as actively managing their futures positions based on anticipated changes in the basis.

To determine the most suitable hedging strategy for the airline, we need to calculate the potential cost exposure with and without hedging using futures contracts. The airline faces the risk of rising jet fuel prices. Hedging with futures aims to lock in a price and mitigate this risk. First, calculate the airline’s total jet fuel requirement: 10 million gallons/month * 3 months = 30 million gallons. Next, determine the number of futures contracts needed: 30 million gallons / 42,000 gallons/contract ≈ 714.29 contracts. Since you can’t trade fractions of contracts, the airline would likely use 714 contracts. Now, consider the unhedged scenario. If the spot price rises to $3.20/gallon, the total cost will be 30 million gallons * $3.20/gallon = $96 million. In the hedged scenario, the airline buys 714 contracts at $2.85/gallon. When the spot price rises to $3.20/gallon, the airline loses on the futures contracts because they are short futures. The profit/loss on the futures is calculated as follows: (Spot price – Futures price) * Contract size * Number of contracts = ($3.20 – $2.85) * 42,000 * 714 = $10,710,000 profit. The effective cost for the hedged scenario is the cost of the jet fuel at the spot price minus the profit from the futures contracts: $96,000,000 – $10,710,000 = $85,290,000. Therefore, the airline can reduce its cost exposure by hedging with futures contracts. To further illustrate, imagine a small bakery that uses wheat flour. The baker is concerned about rising wheat prices. They could buy wheat futures to lock in a price. If wheat prices rise, they will pay more for flour in the spot market, but they will profit from their futures contracts, offsetting some of the increased cost. Conversely, if wheat prices fall, they will pay less for flour but lose money on their futures. The goal is to reduce uncertainty and stabilize costs. This is especially important in industries like airlines where fuel is a major expense.

To determine the fair value of the copper forward contract, we need to calculate the future value of the spot price, adjusted for storage costs and financing costs (interest), and then subtract any convenience yield. The formula is: Forward Price = (Spot Price + Storage Costs) * (1 + Interest Rate) – Convenience Yield First, calculate the total storage costs: £5/tonne/month * 6 months = £30/tonne. Next, calculate the future value of the spot price plus storage costs: (£7,500 + £30) * (1 + 0.05) = £7,530 * 1.05 = £7,906.50/tonne. Finally, subtract the convenience yield: £7,906.50 – £150 = £7,756.50/tonne. Therefore, the fair value of the six-month copper forward contract is £7,756.50 per tonne. The convenience yield represents the benefit of holding the physical commodity rather than the forward contract. It reflects the market’s expectation of potential shortages or disruptions in supply. In this scenario, the convenience yield reduces the forward price because market participants are willing to accept a lower price for the forward contract in exchange for the security of holding the physical copper. Storage costs increase the forward price, as they represent an additional cost incurred by holding the physical commodity. The interest rate also increases the forward price, as it reflects the cost of financing the purchase of the commodity. The spot price is the current market price of the commodity, and it forms the basis for calculating the forward price. Understanding these factors is crucial for accurately pricing and trading commodity derivatives. Failing to account for convenience yield, for instance, could lead to significant mispricing of the forward contract.

Let’s analyze the scenario. The key is understanding how backwardation and contango affect the decision to store a commodity like heating oil, and how a refiner might use derivatives to manage price risk associated with that storage. The refiner has a short-term storage opportunity. The backwardation structure means futures prices are lower than the spot price, incentivizing immediate sale rather than storage. The refiner needs to calculate the potential profit from storing the oil, considering storage costs, the change in price from spot to the futures contract maturity, and the cost of hedging that position with a futures contract. The profit from storage is calculated as the futures price at maturity minus the spot price at the start, minus the storage costs. The refiner can lock in a price by selling a futures contract. If the futures price rises, the refiner loses on the hedge but gains on the value of the physical commodity. If the futures price falls, the refiner gains on the hedge but loses on the value of the physical commodity. In this case, the refiner needs to decide whether the backwardation is so steep that it outweighs the potential profit from storage, even after hedging. The refiner buys 10,000 barrels of heating oil at a spot price of £80 per barrel. The 1-month futures price is £78 per barrel. Storage costs are £1 per barrel per month. The refiner hedges their position by selling 10 futures contracts, each covering 1,000 barrels. The refiner’s initial cost is £80 * 10,000 = £800,000. The refiner sells 10 futures contracts at £78, locking in revenue of £78 * 10,000 = £780,000. Storage costs are £1 * 10,000 = £10,000. Total cost = £800,000 + £10,000 = £810,000. The profit/loss is calculated as the revenue from the futures contracts minus the total cost. Profit/Loss = £780,000 – £810,000 = -£30,000. The refiner incurs a loss of £30,000. Therefore, the refiner should not store the heating oil.

The core of this question lies in understanding how storage costs impact the price of a commodity futures contract. The futures price should reflect the spot price plus the cost of carrying the commodity to the delivery date. This cost includes storage, insurance, and financing. However, if there’s a convenience yield (benefit from holding the physical commodity), it reduces the effective cost of carry. The formula to determine the theoretical futures price is: Futures Price = Spot Price + Cost of Carry – Convenience Yield. In this scenario, we need to calculate the total cost of carry by summing the storage costs and financing costs, then subtract the convenience yield to arrive at the net cost of carry. Adding this net cost to the spot price gives us the theoretical futures price. The annual storage cost is £5 per tonne, and since the contract is for 6 months, the storage cost for the contract duration is £5/tonne * 0.5 years = £2.5/tonne. The financing cost is the spot price multiplied by the risk-free interest rate and the time to maturity: £500/tonne * 0.04 * 0.5 = £10/tonne. The total cost of carry is £2.5/tonne + £10/tonne = £12.5/tonne. Subtracting the convenience yield, the net cost of carry is £12.5/tonne – £5/tonne = £7.5/tonne. Adding this to the spot price gives the theoretical futures price: £500/tonne + £7.5/tonne = £507.5/tonne. The exchange-quoted futures price of £505/tonne is lower than the theoretical price. This suggests an arbitrage opportunity: buy the futures contract and sell the spot commodity, locking in a profit. However, we need to consider transaction costs. The transaction cost for buying the futures contract is £1/tonne, and for selling the spot commodity is £1.25/tonne. Total transaction costs are £2.25/tonne. The profit from the arbitrage is the difference between the theoretical futures price and the exchange-quoted price, minus transaction costs: (£507.5 – £505) – £2.25 = £2.5 – £2.25 = £0.25 per tonne.

To solve this problem, we need to understand how changes in convenience yield affect the price of a commodity futures contract, and how storage costs and risk-free rates interplay. The formula linking these factors is: Futures Price (F) = Spot Price (S) * e^((r + u – c)T), where ‘r’ is the risk-free rate, ‘u’ is the storage cost, ‘c’ is the convenience yield, and ‘T’ is the time to maturity. In this scenario, the spot price (S) is £750, the risk-free rate (r) is 5% (0.05), the storage cost (u) is 2% (0.02), and the time to maturity (T) is 6 months (0.5 years). Initially, the convenience yield (c) is 3% (0.03). We first calculate the initial futures price: F1 = 750 * e^((0.05 + 0.02 – 0.03) * 0.5) = 750 * e^(0.02 * 0.5) = 750 * e^(0.01) ≈ 750 * 1.01005 ≈ £757.54. Next, the convenience yield drops to 1% (0.01). We calculate the new futures price: F2 = 750 * e^((0.05 + 0.02 – 0.01) * 0.5) = 750 * e^((0.06) * 0.5) = 750 * e^(0.03) ≈ 750 * 1.03045 ≈ £772.84. The change in the futures price is F2 – F1 = 772.84 – 757.54 = £15.30. Therefore, the futures price increases by approximately £15.30. This demonstrates that a decrease in convenience yield, while keeping other factors constant, increases the futures price. The concept of convenience yield is crucial here. It reflects the benefit of holding the physical commodity rather than the futures contract. A lower convenience yield means there’s less advantage to holding the physical commodity, making the futures contract relatively more attractive and thus increasing its price. The exponential relationship emphasizes that even small changes in the inputs can lead to significant price differences, especially over longer time horizons. This is because the factors are compounded over time, influencing the final futures price disproportionately.

To determine the most suitable hedging strategy, we need to calculate the implied volatility from the given options prices using an options pricing model (like Black-Scholes). Since this is an exam question, we’ll assume the implied volatility is approximately 25% for both options. Next, we calculate the delta of each option. A call option with a strike price of £750 has a delta closer to 1 as it’s more likely to be in the money if the current futures price is £740. Let’s assume the call option delta is 0.65. The put option with a strike price of £730 has a delta closer to -1 as it’s more likely to be in the money if the futures price falls. Let’s assume the put option delta is -0.40. To hedge a short position in 100,000 barrels of crude oil, we need to offset the price risk. The optimal hedge ratio is calculated as: Hedge Ratio = (Size of position to be hedged / Contract size) * Delta. The contract size for Brent Crude Oil futures is typically 1,000 barrels. For the call option hedge: Number of contracts = (100,000 / 1,000) * 0.65 = 65 contracts. For the put option hedge: Number of contracts = (100,000 / 1,000) * 0.40 = 40 contracts. Since we are short crude oil, we need to buy derivatives to hedge. To hedge with call options, we need to buy call options. To hedge with put options, we also need to buy put options. A delta-neutral strategy involves offsetting the overall delta of the portfolio to zero. In this scenario, since the client is short crude oil futures, a delta-neutral hedge would involve buying call options or buying put options. A short straddle involves selling both a call and a put option, which would increase the risk for a client already short crude oil. A long strangle involves buying both a call and a put option, which can be a suitable hedging strategy but may not be the most cost-effective. Given the need to hedge against downside risk and potentially profit from upside movement, buying put options is the most appropriate strategy. The key here is understanding delta hedging and how to apply it to a real-world commodity trading scenario. It’s not just about plugging numbers into a formula, but about interpreting the results and choosing the right hedging strategy based on the client’s position and risk appetite. The scenario is designed to mimic the complex decisions faced by commodity traders daily, requiring them to consider market dynamics, regulatory constraints, and risk management principles. This example emphasizes the importance of understanding the underlying principles of delta hedging and its application in commodity markets.

The question assesses the understanding of commodity swap valuation, specifically incorporating storage costs and convenience yield. The floating price reset mechanism and the impact of these costs on the swap’s net present value (NPV) are crucial. First, calculate the present value of the fixed payments. The fixed price is £75/tonne, and the contract size is 100 tonnes per month, so the monthly fixed payment is £7,500. The discount rate is 5% per annum, or approximately 0.41% per month (5%/12). The present value of the fixed payments is calculated as the sum of the discounted fixed payments for each month. Next, calculate the expected present value of the floating payments. We’re given the expected floating prices for each month, and we need to discount these back to the present. The monthly floating payment is the expected floating price multiplied by the contract size (100 tonnes). The present value of the floating payments is calculated as the sum of the discounted floating payments for each month. Crucially, the storage costs and convenience yield impact the expected future spot prices. Storage costs increase the future price, while convenience yield decreases it. These adjustments are already factored into the provided expected floating prices, as the question specifies that these prices reflect storage costs and convenience yield. The swap’s NPV is the present value of the floating payments minus the present value of the fixed payments. A positive NPV indicates that the swap is beneficial to the party receiving the floating payments, while a negative NPV indicates it is beneficial to the party paying the fixed payments. The present value of the fixed leg is: \[ PV_{fixed} = \sum_{t=1}^{12} \frac{7500}{(1 + 0.05/12)^t} \] \[ PV_{fixed} \approx £87,854.55 \] The present value of the floating leg is: \[ PV_{floating} = \sum_{t=1}^{12} \frac{P_t \times 100}{(1 + 0.05/12)^t} \] Where \( P_t \) is the expected floating price for month \( t \). \[ PV_{floating} = \frac{70 \times 100}{1.004167} + \frac{71 \times 100}{1.004167^2} + \frac{72 \times 100}{1.004167^3} + \frac{73 \times 100}{1.004167^4} + \frac{74 \times 100}{1.004167^5} + \frac{75 \times 100}{1.004167^6} + \frac{76 \times 100}{1.004167^7} + \frac{77 \times 100}{1.004167^8} + \frac{78 \times 100}{1.004167^9} + \frac{79 \times 100}{1.004167^{10}} + \frac{80 \times 100}{1.004167^{11}} + \frac{81 \times 100}{1.004167^{12}} \] \[ PV_{floating} \approx £90,395.23 \] The NPV of the swap is: \[ NPV = PV_{floating} – PV_{fixed} = £90,395.23 – £87,854.55 \approx £2,540.68 \] Therefore, the NPV of the commodity swap is approximately £2,540.68.

To determine the most suitable hedging strategy, we must first calculate the spot price equivalent of the forward contract and compare it with the predicted spot price. The forward price represents the market’s expectation of the future spot price, adjusted for factors like storage costs, interest rates, and convenience yield. In this scenario, the forward price for Brent Crude Oil is $88.00 per barrel. The refinery expects to purchase 50,000 barrels of Brent Crude Oil. Let’s analyze each hedging option: * **Option a (Short Hedge with Futures):** Selling futures contracts locks in a price but exposes the refinery to basis risk (the difference between the futures price and the spot price at the time of purchase). If the spot price rises above $88, the refinery benefits from the hedge. If the spot price falls below $88, the hedge results in a loss compared to simply buying on the spot market. * **Option b (Long Hedge with Futures):** Buying futures contracts protects against rising prices. If the spot price rises above $88, the refinery benefits. If the spot price falls below $88, the refinery incurs a loss on the hedge. * **Option c (Forward Contract):** Entering a forward contract locks in a price of $88.00. This eliminates price risk but also eliminates the opportunity to benefit from a price decrease. * **Option d (No Hedge):** This exposes the refinery to the full volatility of the spot market. If the spot price increases significantly, the refinery will incur a higher cost. If the spot price decreases, the refinery will benefit. Given that the refinery believes the spot price will be significantly lower than the forward price, not hedging (option d) is the most speculative but potentially the most profitable strategy. However, it carries the highest risk. Entering into a forward contract (option c) would lock in the $88.00 price, which the refinery believes is too high. A short hedge (option a) would be counterintuitive since the refinery is a buyer, not a seller. A long hedge (option b) would protect against price increases but would also lock in a price that the refinery believes is higher than the expected spot price. Therefore, the optimal strategy is to not hedge and purchase on the spot market.

The core of this question lies in understanding how basis risk arises in commodity hedging, particularly when the commodity being hedged and the commodity underlying the futures contract are not perfectly correlated. Basis is the difference between the spot price of an asset and the price of a related futures contract. Basis risk emerges because this difference is not constant and can change unpredictably over time. The calculation involves understanding how changes in the basis affect the effectiveness of the hedge. The initial basis is the spot price minus the futures price at the start of the hedge. The final basis is the spot price minus the futures price at the end of the hedge. The change in basis represents the hedge’s imperfection. In this scenario, a gold refiner is hedging their gold purchases. The refiner buys gold in London (LBMA Gold Price) but hedges using COMEX gold futures. These are similar, but not identical, commodities, creating basis risk. Here’s how to calculate the effective price paid by the gold refiner: 1. **Initial Spot Price:** £1,250/ounce 2. **Initial Futures Price:** £1,275/ounce 3. **Initial Basis:** £1,250 – £1,275 = -£25/ounce 4. **Final Spot Price:** £1,300/ounce 5. **Final Futures Price:** £1,310/ounce 6. **Final Basis:** £1,300 – £1,310 = -£10/ounce 7. **Change in Basis:** -£10 – (-£25) = £15/ounce (Basis strengthened) The refiner locked in the futures at £1,275 and closed out at £1,310. This resulted in a loss of £35/ounce on the futures position (£1,310 – £1,275). However, the spot price increased from £1,250 to £1,300, resulting in a gain of £50/ounce if they hadn’t hedged. The effective price paid is the final spot price (£1,300) plus the loss on the futures contract (£35) which is £1,335/ounce. Alternatively, the initial spot price (£1,250) plus the change in basis (£15) plus the initial future price (£1275) minus the initial spot price (£1250) equals £1,335/ounce. Basis risk is crucial in commodity derivatives. Imagine a coffee roaster hedging arabica coffee prices using robusta futures. The price correlation between arabica and robusta is not perfect. If arabica prices rise sharply while robusta prices remain stable, the roaster’s hedge will underperform, and they will pay more for their coffee than anticipated. Conversely, if robusta prices rise more than arabica, the hedge will overperform, and the roaster will effectively pay less. Understanding basis risk allows companies to make informed decisions about hedging strategies. They might choose to accept some basis risk to reduce transaction costs or find more closely correlated futures contracts, even if they are less liquid. Sophisticated strategies might involve actively managing the basis by trading the spot and futures markets simultaneously.

To determine the break-even price for the refinery, we need to calculate the price at which the refinery’s total revenue equals its total costs. The total costs include the cost of crude oil, the refining costs, and the hedging costs (or savings). The total revenue is the revenue from selling gasoline and jet fuel. First, calculate the cost of crude oil: 100,000 barrels * $80/barrel = $8,000,000. Next, calculate the refining costs: $3/barrel * 100,000 barrels = $300,000. Then, calculate the hedging costs/savings. The refinery hedged 50,000 barrels using futures. The futures price increased from $80 to $84, resulting in a loss on the hedge. The loss is (Futures Price – Initial Futures Price) * Number of Barrels Hedged = ($84 – $80) * 50,000 = $200,000 loss. The remaining 50,000 barrels were unhedged and purchased at the spot price of $80, so there’s no additional gain or loss on those barrels related to hedging. Total costs are the sum of crude oil cost, refining costs, and the hedging loss: $8,000,000 + $300,000 + $200,000 = $8,500,000. Now, calculate the revenue from gasoline and jet fuel. The refinery produces 45,000 barrels of gasoline and 45,000 barrels of jet fuel, so the revenue is (Gasoline Price * Gasoline Barrels) + (Jet Fuel Price * Jet Fuel Barrels). Let ‘x’ be the break-even price. Total Revenue = (x * 45,000) + (x * 45,000) = 90,000x. To break even, Total Revenue = Total Costs, so 90,000x = $8,500,000. Solve for x: x = $8,500,000 / 90,000 = $94.44/barrel. Consider a scenario where a smaller refinery doesn’t hedge at all. If crude oil prices rise significantly before they can refine and sell their products, they face much higher input costs, potentially making their operations unprofitable. This illustrates the risk management aspect of hedging. Conversely, if prices fall, a hedger might miss out on potential profits from buying cheaper crude, but they are protected from significant losses. The key concept here is understanding how hedging strategies impact the overall profitability of a commodity-related business. It’s not just about the initial purchase price of the commodity but also about managing the price risk over time. The break-even calculation combines these elements to provide a comprehensive view of the refinery’s financial performance.

The core of this question revolves around understanding how basis risk arises in hedging strategies using commodity derivatives, specifically futures contracts. Basis risk is the risk that the price of the asset being hedged (the spot price) and the price of the hedging instrument (the futures price) do not move perfectly together. This imperfect correlation can erode the effectiveness of the hedge. The formula for calculating the effective price received is: Effective Price = Spot Price at Sale – (Futures Price at Sale – Futures Price at Purchase). This formula highlights the core mechanism of hedging: locking in a price by offsetting spot market movements with futures market movements. The basis is defined as Spot Price – Futures Price. The change in basis is therefore (Spot Price at Sale – Futures Price at Sale) – (Spot Price at Purchase – Futures Price at Purchase). In this scenario, the company aims to hedge against a potential decline in the price of their copper production. The initial basis is £200/tonne (£8,000 – £7,800). If the basis weakens to £100/tonne (£7,500 – £7,400) at the time of sale, it means the spot price has declined more than the futures price. Calculation: Effective Price = £7,500 – (£7,400 – £7,800) = £7,500 + £400 = £7,900/tonne. The company locked in a price that is close to £7,900/tonne because they bought the future contract at £7,800/tonne and sold at £7,400/tonne, which is a profit of £400/tonne. They use this profit to offset the loss in the spot market. Let’s consider an analogy: Imagine you’re a farmer growing wheat. You want to protect yourself from a potential drop in wheat prices before harvest. You sell wheat futures contracts. Ideally, if wheat prices fall in the spot market, your futures contracts will gain in value, offsetting the loss. However, if the price relationship between the spot market (your actual wheat) and the futures market (the contracts) changes unexpectedly (basis risk), your hedge won’t be perfect. Perhaps a localized drought only affects your region, causing the spot price in your area to fall more than the national futures price. This difference is the basis risk. Another example: Suppose a gold mining company wants to lock in a price for its future gold production. They use gold futures. However, transportation costs from the mine to the delivery point for the futures contract could change. A sudden increase in fuel prices increases transportation costs, widening the basis. The futures price might not fully reflect the price the mining company can actually realize after transportation costs are factored in. Understanding basis risk is crucial for effective hedging. It’s not enough to simply enter a hedge; one must actively manage and monitor the basis to understand the potential for deviations from the intended hedged price. Factors like storage costs, transportation costs, and local supply/demand imbalances all contribute to basis risk.

To determine the profit or loss from the swap, we need to calculate the present value of the cash flows from the fixed and floating legs of the swap. First, calculate the present value of the fixed payments. The fixed rate is 3% per annum, paid semi-annually on a notional principal of £10,000,000. This means each fixed payment is (3%/2) * £10,000,000 = £150,000. The discount rates are 2.8%, 2.9%, 3.0%, and 3.1% for the four periods. The present value of the fixed payments is calculated as follows: \[PV_{fixed} = \frac{150,000}{1 + \frac{0.028}{2}} + \frac{150,000}{(1 + \frac{0.029}{2})^2} + \frac{150,000}{(1 + \frac{0.030}{2})^3} + \frac{150,000}{(1 + \frac{0.031}{2})^4}\] \[PV_{fixed} = \frac{150,000}{1.014} + \frac{150,000}{1.0292} + \frac{150,000}{1.0457} + \frac{150,000}{1.0628}\] \[PV_{fixed} = 147,928.99 + 145,749.94 + 143,431.18 + 141,136.62 = 578,246.73\] Next, calculate the present value of the floating payments. The floating rates are 2.5%, 2.7%, 2.9%, and 3.1% for the four periods. This means the floating payments are (2.5%/2) * £10,000,000 = £125,000, (2.7%/2) * £10,000,000 = £135,000, (2.9%/2) * £10,000,000 = £145,000 and (3.1%/2) * £10,000,000 = £155,000. The discount rates are the same as before. The present value of the floating payments is calculated as follows: \[PV_{floating} = \frac{125,000}{1 + \frac{0.028}{2}} + \frac{135,000}{(1 + \frac{0.029}{2})^2} + \frac{145,000}{(1 + \frac{0.030}{2})^3} + \frac{155,000}{(1 + \frac{0.031}{2})^4}\] \[PV_{floating} = \frac{125,000}{1.014} + \frac{135,000}{1.0292} + \frac{145,000}{1.0457} + \frac{155,000}{1.0628}\] \[PV_{floating} = 123,274.16 + 131,177.51 + 138,664.24 + 145,841.17 = 538,957.08\] The profit or loss is the difference between the present value of the floating payments and the present value of the fixed payments: Profit/Loss = \(PV_{floating} – PV_{fixed}\) Profit/Loss = £538,957.08 – £578,246.73 = -£39,289.65 Therefore, the counterparty would experience a loss of approximately £39,289.65. This calculation highlights the importance of understanding present value calculations in the context of commodity swaps. It goes beyond simple memorization by requiring the application of discounting principles to a series of cash flows determined by fluctuating market rates. The unique aspect lies in applying these calculations to a specific scenario involving commodity-linked interest rates, making it a novel problem-solving challenge.

Let’s consider a hypothetical scenario involving a cocoa bean processor, “ChocoLux,” based in the UK. ChocoLux relies heavily on forward contracts to secure its cocoa bean supply. They enter into a forward contract to purchase 500 metric tons of cocoa beans in 6 months at a price of £2,500 per metric ton. Simultaneously, ChocoLux hedges their price risk by selling cocoa bean futures contracts on the ICE Futures Europe exchange. They sell 50 futures contracts, each representing 10 metric tons, at a price of £2,550 per metric ton. Three months later, due to unforeseen weather conditions in West Africa, the spot price of cocoa beans surges to £2,800 per metric ton. The futures price also increases, but less dramatically, to £2,700 per metric ton, reflecting the market’s anticipation of eventual supply normalization. At this point, ChocoLux decides to unwind its hedge. They buy back the 50 futures contracts at £2,700 per metric ton. The profit/loss on the futures position is calculated as follows: Initial sale price: £2,550/ton Buyback price: £2,700/ton Loss per ton: £2,700 – £2,550 = £150/ton Total loss on futures: 50 contracts * 10 tons/contract * £150/ton = £75,000 However, ChocoLux still has the obligation to purchase the cocoa beans at £2,500 per metric ton through the forward contract. The market price is now £2,800, so they are saving £300 per ton compared to the spot market. The gain on the forward contract is calculated as follows: Market price: £2,800/ton Contract price: £2,500/ton Gain per ton: £2,800 – £2,500 = £300/ton Total gain on forward: 500 tons * £300/ton = £150,000 The net effect of the hedge is the gain on the forward contract minus the loss on the futures contracts: £150,000 – £75,000 = £75,000. This example illustrates how hedging with futures can protect against price volatility, but it also shows that perfect hedges are rare. The basis risk (the difference between the spot price and the futures price) can lead to a net gain or loss. In this case, the basis narrowed, resulting in a net gain for ChocoLux. The key takeaway is that hedging reduces risk but doesn’t eliminate it entirely. The effectiveness of a hedge depends on the correlation between the hedged asset (cocoa beans) and the hedging instrument (cocoa futures). Understanding basis risk and actively managing the hedge are crucial for success.

Let’s consider a hypothetical scenario involving a junior oil trader, Anya, at a UK-based energy firm, “BritOil.” Anya is tasked with hedging BritOil’s exposure to Brent Crude oil price fluctuations. BritOil has a firm commitment to deliver 50,000 barrels of Brent Crude in three months. Anya considers using futures contracts and options on futures to manage this risk. First, let’s analyze the futures hedge. Suppose the current price of Brent Crude is $80 per barrel, and the three-month futures contract is trading at $81 per barrel. Anya could sell 50 Brent Crude futures contracts (each contract representing 1,000 barrels) to lock in a selling price of $81. If the spot price at delivery is lower than $81, the futures hedge will provide a profit to offset the loss in the physical market. Conversely, if the spot price is higher, the futures hedge will result in a loss, but this will be offset by the higher revenue from selling the physical oil. Now, let’s examine using options on futures. Anya could buy put options on Brent Crude futures with a strike price of $80. The put option gives BritOil the right, but not the obligation, to sell futures contracts at $80. If the futures price falls below $80, Anya can exercise the put option and sell futures at $80, effectively setting a floor price for the oil. If the futures price stays above $80, Anya will not exercise the option and will only lose the premium paid for the option. The key difference lies in the flexibility. The futures hedge locks in a specific price, while the put option allows BritOil to benefit from upward price movements while limiting downside risk. Consider a third scenario: a swap. BritOil could enter into a swap agreement with a counterparty, where BritOil agrees to pay a fixed price for the oil and receive a floating price based on the market rate. This is another way to hedge against price volatility. In all three scenarios, UK regulations, specifically those outlined by the Financial Conduct Authority (FCA), dictate reporting requirements, margin requirements, and market conduct rules. Anya must ensure BritOil’s hedging activities comply with these regulations to avoid penalties. For example, BritOil must report large positions in commodity derivatives to the FCA to ensure market transparency. The choice between futures, options, and swaps depends on BritOil’s risk appetite and market outlook. Futures provide a complete hedge, options offer flexibility, and swaps provide a customized hedging solution. Understanding the nuances of each instrument and the relevant regulations is crucial for effective risk management.

The core of this question lies in understanding the impact of contango and backwardation on hedging strategies involving commodity futures. Contango, where futures prices are higher than the expected spot price, creates a roll yield drag for hedgers. Backwardation, where futures prices are lower than the expected spot price, provides a roll yield benefit. The storage costs and convenience yield are crucial factors influencing the shape of the futures curve. A high convenience yield (reflecting a strong immediate need for the commodity) tends to push the market into backwardation. Storage costs, conversely, push the market into contango. In this scenario, the coffee producer is hedging against a price decrease. If the market is in contango, each time the producer rolls the futures contract (i.e., sells the near-term contract and buys the next-term contract), they will be selling low and buying high, incurring a loss. Conversely, if the market is in backwardation, they will be selling high and buying low, generating a profit. The relative magnitudes of the storage costs and convenience yield determine whether the market is in contango or backwardation. The calculation involves comparing the annualized storage costs ($100/ton) with the implied convenience yield. The convenience yield can be inferred from the futures prices. Since the 3-month futures are trading at $2100/ton and the spot price is $2000/ton, the difference of $100/ton represents the market’s expectation of price appreciation over those three months, driven by factors like storage costs and the inverse convenience yield. To annualize the convenience yield, we first determine the convenience yield over the three-month period: Convenience Yield (3 months) = Spot Price + Storage Costs (3 months) – Futures Price (3 months) Convenience Yield (3 months) = $2000 + ($100/4) – $2100 = -$975/4 = -$243.75 Annualized Storage Costs = $100 Annualized Convenience Yield = -$243.75 * 4 = -$975 The net effect is -$975 + $100 = -$875. Since the result is negative, the convenience yield dominates storage costs, putting the market into backwardation. This means the producer benefits from the roll yield. The hedge effectiveness depends on how well the futures price tracks the spot price. A basis risk of $20 means the futures price might not perfectly reflect the spot price movement. This basis risk reduces the effectiveness of the hedge, but the backwardation increases it.

The core of this question revolves around understanding how basis risk arises in hedging strategies using commodity derivatives, specifically when the commodity underlying the derivative doesn’t perfectly match the commodity being hedged. Basis risk is the risk that the price of the hedging instrument (e.g., a futures contract) will not move exactly in correlation with the price of the asset being hedged. This can occur due to differences in location, quality, or timing. In this scenario, a coffee roaster in London needs to hedge their exposure to Arabica coffee prices, but they can only access Robusta coffee futures on the ICE exchange. This mismatch creates basis risk. The roaster needs to understand that changes in the price difference between Arabica and Robusta coffee (the basis) will affect the effectiveness of their hedge. The most effective strategy involves understanding the historical relationship between Arabica and Robusta prices and adjusting the hedge ratio accordingly. The hedge ratio is the ratio of the size of the futures position to the size of the underlying exposure. A naive hedge ratio of 1:1 (hedging one tonne of Arabica with one tonne of Robusta futures) assumes a perfect correlation, which is unlikely. To calculate the appropriate hedge ratio, we need to consider the correlation and volatility of Arabica and Robusta prices. A common approach is to use the following formula: Hedge Ratio = (Correlation between Arabica and Robusta * Volatility of Arabica) / Volatility of Robusta Let’s assume the following: * Correlation between Arabica and Robusta prices: 0.75 * Volatility of Arabica prices: 15% per annum * Volatility of Robusta prices: 20% per annum Hedge Ratio = (0.75 * 0.15) / 0.20 = 0.5625 This means the roaster should sell 0.5625 tonnes of Robusta futures for every 1 tonne of Arabica coffee they need to hedge. In this case, they need to hedge 100 tonnes, so they should sell 100 * 0.5625 = 56.25 tonnes of Robusta futures. Since futures contracts are typically traded in standardized sizes (e.g., 5 tonnes per contract), the roaster would need to round to the nearest whole number of contracts. If each contract is 5 tonnes, they should sell 56.25/5 = 11.25 contracts, which would be rounded to 11 or 12 contracts depending on their risk tolerance. Selling 11 contracts (55 tonnes) would slightly under-hedge, while selling 12 contracts (60 tonnes) would slightly over-hedge. The key takeaway is that a perfect hedge is unlikely due to basis risk, and the optimal hedge ratio aims to minimize the variance of the hedged position, not eliminate price risk entirely. The roaster must continuously monitor the basis and adjust their hedge as needed. Factors such as weather patterns in different coffee-growing regions, changes in consumer preferences, and shifts in global supply and demand can all affect the basis and the effectiveness of the hedge.

1. **Calculate the Expected Net Cash Flows:** The swap involves exchanging a fixed payment for a floating payment linked to the price of Brent Crude oil. We need to estimate the expected floating payments based on the forward curve and then subtract the fixed payments to find the net cash flows for each period. 2. **Incorporate Credit Risk:** The counterparty has a 3% probability of defaulting at the end of each year. This risk reduces the expected value of the cash flows. We will multiply the expected cash flow by (1 – default probability) for each period. 3. **Account for Collateralization:** The swap is collateralized, meaning that if the market value of the swap exceeds a certain threshold (£1 million in this case), the counterparty must post collateral. This reduces the credit exposure. We will assume the collateral fully covers the exposure up to £1 million. 4. **Discount the Expected Cash Flows:** We will discount the expected cash flows back to the present value using the risk-free rate (4% per year). 5. **Illustrative Example:** Let’s assume the following expected net cash flows (without considering credit risk or collateralization): * Year 1: £1,500,000 * Year 2: £1,200,000 * Year 3: £900,000 Now, let’s incorporate the 3% default probability and the £1 million collateral threshold. * **Year 1:** The expected cash flow is £1,500,000. However, due to collateralization, the exposure is capped at £1,000,000. The expected loss due to default is 3% of the exposure exceeding the collateral threshold. In this case, the exposure exceeding collateral is £500,000. So, the expected loss is 0.03 * £500,000 = £15,000. The risk-adjusted cash flow is £1,500,000 – £15,000 = £1,485,000. * **Year 2:** The expected cash flow is £1,200,000. The exposure exceeding collateral is £200,000. So, the expected loss is 0.03 * £200,000 = £6,000. The risk-adjusted cash flow is £1,200,000 – £6,000 = £1,194,000. * **Year 3:** The expected cash flow is £900,000. The exposure is less than the collateral threshold, so there is no expected loss due to default. The risk-adjusted cash flow is £900,000. Now, we discount these risk-adjusted cash flows using the 4% risk-free rate: * Year 1: £1,485,000 / (1.04)^1 = £1,427,884.62 * Year 2: £1,194,000 / (1.04)^2 = £1,102,701.66 * Year 3: £900,000 / (1.04)^3 = £800,720.70 The present value of the swap is the sum of these discounted cash flows: £1,427,884.62 + £1,102,701.66 + £800,720.70 = £3,331,306.98 Therefore, the present value of the commodity swap, considering credit risk and collateralization, is approximately £3,331,306.98. This illustrates how collateralization mitigates credit risk and impacts the valuation of derivative contracts.

Let’s analyze the scenario. A power plant in the UK needs to secure its future coal supply but wants to avoid the upfront capital expenditure of physically purchasing and storing the coal. They opt for a swap to manage price risk. The key here is understanding how the swap works, especially the floating and fixed legs, and how the final settlement is determined. The power plant is paying a fixed price and receiving a floating price tied to the Argus Coal Index. If the average floating price is higher than the fixed price, the swap provider pays the power plant the difference, and vice versa. First, calculate the average floating price: (£95 + £98 + £102 + £105 + £100 + £97) / 6 = £99.50 per tonne. Next, determine the difference between the average floating price and the fixed price: £99.50 – £100 = -£0.50 per tonne. Since the difference is negative, it means the average floating price was lower than the fixed price. Therefore, the power plant owes the swap provider £0.50 per tonne. Finally, calculate the total settlement amount: -£0.50/tonne * 10,000 tonnes = -£5,000. The negative sign indicates that the power plant pays the swap provider. Now, let’s consider the nuances. The swap allows the power plant to hedge against price volatility without taking physical delivery. If coal prices had risen sharply, the swap would have paid the power plant the difference, offsetting their higher fuel costs. Conversely, because prices averaged lower than the fixed rate, the power plant effectively overpaid for its coal relative to the spot market average during the swap period. This highlights the trade-off in using swaps: certainty versus potentially missing out on favorable price movements. The power plant accepted the fixed price to avoid the risk of prices soaring, but in this scenario, that decision resulted in a loss. The UK regulations surrounding commodity derivatives, specifically those overseen by the FCA, require firms offering these swaps to ensure they are suitable for the client and that the client understands the risks involved. This scenario demonstrates a real-world application where even a seemingly small price difference can result in a significant financial impact due to the large notional amount.

The core of this question lies in understanding how backwardation and contango impact hedging strategies using commodity futures. Backwardation (futures price < expected spot price) typically benefits hedgers who are selling (e.g., producers), as they can lock in a price higher than what's currently expected. Contango (futures price > expected spot price) benefits hedgers who are buying (e.g., consumers), as they can lock in a price lower than what’s currently expected. The key here is the roll yield, which is the gain (in backwardation) or loss (in contango) from rolling a futures contract forward as it approaches expiration. In this scenario, the refinery is hedging its future crude oil purchases. They are concerned about rising prices. The initial futures contract price is $85, and the expected spot price is $90. This indicates backwardation. Over the quarter, the spot price increases to $95, and the refinery rolls its position at an average futures price of $92. First, calculate the hedge profit/loss: The refinery bought futures at $85 and closed at $92, resulting in a profit of $7 per barrel. Second, calculate the unhedged cost: The spot price increased from an expected $90 to $95, representing an increase of $5 per barrel. Finally, determine the effective cost: The initial expected cost was $90. The hedge profit was $7, and the spot price increased by $5. Therefore, the effective cost is $90 (expected) + $5 (spot increase) – $7 (hedge profit) = $88. The question tests the candidate’s understanding of backwardation, hedging effectiveness, and the impact of changing spot prices on the overall cost for a hedger. The incorrect options are designed to trap candidates who misinterpret the direction of the hedge, fail to account for the roll yield, or incorrectly calculate the profit/loss.