Commodity Derivatives Quiz Exam Quiz 17

The core of this question revolves around understanding how the London Metal Exchange (LME) warehousing system interacts with physical commodity markets and derivative pricing, specifically when regulatory changes impact warehouse operations. The scenario presented involves a fictional regulatory change that increases the minimum throughput requirements for LME warehouses. This change directly affects the availability of metal for delivery and, consequently, the contango or backwardation in the futures market. The key concept here is the “convenience yield.” Convenience yield represents the benefit of holding the physical commodity rather than a derivative contract. It reflects the value of having immediate access to the metal, avoiding potential delivery delays, and hedging against unexpected demand spikes. In a contango market (futures price higher than spot price), the convenience yield is lower because there’s less urgency to hold the physical commodity. Conversely, in a backwardation market (futures price lower than spot price), the convenience yield is higher. The regulatory change, by potentially restricting metal availability from LME warehouses, increases the perceived risk of relying solely on futures contracts for physical metal delivery. This elevates the importance of holding the physical commodity, driving up the convenience yield. The increased convenience yield will then push the spot price higher relative to the futures price, thus reducing or potentially eliminating the contango, or even creating a backwardation scenario. The magnitude of the impact depends on the severity of the regulatory change and the market’s perception of its long-term effects on metal availability. If the market believes the change is temporary, the impact on the contango will be less pronounced. However, if the market anticipates long-term supply constraints due to the regulatory change, the contango could significantly narrow or even flip into backwardation. The correct answer needs to reflect this understanding of convenience yield, LME warehousing, and the impact of regulatory changes on market dynamics. The other options represent common misconceptions or incomplete understandings of these relationships.

The core of this question lies in understanding how margin calls function in futures contracts, particularly when multiple contracts are held and price movements are adverse. A margin call occurs when the equity in a futures account falls below the maintenance margin level. The trader must then deposit funds to bring the equity back up to the initial margin level. When multiple contracts are involved, the margin call is calculated based on the total loss across all contracts. The key is to calculate the total loss, determine the amount needed to restore the account to the initial margin level, and then consider any excess margin already present. In this scenario, the trader initially holds 10 contracts with a specific initial and maintenance margin. The price movement results in a loss per contract. We need to calculate the total loss, factor in the existing excess margin, and then determine the amount of cash the trader must deposit to meet the margin call. 1. **Calculate the total loss:** The price decreased by £25 per contract. With 10 contracts, the total loss is \(10 \times £25 = £250\). 2. **Calculate the equity after the loss:** The initial equity was \(10 \times £3,000 = £30,000\). After the loss, the equity is \(£30,000 – £250 = £29,750\). 3. **Calculate the total maintenance margin:** The maintenance margin is \(10 \times £2,500 = £25,000\). 4. **Calculate the margin call amount:** The margin call requires bringing the equity back to the initial margin level of £30,000. Since the current equity is £29,750, the trader needs to deposit \(£30,000 – £29,750 = £250\). Therefore, the trader must deposit £250 to meet the margin call.

The core of this question lies in understanding the interplay between storage costs, convenience yield, and the relationship between spot and futures prices, specifically in the context of backwardation. Backwardation occurs when the futures price is lower than the spot price. This situation often arises when there is a high demand for the commodity in the present, leading to a high spot price. However, this also implies that there are significant costs associated with holding the commodity until the delivery date of the futures contract. These costs can include storage, insurance, and financing. Convenience yield represents the benefit of holding the physical commodity rather than a futures contract. This benefit could be due to the ability to profit from unexpected supply shortages or the ability to continue production without interruption. A high convenience yield can also contribute to backwardation. The theoretical futures price is calculated as: Futures Price = Spot Price + Cost of Carry – Convenience Yield. The cost of carry includes storage costs, insurance, and financing costs. In backwardation, the convenience yield exceeds the cost of carry. In this scenario, the spot price of Brent Crude is £85 per barrel. The storage cost is £3 per barrel per month, totaling £9 for three months. The convenience yield must be high enough to offset both the storage costs and the difference between the spot and futures prices. Let \(F\) be the futures price, \(S\) be the spot price, \(C\) be the cost of carry (storage), and \(Y\) be the convenience yield. \[F = S + C – Y\] We are given \(S = 85\), \(F = 82\), and \(C = 9\). We need to find \(Y\). \[82 = 85 + 9 – Y\] \[Y = 85 + 9 – 82\] \[Y = 12\] The convenience yield is £12 per barrel. The key takeaway is that backwardation (futures price < spot price) indicates a high convenience yield relative to the cost of carry. This means that market participants are willing to pay a premium for immediate access to the commodity. A proper understanding of these relationships is crucial for trading and hedging commodity derivatives. Furthermore, UK regulations concerning market manipulation prohibit activities designed to artificially influence spot or futures prices to exploit such backwardation scenarios. This includes practices like hoarding physical commodities to drive up spot prices artificially.

To determine the most suitable hedging strategy, we must first calculate the potential loss without hedging. The expected price change is $90 – $85 = $5 per barrel. Thus, the unhedged loss would be 10,000 barrels * $5/barrel = $50,000. Next, we analyze each hedging strategy’s outcome. Strategy A (Short Futures): A short futures position locks in a selling price. The futures contract settles at $88, resulting in a loss of $88 – $92 = -$4 per barrel on the futures contract. However, the gain from the physical sale is $90 – $85 = $5. The net profit is $5 – $4 = $1 per barrel. Total profit = 10,000 * $1 = $10,000. Strategy B (Long Put Options): Buying put options provides downside protection. The put option with a strike price of $87 costs $2 per barrel. Since the spot price is $90, the put option expires worthless. The net loss is the option premium of $2 per barrel. Total loss = 10,000 * $2 = $20,000. Strategy C (Short Call Options): Selling call options generates premium income but limits upside potential. The call option with a strike price of $93 earns a premium of $1 per barrel. Since the spot price is $90, the option expires worthless. Total profit = 10,000 * $1 = $10,000. Strategy D (Commodity Swap): Entering into a swap at $86 locks in a price of $86. The loss compared to the sale price of $90 is $4 per barrel. Total loss = 10,000 * $4 = $40,000. Comparing the outcomes: – Unhedged loss: $50,000 – Strategy A: Profit $10,000 – Strategy B: Loss $20,000 – Strategy C: Profit $10,000 – Strategy D: Loss $40,000 Strategies A and C both result in a profit of $10,000. However, Strategy A (Short Futures) involves margin requirements and potential margin calls, which can be burdensome if the market moves against the position. Strategy C (Short Call Options) generates premium income and has no margin requirements, making it more cash-flow friendly. This assumes the company is comfortable with the risk of the price exceeding $93, which would require them to deliver at $93. Therefore, strategy C is more suitable. Now, consider a slightly different scenario. Suppose the company anticipates a significant price drop due to an oversupply report. In this case, Strategy B (Long Put Options) would be more attractive, as it would provide substantial downside protection, although in this specific scenario it results in a loss of $20,000. However, if the price dropped to $80, the put option would yield a profit of ($87 – $80) – $2 = $5 per barrel, resulting in a total profit of $50,000. The choice of the hedging strategy depends heavily on the company’s risk tolerance, cash flow situation, and market expectations. In this case, given the information provided, short call options is the most suitable choice.

To determine the optimal strategy, we need to calculate the expected payoff for each possible scenario (price increase, price decrease, and price stability) and then weigh these payoffs by their respective probabilities. The strategy with the highest expected payoff is the most economically rational choice. First, calculate the payoff for each strategy under each scenario: * **Strategy A (Hedge with Futures):** This strategy locks in a price of £82/barrel. * *Price Increase to £90:* Payoff = £82 (locked price) – £82 (original price) = £0 (Hedge is already in place, no additional gain or loss) * *Price Decrease to £70:* Payoff = £82 (locked price) – £82 (original price) = £0 (Hedge is already in place, no additional gain or loss) * *Price Stays at £82:* Payoff = £82 (locked price) – £82 (original price) = £0 (Hedge is already in place, no additional gain or loss) * **Strategy B (Buy Call Options):** This strategy provides the right, but not the obligation, to buy at £85. Premium cost is £3/barrel. * *Price Increase to £90:* Payoff = (£90 – £85) – £3 = £2/barrel * *Price Decrease to £70:* Payoff = £0 – £3 = -£3/barrel (Option expires worthless) * *Price Stays at £82:* Payoff = £0 – £3 = -£3/barrel (Option expires worthless) * **Strategy C (Do Nothing):** This strategy involves no hedging. * *Price Increase to £90:* Payoff = £90 – £82 = £8/barrel * *Price Decrease to £70:* Payoff = £70 – £82 = -£12/barrel * *Price Stays at £82:* Payoff = £82 – £82 = £0/barrel Next, calculate the expected payoff for each strategy: * **Strategy A (Hedge with Futures):** Expected Payoff = (0.3 * £0) + (0.5 * £0) + (0.2 * £0) = £0/barrel * **Strategy B (Buy Call Options):** Expected Payoff = (0.3 * £2) + (0.5 * -£3) + (0.2 * -£3) = £0.6 – £1.5 – £0.6 = -£1.5/barrel * **Strategy C (Do Nothing):** Expected Payoff = (0.3 * £8) + (0.5 * -£12) + (0.2 * £0) = £2.4 – £6 + £0 = -£3.6/barrel Comparing the expected payoffs: Strategy A (£0/barrel) is the highest, making it the most economically rational choice. The example illustrates a fundamental concept in commodity derivatives: hedging aims to reduce risk, even if it means potentially forgoing higher profits in favorable market conditions. Strategy A provides certainty, eliminating both upside and downside risk. Strategy B offers upside potential but limits downside risk at the cost of the premium. Strategy C exposes the company to the full volatility of the market. The optimal choice depends on the company’s risk tolerance and its assessment of market probabilities.

Let’s analyze a scenario involving a UK-based energy company, “Britannia Power,” hedging its natural gas price risk using a combination of futures and options. Britannia Power anticipates needing 1,000,000 MMBtu of natural gas in three months. The current spot price is £2.50/MMBtu. They decide to hedge 60% of their exposure using futures and the remaining 40% using options. First, consider the futures hedge. Britannia Power enters into futures contracts to cover 600,000 MMBtu. The futures price is £2.60/MMBtu. In three months, the spot price is £2.80/MMBtu, and the futures price converges to the spot price. Britannia Power buys the gas at the spot price (£2.80/MMBtu) but profits from the futures contract (£2.80 – £2.60 = £0.20/MMBtu). The net cost for the futures-hedged portion is £2.80 – £0.20 = £2.60/MMBtu. Next, consider the options hedge. Britannia Power buys call options to cover 400,000 MMBtu with a strike price of £2.70/MMBtu. The premium is £0.05/MMBtu. In three months, the spot price is £2.80/MMBtu. Britannia Power exercises the options, paying the strike price of £2.70/MMBtu plus the premium of £0.05/MMBtu, resulting in a total cost of £2.75/MMBtu. If the spot price had been below £2.70, they would have let the options expire, losing only the premium. The total cost is a weighted average of the futures-hedged portion and the options-hedged portion. The futures portion is 600,000 MMBtu at £2.60/MMBtu, and the options portion is 400,000 MMBtu at £2.75/MMBtu. The weighted average is \(\frac{(600,000 \times 2.60) + (400,000 \times 2.75)}{1,000,000} = \frac{1,560,000 + 1,100,000}{1,000,000} = \frac{2,660,000}{1,000,000} = £2.66/MMBtu\). Now, let’s introduce a regulatory twist under UK EMIR (European Market Infrastructure Regulation). Assume Britannia Power is classified as a NFC- and fails to clear the derivative contracts. This could result in a penalty.

The core of this question revolves around understanding how basis risk arises in hedging strategies, specifically when the commodity underlying the futures contract differs from the commodity being hedged. Basis is defined as the difference between the spot price of an asset and the price of a related futures contract. In this scenario, the local wheat variety has a different quality and demand profile than the standard wheat futures contract. The basis risk is the risk that this difference changes unpredictably over time, eroding the effectiveness of the hedge. To calculate the expected profit or loss, we need to consider the initial basis, the final basis, and the hedge position. The farmer sells futures contracts to hedge against a price decline. Initial Basis: Spot Price (Local Wheat) – Futures Price = £210 – £220 = -£10/tonne Final Basis: Spot Price (Local Wheat) – Futures Price = £200 – £215 = -£15/tonne The basis has weakened (become more negative) by £5/tonne. This means the futures price decreased less than the spot price. Hedge Result: The farmer sold futures at £220 and bought them back at £215, resulting in a profit of £5/tonne on the futures position. Spot Market Result: The farmer sold the wheat at £200 instead of £210, resulting in a loss of £10/tonne on the spot position. Net Result: Profit on futures (£5/tonne) – Loss on spot (£10/tonne) = -£5/tonne Total Profit/Loss = -£5/tonne * 500 tonnes = -£2500 Therefore, the farmer experiences a net loss of £2500 due to the weakening basis. This highlights the importance of understanding basis risk and the limitations of hedging with imperfectly correlated assets. A perfect hedge eliminates price risk, but in reality, basis risk is almost always present to some degree, requiring careful management. Using a cross-hedge, as in this case, exacerbates the basis risk because the underlying asset of the futures contract is not identical to the asset being hedged. The farmer’s loss is a direct consequence of this imperfect correlation.

To determine the most suitable hedging strategy for the airline, we need to calculate the potential cost savings or losses associated with each option compared to not hedging at all. First, let’s calculate the airline’s fuel cost without hedging: * Fuel needed: 5,000,000 gallons * Spot price at delivery: $3.50/gallon * Total fuel cost: 5,000,000 * $3.50 = $17,500,000 Now, let’s analyze each hedging strategy: **a) Futures Contract:** * Futures price: $3.20/gallon * Number of contracts: 200 contracts * 42,000 gallons/contract = 8,400,000 gallons (Over-hedged) * Hedge Ratio: 5,000,000/8,400,000 = 0.5952 * Gain on Futures: (3.20-3.50)*8,400,000 = -$2,520,000 * Net Fuel Cost: 17,500,000 + (-2,520,000) = $14,980,000 **b) Options on Futures (Buying Calls):** * Strike price: $3.30/gallon * Premium: $0.15/gallon * Net cost if spot price > strike price: (Spot price – Strike Price) + Premium = (3.50 – 3.30) + 0.15 = $0.35 * Net cost per gallon: Strike Price + Premium + (Spot price – Strike Price) = $3.30 + $0.15 + ($3.50 – $3.30) = $3.65/gallon * Total fuel cost: 5,000,000 gallons * $3.45/gallon = $17,250,000 **c) Swaps:** * Fixed price: $3.35/gallon * Total fuel cost: 5,000,000 gallons * $3.35/gallon = $16,750,000 **d) Forwards:** * Forward price: $3.40/gallon * Total fuel cost: 5,000,000 gallons * $3.40/gallon = $17,000,000 Comparing the total fuel costs under each scenario: * No Hedge: $17,500,000 * Futures: $14,980,000 * Options: $17,250,000 * Swaps: $16,750,000 * Forwards: $17,000,000 The futures contract results in the lowest fuel cost for the airline, making it the most beneficial hedging strategy in this specific scenario. While the airline over-hedged, the drop in price resulted in a net gain on the futures contract that offset the higher spot price of fuel. The key concept tested here is understanding how different derivative instruments (futures, options, swaps, forwards) can be used to hedge commodity price risk. The question requires the candidate to calculate the effective cost of fuel under each hedging strategy, considering factors like contract size, strike prices, premiums, and settlement prices. It also tests the understanding of over-hedging and its potential impact. The scenario is designed to highlight that the best hedging strategy depends on the specific market conditions and the characteristics of each derivative instrument.

The key to solving this problem lies in understanding the concept of contango and backwardation in commodity futures markets, and how storage costs and convenience yields influence these market conditions. Contango, where futures prices are higher than the spot price, typically arises when storage costs are significant and the convenience yield (the benefit of holding the physical commodity) is low. Backwardation, where futures prices are lower than the spot price, occurs when the convenience yield is high and outweighs storage costs. In this scenario, we need to assess how the increase in warehouse capacity and the simultaneous decrease in spot market liquidity affect the contango/backwardation dynamic. Increased warehouse capacity lowers storage costs, which, all else being equal, would reduce contango. However, the decreased spot market liquidity increases the incentive to hold the physical commodity (higher convenience yield), pushing the market towards backwardation. To determine the most likely outcome, we need to weigh the relative impact of these two opposing forces. The problem states that spot market liquidity has “significantly” decreased, implying a substantial increase in the convenience yield. While increased warehouse capacity reduces storage costs, the impact of a significantly reduced spot market liquidity is likely to be more pronounced. Therefore, the market is more likely to shift towards backwardation. Furthermore, the UK regulatory environment, specifically the Financial Conduct Authority (FCA), requires firms dealing in commodity derivatives to understand and manage the risks associated with these market dynamics. A shift towards backwardation can impact hedging strategies and valuation models, necessitating adjustments to risk management frameworks. Understanding the underlying factors driving contango and backwardation is crucial for compliance with FCA regulations regarding market abuse and fair pricing. For example, if a firm is pricing derivatives based on a historical contango market, they need to adjust their models to reflect the new backwardated market to avoid mispricing and potential regulatory scrutiny.

The core of this question revolves around understanding how storage costs, convenience yield, and interest rates interact to determine the theoretical forward price of a commodity. The formula underpinning this relationship is: Forward Price = Spot Price * e^((Cost of Carry) * Time). The Cost of Carry is the sum of storage costs and interest rates less the convenience yield. The convenience yield represents the benefit of holding the physical commodity rather than a forward contract, reflecting factors like supply shortages or production disruptions. Let’s analyze the scenario. A gold refinery in the UK needs to secure its gold supply for the next 18 months (1.5 years). The spot price is £1,800 per ounce. Storage costs are £15 per ounce per year, effectively £22.5 for the entire 18-month period. The annual risk-free interest rate is 4%, translating to a holding cost of 6% over 18 months. The refinery estimates a convenience yield of 2% per year, or 3% over the 18-month period. First, calculate the total cost of carry: Storage costs + Interest – Convenience Yield = £22.5 + (0.06 * £1800) – (0.03 * £1800) = £22.5 + £108 – £54 = £76.5. Next, add the cost of carry to the spot price: £1800 + £76.5 = £1876.5 Therefore, the theoretical forward price should be £1876.5. Now, consider the impact of the Financial Conduct Authority (FCA) regulations. The FCA closely monitors commodity derivative markets to prevent market abuse and ensure fair pricing. If the forward price deviates significantly from the theoretical price, the FCA might investigate potential manipulation or insider trading. A forward price substantially lower than the theoretical price might suggest someone is aggressively selling, potentially due to inside information about future supply increases or demand decreases. Conversely, a forward price significantly higher could indicate hoarding or an artificial squeeze on the market. The refinery, being a regulated entity, must be able to justify its trading activities and demonstrate that its forward price aligns with market fundamentals and reflects a genuine commercial need. Failure to do so could result in scrutiny and potential penalties from the FCA.

The key to solving this problem lies in understanding how margin calls work in futures contracts and how they relate to the initial margin and maintenance margin. The initial margin is the amount required to open the position, and the maintenance margin is the level below which the account cannot fall. When 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 initially deposits £8,000 (initial margin). The maintenance margin is £6,000. The futures contract is on Brent Crude Oil, and each contract represents 1,000 barrels. The initial price is $80 per barrel. First, we need to determine the loss that triggers a margin call. The account balance needs to fall below £6,000. Since the initial deposit is £8,000, the account can lose £2,000 before a margin call is triggered (£8,000 – £6,000 = £2,000). Next, we need to calculate the price decrease per barrel that would result in a £2,000 loss. Since the contract is for 1,000 barrels, a £2,000 loss translates to a £2,000 / 1,000 barrels = £2 per barrel loss. Finally, we need to consider the exchange rate. The initial price is in dollars ($80), and the loss is calculated in pounds (£2). We are given an exchange rate of £1 = $1.25. Therefore, a £2 loss is equivalent to a $2.5 loss ($2 * $1.25 = $2.5). The price decrease required to trigger the margin call is $2.5 per barrel. Therefore, the price at which the margin call will be triggered is $80 – $2.5 = $77.5. Now, let’s consider a different scenario to illustrate the concept. Imagine a trader buys a futures contract for gold. The initial margin is $5,000, and the maintenance margin is $4,000. If the price of gold falls and the trader’s account balance drops to $3,900, a margin call will be issued. The trader must deposit enough funds to bring the account balance back to the initial margin of $5,000. In this case, the trader would need to deposit $1,100 ($5,000 – $3,900 = $1,100). This ensures that the trader has sufficient funds to cover potential further losses and protects the clearinghouse from default risk. The margin system is a crucial risk management tool in futures trading, ensuring the integrity and stability of the market.

The core of this question lies in understanding the implications of backwardation and contango on hedging strategies involving commodity futures, especially within the context of a company managing inventory and future production. Backwardation (futures price < expected spot price) typically incentivizes hedging by producers as they can lock in prices above the expected future spot price. Contango (futures price > expected spot price) generally disincentivizes hedging for producers as they would lock in prices below the expected future spot price. However, the question introduces a nuanced layer: storage costs and convenience yield. Storage costs erode the profitability of holding physical commodities, making futures contracts relatively more attractive to speculators. Convenience yield, on the other hand, reflects the benefit of holding the physical commodity (e.g., ability to meet immediate demand, avoid supply disruptions). A high convenience yield can offset the contango, making holding physical inventory more attractive despite the higher futures price. To calculate the breakeven futures price, we need to consider the expected spot price, storage costs, and convenience yield. The breakeven futures price is the spot price plus storage costs minus the convenience yield. In this case, it’s £75 + £5 – £3 = £77. If the actual futures price is above this breakeven point, hedging is less attractive because the company would be locking in a price lower than what they could effectively achieve by holding the physical commodity and benefiting from the convenience yield. If the actual futures price is below this breakeven point, hedging becomes more attractive. The question also requires understanding the regulatory environment. In the UK, commodity derivatives trading is subject to regulations outlined in the Financial Services and Markets Act 2000 (FSMA) and subsequent legislation implementing MiFID II and EMIR. These regulations aim to ensure market integrity, transparency, and investor protection. The question tests whether the candidate understands how these regulations might influence a company’s decision to hedge. Therefore, the best course of action depends on whether the current futures price is above or below £77 and whether regulatory constraints favor or disfavor hedging.

The correct answer is (a). This question tests the understanding of the impact of contango and backwardation on hedging strategies using commodity futures. A producer hedging in a contango market faces the risk of negative roll yield (selling lower-priced near-term contracts and buying higher-priced later-dated contracts), which erodes their hedging gains. Conversely, a consumer hedging in a backwardated market benefits from a positive roll yield, enhancing their hedging effectiveness. The scenario specifically requires understanding how these market structures influence the hedging outcome for both producers and consumers, demanding more than just memorizing definitions but applying them in a practical hedging context. Consider a gold mining company, “Aurum Ltd,” wanting to hedge its future gold production. If the gold futures market is in contango, Aurum Ltd will be selling near-term futures contracts at a lower price and buying back longer-dated contracts at a higher price to maintain its hedge. This “roll cost” reduces the overall effectiveness of the hedge. Now, imagine a jewelry manufacturer, “Gems & Co,” hedging its future gold purchases. If the gold futures market is in backwardation, Gems & Co. will be buying near-term futures contracts at a higher price and selling longer-dated contracts at a lower price when rolling over the hedge. This “roll benefit” enhances the effectiveness of their hedge. Therefore, the hedging strategy’s success is deeply intertwined with the prevailing market structure. The other options are incorrect because they either misrepresent the impact of contango and backwardation or confuse the roles of producers and consumers in hedging. For instance, option (b) incorrectly suggests that contango always benefits hedgers, while option (c) conflates the effects on producers and consumers. Option (d) introduces an irrelevant factor (storage costs) that, while relevant to commodity pricing in general, doesn’t directly address the core question about hedging effectiveness in different market structures.

The core of this question lies in understanding how basis risk arises in hedging strategies, particularly when the commodity underlying the derivative doesn’t perfectly match the commodity being hedged. Basis risk is the risk that the price of the asset being hedged and the price of the hedging instrument (in this case, a futures contract) will not move in perfect correlation. This difference in price movement is the ‘basis’. The formula to calculate the effective price received is: Sale Price + (Initial Futures Price – Final Futures Price). The initial futures price is the price at which the contract was entered into, and the final futures price is the price at which it was closed out. A strengthening basis means the difference between the spot price and the futures price is increasing, which benefits a short hedge (selling futures). A weakening basis means the difference is decreasing, hurting a short hedge. In this scenario, the farmer is short hedging, so a strengthening basis is beneficial. To calculate the effective price, we first determine the change in the futures price. The basis strengthened by £2.50/tonne, meaning the futures price decreased by £2.50/tonne *less* than the spot price. The spot price decreased by £15/tonne, so the futures price decreased by £15 – £2.50 = £12.50/tonne. The effective price is then the sale price (£210/tonne) plus the profit on the futures contract (£12.50/tonne), resulting in £222.50/tonne. A crucial understanding is that basis risk is *not* eliminated by hedging; it’s merely transformed. The farmer has traded price risk for basis risk. A perfect hedge would only occur if the futures contract was for the exact same grade and location of barley, which is often not possible. Furthermore, understanding the UK regulatory environment is important. While not directly calculating a regulatory penalty, understanding that improper hedging strategies can lead to financial distress, which in turn could trigger regulatory scrutiny from bodies like the FCA (Financial Conduct Authority), is crucial. The question tests the application of basis risk principles in a practical agricultural context, requiring a deep understanding of hedging mechanics and market dynamics, not just memorization of formulas.

Let’s break down this complex scenario. First, we need to understand the implications of a “basis trade” in the context of Brent crude oil and its delivery location, Sullom Voe. A basis trade exploits the price difference between a commodity’s spot price and its futures price, or between futures contracts with different delivery dates or locations. In this case, the trader is anticipating a narrowing of the basis (the difference) between Brent crude futures and the physical Brent crude available at Sullom Voe. The trader buys Brent crude futures, expecting the futures price to increase relative to the spot price at Sullom Voe. Simultaneously, they sell physical Brent crude at Sullom Voe, locking in a profit if the basis narrows as anticipated. This strategy works because the trader believes the market is undervaluing the physical crude at Sullom Voe relative to the futures contract. Several factors can influence the basis. Increased production in the North Sea, logistical bottlenecks at Sullom Voe, or a decrease in demand for Brent crude in the region could all widen the basis. Conversely, a decrease in North Sea production, improved logistical efficiency, or increased demand would narrow the basis. Regulatory changes, such as stricter environmental regulations affecting North Sea oil production, could also impact the basis. The key to calculating the profit or loss lies in comparing the initial basis with the final basis at the time of the trade’s closeout. The initial basis is $2.50/barrel (futures price – spot price). If the final basis is narrower, say $1.00/barrel, the trader profits. If the final basis is wider, say $4.00/barrel, the trader incurs a loss. In this specific case, the basis *widened* to $3.50/barrel. This means the futures price increased *less* than the spot price, or the spot price decreased *more* than the futures price. The loss is the difference between the final basis and the initial basis, multiplied by the number of barrels. Therefore, the loss is ($3.50 – $2.50) * 100,000 = $100,000. It’s crucial to consider the regulatory landscape. The UK’s Financial Conduct Authority (FCA) closely monitors commodity derivatives trading to prevent market abuse, including insider dealing and market manipulation. Traders must adhere to the Market Abuse Regulation (MAR), which prohibits activities that could distort the market. In this scenario, any attempt to artificially widen the basis through manipulative trading practices would be a serious breach of regulations.

The core of this question revolves around understanding how a “basis trade” operates in commodity derivatives, specifically within the context of UK regulations and market dynamics. A basis trade exploits the price difference between a commodity’s spot price and its futures price. The “basis” is this difference (Spot Price – Futures Price). The trader profits if the basis converges as the futures contract approaches expiration. Here’s the breakdown of the scenario and the calculation: 1. **Initial Basis:** Spot Price (£48/barrel) – Futures Price (£50/barrel) = -£2/barrel. This is a negative basis, meaning the futures price is higher than the spot price (contango). 2. **Trader’s Action:** Buys the physical commodity (spot) at £48 and sells the futures contract at £50. 3. **Storage Costs:** £0.50/barrel per month for 3 months = £1.50/barrel total. 4. **Final Prices:** Spot Price at expiration (£49/barrel), Futures Price at expiration (£49.50/barrel). The basis has narrowed. 5. **Profit/Loss Calculation:** * Profit on Spot: £49 (sell) – £48 (buy) = £1/barrel * Profit/Loss on Futures: £50 (sell) – £49.50 (buy back) = £0.50/barrel * Total Gross Profit: £1 + £0.50 = £1.50/barrel * Net Profit: £1.50 (Gross Profit) – £1.50 (Storage Costs) = £0/barrel Therefore, the trader breaks even on this basis trade. Now, let’s discuss why this question tests deeper understanding. It doesn’t just ask for a definition of “basis.” It requires applying the concept in a real-world scenario with costs involved. The storage costs are crucial, as they often determine the profitability of such trades. Furthermore, it subtly touches upon the regulatory aspect. While not explicitly stated, the trader’s actions are subject to market abuse regulations under UK law (e.g., MAR – Market Abuse Regulation). If the trader possessed inside information influencing either the spot or futures price, the trade could be illegal, even if profitable. The question assesses whether the candidate understands that simply making a profit doesn’t guarantee compliance. It tests the ability to synthesize market knowledge, cost considerations, and a fundamental awareness of the regulatory environment in which commodity derivatives operate. A naive trader might focus solely on the price movements and ignore the practical costs and regulatory implications, leading to an incorrect assessment of the trade’s viability and legality. This is a novel problem-solving approach because it combines financial calculation with awareness of external factors.

Let’s consider a scenario where a UK-based artisanal chocolate manufacturer, “Cocoa Dreams Ltd,” sources its cocoa beans primarily from Ghana. They use a combination of forward contracts and options on futures to manage price risk. Cocoa Dreams projects needing 50 tonnes of cocoa beans in six months. Current spot price is £2,000 per tonne. The six-month cocoa futures contract is trading at £2,100 per tonne. They enter into a forward contract to buy 25 tonnes at £2,080 per tonne to secure a portion of their needs. Simultaneously, they purchase 25 ‘at-the-money’ call options on cocoa futures contracts (each contract representing 10 tonnes) with a strike price of £2,100 per tonne, paying a premium of £100 per tonne. In six months, two scenarios unfold: Scenario 1: The spot price of cocoa rises to £2,300 per tonne. The futures price converges to the spot price, also at £2,300. Cocoa Dreams exercises its call options. The profit on each call option is (£2,300 – £2,100) – £100 = £100 per tonne. For 25 tonnes (2.5 contracts * 10 tonnes), the profit is 25 * £100 = £2,500. The forward contract secures 25 tonnes at £2,080. The remaining 25 tonnes are effectively bought at £2,100 (through the option) + £100 (premium) = £2,200. Their total cost is (25 * £2,080) + (25 * £2,200) = £52,000 + £55,000 = £107,000. Without hedging, purchasing 50 tonnes at £2,300 would have cost £115,000. Scenario 2: The spot price of cocoa falls to £1,900 per tonne. The futures price converges to the spot price, also at £1,900. Cocoa Dreams lets the call options expire worthless, losing the premium of £100 per tonne. The loss on the options is 25 * £100 = £2,500. The forward contract still obligates them to buy 25 tonnes at £2,080. They buy the remaining 25 tonnes at the spot price of £1,900. Their total cost is (25 * £2,080) + (25 * £1,900) + £2,500 = £52,000 + £47,500 + £2,500 = £102,000. Without hedging, purchasing 50 tonnes at £1,900 would have cost £95,000. The hedge increased their cost but provided price certainty for a portion of their cocoa. This example demonstrates how a company can use a combination of forward contracts and options on futures to manage price risk, balancing cost certainty with the potential to benefit from favorable price movements. The Financial Conduct Authority (FCA) regulates firms offering commodity derivatives in the UK. Firms must comply with MiFID II regulations, including reporting requirements and best execution standards.

The question assesses understanding of commodity swap valuation, specifically focusing on the impact of changes in the forward curve and correlation between different commodities on cross-commodity swaps. The core principle is that a swap’s value is the present value of the difference between the fixed rate and the expected floating rate payments over the swap’s life. Changes in the forward curve directly affect the expected floating rate payments. Furthermore, the correlation between the prices of the two commodities in a cross-commodity swap influences the volatility of the expected cash flows and, consequently, the swap’s overall value. In this scenario, the oil producer entered a swap to hedge against price fluctuations. The initial valuation was based on the forward curve at that time. As the forward curve shifts upwards, the expected floating rate payments (based on the Brent crude price) increase. This benefits the oil producer, who is receiving these higher floating payments in exchange for a fixed payment. The increase in the forward curve directly translates to a positive change in the swap’s value for the oil producer. The increased correlation between Brent crude and natural gas prices affects the uncertainty surrounding the net cash flows of the swap. Higher correlation reduces the diversification benefit of the swap and increases the overall risk. This higher risk should theoretically increase the value of the swap to the oil producer. However, the primary driver of the change in value is the shift in the forward curve. The discount rate used to calculate the present value of the expected cash flows also plays a crucial role. A higher discount rate would reduce the present value of future cash flows, partially offsetting the positive impact of the forward curve shift. The calculation is as follows (simplified for exam purposes, assuming annual payments and a single-period change): 1. **Initial Expected Floating Rate (based on initial forward curve):** Let’s assume this was initially £60/barrel. 2. **Fixed Rate:** £62/barrel (the rate agreed upon in the swap). 3. **New Expected Floating Rate (based on the shifted forward curve):** £68/barrel. 4. **Notional Amount:** 100,000 barrels. 5. **Discount Rate:** 5% (assumed). * **Initial Value (simplified):** \[(60 – 62) \times 100,000 / (1 + 0.05) = -£190,476\] (Negative for the oil producer initially). * **New Value (simplified):** \[(68 – 62) \times 100,000 / (1 + 0.05) = £571,429\] * **Change in Value:** \[£571,429 – (-£190,476) = £761,905\] Therefore, the value of the swap increases significantly for the oil producer.

The core of this question revolves around understanding the implications of basis risk within commodity derivatives, specifically in the context of hedging. Basis risk arises when the price of the asset being hedged (e.g., physical Brent Crude) doesn’t move perfectly in sync with the price of the hedging instrument (e.g., a WTI Crude futures contract). This imperfect correlation can lead to hedging outcomes that deviate from expectations. The scenario presented involves a refiner hedging Brent Crude purchases with WTI Crude futures. The key is to calculate the effective price paid, considering the initial hedge, the basis change, and the subsequent liquidation of the futures position. First, calculate the initial cost of the crude: 1000 barrels * $85/barrel = $85,000. The initial hedge profit is calculated as (selling price – purchase price) * number of barrels = ($84 – $82) * 1000 = $2,000. The change in basis is the difference between the change in Brent price and the change in WTI price: ($88 – $85) – ($86 – $82) = $3 – $4 = -$1. This means the basis weakened by $1 per barrel. The impact of the basis change on the hedge is -$1/barrel * 1000 barrels = -$1,000. The net profit from the hedge is the initial profit minus the impact of the basis change: $2,000 – $1,000 = $1,000. Therefore, the effective cost is the initial cost minus the net hedge profit: $85,000 – $1,000 = $84,000. The effective price per barrel is $84,000 / 1000 barrels = $84/barrel. This example highlights that even with a hedge in place, changes in the basis can significantly impact the final cost. A weakening basis, as in this case, erodes the effectiveness of the hedge. The question emphasizes the practical application of understanding basis risk, rather than simply defining it. It requires the candidate to integrate the concepts of hedging, futures contracts, and basis fluctuations to arrive at the correct answer. The incorrect options are designed to reflect common errors in calculating hedge effectiveness, such as ignoring the basis change or misinterpreting its impact.

The core of this question revolves around understanding how storage costs impact the price of commodity futures contracts, particularly within the context of contango and backwardation. Contango, where futures prices are higher than spot prices, typically reflects storage costs, insurance, and the time value of money. Backwardation, where futures prices are lower than spot prices, often indicates a strong immediate demand for the commodity. The calculation involves determining the breakeven futures price, considering the spot price, storage costs (including the opportunity cost of capital tied up in storage), and insurance. The formula to calculate the theoretical futures price is: Futures Price = Spot Price + Storage Costs + Insurance Costs – Convenience Yield Since convenience yield is not given, it is assumed to be zero for simplicity. Storage costs consist of direct costs and the opportunity cost of capital. The opportunity cost is calculated by multiplying the spot price by the risk-free rate (representing the return an investor could earn elsewhere). In this scenario, the spot price is £80 per barrel. The direct storage cost is £3 per barrel per year, and insurance is £1 per barrel per year. The risk-free rate is 5% per annum. The futures contract is for delivery in 6 months (0.5 years). First, calculate the total storage and insurance costs for the 6-month period: Total Storage Cost = £3/year * 0.5 year = £1.50 Total Insurance Cost = £1/year * 0.5 year = £0.50 Next, calculate the opportunity cost of capital for the 6-month period: Opportunity Cost = Spot Price * Risk-Free Rate * Time = £80 * 0.05 * 0.5 = £2 Now, calculate the theoretical futures price: Futures Price = £80 + £1.50 + £0.50 + £2 = £84 The breakeven futures price is £84. A futures price above this level would generate a profit for someone buying the commodity spot and storing it to deliver against the futures contract, while a price below this level would create an arbitrage opportunity in the opposite direction. Now, consider the impact of regulatory changes. If new UK regulations increase the capital requirements for commodity trading firms, it may lead to higher financing costs for these firms. This increased cost of capital could affect their willingness to hold inventory, potentially reducing the supply of the commodity available for future delivery. This, in turn, could decrease the futures price as firms are less willing to store the commodity. The magnitude of this effect would depend on the elasticity of supply and demand for the commodity and the extent of the regulatory impact on financing costs.

The question assesses understanding of the interrelationship between storage costs, convenience yield, and the theoretical futures price. The formula that connects these concepts is: Futures Price = Spot Price * e^( (Cost of Carry – Convenience Yield) * Time). The Cost of Carry includes storage costs, while the Convenience Yield reflects the benefit of holding the physical commodity. A higher convenience yield lowers the futures price relative to the spot price, reflecting the market’s expectation of readily available supply. The storage cost directly increases the cost of carry, thus increasing the futures price. The question requires the candidate to apply these concepts in a scenario involving changing storage costs and a given convenience yield to determine the impact on the futures price. First, calculate the initial futures price: Initial Futures Price = Spot Price * e^((Storage Cost – Convenience Yield) * Time) Initial Futures Price = 100 * e^((0.05 – 0.02) * 0.5) Initial Futures Price = 100 * e^(0.03 * 0.5) Initial Futures Price = 100 * e^(0.015) Initial Futures Price ≈ 100 * 1.015113 ≈ 101.51 Next, calculate the new futures price with increased storage costs: New Futures Price = Spot Price * e^((New Storage Cost – Convenience Yield) * Time) New Futures Price = 100 * e^((0.08 – 0.02) * 0.5) New Futures Price = 100 * e^(0.06 * 0.5) New Futures Price = 100 * e^(0.03) New Futures Price ≈ 100 * 1.030455 ≈ 103.05 Finally, calculate the difference between the new and initial futures prices: Difference = New Futures Price – Initial Futures Price Difference = 103.05 – 101.51 ≈ 1.54 The increase in storage costs leads to an increase in the futures price. This reflects the increased cost of carrying the physical commodity over time. The convenience yield partially offsets the storage cost, but the net effect of the increased storage cost is still an increase in the futures price. The correct answer is approximately 1.54. This demonstrates an understanding of how changes in storage costs affect futures prices, accounting for the moderating effect of convenience yield. A real-world example would be the impact of increased warehousing costs on the price of agricultural commodities futures contracts. If the cost of storing grain increases significantly due to factors like increased demand for storage space or new regulations, the futures price for grain would likely increase, all other factors being equal.

Let’s analyze a scenario involving a UK-based energy company, “Britannia Power,” hedging its natural gas purchases using a combination of futures contracts and options on futures. Britannia Power needs to secure a supply of 500,000 MMBtu of natural gas for delivery in December. They decide to hedge 60% of their exposure using December natural gas futures contracts listed on ICE Futures Europe and the remaining 40% using call options on those same futures contracts. Futures Contracts: Britannia Power sells short 300 contracts, each representing 1,000 MMBtu (300 contracts * 1,000 MMBtu/contract = 300,000 MMBtu), at a price of £2.50/MMBtu. Options on Futures: To hedge the remaining 200,000 MMBtu, Britannia Power buys 200 call option contracts (200 contracts * 1,000 MMBtu/contract = 200,000 MMBtu) with a strike price of £2.60/MMBtu at a premium of £0.05/MMBtu. Scenario 1: The price of December natural gas futures rises to £2.75/MMBtu. Britannia Power closes out its futures position at £2.75/MMBtu. The loss on the futures position is (£2.75 – £2.50) * 300,000 MMBtu = £75,000. The call options are in the money. The profit on the call options is (£2.75 – £2.60) * 200,000 MMBtu – (£0.05 * 200,000 MMBtu) = £30,000 – £10,000 = £20,000. The net loss is £75,000 – £20,000 = £55,000. Scenario 2: The price of December natural gas futures falls to £2.40/MMBtu. Britannia Power closes out its futures position at £2.40/MMBtu. The profit on the futures position is (£2.50 – £2.40) * 300,000 MMBtu = £30,000. The call options expire worthless. The loss on the call options is £0.05 * 200,000 MMBtu = £10,000. The net profit is £30,000 – £10,000 = £20,000. Scenario 3: The price of December natural gas futures settles at £2.60/MMBtu. Britannia Power closes out its futures position at £2.60/MMBtu. The loss on the futures position is (£2.60 – £2.50) * 300,000 MMBtu = £30,000. The call options are at the money. The loss on the call options is £0.05 * 200,000 MMBtu = £10,000. The net loss is £30,000 + £10,000 = £40,000. The key takeaway is that the combined strategy provides Britannia Power with downside protection (profit from futures if prices fall) and upside participation (potential profit from options if prices rise), but this comes at the cost of the option premium. The optimal strategy depends on Britannia Power’s risk aversion and their view on the future price volatility of natural gas. The choice of hedging 60% with futures and 40% with options allows Britannia Power to balance cost and risk management effectively.

To determine the most suitable hedging strategy, we need to analyze the exposure and the available derivative instruments. The refinery faces the risk of declining crack spreads, meaning the difference between the price of refined products (gasoline and heating oil) and the price of crude oil narrows. To hedge against this, the refinery needs to sell refined products and buy crude oil futures. The optimal strategy involves a combination of shorting gasoline and heating oil futures and longing crude oil futures. The hedge ratio should reflect the refinery’s output mix. Given the refinery’s output ratio of 2:1 (gasoline to heating oil), we need to weight the futures contracts accordingly. Let’s assume the refinery wants to hedge 1,000,000 barrels of crude oil equivalent. This translates to hedging 666,667 barrels of gasoline and 333,333 barrels of heating oil. A gasoline futures contract typically covers 42,000 gallons (or 1,000 barrels), and a heating oil futures contract also covers 42,000 gallons (or 1,000 barrels). A crude oil futures contract covers 1,000 barrels. To hedge the gasoline output, the refinery needs to short \( \frac{666,667}{1,000} = 667 \) gasoline futures contracts. To hedge the heating oil output, the refinery needs to short \( \frac{333,333}{1,000} = 333 \) heating oil futures contracts. To hedge the crude oil input, the refinery needs to long \( \frac{1,000,000}{1,000} = 1,000 \) crude oil futures contracts. However, the question specifies a strategy involving options on futures. The refinery can use put options on gasoline and heating oil futures to protect against a decline in refined product prices, and call options on crude oil futures to protect against an increase in crude oil prices. Buying put options gives the refinery the right, but not the obligation, to sell futures contracts at a specified price (strike price). Buying call options gives the refinery the right, but not the obligation, to buy futures contracts at a specified price. The most appropriate strategy is to buy put options on gasoline and heating oil futures and buy call options on crude oil futures, with the number of contracts reflecting the refinery’s output mix and crude oil input. The strike prices should be chosen based on the refinery’s risk tolerance and expectations for future price movements. A strike price slightly below the current market price for the put options and slightly above the current market price for the call options would provide downside protection while allowing the refinery to benefit from favorable price movements.

The core of this question lies in understanding how the contango or backwardation of a commodity futures curve impacts the hedging strategy of a gold producer. When a market is in contango (futures prices are higher than spot prices, and increase with delivery date), the producer faces a potential loss due to the negative roll yield when hedging by selling futures contracts. This roll yield arises because, as the futures contract nears expiration, its price converges to the spot price. The producer must continually “roll” their hedge by selling the expiring contract and buying a further-dated one. In contango, this means selling low (expiring contract) and buying high (further-dated contract), resulting in a loss. Conversely, in backwardation, futures prices are lower than spot prices and decrease with delivery date, the roll yield is positive, benefiting the hedger. To calculate the impact of the roll yield, we need to determine the price difference between the expiring contract and the new contract to which the hedge is rolled. In this case, the gold producer rolls 100 contracts. Each contract represents 100 troy ounces of gold. Therefore, the total gold hedged is 100 contracts * 100 ounces/contract = 10,000 troy ounces. The contango is $15/ounce (2024 contract price – 2023 contract price). This represents the cost of rolling the hedge for each ounce of gold. Therefore, the total roll cost is $15/ounce * 10,000 ounces = $150,000. The producer also incurs brokerage fees of $5 per contract. For 100 contracts, the total brokerage fees are 100 contracts * $5/contract = $500. The total cost of hedging, considering both the roll yield and brokerage fees, is $150,000 + $500 = $150,500. This is the amount by which the gold producer’s realized revenue will be reduced due to the hedging strategy. Now, consider a contrasting scenario. Suppose the gold market was in backwardation with the 2023 contract at $1,850 and the 2024 contract at $1,835. The roll yield would be positive ($15 per ounce), benefiting the producer. The revenue would increase by $150,000, partially offset by the $500 brokerage fee, resulting in a net gain of $149,500. This illustrates how market structure significantly impacts hedging outcomes.

The core of this question lies in understanding how contango and backwardation impact hedging strategies, specifically when a producer is selling forward. Contango, where future prices are higher than spot prices, erodes the benefit of a short hedge because the producer receives less than expected when closing out the hedge. Backwardation, where future prices are lower than spot prices, enhances the benefit of a short hedge, as the producer receives more than expected. The key is calculating the net realized price by considering the initial futures price, the change in the futures price over the hedging period, and the spot price at the time of sale. In this scenario, the producer initially hedges at £85/barrel. Over the three months, the futures price decreases by £5/barrel, meaning the producer gains £5/barrel on the hedge. However, the spot price at the time of sale is £82/barrel. The net realized price is the initial hedge price (£85) plus the gain on the hedge (£5) minus the difference between the initial spot price and the spot price at the sale (£0, since we are only concerned with the hedge impact), resulting in £90/barrel. This illustrates how backwardation benefits a short hedger. Consider a different scenario: Imagine a consumer hedging their future purchase of oil. If the market is in contango, they lock in a higher future price, but if the spot price rises even higher, they are still protected. Conversely, in backwardation, they might regret hedging if the spot price falls below the futures price they locked in. The decision to hedge depends on their risk aversion and expectation of future price movements. Now, consider a more complex situation involving cross-hedging. A company using jet fuel might hedge with crude oil futures. The effectiveness of this hedge depends on the correlation between jet fuel and crude oil prices. If the correlation is weak, the hedge might not provide the desired protection and could even increase the company’s risk. Understanding the basis risk (the risk that the price difference between the hedged asset and the hedging instrument will change) is crucial in such cases. Finally, think about the regulatory implications. In the UK, commodity derivatives trading is subject to regulations designed to prevent market manipulation and ensure fair trading practices. These regulations might include position limits, reporting requirements, and restrictions on certain types of trading activity. Failure to comply with these regulations can result in significant penalties.

The core of this question lies in understanding the interplay between storage costs, convenience yield, and the theoretical futures price. The futures price, in a simplified world, reflects the spot price compounded by the cost of carry (storage, insurance, financing) less any benefits derived from holding the physical commodity (convenience yield). A key nuance is that the convenience yield isn’t directly observable but is inferred from market prices. The formula connecting these elements is: Futures Price = Spot Price * exp((Cost of Carry – Convenience Yield) * Time to Maturity). In this scenario, the cost of carry is primarily storage, and we need to solve for the implied convenience yield. First, calculate the implied cost of carry: 8% financing + 2% insurance + 5% storage = 15%. Next, we use the futures price and spot price to back out the convenience yield. The futures price is 98, and the spot price is 90, and the time to maturity is 0.5 years. Using the formula: 98 = 90 * exp((0.15 – Convenience Yield) * 0.5) Divide both sides by 90: 98/90 = exp((0.15 – Convenience Yield) * 0.5) Take the natural logarithm of both sides: ln(98/90) = (0.15 – Convenience Yield) * 0.5 ln(98/90) ≈ 0.08515 Divide by 0.5: 0.08515 / 0.5 = 0.15 – Convenience Yield 0. 1703 ≈ 0.15 – Convenience Yield Convenience Yield ≈ 0.15 – 0.1703 Convenience Yield ≈ -0.0203 or -2.03% Since the question asks for the *net* cost of carry, we combine the storage costs with the (negative) convenience yield: 15% (cost of carry) – 2.03% (convenience yield) = 12.97%. Therefore, the closest answer is 12.97%. The negative convenience yield indicates a backwardation scenario where the futures price is lower than what the cost of carry would suggest, implying a high premium for immediate availability of the commodity. This might occur due to anticipated supply shortages or high immediate demand.

The core of this question lies in understanding how the contango or backwardation of a commodity market impacts the hedging strategy of a producer. When a market is in contango (futures price higher than the spot price), a producer selling futures to hedge faces the risk that the futures price converges towards the lower spot price as the contract nears expiry. This convergence erodes the initial hedging advantage. Conversely, in backwardation (futures price lower than the spot price), the futures price tends to rise toward the spot price, benefiting the hedger. The key is calculating the net effect of these price movements combined with storage costs and the producer’s minimum acceptable price. Let \(S_0\) be the initial spot price, \(F_0\) the initial futures price, \(S_T\) the spot price at delivery, and \(F_T\) the futures price at delivery. The producer sells futures at \(F_0\). Their effective selling price is \(F_0 + S_T – F_T – C\), where \(C\) is the storage cost. We want to find the minimum \(F_0\) such that the effective selling price is at least \(P\), the producer’s minimum acceptable price. So, \(F_0 + S_T – F_T – C \ge P\). Given \(S_0 = 80\), \(F_0 = 82\), \(S_T = 78\), \(C = 3\), and \(P = 79\). We need to calculate \(F_T\). Since the market is in contango and prices converge at delivery, we can approximate \(F_T\) by considering the relationship between the initial spot and futures prices and the final spot price. The initial spread was \(F_0 – S_0 = 2\). Assuming this spread narrows proportionally, we can estimate \(F_T = S_T + (F_0 – S_0) = 78 + 2 = 80\). Now, the effective selling price is \(82 + 78 – 80 – 3 = 77\). Since this is less than the producer’s minimum acceptable price of 79, the hedge was not successful. To find the minimum futures price needed, we set \(F_0 + 78 – 80 – 3 = 79\), which gives \(F_0 = 84\). The difference between the initial futures price (82) and the minimum required futures price (84) is 2. Therefore, the initial futures price would need to be at least £2 higher for the hedge to be successful. A useful analogy is to think of the futures contract as a “promise” to deliver at a future price. If the market conditions change unfavorably, the value of that promise erodes. The producer must factor in these potential erosions, along with storage costs, when deciding whether to hedge.

The core of this problem lies in 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 is defined as the difference between the spot price of an asset and the price of a related futures contract. Basis risk occurs because this difference is not constant and can change over time, affecting the effectiveness of the hedge. In this scenario, the coffee roaster is hedging their Arabica bean purchases using Robusta coffee futures. Arabica and Robusta are related, but their prices don’t move in perfect lockstep. Factors like weather patterns affecting specific growing regions, changes in consumer preferences (e.g., a shift towards higher-quality Arabica), or supply chain disruptions unique to each type of bean can cause the basis to fluctuate. To calculate the expected profit/loss, we need to consider the following: 1. **Initial Basis:** The initial basis is the difference between the spot price of Arabica and the futures price of Robusta at the time the hedge is initiated: £2100 – £1850 = £250. 2. **Final Basis:** The final basis is the difference between the spot price of Arabica and the futures price of Robusta at the time the hedge is lifted: £2250 – £2020 = £230. 3. **Change in Basis:** The change in basis is the difference between the final basis and the initial basis: £230 – £250 = -£20. This negative value indicates that the basis has *narrowed*. 4. **Hedge Outcome:** Since the roaster *bought* Robusta futures to hedge against rising Arabica prices, a narrowing basis means the futures position *underperformed* relative to the Arabica price movement. The roaster gained £2020 – £1850 = £170 on the futures contract. 5. **Spot Market Outcome:** The roaster had to pay £2250 instead of £2100 for Arabica, leading to a loss of £2250 – £2100 = £150 in the spot market. 6. **Net Outcome:** The net outcome is the sum of the futures profit and the spot market loss: £170 – £150 = £20 profit. Therefore, despite hedging, the roaster experienced a net profit of £20 per tonne due to the narrowing of the basis. This highlights that hedging with imperfectly correlated assets reduces, but doesn’t eliminate, price risk. The success of such a strategy depends heavily on understanding and managing basis risk. A wider basis would have resulted in a loss, demonstrating the inherent uncertainty. The roaster could explore other hedging instruments like options to further refine their risk management strategy. They could also investigate strategies to dynamically adjust their hedge ratio as the basis changes.

Let’s analyze a scenario involving a UK-based artisanal chocolate maker, “Cocoa Dreams,” who sources cocoa beans from Ghana. Cocoa Dreams wants to protect itself against potential price increases in cocoa beans over the next six months. They are considering using commodity derivatives. The current spot price of cocoa beans is £2,500 per tonne. The six-month cocoa futures contract is trading at £2,650 per tonne. Cocoa Dreams needs 50 tonnes of cocoa beans in six months. If Cocoa Dreams enters into a futures contract to buy 50 tonnes of cocoa at £2,650 per tonne, they lock in that price. If the spot price at the end of six months is higher than £2,650, Cocoa Dreams benefits. Conversely, if the spot price is lower, they lose out compared to buying on the spot market. Alternatively, Cocoa Dreams could buy call options on cocoa futures. Suppose a six-month call option on cocoa futures with a strike price of £2,700 costs £100 per tonne. This gives Cocoa Dreams the right, but not the obligation, to buy cocoa futures at £2,700. If the futures price at expiration is above £2,700, Cocoa Dreams will exercise the option, limiting their maximum purchase price to £2,700 plus the option premium (£100), or £2,800 per tonne. If the futures price is below £2,700, they will let the option expire and buy cocoa on the spot market. Another option is a swap. Cocoa Dreams could enter into a swap agreement with a bank where they agree to pay a fixed price of, say, £2,750 per tonne for 50 tonnes of cocoa in six months, while the bank pays them the prevailing spot price at that time. This effectively fixes Cocoa Dreams’ cocoa bean cost at £2,750 per tonne, regardless of the spot price in six months. Finally, Cocoa Dreams could enter into a forward contract with a local supplier to purchase 50 tonnes of cocoa in six months at a price of £2,700 per tonne. This is a private agreement between Cocoa Dreams and the supplier, customized to their specific needs. The best strategy depends on Cocoa Dreams’ risk appetite and their expectations for future cocoa prices. Futures offer price certainty but eliminate potential gains from price decreases. Options limit upside risk while allowing participation in price decreases (minus the premium). Swaps provide price stability and can be tailored to specific needs. Forwards offer customization but carry counterparty risk.

Let’s consider a scenario involving a power generation company, “Evergreen Energy,” that relies heavily on natural gas to fuel its power plants. Evergreen Energy anticipates a surge in electricity demand during the upcoming winter months. To mitigate the risk of increased natural gas prices, Evergreen Energy enters into a natural gas swap agreement with “Global Commodities Bank.” The swap is structured such that Evergreen Energy pays a fixed price of £0.75 per therm of natural gas, while Global Commodities Bank pays a floating price based on the average monthly Henry Hub natural gas spot price. The notional amount of the swap is 1,000,000 therms per month for six months. Now, let’s assume that the average monthly Henry Hub spot prices for the six months turn out to be: Month 1: £0.70, Month 2: £0.80, Month 3: £0.90, Month 4: £0.85, Month 5: £0.78, Month 6: £0.72. To determine the net cash flow for Evergreen Energy, we need to calculate the difference between the fixed price paid and the floating price received for each month, and then multiply by the notional amount. Month 1: (£0.70 – £0.75) * 1,000,000 = -£50,000 (Evergreen pays) Month 2: (£0.80 – £0.75) * 1,000,000 = £50,000 (Evergreen receives) Month 3: (£0.90 – £0.75) * 1,000,000 = £150,000 (Evergreen receives) Month 4: (£0.85 – £0.75) * 1,000,000 = £100,000 (Evergreen receives) Month 5: (£0.78 – £0.75) * 1,000,000 = £30,000 (Evergreen receives) Month 6: (£0.72 – £0.75) * 1,000,000 = -£30,000 (Evergreen pays) Total Net Cash Flow = -£50,000 + £50,000 + £150,000 + £100,000 + £30,000 – £30,000 = £250,000 Therefore, Evergreen Energy receives a net cash flow of £250,000 over the six-month period. This net positive cash flow indicates that the floating prices were, on average, higher than the fixed price, benefiting Evergreen Energy. Now consider how UK regulations, specifically those under the Financial Conduct Authority (FCA), would view Evergreen Energy’s activities. The FCA would be concerned with ensuring Evergreen Energy adequately discloses the risks associated with the swap, has sufficient capital to meet its obligations, and does not engage in market manipulation. Furthermore, the FCA would scrutinize whether the swap is used for genuine hedging purposes or speculative trading, with potential implications for Evergreen’s regulatory classification and reporting requirements. The swap’s documentation must comply with EMIR regulations, including mandatory clearing and reporting obligations.