Commodity Derivatives Quiz Exam Quiz 14

The core of this question revolves around understanding the implications of backwardation in commodity markets, specifically concerning storage costs and the behaviour of futures prices over time. Backwardation occurs when the spot price of a commodity is higher than its futures price, incentivizing immediate delivery and discouraging storage. The calculation to determine the break-even storage cost involves comparing the spot price with the futures price. If the futures price is *lower* than the spot price, the market is in backwardation. The difference between the spot and futures prices represents the *maximum* amount a storage company can charge before it becomes unprofitable to store the commodity. Any storage cost exceeding this difference would mean the storage company is better off selling the commodity immediately at the spot price rather than storing it and selling it later at the lower futures price. In this scenario, the spot price of copper is £8,500 per tonne, and the six-month futures price is £8,350 per tonne. The difference is £150 per tonne. This £150 represents the maximum storage cost a company can absorb over six months while still breaking even. To determine the monthly break-even cost, we divide the total six-month difference by six: £150 / 6 = £25 per tonne per month. This monthly figure represents the maximum storage cost that can be sustained before storage becomes economically unviable. A crucial element to consider is the risk-averse nature of storage companies. They typically demand a profit margin to compensate for risks such as spoilage, theft, or unexpected changes in market conditions. This profit margin reduces the maximum break-even storage cost. If a storage company requires a profit margin of, say, £5 per tonne per month, the maximum storage cost they can offer is reduced to £20 per tonne per month (£25 – £5 = £20). This highlights that backwardation not only indicates a current shortage but also directly influences storage economics, setting an upper limit on what storage providers can realistically charge. It also shows how futures prices act as a benchmark for storage costs and inventory management decisions.

The question explores the concept of a basis trade, specifically focusing on the impact of storage costs and convenience yield on the profitability of the trade. The basis is the difference between the spot price of a commodity and the price of a futures contract on that commodity. A trader attempts to exploit discrepancies between these prices, aiming to profit from their convergence. Storage costs directly increase the cost of holding the physical commodity, thereby widening the basis (futures price higher than spot). A higher convenience yield, reflecting the benefit of holding the physical commodity (e.g., to meet unexpected demand), narrows the basis (spot price higher relative to futures). The initial basis is calculated as Futures Price – Spot Price = £85 – £80 = £5. The trader enters a long spot/short futures position, meaning they buy the physical commodity at £80 and simultaneously sell a futures contract at £85. Over the contract period, storage costs amount to £2.50. This increases the effective cost of holding the physical commodity, impacting the basis. The convenience yield is £1. This offsets some of the storage costs, reflecting the value derived from holding the physical commodity. The adjusted basis at the contract’s expiration is calculated as: Initial Basis + Storage Costs – Convenience Yield = £5 + £2.50 – £1 = £6.50. At expiration, the spot price is £82 and the futures price is £88.50. The trader closes out their positions. They sell the physical commodity at the spot price of £82 and buy back the futures contract at £88.50. The profit/loss from the spot position is the difference between the selling price and the initial purchase price: £82 – £80 = £2. The profit/loss from the futures position is the difference between the initial selling price and the final purchase price: £85 – £88.50 = -£3.50. The total profit/loss is the sum of the profit/loss from the spot and futures positions: £2 – £3.50 = -£1.50. However, we must consider the initial expectation based on the initial basis and the adjusted basis. The trader expected the basis to converge, resulting in a profit equal to the initial basis. The change in the basis due to storage and convenience yield altered the outcome. The trader lost £1.50.

The core of this question revolves around understanding how storage costs, convenience yield, and interest rates interact to determine the theoretical price of a commodity futures contract. The formula that governs this relationship is: Futures Price = Spot Price * e^( (Cost of Carry) * Time to Maturity), where Cost of Carry = Storage Costs + Interest Rate – Convenience Yield. The question requires calculating the futures price based on given parameters, factoring in the impact of storage costs, interest rates, and the crucial, often overlooked, convenience yield. The convenience yield represents the benefit of holding the physical commodity rather than the futures contract. In this scenario, calculating the cost of carry is the first step. Storage costs are given as £5/tonne/year, and the annual interest rate is 3%. The convenience yield, which reflects the market’s expectation of future spot price increases or potential shortages, is estimated at 1.5%. Therefore, the cost of carry is £5 + 3% – 1.5% = 3.5% per year. Next, we apply the formula to calculate the futures price for a contract expiring in 9 months (0.75 years). Futures Price = £450 * e^(0.035 * 0.75). Calculating the exponent: 0.035 * 0.75 = 0.02625 e^(0.02625) ≈ 1.0266 Futures Price ≈ £450 * 1.0266 ≈ £461.97 Therefore, the theoretical futures price is approximately £461.97 per tonne. Understanding the impact of each component – storage costs, interest rates, and convenience yield – is crucial for accurately pricing commodity futures and understanding market dynamics. For instance, a higher convenience yield would reduce the futures price, reflecting a greater incentive to hold the physical commodity. Conversely, higher storage costs or interest rates would increase the futures price.

To determine the most suitable hedging strategy, we need to calculate the potential profit or loss from each strategy under different price scenarios and then assess the risk-reward profile. The key is to understand how the derivative instruments (futures and options) will behave as the underlying commodity price changes. * **Scenario 1: Price increases to £85/tonne:** * **No Hedge:** Profit = £5/tonne. * **Futures Hedge:** Locked in £80/tonne. No additional profit or loss. * **Call Option:** The call option with a strike price of £82/tonne will be exercised. Profit = £85 – £82 – £2 = £1/tonne. Net Price = £80 (initial sale) + £1 = £81/tonne. * **Put Option:** The put option will expire worthless. Net Price = £80 (initial sale) – £1 = £79/tonne. * **Scenario 2: Price decreases to £75/tonne:** * **No Hedge:** Loss = £5/tonne. * **Futures Hedge:** Locked in £80/tonne. No additional profit or loss. * **Call Option:** The call option will expire worthless. Net Price = £80 (initial sale) – £2 = £78/tonne. * **Put Option:** The put option with a strike price of £78/tonne will be exercised. Profit = £78 – £75 – £1 = £2/tonne. Net Price = £80 (initial sale) + £2 = £82/tonne. * **Scenario 3: Price remains at £80/tonne:** * **No Hedge:** No profit or loss. * **Futures Hedge:** Locked in £80/tonne. No additional profit or loss. * **Call Option:** The call option will expire worthless. Net Price = £80 (initial sale) – £2 = £78/tonne. * **Put Option:** The put option will expire worthless. Net Price = £80 (initial sale) – £1 = £79/tonne. Now, let’s analyze the risk-reward profiles: * **No Hedge:** Unlimited upside and downside. Highest risk, highest potential reward. * **Futures Hedge:** Eliminates both upside and downside. Lowest risk, but no potential for additional profit. * **Call Option:** Limits upside potential (capped at strike price + option premium) but allows for some downside protection (reduced by premium). * **Put Option:** Limits downside risk (floor at strike price – option premium) but sacrifices upside potential (reduced by premium). Given the farmer’s primary concern is to protect against downside risk while retaining some upside potential, the put option strategy is generally the most suitable. It provides a price floor, ensuring a minimum selling price, while still allowing the farmer to benefit if prices rise (albeit with a reduced profit due to the premium paid). The futures hedge eliminates all risk and reward, which might not be desirable if the farmer believes prices could increase significantly. The call option offers limited downside protection and caps potential profit. A key consideration is basis risk, which isn’t directly addressed in this simplified scenario. In reality, the futures price might not perfectly correlate with the farmer’s local selling price. The farmer must also consider margin requirements for futures contracts, which could tie up capital. Option strategies require paying a premium upfront, which is a guaranteed cost regardless of price movements.

Let’s consider a scenario where a UK-based artisanal chocolate manufacturer, “ChocoArtisan,” relies heavily on cocoa beans sourced from Ghana. ChocoArtisan wants to hedge against potential price increases in cocoa beans over the next 12 months. They decide to use cocoa futures contracts traded on the ICE Futures Europe exchange. To determine the number of contracts needed, we must first calculate ChocoArtisan’s total cocoa bean requirement. Assume ChocoArtisan uses 50 metric tons of cocoa beans per month, totaling 600 metric tons annually. One ICE cocoa futures contract represents 10 metric tons of cocoa. Therefore, ChocoArtisan needs to hedge 600/10 = 60 contracts. However, ChocoArtisan’s financial advisor suggests a “delta-neutral” approach to account for the possibility that ChocoArtisan might slightly reduce production if cocoa prices rise significantly, thus reducing their need for cocoa beans. The advisor estimates that for every 1% increase in cocoa prices, ChocoArtisan will reduce production by 0.2%. This is their “price elasticity of demand” for cocoa. Now, suppose ChocoArtisan initially hedges with 60 contracts. If cocoa prices increase by 10%, ChocoArtisan will reduce their cocoa bean usage by 10% * 0.2% = 2%. This means their new annual cocoa bean requirement is 600 * (1 – 0.02) = 588 metric tons. The initial hedge of 60 contracts covers 60 * 10 = 600 metric tons. The “over-hedged” amount is 600 – 588 = 12 metric tons. To achieve delta neutrality, ChocoArtisan should reduce their hedge by 12/10 = 1.2 contracts. Since they can’t trade fractional contracts, they should reduce the hedge by 1 contract. Therefore, the adjusted number of contracts for a delta-neutral hedge is 60 – 1 = 59 contracts.

Let’s consider a hypothetical scenario involving a UK-based energy company, “GreenPower UK,” which relies on natural gas for electricity generation. GreenPower UK wants to hedge against volatile natural gas prices using commodity derivatives. They use a combination of futures contracts, options, and swaps to manage their price risk. The company’s strategy involves a layered approach: they hedge a base level of consumption with futures, use options to protect against price spikes while still benefiting from price drops, and employ swaps to lock in a fixed price for a portion of their long-term gas needs. The key concept here is the combined use of different derivative instruments to create a comprehensive hedging strategy. Futures provide a baseline hedge, but lock in a specific price, removing upside potential. Options allow participation in favorable price movements while limiting downside risk, but require paying a premium. Swaps offer price certainty for the long term, but may not be flexible enough to adapt to changing consumption patterns. The optimal strategy balances these factors based on the company’s risk appetite, market outlook, and operational needs. Now, let’s examine the impact of market regulations on GreenPower UK’s hedging activities. Under UK EMIR regulations, GreenPower UK, as a financial counterparty (due to its derivatives activity exceeding certain thresholds), is required to report its derivatives transactions to a trade repository, implement risk mitigation techniques, and clear certain standardized OTC derivatives through a central counterparty (CCP). Suppose GreenPower UK fails to accurately report its transactions to the trade repository within the required timeframe. This would result in regulatory penalties. Furthermore, if GreenPower UK does not adequately collateralize its uncleared OTC derivatives, it would face increased counterparty credit risk and potential regulatory sanctions. The interaction of these derivatives and the regulatory landscape creates a complex environment for GreenPower UK to navigate.

To determine the fair value of the swap, we need to calculate the present value of the expected future cash flows. The key is to forecast the future price of crude oil using the forward curve and then determine the swap’s cash flows based on the difference between the fixed swap price and the forecasted future price. We then discount these cash flows back to the present to find the swap’s fair value. First, we need to understand the forward curve. The forward curve represents the market’s expectation of future prices. In this case, the forward curve is given as \(F(t) = 80 + 2t\), where \(t\) is the time in years. Next, we calculate the expected future prices for each year of the swap: – Year 1: \(F(1) = 80 + 2(1) = 82\) – Year 2: \(F(2) = 80 + 2(2) = 84\) – Year 3: \(F(3) = 80 + 2(3) = 86\) Now, we calculate the cash flows for each year. The swap price is fixed at $83. The cash flow is the difference between the future price and the swap price: – Year 1: \(82 – 83 = -1\) – Year 2: \(84 – 83 = 1\) – Year 3: \(86 – 83 = 3\) These cash flows need to be discounted back to the present using the risk-free rate of 5%. The present value of each cash flow is calculated as: – Year 1: \(\frac{-1}{(1 + 0.05)^1} = -0.9524\) – Year 2: \(\frac{1}{(1 + 0.05)^2} = 0.9070\) – Year 3: \(\frac{3}{(1 + 0.05)^3} = 2.5915\) Finally, we sum the present values of all cash flows to find the fair value of the swap: Fair Value = \(-0.9524 + 0.9070 + 2.5915 = 2.5461\) Therefore, the fair value of the swap is approximately $2.55. This calculation illustrates how commodity swaps are valued by considering the forward curve to estimate future prices and then discounting the expected cash flows. The result shows the present value of entering into the swap, reflecting the expected gains or losses based on the current market conditions. The discounting process is crucial as it accounts for the time value of money, ensuring that future cash flows are appropriately valued in today’s terms. The scenario also highlights the importance of understanding forward curves and risk-free rates in derivatives valuation.

The question focuses on the interplay between storage costs, convenience yield, and the equilibrium futures price. It tests the understanding of how these factors combine to influence the pricing of commodity futures contracts, and how changes in one factor impact the others. The calculation is based on the cost of carry model, adjusted for convenience yield. The convenience yield represents the benefit of holding the physical commodity rather than the futures contract. The formula used is: Futures Price = Spot Price * (1 + Risk-Free Rate + Storage Costs – Convenience Yield). The risk-free rate is the return an investor can expect from a risk-free investment over the life of the futures contract. The storage costs are the costs associated with storing the physical commodity over the life of the futures contract. The convenience yield represents the benefit of holding the physical commodity rather than the futures contract. In this scenario, the spot price is £450/tonne, the risk-free rate is 5% per annum (2.5% for 6 months), storage costs are £15/tonne for 6 months, and the convenience yield is 3% per annum (1.5% for 6 months). Therefore, the futures price is calculated as follows: Futures Price = £450 * (1 + 0.025 + (15/450) – 0.015) Futures Price = £450 * (1 + 0.025 + 0.0333 – 0.015) Futures Price = £450 * (1.0433) Futures Price = £469.49 Now, consider a scenario where unforeseen logistical bottlenecks significantly increase storage costs. These bottlenecks reduce the availability of storage, driving up prices. If the market anticipates these bottlenecks will persist, the convenience yield might also be affected, as immediate access to the commodity becomes even more valuable. For example, a manufacturer needing the commodity for production may be willing to pay a premium to avoid disruptions. In this case, the increased storage costs and potentially a lower convenience yield will drive up the futures price. If storage costs increase to £30/tonne and the market assesses the convenience yield to decrease to 1% per annum (0.5% for 6 months) due to the increased value of having the physical commodity readily available, the new futures price would be: Futures Price = £450 * (1 + 0.025 + (30/450) – 0.005) Futures Price = £450 * (1 + 0.025 + 0.0667 – 0.005) Futures Price = £450 * (1.0867) Futures Price = £489.02 This increase in futures price reflects the higher cost of carry and the reduced benefit of holding the physical commodity.

The core of this question lies in understanding how contango and backwardation, combined with storage costs and the convenience yield, influence the decision-making process of a commodity trader using a calendar spread strategy. A calendar spread involves simultaneously buying and selling futures contracts of the same commodity but with different expiration dates. Contango is a market situation where future prices are higher than the spot price, or distant delivery prices are higher than near delivery prices. Backwardation is the opposite, where future prices are lower than the spot price. Storage costs are the expenses incurred in storing the physical commodity, while convenience yield represents the benefit of holding the physical commodity rather than a futures contract. In this scenario, the trader is evaluating whether to roll their near-month contract into a far-month contract. The decision hinges on whether the difference in prices between the two contracts (the spread) adequately compensates for the costs associated with storage and the forgone convenience yield. Here’s the breakdown of the calculation: 1. **Calculate the spread:** The far-month contract is priced at £85 per tonne, and the near-month contract is priced at £80 per tonne. The spread is £85 – £80 = £5 per tonne. 2. **Calculate the total cost of carry:** The storage cost is £3 per tonne, and the convenience yield is £4 per tonne. The net cost of carry is storage cost minus convenience yield: £3 – £4 = -£1 per tonne. A negative cost of carry indicates that the convenience yield outweighs the storage cost, making it more attractive to hold the physical commodity. 3. **Evaluate the profitability:** The trader needs to determine if the spread is greater than the cost of carry. In this case, the spread (£5) is greater than the cost of carry (-£1). Therefore, the calendar spread is profitable. The profit is the spread minus the cost of carry: £5 – (-£1) = £6 per tonne. The key here is recognizing that the convenience yield reduces the effective cost of carry. Even with storage costs, the significant benefit derived from having the physical commodity available (convenience yield) makes the overall cost of carry negative. This makes the calendar spread, capturing the contango, an attractive opportunity. Therefore, the trader should roll the near-month contract into the far-month contract, as the £5 spread more than covers the net cost of carry, resulting in a profit of £6 per tonne. This decision is based on the market structure, storage economics, and the inherent value of physical commodity availability.

The core of this question revolves around understanding how margin requirements function in commodity futures trading, particularly in the context of adverse price movements and the potential for margin calls. The initial margin is the deposit required to open a futures position. The maintenance margin is the minimum amount of equity that must be maintained in the account. If the equity falls below this level, a margin call is triggered, requiring the trader to deposit additional funds to bring the account back to the initial margin level. In this scenario, we must calculate the cumulative losses incurred over the three days and determine if these losses trigger a margin call. The trader starts with an initial margin of £6,000. On day 1, they lose £1,200, reducing their equity to £4,800. On day 2, they lose an additional £1,500, further reducing their equity to £3,300. Finally, on day 3, they lose £1,800, bringing their equity down to £1,500. The maintenance margin is £4,000. Since the equity of £1,500 is below the maintenance margin, a margin call is triggered. To calculate the amount of the margin call, we need to determine how much money the trader needs to deposit to bring the account back to the initial margin level of £6,000. The difference between the initial margin and the current equity is £6,000 – £1,500 = £4,500. Therefore, the trader needs to deposit £4,500 to satisfy the margin call. This question tests the understanding of margin mechanics, including initial margin, maintenance margin, and margin calls. It goes beyond simple definitions by requiring the application of these concepts in a practical scenario with multiple price fluctuations. It also tests the understanding of the consequences of failing to meet a margin call, which can include the liquidation of the position. A common misconception is to calculate the margin call based on the maintenance margin instead of the initial margin. Another is to only consider the loss on the final day.

Let’s consider a hypothetical energy company, “NovaFuel UK,” operating under UK regulations. NovaFuel UK needs to hedge its exposure to price fluctuations in Brent Crude oil. They enter into a swap agreement with a financial institution, “Global Derivatives Ltd.” The swap is a fixed-for-floating swap where NovaFuel UK pays a fixed price of $80 per barrel and receives a floating price based on the average monthly Brent Crude price. The notional amount is 100,000 barrels per month for 12 months. To analyze the cash flows, we need to consider the floating price each month. Let’s assume the average monthly Brent Crude prices for the first three months are $75, $82, and $85 respectively. Month 1: Floating price = $75. NovaFuel UK pays $80 and receives $75, resulting in a net payment of $5 per barrel. Total payment = $5 * 100,000 = $500,000. Month 2: Floating price = $82. NovaFuel UK pays $80 and receives $82, resulting in a net receipt of $2 per barrel. Total receipt = $2 * 100,000 = $200,000. Month 3: Floating price = $85. NovaFuel UK pays $80 and receives $85, resulting in a net receipt of $5 per barrel. Total receipt = $5 * 100,000 = $500,000. Now, let’s introduce a regulatory change. Assume that halfway through the swap’s term, the UK government, in response to concerns about speculative trading in commodity derivatives as outlined in updated guidelines from the Financial Conduct Authority (FCA), imposes a new transaction tax of £0.50 per barrel on all commodity derivative transactions settled physically or financially. The exchange rate at the time of the transaction is 1.25 USD/GBP. This tax impacts the cash flows. For example, in month 2, the net receipt was $200,000. The tax will reduce the receipts. Tax per barrel = £0.50 * 1.25 = $0.625. Total tax = $0.625 * 100,000 = $62,500. The net receipt after tax becomes $200,000 – $62,500 = $137,500. The key takeaway is that regulatory changes can significantly affect the profitability and hedging effectiveness of commodity derivatives. Companies must stay informed about evolving regulations and adjust their strategies accordingly. This example illustrates how a seemingly small tax per barrel can have a substantial impact on the overall cash flows of a large commodity swap. This highlights the need for robust risk management and compliance frameworks within commodity trading firms. Furthermore, it underscores the importance of understanding the legal and regulatory landscape surrounding commodity derivatives trading, as non-compliance can lead to significant financial penalties and reputational damage.

The core of this question revolves around understanding how basis risk arises in hedging strategies using commodity derivatives, particularly when the commodity underlying the derivative doesn’t perfectly match the commodity being hedged. Basis risk is the risk that the price of the hedging instrument (e.g., a futures contract on West Texas Intermediate (WTI) crude oil) will not move exactly in tandem with the price of the asset being hedged (e.g., Brent crude oil or jet fuel). This discrepancy can arise due to differences in quality, location, or timing. The formula to estimate the effective hedge ratio, considering basis risk, involves calculating the correlation between the changes in the spot price of the asset being hedged and the changes in the futures price of the hedging instrument, then multiplying this correlation by the ratio of the standard deviation of the spot price changes to the standard deviation of the futures price changes. This adjusted hedge ratio aims to minimize the variance of the hedged position. In this scenario, the refinery is hedging jet fuel (derived from Brent crude) with WTI futures. The correlation factor reflects the degree to which WTI futures price movements reflect Brent-related jet fuel price movements. The standard deviation ratio adjusts for the relative volatility of jet fuel versus WTI. Let’s assume the refinery decides to hedge 80% of its anticipated jet fuel production for the next quarter. They expect to produce 1,000,000 barrels of jet fuel. The current spot price of jet fuel is $90/barrel. They use WTI crude oil futures to hedge, as there are no liquid jet fuel futures contracts available. The correlation between jet fuel price changes and WTI futures price changes is 0.8. The standard deviation of jet fuel price changes is $2.50/barrel, and the standard deviation of WTI futures price changes is $3.00/barrel. First, we calculate the optimal hedge ratio: \[ \text{Hedge Ratio} = \text{Correlation} \times \frac{\text{Standard Deviation of Spot Price}}{\text{Standard Deviation of Futures Price}} \] \[ \text{Hedge Ratio} = 0.8 \times \frac{2.50}{3.00} = 0.8 \times 0.8333 = 0.6666 \] This suggests the refinery should hedge approximately 66.66% of its exposure to minimize variance. However, the refinery initially intended to hedge 80%. The question asks us to assess the implications of hedging more than the variance-minimizing hedge ratio. Hedging more than the optimal ratio means the refinery is over-hedging. Over-hedging can reduce potential gains if jet fuel prices rise because the refinery has locked in a price on a larger portion of its production. It also increases transaction costs associated with the larger hedge position. The refinery is essentially betting that jet fuel prices will decline. Conversely, hedging less than the optimal ratio (under-hedging) leaves the refinery exposed to potential losses if jet fuel prices fall, but it also allows them to benefit more if prices rise.

The core of this question lies in understanding how basis risk arises in hedging strategies, particularly when the commodity being hedged and the commodity underlying the futures contract are not perfectly correlated. Basis is defined as the difference between the spot price of the commodity being hedged and the price of the related futures contract. Basis risk arises because this difference is not constant and can change unpredictably over time. The formula to calculate the hedge ratio, which minimizes risk, is given by: \[ \text{Hedge Ratio} = \rho \cdot \frac{\sigma_{\text{spot}}}{\sigma_{\text{futures}}} \] where: – \(\rho\) is the correlation coefficient between the spot price changes and the futures price changes. – \(\sigma_{\text{spot}}\) is the standard deviation of the spot price changes. – \(\sigma_{\text{futures}}\) is the standard deviation of the futures price changes. In this scenario, the refinery is hedging jet fuel using crude oil futures. The correlation between jet fuel and crude oil is 0.8. The standard deviation of jet fuel price changes is 0.03, and the standard deviation of crude oil futures price changes is 0.04. Plugging these values into the formula: \[ \text{Hedge Ratio} = 0.8 \cdot \frac{0.03}{0.04} = 0.8 \cdot 0.75 = 0.6 \] This means that for every unit of jet fuel the refinery wants to hedge, they should short 0.6 units of crude oil futures contracts to minimize basis risk. To hedge 1,000,000 gallons of jet fuel, the refinery needs to short: \[ 1,000,000 \text{ gallons} \cdot 0.6 = 600,000 \text{ gallons equivalent of crude oil futures} \] Since each futures contract is for 1,000 barrels and each barrel contains 42 gallons, each contract covers \(1,000 \cdot 42 = 42,000\) gallons. Therefore, the number of contracts needed is: \[ \frac{600,000 \text{ gallons}}{42,000 \text{ gallons/contract}} \approx 14.29 \text{ contracts} \] Since futures contracts can only be traded in whole numbers, the refinery would need to short 14 contracts. The critical aspect here is understanding that the hedge ratio isn’t simply a 1:1 relationship due to the imperfect correlation and differing volatilities. It’s a calculated ratio that minimizes the variance of the hedged position, accounting for the basis risk. Failing to account for the correlation or the standard deviations would lead to an under- or over-hedged position, increasing the refinery’s exposure to price fluctuations. The rounding to the nearest whole number of contracts introduces a slight imperfection in the hedge, but it is unavoidable in practice.

The question explores the impact of contango and backwardation on hedging strategies using commodity futures, specifically within the context of a UK-based energy company. The optimal hedging strategy depends on the shape of the futures curve and the company’s risk appetite. In contango, futures prices are higher than expected spot prices at delivery. This means that hedging by selling futures contracts locks in a price that is initially higher than the expected spot price. However, as the contract approaches expiration, the futures price converges towards the spot price. This convergence erodes the initial profit, resulting in a “roll yield” loss. The energy company needs to sell more contracts to cover the same volume of commodity as time goes on, increasing the cost of hedging. In backwardation, futures prices are lower than expected spot prices at delivery. Hedging by selling futures contracts locks in a price that is initially lower than the expected spot price. As the contract approaches expiration, the futures price converges towards the spot price, resulting in a “roll yield” gain. The energy company can sell fewer contracts to cover the same volume of commodity as time goes on, decreasing the cost of hedging. Risk appetite plays a crucial role. A risk-averse company might prioritize certainty and accept the roll yield loss in contango to lock in a price. A risk-seeking company might prefer to remain unhedged or use more complex strategies involving options to potentially benefit from price movements. The calculation involves comparing the outcomes of hedging in contango and backwardation, considering the roll yield and the company’s risk tolerance. The best strategy is the one that aligns with the company’s risk profile and market expectations. The question is designed to assess not just the understanding of contango and backwardation, but also the ability to apply this knowledge in a practical hedging scenario and to consider the impact of risk appetite on hedging decisions.

The core of this question lies in understanding how basis risk arises in hedging strategies, specifically when the commodity underlying the futures contract differs from 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. The formula to determine the effective price received is: Effective Price = Spot Price at Sale + Initial Futures Price – Final Futures Price. The key here is to recognize that the refinery is hedging jet fuel (a refined product), with crude oil futures. The price difference between crude oil and jet fuel is the source of basis risk. The refinery locks in a profit margin by hedging. The initial futures price is £80/barrel, and the refinery sells the jet fuel when crude is £75/barrel and the futures contract closes at £77/barrel. The effective price is £75 + £80 – £77 = £78. The refinery needs to consider the basis risk, which is the difference between the price movement of crude oil futures and jet fuel. The refinery also needs to consider the storage cost, transportation cost, and refining costs. Let’s consider an analogy: Imagine a baker who wants to hedge the price of flour using wheat futures. If the price of wheat goes up, the baker expects the price of flour to go up as well. However, the price of flour may not go up by the same amount as the price of wheat, due to factors such as milling costs, transportation costs, and demand for flour. This difference in price movement is basis risk. The baker can reduce basis risk by using a hedging strategy that is more closely correlated with the price of flour, such as using flour futures (if available) or using a combination of wheat futures and other hedging instruments. Another example would be an airline hedging jet fuel costs using crude oil futures. Jet fuel is derived from crude oil, but the refining process and market demand can create price discrepancies. The airline faces basis risk because jet fuel prices may not perfectly track crude oil prices. Factors like refinery capacity, seasonal demand for heating oil, and geopolitical events can influence the spread between crude oil and jet fuel.

To determine the impact on the refinery’s profit, we need to calculate the change in revenue from processing the crude oil and subtract the change in the cost of the crude oil itself, considering the hedging strategy. First, calculate the unhedged profit impact: * Change in crack spread: $5/barrel * Unhedged profit impact: 100,000 barrels * $5/barrel = $500,000 Next, determine the impact of the futures contracts: * Number of contracts: 100,000 barrels / 1,000 barrels/contract = 100 contracts * Change in futures price: $4/barrel * Profit on futures contracts: 100 contracts * 1,000 barrels/contract * $4/barrel = $400,000 Now, consider the option contracts. Since the refinery bought put options, they benefit if the price *decreases*. The strike price is $80, and the final price is $74, so the put options are in the money. * Profit per barrel from options: $80 – $74 – $2 = $4/barrel (Strike Price – Final Price – Premium) * Total profit from options: 100,000 barrels * $4/barrel = $400,000 The combined impact of the futures and options is $400,000 + $400,000 = $800,000. This is *additional* profit because the hedge protected against a price decrease. Finally, determine the overall profit impact by adding the unhedged profit impact and the hedging profit: * Overall profit impact: $500,000 (unhedged) + $800,000 (hedged) = $1,300,000 Therefore, the refinery’s overall profit is increased by $1,300,000 due to the combined effect of the change in the crack spread and the hedging strategy using futures and options. This scenario highlights the importance of understanding how different hedging instruments interact. Futures contracts provide a linear hedge, while options provide asymmetric protection, allowing participation in favorable price movements while limiting downside risk. The key is to carefully consider the specific risk profile and objectives when designing a hedging strategy. A refinery seeking to protect its profit margin needs to assess the potential impact of price fluctuations in both crude oil and refined products, and then choose the appropriate combination of hedging instruments to achieve the desired level of protection. The choice between futures, options, or a combination thereof depends on the refinery’s risk tolerance and its view on future price movements.

Let’s analyze the hedging strategy of the hypothetical artisanal chocolate maker, “Cocoa Dreams,” against cocoa price volatility using futures contracts. Cocoa Dreams needs 50 tonnes of cocoa in six months. One cocoa futures contract is for 10 tonnes. They decide to hedge by buying futures contracts. The current spot price is £3,000 per tonne, and the six-month futures price is £3,100 per tonne. Six months later, the spot price is £2,800 per tonne, and the futures price is £2,850 per tonne. Cocoa Dreams buys 50 tonnes of cocoa in the spot market at £2,800 per tonne. Simultaneously, they close out their futures position by selling the futures contracts at £2,850 per tonne. First, calculate the number of futures contracts: 50 tonnes / 10 tonnes per contract = 5 contracts. Next, calculate the profit or loss on the futures contracts: Selling price: £2,850 per tonne Purchase price: £3,100 per tonne Loss per tonne: £3,100 – £2,850 = £250 per tonne Total loss on futures contracts: 5 contracts * 10 tonnes/contract * £250/tonne = £12,500 Then, calculate the cost of buying cocoa in the spot market: 50 tonnes * £2,800 per tonne = £140,000 Finally, calculate the effective cost of cocoa after hedging: £140,000 (spot market cost) + £12,500 (futures loss) = £152,500 Effective price per tonne: £152,500 / 50 tonnes = £3,050 per tonne. This example illustrates how hedging with futures contracts can provide price certainty but doesn’t guarantee the best possible price. Cocoa Dreams effectively paid £3,050 per tonne, which is less than the initial futures price (£3,100) but more than the final spot price (£2,800). The futures market acted as a risk management tool, mitigating the impact of price fluctuations. The key takeaway is that hedging locks in a price range, offering protection against adverse price movements, but forgoing potential benefits from favorable price changes. This is especially important in the context of regulations like those outlined by the FCA, which require firms to demonstrate sound risk management practices.

The core of this question revolves around understanding how regulatory changes, specifically those impacting position limits and reporting requirements under UK law (derived from MiFID II and potentially amended post-Brexit by UK legislation), affect a commodity trading firm’s operational costs and hedging strategies. Increased regulatory scrutiny, exemplified by stricter position limits and more frequent reporting, leads to several direct and indirect cost increases. Direct costs include the expenses associated with enhanced monitoring systems needed to track positions in real-time and ensure compliance with the new limits. Firms also incur costs related to increased staffing or training to handle the expanded reporting obligations to regulatory bodies like the FCA. These reports often require detailed breakdowns of trading activity, counterparties, and underlying exposures. Indirect costs are more subtle. Stricter position limits can constrain a firm’s ability to execute large hedging strategies efficiently. For example, a firm hedging a large physical commodity inventory might need to use more derivative contracts and spread them across different delivery months or exchanges to stay within the position limits. This can increase transaction costs and potentially reduce the effectiveness of the hedge. Furthermore, increased reporting frequency can divert resources from core trading activities, leading to opportunity costs. The scenario presented involves a UK-based commodity trading firm dealing in Brent Crude Oil futures. The question tests the candidate’s ability to assess how these regulatory changes impact the firm’s overall cost structure and hedging effectiveness. A key aspect is recognizing that the regulatory changes force the firm to adjust its hedging strategies, which can have both cost and risk management implications. The correct answer identifies the combined impact of increased monitoring and reporting costs, coupled with the potential inefficiencies introduced into hedging strategies due to position limits. The incorrect options focus on only one aspect of the impact or misunderstand the nature of the regulatory changes.

To determine the most suitable hedging strategy, we need to analyze the refinery’s exposure to price fluctuations in both crude oil (input) and gasoline (output). The refinery profits from the “crack spread,” which is the difference between the price of gasoline and the price of crude oil. The refinery’s goal is to lock in a profitable crack spread to protect its margins. A short hedge in crude oil futures protects against a decrease in crude oil prices, which would negatively impact the refinery’s input costs. A long hedge in gasoline futures protects against a decrease in gasoline prices, which would negatively impact the refinery’s revenue. Combining these two strategies allows the refinery to lock in a specific crack spread. Let’s analyze the different hedging strategies: * **Short hedge in crude oil futures, long hedge in gasoline futures:** This strategy protects against both a decrease in crude oil prices and a decrease in gasoline prices, effectively locking in the crack spread. If crude oil prices fall, the refinery profits from the short hedge, offsetting the decrease in the value of its crude oil inventory. If gasoline prices fall, the refinery profits from the long hedge, offsetting the decrease in revenue from gasoline sales. * **Long hedge in crude oil futures, short hedge in gasoline futures:** This strategy is the opposite of the correct strategy and would expose the refinery to losses if crude oil prices rise and gasoline prices fall. * **Short hedge in both crude oil and gasoline futures:** This strategy protects against a decrease in both crude oil and gasoline prices, but it does not lock in the crack spread. The refinery would still be exposed to changes in the difference between the two prices. * **Long hedge in both crude oil and gasoline futures:** This strategy protects against an increase in both crude oil and gasoline prices, but it does not lock in the crack spread. The refinery would still be exposed to changes in the difference between the two prices. The optimal strategy for the refinery is to use a short hedge in crude oil futures and a long hedge in gasoline futures to lock in a profitable crack spread. This protects the refinery from adverse price movements in both its input and output markets.

Let’s analyze a scenario involving a junior trader, Anya, at a UK-based trading firm, “Thames Commodities Ltd,” who’s tasked with managing the firm’s exposure to Brent crude oil price fluctuations. Thames Commodities has a long-term contract to supply jet fuel to several airlines, effectively making them short Brent crude (the primary component of jet fuel). Anya decides to use a combination of futures and options to hedge this exposure, but she’s relatively new to the complexities of commodity derivatives. First, Anya calculates the firm’s total exposure: Thames Commodities is obligated to supply 500,000 barrels of jet fuel per month for the next 12 months. To hedge this, she needs to consider rolling futures contracts. She decides to use Brent crude oil futures contracts, each representing 1,000 barrels. Therefore, she needs to hedge 500 contracts per month. To manage the risk associated with potential price increases, Anya initially considers a simple futures hedge, shorting 500 Brent crude futures contracts for each month. However, she’s concerned about the possibility of a significant price *decrease*, as this would mean Thames Commodities would be locked into selling jet fuel at a higher price than the market price of crude oil. This is where options come in. Anya decides to implement a collar strategy. She buys call options with a strike price of $85 per barrel (to protect against price increases) and sells put options with a strike price of $75 per barrel (to generate income and partially offset the cost of the call options). Both options expire in one month. The call options cost $2 per barrel, and the put options generate $1 per barrel. Now, consider a scenario where, at the option expiry date, Brent crude oil is trading at $90 per barrel. Anya will exercise her call options, limiting Thames Commodities’ exposure to the price increase above $85. She will not be assigned on her short put options, as the price is above $75. The effective price Thames Commodities pays for crude oil is capped at $85 (strike price of the call) + $2 (call premium) – $1 (put premium) = $86 per barrel. If, instead, the price had fallen to $70, Anya would be assigned on her short put options, obligating her to buy crude at $75. The effective price she pays would then be $75 + $2 (call premium) – $1 (put premium) = $76 per barrel. This strategy aims to provide Thames Commodities with a range within which their crude oil costs are relatively stable, balancing the need for protection against price increases with the desire to benefit from potential price decreases. The key is understanding the interplay between futures, calls, and puts, and how they can be combined to create a tailored hedging strategy.

The core of this question lies in understanding how a commodity swap allows counterparties to manage price risk and achieve desired price exposures. The calculation involves determining the equivalent fixed price a company would be willing to pay in a swap to hedge against fluctuating spot prices, given its risk aversion and market expectations. The forward curve provides a benchmark for future spot prices. However, the company’s risk aversion dictates a premium it’s willing to pay above the forward curve to secure price certainty. This premium is reflected in the risk premium. The Equivalent Fixed Price (EFP) is calculated by summing the forward prices for each period, adding the risk premium for each period, and then averaging the total. This average represents the fixed price the company is willing to pay to eliminate price volatility. The calculation ensures the company’s overall cost remains predictable, despite market fluctuations. The formula is: \[EFP = \frac{\sum_{i=1}^{n} (F_i + RP_i)}{n}\] where \(F_i\) is the forward price for period \(i\), \(RP_i\) is the risk premium for period \(i\), and \(n\) is the number of periods. In this case: EFP = \(\frac{(50 + 2) + (52 + 3) + (54 + 4) + (56 + 5)}{4}\) = \(\frac{52 + 55 + 58 + 61}{4}\) = \(\frac{226}{4}\) = 56.5 The correct answer is therefore £56.50. The incorrect options are designed to reflect common errors in understanding or calculation. Option b) neglects the risk premium, focusing solely on the forward curve. Option c) incorrectly applies the risk premium, possibly subtracting it instead of adding it. Option d) misinterprets the averaging process, potentially weighting the forward prices or risk premiums incorrectly. These errors represent typical misunderstandings of how risk aversion and market expectations are incorporated into commodity swap pricing.

The core of this question revolves around understanding how storage costs impact the relationship between spot prices and futures prices in commodity markets, particularly within the context of the UK regulatory environment. The cost of carry model dictates that the futures price should approximate the spot price plus the costs of storing the commodity until the delivery date. These costs include warehousing, insurance, financing, and any potential spoilage. In this scenario, the additional regulation imposing stricter environmental controls on storage facilities directly increases the cost of storage. This increased cost needs to be factored into the futures price. If the market participants believe that the new regulations are permanent and will consistently increase storage costs, then the futures price will increase to reflect these higher costs. Let’s break down the calculation: 1. **Initial Cost of Carry:** Assume the initial cost of carry (storage, insurance, financing) is £5 per tonne per month. For 6 months, this totals £30 per tonne. 2. **New Regulatory Costs:** The new regulations add an additional £2 per tonne per month, totaling £12 per tonne over 6 months. 3. **Total Cost of Carry:** The new total cost of carry becomes £30 + £12 = £42 per tonne. 4. **Impact on Futures Price:** The futures price should increase by the amount of the increased cost of carry. Therefore, the futures price should increase by approximately £12 per tonne. The incorrect answers are designed to test common misunderstandings. Option B suggests a decrease, which is incorrect as increased costs should lead to higher futures prices. Option C incorrectly attributes the price change solely to increased demand, ignoring the direct impact of storage costs. Option D considers only the initial storage cost and fails to account for the impact of the new regulations. The question tests the candidate’s ability to apply the cost of carry model in a real-world scenario with regulatory changes.

To determine the most suitable hedging strategy, we need to calculate the hedge ratio and then assess the impact of basis risk. The hedge ratio is calculated as the correlation between the spot price and the futures price multiplied by the ratio of the standard deviation of the spot price changes to the standard deviation of the futures price changes. This gives us the number of futures contracts needed to hedge the exposure. The formula is: Hedge Ratio = Correlation * (σ_spot / σ_futures). In this scenario, the correlation is 0.8, the standard deviation of spot price changes is £0.06/tonne, and the standard deviation of futures price changes is £0.08/tonne. Therefore, the hedge ratio is 0.8 * (0.06 / 0.08) = 0.6. The company needs to hedge 5,000 tonnes of copper. The contract size is 25 tonnes. So, without considering the hedge ratio, the company would need 5,000 / 25 = 200 contracts. However, with the hedge ratio of 0.6, the company needs 200 * 0.6 = 120 contracts. Next, we must evaluate the impact of basis risk. Basis risk arises because the spot price and the futures price do not always move perfectly in tandem. The risk is that the basis (the difference between the spot and futures price) can change unexpectedly, reducing the effectiveness of the hedge. A perfect hedge eliminates all price risk, but basis risk introduces some residual risk. The extent of basis risk is proportional to the correlation between spot and futures prices; a lower correlation implies higher basis risk. Given the correlation is 0.8, the basis risk is moderate. The company should implement a hedging strategy using 120 futures contracts. This strategy will reduce the price risk associated with the copper inventory, but it will not eliminate it entirely due to basis risk. Understanding the degree of basis risk is critical for assessing the overall effectiveness of the hedge. If the correlation were significantly lower (e.g., 0.3), the basis risk would be much higher, and the company might consider alternative hedging strategies or accept a higher level of price risk.

The core of this question revolves around understanding the interplay between storage costs, convenience yield, and the resulting impact on futures prices within a commodity market, specifically concerning UK regulations and market practices. The formula to calculate the theoretical futures price is: Futures Price = Spot Price * e^( (Cost of Carry – Convenience Yield) * Time to Maturity). The cost of carry includes storage, insurance, and financing costs. Convenience yield reflects the benefit of holding the physical commodity. In this scenario, we are given the spot price of Brent Crude, the storage costs, the risk-free rate (used for financing costs), and the convenience yield. We need to calculate the theoretical futures price for a contract expiring in 6 months (0.5 years). First, calculate the cost of carry: * Storage Costs: £3/barrel/year * Financing Costs: Spot Price * Risk-Free Rate = £80 * 0.05 = £4/barrel/year * Total Cost of Carry = £3 + £4 = £7/barrel/year Next, calculate the net cost of carry by subtracting the convenience yield: * Net Cost of Carry = Cost of Carry – Convenience Yield = £7 – £5 = £2/barrel/year Now, calculate the futures price using the formula: * Futures Price = £80 * e^(2 * 0.5) = £80 * e^(1) = £80 * 2.71828 ≈ £82.16 However, the question introduces a regulatory change: increased scrutiny on storage facilities, leading to higher compliance costs. This directly impacts storage costs, a key component of the cost of carry. The compliance costs increase storage by £1.50/barrel/year. The new cost of carry becomes: * Storage Costs: £3 + £1.50 = £4.50/barrel/year * Financing Costs: £4/barrel/year (unchanged) * Total Cost of Carry = £4.50 + £4 = £8.50/barrel/year The new net cost of carry is: * Net Cost of Carry = £8.50 – £5 = £3.50/barrel/year Finally, the new theoretical futures price is: * Futures Price = £80 * e^(3.50 * 0.5) = £80 * e^(1.75) = £80 * 5.7546 ≈ £84.60 Therefore, the new theoretical futures price, considering the regulatory change, is approximately £84.60. This highlights how regulatory changes affecting storage directly influence commodity derivatives pricing. The convenience yield represents the benefit to the holder of physically owning the commodity instead of a derivative, and it can fluctuate based on supply and demand dynamics. Higher compliance costs for storage decrease the incentive to hold physical inventory, potentially increasing the convenience yield, but this is not directly factored into the calculation here as the convenience yield is provided. This question tests the candidate’s ability to integrate regulatory impacts into standard commodity pricing models.

The core of this question lies in understanding how contango and backwardation, along with storage costs, influence the decision-making process of a commodity trading firm when evaluating the profitability of storing a physical commodity and simultaneously selling a futures contract. The trader needs to compare the total cost of storage, including financing, with the potential profit derived from the spread between the spot price and the futures price. The trader must also take into account the time value of money, discounting future profits to their present value for an accurate comparison. First, calculate the total storage cost per tonne: £5 (insurance) + £15 (warehouse) = £20. Next, determine the financing cost per tonne: £500 (spot price) * 0.05 (annual interest rate) * (6/12) (6-month period) = £12.50. The total cost of carry per tonne is then: £20 (storage) + £12.50 (financing) = £32.50. The futures price needs to cover this cost to make the strategy viable. The current spread is £520 – £500 = £20. The trader requires an additional £32.50 – £20 = £12.50 price increase in the futures contract to break even. Considering the regulations, the trader must also factor in potential margin calls and position limits imposed by UK regulatory bodies like the FCA. These rules can restrict the size of the position and increase the capital required, influencing the overall profitability and risk assessment. The trader must also consider the impact of the Market Abuse Regulation (MAR) which prohibits insider dealing and market manipulation. Any information about a significant supply disruption, for instance, that isn’t public, can’t be used to justify a trading decision. The breakeven futures price would need to be £500 + £32.50 = £532.50. Therefore, the trader needs to evaluate if the futures price is expected to reach at least £532.50 in six months to make the storage and hedging strategy worthwhile, considering the inherent risks and regulatory landscape. This is a nuanced decision that requires careful analysis of market conditions, storage costs, financing rates, and regulatory constraints.

The core of this question revolves around understanding the implications of contango and backwardation on hedging strategies using commodity futures, specifically within the context of a UK-based energy company navigating the complexities of the Brent crude oil market under FCA regulations. When a market is in contango, the futures price is higher than the spot price. This means that a hedger selling futures to lock in a price for future production will effectively receive a lower price than the current spot price, as the futures price converges towards the spot price at expiration. This difference represents a cost of carry, which includes storage, insurance, and financing costs. Conversely, in backwardation, the futures price is lower than the spot price, benefiting the hedger who sells futures. In this scenario, the energy company needs to determine the optimal hedging strategy considering the market’s contango, storage limitations, and the impact of rolling futures contracts. Rolling futures involves closing out an expiring contract and opening a new one further into the future. In a contango market, each roll results in selling the expiring contract at a lower price and buying the new contract at a higher price, leading to a roll yield loss. To minimize the cost of hedging in contango, the company might consider strategies such as selective hedging (hedging only a portion of their production), using shorter-dated futures contracts (although this increases roll frequency), or exploring alternative hedging instruments like options to provide price protection with limited downside. The FCA requires firms to demonstrate that their hedging strategies are prudent and aligned with their risk management objectives. The optimal strategy depends on the company’s risk appetite, storage capacity, and expectations regarding future price movements. For example, if the company anticipates that the contango will widen, it might be more beneficial to delay hedging or use options strategies to capitalize on potential price increases while limiting downside risk. The correct answer needs to consider the cost of carry implied by the contango, the roll yield loss from rolling futures contracts, and the limitations imposed by storage capacity. It should also reflect the company’s need to comply with FCA regulations regarding prudent risk management.

The core of this question lies in understanding the interplay between contango, backwardation, storage costs, and the decision-making process of a physical commodity trader. The trader’s arbitrage opportunity arises from the difference between the future price and the spot price, adjusted for storage and financing costs. First, calculate the total storage cost: £0.15/barrel/month * 6 months = £0.90/barrel. Next, calculate the total financing cost: £45/barrel * 0.05 (annual interest rate) * (6/12) (fraction of year) = £1.125/barrel. The total cost of carry is the sum of storage and financing costs: £0.90 + £1.125 = £2.025/barrel. The theoretical future price should be the spot price plus the cost of carry: £45 + £2.025 = £47.025/barrel. Since the actual future price is £48.50/barrel, the future price is higher than the theoretical future price. This indicates contango, but more importantly, an arbitrage opportunity. The trader can buy the commodity at the spot price (£45), store it for six months, and simultaneously sell a six-month futures contract at £48.50. This locks in a profit. After six months, the trader delivers the commodity against the futures contract, receiving £48.50. The total cost of buying, storing, and financing the commodity is £45 + £2.025 = £47.025. The profit is the difference between the futures price and the total cost: £48.50 – £47.025 = £1.475/barrel. However, we must consider the margin requirements. The initial margin is £4/barrel. This margin is essentially a performance bond and is returned to the trader (with interest or adjustments) when the contract is closed. It does not represent a cost in the same way as storage or financing. The variation margin is only applicable if the price moves against the trader’s position during the contract’s life. In this scenario, we assume that the trader is able to meet all margin calls, and we are only looking at the final profit upon delivery. Therefore, the trader’s arbitrage profit is £1.475 per barrel. This assumes perfect execution and no unexpected costs. It’s crucial to note that in real-world scenarios, transaction costs (brokerage fees, exchange fees) would further reduce the profit. Also, the interest earned on the margin account could slightly increase the overall return. The key takeaway is that the arbitrage opportunity arises because the futures price is sufficiently high to cover all costs associated with buying, storing, and financing the commodity, leaving a profit margin. This demonstrates a deep understanding of cost of carry model and arbitrage in commodity derivatives.

The question explores the concept of basis risk in commodity futures trading, specifically in the context of hedging jet fuel purchases. Basis risk arises because the price movement of the futures contract used for hedging (Brent crude oil in this case) may not perfectly correlate with the price movement of the underlying commodity being hedged (jet fuel). Several factors contribute to basis risk, including differences in location (jet fuel at Heathrow vs. Brent crude pricing point), quality (specific jet fuel specifications vs. generic crude oil), and timing (futures contract maturity vs. actual jet fuel purchase date). The calculation of the expected hedge effectiveness involves several steps. First, we need to determine the expected change in the spot price of jet fuel. The problem states that jet fuel prices are expected to increase by 5%. The initial spot price of jet fuel is £800/tonne, so the expected increase is \(0.05 \times £800 = £40\). Therefore, the expected spot price at the purchase date is \(£800 + £40 = £840\). Next, we determine the expected change in the futures price of Brent crude oil. The problem states that Brent crude oil futures are expected to increase by 7%. The initial futures price is £700/tonne, so the expected increase is \(0.07 \times £700 = £49\). Therefore, the expected futures price at the delivery date is \(£700 + £49 = £749\). The airline hedges its purchase by buying futures contracts. Therefore, the profit or loss on the futures contracts is the difference between the selling price (the initial futures price) and the buying price (the expected futures price). In this case, the airline sells at £700 and buys back at £749, resulting in a loss of \(£749 – £700 = -£49\) per tonne. The effective price paid by the airline is the expected spot price minus the profit or loss on the futures contracts. In this case, it’s \(£840 – £49 = £791\). Hedge effectiveness is calculated as the percentage reduction in price volatility achieved by the hedge. In this scenario, we calculate it as the difference between the unhedged price and the hedged price, divided by the unhedged price increase. The unhedged price increase is £40 (from £800 to £840). The reduction in price due to hedging is \(£40 – (£791 – £800) = £40 – (-£9) = £49\). Hedge effectiveness is therefore \(£49 / £40 = 1.225\), or 122.5%. However, since the effective price is lower than the initial price, the hedge effectiveness is greater than 100%. To correctly interpret this, we consider the hedge’s impact relative to the expected price increase. The hedge not only offset the expected increase but also resulted in a lower effective price than the initial spot price. The question asks for the *expected* hedge effectiveness, focusing on the anticipated outcome based on the given price movements.

To determine the optimal hedging strategy, we need to calculate the hedge ratio that minimizes the variance of the hedged portfolio. The hedge ratio is calculated as the correlation between the spot price and the futures price, multiplied by the ratio of the standard deviation of the spot price to the standard deviation of the futures price. In this case, the correlation is 0.8, the standard deviation of the spot price is 0.15, and the standard deviation of the futures price is 0.20. Hedge Ratio = Correlation * (Standard Deviation of Spot Price / Standard Deviation of Futures Price) Hedge Ratio = 0.8 * (0.15 / 0.20) = 0.8 * 0.75 = 0.6 Since the company wants to hedge 100,000 barrels of crude oil and each futures contract is for 1,000 barrels, the number of contracts needed is the hedge ratio multiplied by the exposure divided by the contract size. Number of Contracts = Hedge Ratio * (Exposure / Contract Size) Number of Contracts = 0.6 * (100,000 / 1,000) = 0.6 * 100 = 60 Therefore, the company should short 60 futures contracts to minimize its risk exposure. This strategy aims to offset potential losses in the physical crude oil market due to price declines by gains in the futures market. For instance, consider a scenario where the spot price of crude oil falls by 10%. Without hedging, the company would experience a direct loss on its inventory. However, by shorting futures contracts, the company can profit from the decline in futures prices, offsetting a portion of the loss in the physical market. The hedge ratio of 0.6 indicates that for every $1 change in the spot price, the futures price is expected to change by $0.6, thus requiring a smaller position in the futures market to effectively hedge the exposure. The use of futures contracts allows the company to transfer the price risk associated with its crude oil inventory to speculators willing to take on that risk. The effectiveness of the hedge depends on the correlation between the spot and futures prices remaining relatively stable. If the correlation weakens, the hedge may become less effective, leading to basis risk.