Leveraged Trading Quiz Exam Quiz 02

The question assesses understanding of how leverage affects margin requirements and potential losses in a volatile market. A higher leverage ratio means a smaller initial margin is required, but it also amplifies both potential gains and losses. The initial margin is calculated as the position value divided by the leverage ratio. In this case, the initial margin is £200,000 / 20 = £10,000. If the asset’s value drops by 6%, the loss is 6% of £200,000, which equals £12,000. Since the loss (£12,000) exceeds the initial margin (£10,000), the client will receive a margin call. The client must deposit enough funds to restore the account to the initial margin level. The shortfall is £12,000 (loss) – £10,000 (initial margin) = £2,000. To bring the account back to the initial margin requirement of £10,000, the client needs to deposit £2,000. Let’s consider an analogy. Imagine you’re using a small down payment (the margin) to control a large house (the asset). High leverage is like using a tiny down payment. If the house price drops even a little, the value of your house could fall below what you owe, and you’d need to add more money (margin call) to cover the difference. A lower leverage ratio is like a larger down payment. You have more equity at risk, but you’re less likely to face a margin call if the house price fluctuates. Now, let’s consider a scenario where the leverage was 10. The initial margin would be £200,000 / 10 = £20,000. A 6% drop would still result in a £12,000 loss, but because the initial margin is £20,000, no margin call would be triggered. This illustrates how lower leverage provides a buffer against market volatility.

The Net Free Equity (NFE) is calculated by subtracting the total liabilities from the total assets. In this scenario, the total assets are the initial margin plus the profit or loss from the trade. The total liabilities are the initial margin requirement. The leverage ratio is then calculated by dividing the total value of the position by the NFE. Here’s the calculation: 1. **Calculate the Profit/Loss:** The trader bought 10,000 shares at £5.00 and sold them at £5.50, resulting in a profit of (£5.50 – £5.00) * 10,000 = £5,000. 2. **Calculate Total Assets:** The total assets are the initial margin (£10,000) plus the profit (£5,000), which equals £15,000. 3. **Calculate Net Free Equity (NFE):** The NFE is the total assets (£15,000) minus the initial margin requirement (£10,000), resulting in £5,000. 4. **Calculate Total Value of Position:** The total value of the position is the number of shares (10,000) multiplied by the initial purchase price (£5.00), which equals £50,000. 5. **Calculate Leverage Ratio:** The leverage ratio is the total value of the position (£50,000) divided by the NFE (£5,000), resulting in a leverage ratio of 10:1. This example illustrates how profits and losses affect the net free equity and, consequently, the leverage ratio. A higher profit increases NFE, reducing the leverage ratio, while a loss would decrease NFE, increasing the leverage ratio. Understanding this relationship is crucial for managing risk in leveraged trading. The initial margin acts as a security deposit, while the NFE represents the trader’s actual equity available to absorb potential losses. The leverage ratio is a dynamic measure that reflects the risk exposure relative to the trader’s capital. Regulatory bodies like the FCA in the UK often impose limits on leverage ratios to protect retail investors from excessive risk.

The core concept tested is the understanding of how margin requirements and leverage interact to determine the maximum potential loss a client faces in leveraged trading, specifically within the context of UK regulations and a firm’s internal risk management policies. The question requires calculating the total potential loss, considering the initial margin, the potential price movement against the trader’s position, and the impact of the firm’s specific close-out policy. First, determine the total value of the position: 5000 shares * £20/share = £100,000. The initial margin is 5% of this value: £100,000 * 0.05 = £5,000. The price movement against the position is £20 – £17 = £3 per share. The total loss due to price movement is 5000 shares * £3/share = £15,000. However, the firm has a close-out policy of 80% of the initial margin. This means the position will be closed out when the loss reaches 20% of the initial margin. The initial margin is £5,000, so the close-out trigger is when the account equity falls to £5,000 * 0.20 = £1,000. This implies a loss of £5,000 – £1,000 = £4,000 before close-out. The question asks for the *maximum* potential loss. The maximum loss will occur *before* the close-out policy is triggered if the price moves significantly against the position. In this scenario, the trader deposited £5,000 and the price moved from £20 to £17. The loss due to the price movement of £3 per share is calculated as: 5000 * £3 = £15,000. However, the trader only deposited £5,000, so the maximum loss cannot exceed the initial deposit. The close-out policy aims to prevent losses exceeding the initial margin by a substantial amount. The maximum potential loss, considering the close-out policy, is the initial margin plus any additional loss incurred before the position is closed. The key is to understand that the close-out policy is designed to *limit* losses, not eliminate them entirely. The firm’s policy allows a loss of 80% of the initial margin before close-out. Therefore, the trader could lose the entire initial margin (£5,000) before the close-out is triggered. The maximum potential loss is capped by the initial margin deposit. Therefore, the maximum potential loss is £5,000.

The core of this question revolves around understanding how leverage impacts the Net Asset Value (NAV) of a fund employing derivatives, particularly in the context of potential market shocks and regulatory limits. The fund’s initial state is crucial: it’s leveraged 3:1, meaning for every £1 of investor capital, it controls £3 of assets. The key is to calculate the impact of a 15% market decline on those assets and, consequently, on the fund’s NAV. First, calculate the total asset value controlled by the fund: £100 million (NAV) * 3 (leverage) = £300 million. A 15% decline in these assets results in a loss of £300 million * 0.15 = £45 million. This loss directly reduces the fund’s NAV. The new NAV becomes £100 million (initial NAV) – £45 million (loss) = £55 million. Next, assess the leverage ratio after the market decline. The fund still controls the same £300 million in assets (although their value has decreased). The leverage ratio is now £300 million (assets) / £55 million (NAV) = 5.45:1. Finally, determine if the fund breaches the FCA’s 6:1 leverage limit. Since 5.45:1 is less than 6:1, the fund remains within the regulatory limit. The fund manager must still take action to reduce the leverage to the target of 3:1, but they have not breached the limit yet. This scenario highlights the amplified impact of market movements on leveraged funds and the importance of regulatory oversight. Consider a tightrope walker using a long pole for balance (leverage). A slight gust of wind (market volatility) can be easily corrected. However, a sudden strong gust (market shock) can dramatically shift their center of gravity, making it harder to stay balanced. The regulatory limit acts as a safety net, preventing the tightrope walker from straying too far and potentially falling. This question isn’t just about calculations; it’s about understanding the interplay between leverage, market risk, and regulatory constraints in a practical setting.

To determine the maximum potential loss, we first need to calculate the total exposure created by the leveraged trade. The trader used a leverage ratio of 15:1 on an initial margin of £8,000. This means the total value of the assets controlled is 15 times the margin. Therefore, the total exposure is \( 15 \times £8,000 = £120,000 \). Now, we need to determine the price at which the trader would face a margin call. A margin call occurs when the equity in the account falls below the maintenance margin. In this case, the maintenance margin is 4% of the total exposure. So, the maintenance margin level is \( 0.04 \times £120,000 = £4,800 \). The amount the trader can lose before a margin call is triggered is the difference between the initial margin and the maintenance margin: \( £8,000 – £4,800 = £3,200 \). Finally, we need to calculate the percentage price decrease that would result in this loss. The percentage decrease is calculated as the loss divided by the total exposure: \( \frac{£3,200}{£120,000} \times 100\% \approx 2.67\% \). Therefore, the maximum percentage price decrease the trader can withstand before a margin call is triggered is approximately 2.67%. This calculation demonstrates the amplified risk associated with leveraged trading. Even a small percentage decrease in the asset’s value can lead to a significant loss relative to the initial margin, potentially triggering a margin call. The leverage magnifies both potential gains and potential losses, making risk management crucial in leveraged trading. Understanding these calculations is vital for traders to assess and manage their exposure effectively, especially in volatile markets. Ignoring these calculations can result in unexpected losses and forced liquidation of positions.

The question tests the understanding of how leverage impacts both potential profits and losses, and the risk management considerations when using leveraged ETFs. The calculation involves determining the daily percentage change of the index, applying the leverage factor of the ETF, and then calculating the resulting price of the ETF. The key is understanding that leveraged ETFs rebalance daily, which means the leverage factor is applied to the *daily* return, not the cumulative return over multiple days. Here’s the calculation: Day 1: Index starts at 8000, ends at 8080. Percentage change = \[\frac{8080-8000}{8000} \times 100 = 1\%\] ETF percentage change = 3 * 1% = 3% ETF price at end of Day 1 = 100 + (3% of 100) = 103 Day 2: Index starts at 8080, ends at 7999. Percentage change = \[\frac{7999-8080}{8080} \times 100 = -1.002475\%\] (approximately -1.00%) ETF percentage change = 3 * -1.002475% = -3.007425% (approximately -3.01%) ETF price at end of Day 2 = 103 + (-3.007425% of 103) = 103 – 3.09764775 = 99.90235225 (approximately 99.90) Day 3: Index starts at 7999, ends at 8055. Percentage change = \[\frac{8055-7999}{7999} \times 100 = 0.7001\%\] (approximately 0.70%) ETF percentage change = 3 * 0.7001% = 2.1003% (approximately 2.10%) ETF price at end of Day 3 = 99.90235225 + (2.1003% of 99.90235225) = 99.90235225 + 2.0982 = 101.99 (approximately 102.00) Therefore, the approximate price of the ETF at the end of Day 3 is £102.00. A crucial point is that leveraged ETFs are designed for short-term trading. The daily rebalancing means that over longer periods, the cumulative return of the ETF can deviate significantly from three times the cumulative return of the underlying index, due to the compounding effect of daily returns. This phenomenon, known as volatility drag, can erode returns, especially in volatile markets. Consider a scenario where an index fluctuates significantly up and down over a month but ends up at roughly the same level it started. A 3x leveraged ETF tracking this index could experience substantial losses during that month, even though the index itself saw little net change. This highlights the importance of active monitoring and risk management when trading leveraged ETFs.

The question explores the impact of operational leverage on a firm’s sensitivity to changes in sales volume, particularly when combined with financial leverage. Operational leverage arises from fixed operating costs. High operational leverage means a large portion of costs are fixed, so a small change in sales volume leads to a larger change in operating income (EBIT). Financial leverage, on the other hand, arises from the use of debt financing. Higher financial leverage means a larger portion of financing comes from debt, increasing the sensitivity of net income to changes in EBIT. The degree of operating leverage (DOL) is calculated as: \[DOL = \frac{\% \Delta EBIT}{\% \Delta Sales}\] The degree of financial leverage (DFL) is calculated as: \[DFL = \frac{\% \Delta Net Income}{\% \Delta EBIT}\] The degree of total leverage (DTL) is calculated as: \[DTL = DOL \times DFL = \frac{\% \Delta Net Income}{\% \Delta Sales}\] In this scenario, we need to determine the combined impact of operational and financial leverage on the change in net income given a change in sales. The firm’s fixed operating costs and interest expenses are crucial in determining the degree of operational and financial leverage, respectively. The combined leverage effect magnifies the impact of sales changes on net income. A higher degree of total leverage implies a greater sensitivity of net income to sales fluctuations. The question challenges the understanding of how these two types of leverage interact and amplify the effects of changes in sales on a firm’s profitability. To solve this, we first calculate the new EBIT and Net Income based on the increased sales. Original Sales: £5,000,000 Original Variable Costs: £2,000,000 Original Fixed Operating Costs: £1,500,000 Original EBIT: £5,000,000 – £2,000,000 – £1,500,000 = £1,500,000 Interest Expense: £500,000 Original Net Income: £1,500,000 – £500,000 = £1,000,000 New Sales: £5,000,000 * 1.05 = £5,250,000 New Variable Costs: £2,000,000 * 1.05 = £2,100,000 Fixed Operating Costs remain the same: £1,500,000 New EBIT: £5,250,000 – £2,100,000 – £1,500,000 = £1,650,000 Interest Expense remains the same: £500,000 New Net Income: £1,650,000 – £500,000 = £1,150,000 Percentage Change in Net Income: \[ \frac{New\,Net\,Income – Original\,Net\,Income}{Original\,Net\,Income} \times 100 = \frac{1,150,000 – 1,000,000}{1,000,000} \times 100 = 15\% \]

Let’s break down the mechanics of margin calls and their impact on leveraged trading. A margin call occurs when the equity in a trader’s account falls below the maintenance margin requirement. This requirement is set by the broker to protect them from losses if the trader’s position moves against them. The maintenance margin is usually a percentage of the total value of the position. In this scenario, we’re looking at a situation where a trader, Amelia, uses significant leverage. The initial margin is what Amelia deposited to open the position. The maintenance margin is the minimum equity Amelia must maintain in her account to keep the position open. If the market moves against Amelia and her equity drops below the maintenance margin, she will receive a margin call. She will then need to deposit additional funds to bring her equity back up to the initial margin level (or close the position). To calculate the price at which Amelia will receive a margin call, we need to determine how much the asset’s price can fall before her equity drops below the maintenance margin. The formula to calculate the margin call price is: Margin Call Price = Purchase Price * (1 – (Initial Margin – Maintenance Margin) / Leverage) In Amelia’s case, the purchase price is £25, the initial margin is 40% (0.40), the maintenance margin is 25% (0.25), and the leverage is 10. Plugging these values into the formula: Margin Call Price = £25 * (1 – (0.40 – 0.25) / 10) Margin Call Price = £25 * (1 – (0.15 / 10)) Margin Call Price = £25 * (1 – 0.015) Margin Call Price = £25 * 0.985 Margin Call Price = £24.625 Therefore, Amelia will receive a margin call when the asset’s price falls to £24.625. Let’s illustrate with an analogy: Imagine Amelia is buying a house worth £250,000 and taking out a mortgage (leverage). Her initial deposit (initial margin) is £100,000 (40%). The bank (broker) has a minimum equity requirement (maintenance margin) of £62,500 (25% of £250,000). If the house price falls, reducing Amelia’s equity below £62,500, the bank will ask Amelia to deposit more money to bring her equity back up, or they will foreclose (close the position). The margin call price calculation determines at what house price this would happen.

The core of this question lies in understanding how leverage impacts the margin requirements and potential losses in a short selling scenario involving a Contract for Difference (CFD). A CFD allows traders to speculate on the price movement of an asset without owning it. Short selling a CFD means betting that the price of the asset will decrease. Leverage amplifies both potential profits and losses. Initial margin is the upfront capital required to open the position, while variation margin is the additional capital needed to cover losses as the price moves against the trader. In this scenario, the trader shorts 5000 shares of company XYZ at £5.00 per share using a CFD with a leverage ratio of 10:1. This means the trader only needs to deposit 1/10th of the total value of the position as initial margin. The initial margin is calculated as (5000 shares * £5.00/share) / 10 = £2500. The price then increases to £5.50. The loss on the short position is (5000 shares * (£5.50 – £5.00)) = £2500. The question asks for the total margin required to maintain the position. This includes the initial margin plus any variation margin required to cover losses. In this case, the variation margin is equal to the loss of £2500. Therefore, the total margin required is £2500 (initial margin) + £2500 (variation margin) = £5000. Now consider a slightly different scenario: a trader using leverage is like a driver speeding down a winding road. The leverage is the speed. A small miscalculation (a slight turn of the wheel) at high speed (high leverage) can lead to a much larger deviation from the intended path (larger losses). The initial margin is like the driver’s initial fuel in the tank. If the road gets unexpectedly long and winding (the price moves significantly against the trader), the driver needs more fuel (variation margin) to continue the journey (maintain the position). If the driver runs out of fuel (margin call), the journey ends abruptly (the position is closed).

To determine the required initial margin, we must first calculate the total exposure of the leveraged positions. Trader X has two positions: a long position in Alpha shares valued at £150,000 and a short position in Beta shares valued at £100,000. The total exposure is the sum of these two positions: £150,000 + £100,000 = £250,000. The initial margin requirement is 10% of the total exposure. Therefore, the initial margin required is 10% of £250,000, which is calculated as 0.10 * £250,000 = £25,000. Now, let’s consider the rationale behind this calculation. Leverage, in essence, magnifies both potential gains and potential losses. In this scenario, Trader X controls £250,000 worth of assets with a smaller amount of their own capital. The initial margin serves as a buffer to protect the broker against potential losses. A 10% margin implies that Trader X needs to deposit £25,000 to cover potential adverse movements in the prices of Alpha and Beta shares. If the losses exceed this margin, the broker may issue a margin call, requiring Trader X to deposit additional funds or risk having their positions closed. The Financial Conduct Authority (FCA) mandates these margin requirements to ensure market stability and protect individual investors from excessive risk. The specific percentage can vary depending on the asset class, the client’s risk profile, and the broker’s internal policies. The FCA’s regulations aim to strike a balance between allowing investors to utilize leverage to enhance returns and mitigating the risks associated with highly leveraged trading. This balance is crucial for maintaining a fair and orderly market.

The question explores the concept of leverage ratios, specifically focusing on how changes in asset value impact the equity base and consequently, the leverage ratio of a trading firm. The calculation involves determining the initial equity, calculating the profit from the asset sale, adding the profit to the equity, and then calculating the new leverage ratio. The leverage ratio is calculated as total assets divided by equity. Initial Equity = Total Assets / Initial Leverage Ratio = £50,000,000 / 5 = £10,000,000 Profit from Asset Sale = 20% of £10,000,000 = £2,000,000 New Equity = Initial Equity + Profit = £10,000,000 + £2,000,000 = £12,000,000 New Total Assets = Initial Total Assets – Asset Sale + Profit = £50,000,000 – £10,000,000 + £2,000,000 = £42,000,000 New Leverage Ratio = New Total Assets / New Equity = £42,000,000 / £12,000,000 = 3.5 The example illustrates how a trading firm’s leverage ratio can fluctuate based on asset performance and strategic asset sales. Imagine “Starlight Trading,” a firm specializing in emerging market bonds. Initially, Starlight operates with a leverage ratio of 5, managing £50 million in assets with an equity base of £10 million. This means for every £1 of equity, they control £5 of assets. Now, consider Starlight decides to liquidate a portion of its portfolio, specifically £10 million worth of bonds. These bonds, purchased at a discount, have appreciated significantly, yielding a 20% profit upon sale. This profit, amounting to £2 million, directly increases Starlight’s equity. The challenge lies in understanding how this asset sale and subsequent profit impact Starlight’s overall leverage. The key is to recognize that the asset base decreases by the amount sold, while the equity increases by the profit generated. This dynamic interaction between asset reduction and equity growth determines the new leverage ratio, reflecting Starlight’s adjusted risk profile. The question requires a comprehensive understanding of how leverage ratios are calculated and how they are affected by changes in both assets and equity, offering a practical application of theoretical knowledge.

Let’s analyze the impact of operational leverage on a firm’s profitability. Operational leverage reflects the extent to which a company uses fixed costs in its operations. A higher degree of operational leverage means that a larger proportion of the company’s costs are fixed, rather than variable. This can lead to significant profit swings as sales volume changes. The degree of operational leverage (DOL) is calculated as: \[DOL = \frac{\% \text{ Change in Operating Income}}{\% \text{ Change in Sales}}\] A DOL of 3 means that for every 1% change in sales, the operating income will change by 3%. Companies with high fixed costs (like airlines or manufacturers with automated factories) tend to have high operational leverage. Consider two hypothetical artisanal cheese producers: “Fromage Fantastique” and “Cheddar Champions.” Fromage Fantastique invests heavily in automated aging caves and specialized packaging equipment, resulting in high fixed costs but lower variable costs per unit. Cheddar Champions, on the other hand, relies on traditional methods with more manual labor, leading to lower fixed costs but higher variable costs per unit. If both companies initially have the same operating income, a small increase in sales will benefit Fromage Fantastique more due to its high operational leverage. However, a small decrease in sales will hurt Fromage Fantastique more. Now, imagine a scenario where the UK government introduces a new regulation requiring all cheese producers to implement expensive traceability software. This increases the fixed costs for both companies. The impact will be more pronounced for Cheddar Champions, as the increase in fixed costs will significantly change its cost structure and operational leverage, making it more sensitive to changes in sales volume. Fromage Fantastique, already operating with high fixed costs, will see a smaller relative change in its operational leverage. The key takeaway is that operational leverage amplifies the impact of sales changes on operating income, and this effect is more pronounced for companies with a higher proportion of fixed costs. Understanding a company’s operational leverage is crucial for assessing its risk and potential profitability.

The core of this question lies in understanding the interaction between initial margin, maintenance margin, and the potential for margin calls when trading leveraged products like Contracts for Difference (CFDs). We need to calculate the point at which the account equity falls below the maintenance margin requirement, triggering a margin call. First, determine the initial margin deposit: £20,000. Second, calculate the total notional value of the position: 500 shares * £120/share = £60,000. Third, calculate the maintenance margin requirement: £60,000 * 8% = £4,800. Fourth, calculate the amount the account equity can decline before a margin call: £20,000 (initial margin) – £4,800 (maintenance margin) = £15,200. Fifth, calculate the loss per share that would trigger the margin call: £15,200 / 500 shares = £30.40/share. Sixth, calculate the share price at which the margin call will occur: £120 (initial price) – £30.40 (loss per share) = £89.60. Therefore, the margin call will be triggered when the share price falls to £89.60. Consider a different, completely original analogy: Imagine you’re operating a highly leveraged delivery service using borrowed e-bikes. Your initial deposit (margin) is like a security deposit on the bikes. The maintenance margin is the minimum operating capital you need to keep the bikes running (charging, minor repairs). If your earnings (share price) plummet due to unexpected competition or a sudden surge in electricity costs, you start dipping into your security deposit. Once your security deposit falls below the minimum operating capital, the bike rental company (broker) demands more money (margin call) to ensure you can continue operating. If you can’t provide it, they repossess the bikes (close the position). This question tests understanding of margin requirements, how they relate to leverage, and the consequences of adverse price movements. It goes beyond simple definitions by requiring a calculation and understanding of the practical implications of these concepts.

The core of this question lies in understanding how leverage amplifies both gains and losses, and how margin requirements act as a buffer against potential losses. The initial margin is the equity the investor must deposit, and the maintenance margin is the minimum equity level that must be maintained. When the equity falls below the maintenance margin, a margin call is triggered, requiring the investor to deposit additional funds to bring the equity back to the initial margin level. In this scenario, we need to calculate the price at which the investor receives a margin call. The investor uses leverage, so a small movement in the underlying asset’s price can significantly impact the equity in the account. Here’s how to calculate the margin call price: 1. **Calculate the initial equity:** The investor deposits £25,000 as initial margin. 2. **Calculate the total position value:** With a leverage of 5:1, the investor controls a position worth 5 * £25,000 = £125,000. 3. **Calculate the number of units purchased:** The investor buys units of the asset at £125 each, so they purchase £125,000 / £125 = 1000 units. 4. **Calculate the equity at the maintenance margin:** The maintenance margin is 30%, meaning the equity must not fall below 30% of the total position value. 5. **Calculate the minimum equity:** The minimum equity allowed is 30% * £125,000 = £37,500. 6. **Calculate the maximum loss before margin call:** The maximum loss the investor can sustain before a margin call is triggered is the initial equity minus the minimum equity: £25,000 – £37,500 = -£12,500. Note that this is a negative number representing the maximum loss. Since the margin is 30%, the equity can not fall below 30% of the total position value. 7. **Calculate the loss per unit:** The loss of £12,500 is spread across 1000 units, so the loss per unit is £12,500 / 1000 = £12.50. 8. **Calculate the margin call price:** Subtract the loss per unit from the initial purchase price to find the price at which a margin call is triggered: £125 – £12.50 = £112.50. Therefore, the investor will receive a margin call if the asset price falls to £112.50. The margin call will require the investor to deposit enough funds to bring the equity back to the initial margin level of £25,000. This calculation demonstrates the crucial role of understanding leverage and margin requirements in leveraged trading. Failing to monitor the equity level and asset price can lead to unexpected margin calls and forced liquidation of positions.

The question assesses the understanding of how leverage impacts the margin requirements and potential losses in a complex trading scenario involving multiple asset classes and margin tiers. It requires calculating the total margin required and the potential loss, considering the leverage provided by the broker and the specific margin rates for each asset. The question involves understanding the relationship between leverage, margin, and risk in a multi-asset portfolio. First, calculate the margin requirement for each asset class: * Equities: £200,000 * 20% = £40,000 * Bonds: £150,000 * 5% = £7,500 * FX: £100,000 * 2% = £2,000 Total margin required = £40,000 + £7,500 + £2,000 = £49,500 Next, calculate the loss for each asset class: * Equities: £200,000 * 12% = £24,000 * Bonds: £150,000 * 3% = £4,500 * FX: £100,000 * 1% = £1,000 Total loss = £24,000 + £4,500 + £1,000 = £29,500 The trader’s initial capital is £60,000. Since the total margin required is £49,500, the remaining capital after margin = £60,000 – £49,500 = £10,500. After the losses, the remaining capital will be £10,500 – £29,500 = -£19,000. This means the trader has a negative balance of £19,000. The leverage provided by the broker amplifies both the potential gains and losses. In this scenario, the trader experienced losses across all asset classes, resulting in a significant depletion of capital. The initial margin covered part of the losses, but the magnitude of the losses exceeded the remaining capital, leading to a negative balance. This demonstrates the risk associated with leveraged trading, where even small percentage changes in asset prices can result in substantial losses. The calculation illustrates how leverage can quickly erode a trader’s capital if the trades move against them.

The core concept here is understanding how leverage affects both potential gains and potential losses, especially when margin calls are involved. The initial margin is the percentage of the total investment that the investor must deposit, while the maintenance margin is the minimum percentage that the investor’s equity must represent of the total position value to avoid a margin call. When the equity falls below the maintenance margin, a margin call is triggered, requiring the investor to deposit additional funds to bring the equity back to the initial margin level. Failure to meet the margin call can result in the liquidation of the position. In this scenario, the investor initially deposits £20,000 (20% of £100,000), and the maintenance margin is 10%. This means the investor’s equity must not fall below £10,000 (10% of £100,000). The maximum loss the investor can sustain before a margin call is triggered is £10,000 (initial equity of £20,000 – maintenance margin of £10,000). This corresponds to a 10% decrease in the asset’s value (loss of £10,000 on a £100,000 position). If the asset’s value drops by 12%, the position is now worth £88,000 (£100,000 – 12% of £100,000). The investor’s equity is now £8,000 (£88,000 – £80,000 borrowed). Because £8,000 is below the maintenance margin of £10,000, a margin call is triggered. To meet the margin call, the investor needs to bring their equity back to the initial margin level of 20% of the current position value, which is 20% of £88,000 = £17,600. The investor’s equity is currently £8,000, so they need to deposit an additional £9,600 (£17,600 – £8,000) to meet the margin call.

The core of this question lies in understanding how leverage impacts the margin required for trading, especially when considering regulatory constraints like those imposed by the FCA. The FCA mandates specific margin requirements based on the asset class and the client’s classification (retail vs. professional). These requirements directly affect the maximum leverage a trader can utilize. Let’s break down the calculation: 1. **Calculate the initial margin requirement without leverage:** If Amelia wants to control £500,000 worth of FTSE 100 index CFDs, without any leverage, she would need to deposit the full £500,000. 2. **Determine the FCA’s margin requirement for retail clients:** The FCA mandates a minimum margin of 5% for major indices like the FTSE 100 for retail clients. 3. **Calculate the margin required with FCA-mandated leverage:** With the 5% margin requirement, Amelia needs to deposit only 5% of £500,000, which is \(0.05 \times £500,000 = £25,000\). 4. **Calculate the maximum leverage:** Leverage is calculated as the total value of the position divided by the margin required. In this case, it’s \(£500,000 / £25,000 = 20\). Therefore, the maximum leverage Amelia can use is 20:1. 5. **The impact of increased margin:** If the brokerage increases the margin requirement to 10%, Amelia would need to deposit \(0.10 \times £500,000 = £50,000\). This reduces the maximum leverage to \(£500,000 / £50,000 = 10\). The maximum leverage Amelia can use is now 10:1. 6. **The impact of Amelia being classified as a professional client:** If Amelia is classified as a professional client, the margin requirements are lowered. For example, let’s say the margin requirement is lowered to 1%. Amelia would need to deposit \(0.01 \times £500,000 = £5,000\). This increases the maximum leverage to \(£500,000 / £5,000 = 100\). The maximum leverage Amelia can use is now 100:1. Understanding these calculations and the impact of regulatory changes is critical for any leveraged trader. It’s not just about the numbers; it’s about understanding the risk management implications and how regulatory frameworks shape the trading landscape. The analogy here is a seesaw: as the margin requirement goes up (the weight on one side), the leverage goes down (the other side rises), and vice versa. This interplay is crucial for managing risk effectively.

The key to answering this question lies in understanding how leverage magnifies both profits and losses, and how margin requirements work in practice. The initial margin is the amount required to open the position, and the maintenance margin is the minimum equity that must be maintained in the account. When the equity falls below the maintenance margin, a margin call is triggered, requiring the investor to deposit additional funds to bring the equity back up to the initial margin level. First, calculate the initial equity in the account: 10,000 shares * £5.00/share = £50,000. With a 20% initial margin requirement, the investor needed to deposit £50,000 * 20% = £10,000. This means the investor borrowed £40,000. Next, calculate the equity at the time of the margin call. The price decreased by 15%, so the new share price is £5.00 * (1 – 0.15) = £4.25. The total value of the shares is now 10,000 shares * £4.25/share = £42,500. The investor still owes £40,000, so the equity in the account is £42,500 – £40,000 = £2,500. The maintenance margin is 10%, so the minimum equity required is £50,000 * 10% = £5,000. The investor’s equity is £2,500, which is below the maintenance margin. To meet the margin call, the investor must deposit enough funds to bring the equity back up to the *initial* margin level of £10,000. Therefore, the investor must deposit £10,000 – £2,500 = £7,500. A common mistake is to calculate the deposit needed to reach the maintenance margin level (£5,000), but the margin call requires the equity to be restored to the initial margin level. Another mistake is to calculate the deposit needed to cover the losses, but the margin call is triggered by the equity falling below the maintenance margin, not necessarily by the entire loss needing to be covered immediately. This scenario highlights the significant risk of leveraged trading and the importance of understanding margin requirements.

Let’s analyze the impact of operational leverage on a company’s earnings volatility. Operational leverage refers to the extent to which a company uses fixed costs in its operations. A high degree of operational leverage means that a large proportion of a company’s costs are fixed, while a low degree of operational leverage means that a large proportion of a company’s costs are variable. A company with high operational leverage will experience greater fluctuations in its earnings before interest and taxes (EBIT) as sales volume changes, compared to a company with low operational leverage. The degree of operating leverage (DOL) measures the sensitivity of a company’s operating income to changes in sales. It is calculated as: \[DOL = \frac{\% \text{ Change in EBIT}}{\% \text{ Change in Sales}} \] In this scenario, we are comparing two companies, Alpha and Beta, with different cost structures. Alpha has higher fixed costs and lower variable costs, indicating higher operational leverage. Beta has lower fixed costs and higher variable costs, indicating lower operational leverage. We need to determine which company’s EBIT will be more sensitive to changes in sales volume. The key is understanding that with higher operational leverage, a small change in sales will result in a larger change in EBIT. This is because the fixed costs are spread over a larger or smaller number of units sold, amplifying the effect on profitability. For example, consider two scenarios: Scenario 1: Sales increase by 10%. Alpha’s EBIT increases by 20% (DOL = 2). Beta’s EBIT increases by 12% (DOL = 1.2). Scenario 2: Sales decrease by 10%. Alpha’s EBIT decreases by 20%. Beta’s EBIT decreases by 12%. Alpha’s EBIT is more volatile than Beta’s EBIT because of Alpha’s higher operational leverage. This means that Alpha’s earnings are more sensitive to changes in sales volume, making it riskier during economic downturns but also potentially more profitable during economic booms. The company with higher operational leverage will experience greater earnings volatility.

To determine the maximum potential loss, we need to calculate the total exposure created by the leveraged trade and then apply the percentage loss to that exposure. The initial margin of £20,000 controls a position worth £200,000 (since the leverage is 10:1). A 15% decline in the asset’s value directly impacts this £200,000 exposure. Therefore, the potential loss is 15% of £200,000, which equals £30,000. However, the client only deposited £20,000 as initial margin. This means the maximum loss the client can incur is capped at their initial investment of £20,000, as any loss beyond that would trigger a margin call and subsequent liquidation of the position to prevent further losses for the broker. This illustrates the importance of understanding leverage; while it amplifies potential gains, it also magnifies potential losses, but losses are limited to the initial margin deposited. Imagine leverage as a double-edged sword: it can cut both ways with significant force. A small movement against the position can quickly erode the initial margin. Risk management strategies, such as stop-loss orders, are crucial to mitigate these risks. Without them, even a seemingly modest market fluctuation can lead to substantial financial consequences.

1. **Initial Situation:** * Total Assets: £5,000,000 * Total Liabilities: £3,000,000 * Total Equity: £2,000,000 (Assets – Liabilities) * Financial Leverage Ratio: £5,000,000 / £2,000,000 = 2.5 2. **After Transaction:** * New Debt: £500,000 * Total Liabilities: £3,000,000 + £500,000 = £3,500,000 * Total Assets: £5,000,000 + £500,000 = £5,500,000 (Assets increase by the amount of debt raised) * Total Equity: £5,500,000 – £3,500,000 = £2,000,000 (Equity remains unchanged as the debt is used to acquire assets) * New Financial Leverage Ratio: £5,500,000 / £2,000,000 = 2.75 3. **Impact on ROE:** The increase in the financial leverage ratio from 2.5 to 2.75 indicates higher financial leverage. Assuming profitability remains constant, the ROE will increase. This is because the company is using more debt to finance its assets, and if the return on those assets exceeds the cost of debt, the excess return accrues to equity holders, boosting ROE. Conversely, if the assets perform poorly, the losses are amplified, and the ROE will decrease. The question does not ask about the exact calculation of ROE, but rather the directional impact of the change in the leverage ratio. Analogy: Imagine two farmers, Alice and Bob. Both have £100,000 to invest in their farms. Alice uses only her £100,000 (no debt). Bob uses £50,000 of his own money and borrows £50,000. If both farms generate a 10% return, Alice makes £10,000. Bob makes £10,000, but he also has to pay interest on his loan. If the interest rate is 5%, he pays £2,500 in interest, leaving him with £7,500 profit on his £50,000 investment, which is a 15% return on his equity. However, if both farms lose 10%, Alice loses £10,000. Bob loses £10,000 plus £2,500 in interest, resulting in a greater loss on his equity. This illustrates how leverage amplifies both gains and losses.

The core of this question lies in understanding how leverage magnifies both potential gains and losses, and how margin requirements function as a safety net for the lender. The investor’s initial margin of £50,000 represents their equity in the position. The loan of £200,000, combined with the initial margin, allows the investor to control an asset worth £250,000. If the asset’s value declines, the investor’s equity erodes. When the equity falls below the maintenance margin, a margin call is triggered, requiring the investor to deposit additional funds to restore the equity to the initial margin level. The formula for calculating the percentage decline triggering a margin call is: Percentage Decline = (Initial Margin – (Loan Amount * (Maintenance Margin Percentage / (1 – Maintenance Margin Percentage)))) / (Initial Margin + Loan Amount) In this scenario, the initial margin is £50,000, the loan amount is £200,000, and the maintenance margin is 25%. Plugging these values into the formula: Percentage Decline = \[ \frac{50,000 – (200,000 * (0.25 / (1 – 0.25)))}{50,000 + 200,000} \] Percentage Decline = \[ \frac{50,000 – (200,000 * (0.25 / 0.75))}{250,000} \] Percentage Decline = \[ \frac{50,000 – (200,000 * 0.3333)}{250,000} \] Percentage Decline = \[ \frac{50,000 – 66,666.67}{250,000} \] Percentage Decline = \[ \frac{-16,666.67}{250,000} \] Percentage Decline = -0.06666668 or -6.67% Therefore, a decline of approximately 6.67% in the asset’s value will trigger a margin call. This calculation demonstrates the inverse relationship between leverage and the buffer against losses. Higher leverage (in this case, a loan four times the initial margin) means a smaller percentage decline is needed to trigger a margin call. The maintenance margin acts as a threshold to protect the lender from excessive losses, ensuring that the investor maintains a certain level of equity in the position. Understanding this interplay is crucial for managing risk in leveraged trading.

The question assesses the understanding of leverage ratios, specifically the debt-to-equity ratio, in the context of a leveraged trading firm operating under UK regulations. The debt-to-equity ratio is calculated as Total Debt / Shareholder’s Equity. A higher ratio indicates greater financial risk. The scenario involves a firm exceeding its regulatory limit, requiring the calculation of the current ratio and the determination of the equity injection needed to comply with the limit. In this case, the firm’s total debt is £90 million, and its shareholder’s equity is £30 million, resulting in a debt-to-equity ratio of 3:1. The regulatory limit is 2:1. To achieve this limit, the firm needs to increase its equity. Let \(x\) be the amount of equity injection needed. The new debt-to-equity ratio will be \(90 / (30 + x) = 2\). Solving for \(x\): \[ 90 = 2(30 + x) \\ 90 = 60 + 2x \\ 30 = 2x \\ x = 15 \] Therefore, the firm needs to inject £15 million of equity to meet the regulatory requirement. A useful analogy is to consider a seesaw. Debt is like one side of the seesaw, and equity is the other. Leverage is the balance point. If the debt side is too heavy (high debt-to-equity ratio), the seesaw becomes unstable, representing higher financial risk. Regulators set limits to ensure the seesaw remains relatively balanced, preventing the firm from becoming overly exposed to potential losses. Injecting equity is like adding weight to the equity side of the seesaw, restoring balance and reducing the risk. This ensures the firm operates within acceptable risk parameters as defined by regulations.

The Net Stable Funding Ratio (NSFR) is a regulatory requirement designed to ensure that banks maintain a stable funding profile in relation to their assets and off-balance sheet exposures. It aims to limit excessive reliance on short-term wholesale funding, encouraging banks to fund their activities with more stable sources of funding over a one-year horizon. The NSFR is calculated as the ratio of Available Stable Funding (ASF) to Required Stable Funding (RSF). ASF represents the portion of an institution’s liabilities and capital expected to be reliable over the coming year. Different types of liabilities and capital are assigned different ASF factors, reflecting their stability. For example, common equity tier 1 capital receives a 100% ASF factor, while short-term wholesale funding from financial institutions receives a 0% ASF factor. RSF represents the amount of stable funding needed to support an institution’s assets and off-balance sheet exposures over the coming year. Different types of assets are assigned different RSF factors, reflecting their liquidity and the potential need for stable funding. For instance, high-quality liquid assets (HQLA) may receive a 0% RSF factor, while less liquid assets like loans to corporations may receive a higher RSF factor (e.g., 50% or more). Off-balance sheet exposures, such as commitments to extend credit, also require stable funding, with RSF factors assigned based on the likelihood of the commitment being drawn down. A higher NSFR indicates a more stable funding profile. The minimum required NSFR is typically 100%, meaning that a bank’s available stable funding must be at least equal to its required stable funding. If a bank’s NSFR falls below 100%, it may need to reduce its reliance on short-term funding, increase its holdings of liquid assets, or reduce its lending activities. For example, consider a hypothetical leveraged trading firm, “Apex Investments.” Apex has £50 million in CET1 capital (100% ASF), £100 million in one-year corporate bonds (50% ASF), £200 million in loans to hedge funds (85% RSF), and £50 million in HQLA (0% RSF). Apex’s ASF is (£50m * 1.0) + (£100m * 0.5) = £100m. Apex’s RSF is (£200m * 0.85) + (£50m * 0) = £170m. Apex’s NSFR is (£100m / £170m) = 58.82%. This would require Apex to take action to improve its funding profile.

To determine the impact of a change in the margin requirement on the maximum leverage achievable, we first need to understand how margin requirements and leverage are related. The initial margin requirement is the percentage of the total trade value that an investor must deposit with the broker. The maximum leverage is the inverse of this percentage. In this case, the initial margin requirement is 20%, which means the maximum leverage is \(1 / 0.20 = 5\). When the margin requirement increases to 40%, the maximum leverage decreases. The new maximum leverage is \(1 / 0.40 = 2.5\). The question asks for the *reduction* in maximum leverage. To find this, we subtract the new leverage from the old leverage: \(5 – 2.5 = 2.5\). Now, let’s consider an analogy. Imagine you’re renting tools. Initially, you need to pay a 20% deposit on the tool’s value, allowing you to “leverage” the tool’s use. If the deposit increases to 40%, you can rent fewer tools with the same amount of money, effectively reducing your leverage. This reduction in leverage impacts the scale of trades an investor can undertake, influencing both potential profits and losses. A higher margin requirement acts as a risk control measure for both the investor and the broker. Furthermore, this reduction in leverage can have a significant impact on trading strategies. For example, a trader who previously employed a high-frequency trading strategy relying on high leverage may find that the increased margin requirements make the strategy unfeasible due to the reduced scale of positions they can take. Similarly, a portfolio manager using leverage to enhance returns may need to re-evaluate their asset allocation and risk management practices to adapt to the new leverage constraints. The change also affects the broker’s risk exposure, as they are now lending a smaller proportion of the total trade value.

To determine the maximum potential loss, we first need to calculate the total value of the shares purchased using leverage. A margin of 25% means the investor only needs to deposit 25% of the total value, with the remaining 75% borrowed. If the investor deposits £50,000, this represents 25% of the total investment. Therefore, the total value of shares purchased is calculated as: Total Value = Deposit / Margin Percentage = £50,000 / 0.25 = £200,000. Now, if the share price falls to zero, the investor loses the entire value of the shares. However, the loss is capped at the total value of the shares purchased, not an infinite amount. The maximum loss is the total value of the shares minus any potential dividends received during the holding period. In this case, no dividends are mentioned, so the maximum potential loss is simply the total value of the shares, which is £200,000. However, we must also consider the interest paid on the borrowed funds. The interest rate is 8% per annum, and the investment period is 6 months (0.5 years). The amount borrowed is 75% of £200,000, which is £150,000. The interest paid is calculated as: Interest = Principal * Rate * Time = £150,000 * 0.08 * 0.5 = £6,000. Therefore, the total maximum potential loss is the total value of the shares plus the interest paid on the borrowed funds: Total Loss = £200,000 + £6,000 = £206,000. This represents the worst-case scenario where the share price drops to zero and the investor loses their entire investment, including the initial deposit and the interest paid on the borrowed funds.

The core of this question revolves around understanding how changes in initial margin requirements impact the maximum leverage a trader can employ and, consequently, the potential profit or loss on a given investment. A higher initial margin necessitates a smaller leverage ratio, and vice versa. The calculation is straightforward: Leverage Ratio = 1 / Initial Margin Percentage. This ratio then determines the maximum position size a trader can control with their available capital. The potential profit or loss is calculated by multiplying the position size by the price change of the asset. In this specific scenario, the initial margin increases, reducing the allowable leverage. This directly affects the position size the trader can take. The problem requires calculating the initial leverage, the new leverage, the initial position size, the new position size, and then the change in potential profit due to the reduced leverage. Initial Margin = 2% = 0.02 New Margin = 5% = 0.05 Capital = £20,000 Price Change = 3% = 0.03 Asset Price = £50 1. Initial Leverage = 1 / 0.02 = 50 2. New Leverage = 1 / 0.05 = 20 3. Initial Position Size = £20,000 * 50 = £1,000,000 4. New Position Size = £20,000 * 20 = £400,000 5. Initial Profit = £1,000,000 * 0.03 = £30,000 6. New Profit = £400,000 * 0.03 = £12,000 7. Difference in Profit = £30,000 – £12,000 = £18,000 Therefore, the trader’s potential profit decreases by £18,000 due to the increase in initial margin requirements. Imagine a seesaw. Leverage is the length of the board on either side of the fulcrum. Your capital is the weight you put on one end. If the initial margin (fulcrum point) moves closer to your weight (capital), you need less effort (capital) to lift a heavier object (larger position size) on the other end. But if the fulcrum moves further away (higher margin), you can’t lift as much with the same effort. The question tests if you understand this inverse relationship and its impact on potential gains.

The question tests the understanding of how leverage affects the margin required for trading a currency pair and how changes in the exchange rate impact the available margin. The initial margin is calculated based on the leverage ratio and the notional value of the trade. A favorable movement in the exchange rate increases the equity in the account, which in turn increases the available margin. The calculation involves determining the initial margin, calculating the profit from the exchange rate movement, and then adding the profit to the initial margin to find the new available margin. Initial Margin = Notional Value / Leverage Ratio = \(£500,000 / 50 = £10,000\) Profit from Exchange Rate Change: The trader bought GBP/USD at 1.2500 and the rate moved to 1.2550. The profit is the difference in the exchange rate multiplied by the notional value in GBP, converted to GBP. Change in Exchange Rate = 1.2550 – 1.2500 = 0.0050 Profit in USD = Change in Exchange Rate * Notional Value in GBP = \(0.0050 * £500,000 = $2,500\) Convert Profit to GBP: To determine how much the available margin increased, convert the profit from USD back to GBP using the new exchange rate of 1.2550. Profit in GBP = Profit in USD / New Exchange Rate = \($2,500 / 1.2550 = £1,992.03\) New Available Margin = Initial Margin + Profit in GBP = \(£10,000 + £1,992.03 = £11,992.03\) Therefore, the new available margin is approximately £11,992.03. Understanding how leverage impacts margin is crucial in leveraged trading. A higher leverage ratio reduces the initial margin requirement but also magnifies both profits and losses. Changes in the exchange rate directly affect the equity in the trading account, which in turn influences the available margin. Traders must carefully monitor their margin levels to avoid margin calls and potential liquidation of their positions. This scenario highlights the dynamic relationship between leverage, exchange rates, and margin in leveraged trading. It emphasizes the need for traders to understand these concepts thoroughly to manage risk effectively and make informed trading decisions.

The question assesses the understanding of leverage ratios, specifically the debt-to-equity ratio, and its implications for a company’s financial risk profile. The debt-to-equity ratio is calculated as Total Debt / Shareholders’ Equity. A higher ratio indicates greater financial leverage and potentially higher risk. We need to calculate the debt-to-equity ratio for both companies (A and B) and then analyze how a change in operating profit affects their respective Earnings Per Share (EPS). For Company A: Debt-to-Equity Ratio = £5,000,000 / £10,000,000 = 0.5 Interest Expense = £5,000,000 * 5% = £250,000 Initial Profit Before Tax = £2,000,000 Profit After Interest = £2,000,000 – £250,000 = £1,750,000 Tax (20%) = £1,750,000 * 0.20 = £350,000 Net Income = £1,750,000 – £350,000 = £1,400,000 EPS = £1,400,000 / 1,000,000 shares = £1.40 New Profit Before Tax = £2,500,000 Profit After Interest = £2,500,000 – £250,000 = £2,250,000 Tax (20%) = £2,250,000 * 0.20 = £450,000 New Net Income = £2,250,000 – £450,000 = £1,800,000 New EPS = £1,800,000 / 1,000,000 shares = £1.80 EPS Change for A = £1.80 – £1.40 = £0.40 For Company B: Debt-to-Equity Ratio = £2,000,000 / £13,000,000 = 0.1538 (approximately 0.15) Interest Expense = £2,000,000 * 5% = £100,000 Initial Profit Before Tax = £2,000,000 Profit After Interest = £2,000,000 – £100,000 = £1,900,000 Tax (20%) = £1,900,000 * 0.20 = £380,000 Net Income = £1,900,000 – £380,000 = £1,520,000 EPS = £1,520,000 / 1,000,000 shares = £1.52 New Profit Before Tax = £2,500,000 Profit After Interest = £2,500,000 – £100,000 = £2,400,000 Tax (20%) = £2,400,000 * 0.20 = £480,000 New Net Income = £2,400,000 – £480,000 = £1,920,000 New EPS = £1,920,000 / 1,000,000 shares = £1.92 EPS Change for B = £1.92 – £1.52 = £0.40 Both companies experience the same absolute change in EPS (£0.40). However, the percentage change in EPS is higher for Company A due to its higher leverage. Percentage Change in EPS for A = (£0.40 / £1.40) * 100% = 28.57% Percentage Change in EPS for B = (£0.40 / £1.52) * 100% = 26.32% Therefore, Company A, with the higher debt-to-equity ratio, experiences a greater percentage increase in EPS due to the increased operating profit. This demonstrates the magnifying effect of financial leverage on shareholder returns when operating profits increase. The higher the leverage, the greater the impact (positive or negative) on EPS for a given change in operating profit.

The key to answering this question lies in understanding how leverage magnifies both potential gains and potential losses, and how margin requirements act as a buffer against these magnified losses. The initial margin is the amount of equity the investor must deposit, and the maintenance margin is the minimum equity level that must be maintained in the account. If the equity falls below the maintenance margin, a margin call is issued, requiring the investor to deposit additional funds to bring the equity back up to the initial margin level. In this scenario, we need to calculate the price at which the investor will receive a margin call. First, determine the initial equity: £20,000. The initial loan is £80,000 (since the leverage is 4:1, meaning for every £1 of equity, there’s £4 of debt). The total value of shares purchased is £100,000 (£20,000 + £80,000). The number of shares purchased is 100,000 shares / £10 per share = 10,000 shares. Next, determine the equity value at which a margin call is triggered. The maintenance margin is 30%, so the equity must not fall below 30% of the total value of the shares. Let ‘P’ be the price per share at which the margin call is triggered. The total value of the shares at this point is 10,000 * P. The equity at this point is (10,000 * P) – £80,000 (the loan amount remains constant). The margin call is triggered when: (10,000 * P) – £80,000 = 0.30 * (10,000 * P). Solving for P: 10,000P – 80,000 = 3,000P => 7,000P = 80,000 => P = 80,000 / 7,000 = £11.43 (rounded to two decimal places). Therefore, the investor will receive a margin call when the share price rises to £11.43.