Leveraged Positions

Leveraged positions involve the use of margin, allowing investors to control a larger position with a smaller amount of their own capital. There are several important concepts to understand:

• Margin loan: The borrowed funds used to establish the position.
• Call money rate: The interest rate paid on the margin loan.
• Trader's equity: The investor's own capital invested in the position.
• Initial margin requirement: The minimum proportion of capital the trader must contribute.
• Financial leverage: Increases both the potential gains and losses.

Calculating Leverage Ratio

For example, if a position requires 40% margin, and the total exposure is $100,000, only $40,000 needs to be provided. Financial leverage is calculated as \(1/0.40 = 2.5\). Thus, a 10% price change results in a 25% profit or loss for the investor. Practice these simple calculations to avoid mistakes on the exam.

Example: Leveraged Stock Purchase Return

Suppose an investor buys 1,000 shares at $27 each and sells at $20, using 3x leverage. The loan interest rate is 5%, dividends are $0.10 per share, and commission is $0.01 per share.

Steps to calculate total return:

1. Total Sales: $20 × 1,000 = $20,000.
2. Total Purchase Price: $27 × 1,000 = $27,000.
3. Equity Used: $27,000 / 3 = $9,000.
4. Loan Amount: $27,000 − $9,000 = $18,000.
5. Interest Paid: $18,000 × 5% = $900.
6. Commission: $0.01 × 1,000 = $10.
7. Dividends: $0.10 × 1,000 = $100.

Final equity: $20,000 (sales) − $18,000 (loan repayment) − $900 (interest) − $10 (commission) + $100 (dividends) = $1,190.
Return on initial $9,000 equity: \((1,190 / 9,000) - 1 = -0.87\), i.e., −87%. This shows how a 25% drop in the stock price translates to an 88% loss due to leverage.

If the price drops further, the investor could end up owing money. This brings in the maintenance margin requirement – if equity falls below this level, a margin call is triggered. If additional equity isn’t deposited, the broker will liquidate the position.

Margin Call Calculation Example

Suppose a trader buys stock at $30, with a 40% initial margin and a 20% maintenance margin. The key question: below what price will a margin call occur?

Formula: \[ \text{Initial Price} \times (1 - \text{Initial Margin}) = \text{Maintenance Price} \times (1 - \text{Maintenance Margin}) \]

Plugging in the values: \[ 30 \times (1 - 0.40) = P_{maint} \times (1 - 0.20) \] \[ 18 = P_{maint} \times 0.8 \] \[ P_{maint} = \frac{18}{0.8} = 22.50 \]

A margin call will occur if the stock price falls below $22.50. The logic: a price drop from $30 to $22.50 reduces the investor’s equity from $12 to $4.50, i.e., to 20% of the position. Falling further requires depositing more collateral. This is the logic behind this calculation.