Explanation

To solve this margin call problem, we need to understand the relationship between leverage ratio, initial margin, and maintenance margin.

Step 1: Calculate the initial margin

The leverage ratio is given as 2.5. The leverage ratio formula is:

$\text{Leverage Ratio} = \frac{1}{\text{Initial Margin}}$

Rearranging: $\text{Initial Margin} = \frac{1}{\text{Leverage Ratio}} = \frac{1}{2.5} = 0.40 = 40\%$

So the initial margin is 40%.

Step 2: Set up the margin call equation

Let:

• P₀ = Initial stock price = $80
• P₁ = Stock price at margin call = $60 (given as "below $60", so we use $60 as the threshold)
• IM = Initial margin = 40%
• MM = Maintenance margin (what we need to find)

The margin call occurs when: $\frac{\text{Equity}}{\text{Market Value}} = \frac{P₁ - (1 - \text{IM}) \times P₀}{P₁} \leq \text{MM}$

Where:

• Equity = Current market value - Loan amount
• Loan amount = (1 - IM) × P₀

Step 3: Calculate the loan amount

Loan amount = (1 - 0.40) × $80 = 0.60 × $80 = $48

Step 4: Calculate equity at P₁ = $60

Equity = P₁ - Loan amount = $60 - $48 = $12

Step 5: Calculate the actual margin at P₁

Actual margin = Equity / Market Value = $12 / $60 = 0.20 = 20%

Step 6: Determine maintenance margin

At the margin call price, the actual margin equals the maintenance margin (or falls just below it). Therefore:

$\text{MM} = 20\%$

Step 7: Verify with the margin call formula

The general formula for margin call price is: $P_{\text{margin call}} = P₀ \times \frac{1 - \text{IM}}{1 - \text{MM}}$

Plugging in our values: $60 = 80 \times \frac{1 - 0.40}{1 - \text{MM}}$ $60 = 80 \times \frac{0.60}{1 - \text{MM}}$ $\frac{60}{80} = \frac{0.60}{1 - \text{MM}}$ $0.75 = \frac{0.60}{1 - \text{MM}}$ $1 - \text{MM} = \frac{0.60}{0.75} = 0.80$ $\text{MM} = 1 - 0.80 = 0.20 = 20\%$

Conclusion: The maintenance margin is 20.0%, which corresponds to option B.