Answer: 20.0%

## 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.

Author: LeetQuiz .