You sold short 100 shares of common stock at $70 per share. The initial margin is 50%. At what stock price would you receive a margin call if the maintenance margin is 40%?[Fill in the blank]单项选择题
A
a. $45
B
b. $52.5
C
c. $60
D
d. $75
E
e. $65

Question

You sold short 100 shares of common stock at $70 per share. The initial margin is 50%. At what stock price would you receive a margin call if the maintenance margin is 40%?[Fill in the blank]

BlackTom AI · Accepted Answer

For a short sale the investor’s equity = proceeds from sale + margin deposit − current market value of the shorted shares. The maintenance rule triggers a margin call when equity falls to the maintenance margin percentage of the current market value.

1. Relevant concepts
- Proceeds from short sale = number of shares × initial sale price.
- Initial margin deposit = initial margin % × sale proceeds.
- Equity in a short position = proceeds + deposit − current market value.
- Margin call when Equity / (current market value) ≤ maintenance margin.

2. Step-by-step reasoning and intermediate calculations
- Proceeds from selling short 100 shares at $70: 100 × $70 = $7,000.
- Initial margin (50%): 0.50 × $7,000 = $3,500 (this is the additional deposit required).
- Total funds in margin account initially = proceeds + deposit = $7,000 + $3,500 = $10,500.
- Current market value of the short position at price P = 100 × P = 100P.
- Equity at price P = total funds − market value = 10,500 − 100P.

3. Apply maintenance margin condition
- Maintenance margin requirement: Equity = 0.40 × (market value) = 0.40 × 100P = 40P.
- Set equality to find the trigger price: 10,500 − 100P = 40P.
- Solve: 10,500 = 140P → P = 10,500 / 140 = 75.

4. Why this is correct
At P = $75 the equity is exactly 40% of the current market value: equity = 10,500 − 100(75) = 3,000; market value = 7,500; equity/market value = 3,000/7,500 = 0.40. Any price above $75 makes the equity ratio fall below 40% and produces a margin call.

5. Why the other choices are incorrect (brief)
- $45, $52.50, $60, $65 all give equity/market ratios well above 40% (no margin call). Example at $60: equity = 10,500 − 6,000 = 4,500; ratio = 4,500/6,000 = 75% > 40%.

Conclusion: The margin-call trigger price is $75, matching answer d.

You sold short 100 shares of common stock at $70 per share. The initial margin is 50%. At what stock price would you receive a margin call if the maintenance margin is 40%?[Fill in the blank]单项选择题

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