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. $52.5
B
b. $60
C
c. $65
D
d. $45
E
e. $75

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 equals the sale proceeds plus the initial margin deposit minus the current market value of the shorted shares.

1. Relevant concepts
- Sale proceeds = number of shares × initial short price.
- Initial margin deposit is a percentage of the sale proceeds.
- Account equity (for a short position) = proceeds + margin deposit − current market value.
- A margin call occurs when equity / current market value < maintenance margin; the trigger price satisfies equality.

2. Step-by-step reasoning
- Number of shares = 100, initial short price = $70.
- Sale proceeds = 100 × $70 = $7,000.
- Initial margin = 50% of proceeds → margin deposit = 0.50 × $7,000 = $3,500.
- Current market value when price = P: 100 × P = 100P.
- Equity at price P = proceeds + deposit − market value = 7,000 + 3,500 − 100P = 10,500 − 100P.
- Maintenance margin requirement: equity / market value = 0.40 at the call threshold.

3. Algebraic calculation (all intermediate steps)
Set (10,500 − 100P) / (100P) = 0.40
Multiply both sides by 100P: 10,500 − 100P = 0.40 × 100P = 40P
Bring terms together: 10,500 = 100P + 40P = 140P
Solve for P: P = 10,500 / 140 = 75

4. Why this answer is correct
At P = $75 the equity is 10,500 − 7,500 = $3,000 and the market value is $7,500. Equity/market value = 3,000/7,500 = 0.40, exactly the maintenance requirement. Any price above $75 would make the ratio fall below 40% and produce a margin call.

5. Why the other options are incorrect
- $52.50, $60, $65, $45 all produce equity/market value ratios well above 40% (e.g., at $65 equity = $4,000 and ratio = 4,000/6,500 ≈ 61.5%), so no margin call occurs at those prices. Only $75 satisfies the equality.

6. Conclusion
Therefore the margin call price is $75, matching the provided correct answer (e. $75).

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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