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]Single choice
A
a. $52.5
B
b. $65
C
c. $75
D
d. $60
E
e. $45

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 initial margin deposit plus the sale proceeds minus the current market value of the short position.

1) Relevant knowledge points and concepts
- Proceeds from short sale = number of shares × initial sale price.
- Initial margin deposit is a percentage of the proceeds (here 50%).
- Equity in a short position = margin deposit + proceeds − current market value (number of shares × current price).
- A margin call occurs when Equity / Current Market Value < maintenance margin (here 40%). Solve equality to find the trigger price.

2) Complete reasoning process (step by step)
- Number of shares = 100. Initial sale price = $70.
- Proceeds = 100 × $70 = $7,000.
- Initial margin deposit = 50% × $7,000 = $3,500.
- Let P be the stock price that triggers the margin call. Current market value = 100 × P = 100P.
- Equity at price P = margin deposit + proceeds − current market value = 3,500 + 7,000 − 100P = 10,500 − 100P.
- Set the equity ratio equal to the maintenance margin to find the trigger:
  (Equity) / (Current Market Value) = 0.40
  (10,500 − 100P) / (100P) = 0.40

3) Algebraic calculation (all intermediate steps)
- 10,500 − 100P = 0.40 × 100P = 40P
- 10,500 = 100P + 40P = 140P
- P = 10,500 / 140 = 75

4) Why the correct answer is correct
- At P = $75 the equity equals 10,500 − 100×75 = 3,000. Current market value = 7,500. Equity ratio = 3,000 / 7,500 = 0.40, exactly the maintenance requirement; any higher price would push the ratio below 40% and trigger a margin call.

5) Why other options are incorrect
- $65: equity = 10,500 − 6,500 = 4,000; ratio = 4,000/6,500 ≈ 0.615 (>0.40), no call.
- $60: ratio = (10,500 − 6,000)/6,000 = 4,500/6,000 = 0.75, no call.
- $52.50 and $45: ratios are even higher (1.0 and 1.333), so far above maintenance.

6) Conclusion
- Therefore the margin-call trigger price is $75, matching the provided correct answer (c. $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]Single choice

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