Assume you sell short 100 shares of common stock at $30 per share, with initial margin at 50%. What would be your rate of return if you repurchase the stock at $35 per share? The stock paid no dividends during the period, and assume no other transaction costs.

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BlackTom AI · Accepted Answer

To tackle this problem, I’ll lay out the scenario and then evaluate each answer choice.
First, consider the initial trade: you short 100 shares at $30 each. This generates proceeds of 100 × $30 = $3,000. You must post an initial margin of 50%, which means you commit 50% of the short value as collateral: 0.50 × $3,000 = $1,500. So your account at the outset has $3,000 in proceeds from the short plus $1,500 of your own funds as margin, for a total of $4,500 in value, while you owe to buy back the shares later (short liability) of $3,000.
Now, the stock is repurchased at $35 per share to cover the short: cost to cover = 100 × $35 = $3,500.
Profit or loss on the short position equals the initial proceeds minus the cost to cover: $3,000 − $3,500 = −$500. This is a loss.
Next, compute the rate of return relative to the initial margin requirement (the amount you actually invested in the trade as margin): initial margin = $1,500. Rate of return = (profit or loss) / (initial margin) = (−$500) / ($1,500) = −0.3333, or −33.33%.
Now, examine each answer choice:
A. −33.33%: This matches the calculation above as the gain/loss divided by the initial margin.
B. −25.63%: This would imply a smaller loss relative to margin, which would occur if the numbers or formulas were different (for example, if the margin or proceeds were treated differently). However, with $500 loss on a $1,500 margin, the rate is −33.33%, not −25.63%.
C. −57.14%: This would correspond to a loss of $857.14 on a $1,500 margin, which does not align with the actual $500 absolute loss from the price move from 30 to 35.
D. −77.23%: This would require a much larger loss relative to the margin (nearly ¾ of the margin), which again is not consistent with a $500 loss on a $1,500 margin.
E. 66.67%: This is a positive return, inconsistent with the fact you lost money on covering the short at a higher price than you sold.
In summary, option A correctly represents the rate of return on your initial margin given a move from $30 to $35 in a short sale of 100 shares with no dividends and no other costs.

FINS5513-Investments & Portfolio Sel. - T3 2025

Assume you sell short 100 shares of common stock at $30 per share, with initial margin at 50%. What would be your rate of return if you repurchase the stock at $35 per share? The stock paid no dividends during the period, and assume no other transaction costs.

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Shorting a stock, where you only make money if the stock goes down, has never been a successful investment strategy, based on the case studies we reviewed in class.

How does a short seller "cover" a short?

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