Investment Analysis and
Portfolio Management
Lecture 2a
Gareth Myles
Return on a short sale
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The calculation of the return for a short sales
raises some questions
Considering this issue gives an insight into the
meaning of “return”
Assume an investor sells short 100 stock at a
price of £1 each
A year later the short sale is reversed when
the stock are trading at £0.50
What is the return?
Return on a short sale
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It is clear the investment has been successful
The investor received £100 at the time of the
short sale
The borrowed stock were replaced for £50
The investor has gained £50
So the return must be positive?
Return on a short sale
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It was claimed that the formula would always
work
Return = (Final value – Initial value)/Initial value
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For the short sale:
Initial value = -100
Final value = -50
Return on a short sale
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These values give
Return = (-50 – (-100))/(-100) = - 0.5
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The calculated return is negative
 How does this fit with the fact that the trade
has lead to a profit?
 The explanation lies with the meaning of a
return
Return on a short sale
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Consider placing £100 in a bank account for 1
year at an interest rate of 10%
Then 100 (1.1) = 110
Equivalently
Return = (110 – 100)/100 = 0.1
The return is the interest rate
More generally the return, r, solves
Initial (1 + r) = Final
Return on a short sale
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Apply this logic to the example of a short sale
-100 (1 + r) = -50
 Solving gives r = -0.5
 Interpretation: if I have an overdraft of £100
what interest rate will reduce this to an
overdraft of £50 in one year?
 So a negative return on negative quantities is
good
Return on a short sale
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And remember the calculation of portfolio
return
 This is composed of the sum of terms Xiri
 For a short sale Xi is negative
 If ri is also negative then Xiri is positive