Investment Analysis and Portfolio Management

1. Investment Analysis and Portfolio Management Lecture 2a Gareth Myles

2. Return on a short sale • 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?

3. Return on a short sale • 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?

4. Return on a short sale • It was claimed that the formula would always work Return = (Final value – Initial value)/Initial value • For the short sale: Initial value = -100 Final value = -50

5. Return on a short sale • These values give Return = (-50 – (-100))/(-100) = - 0.5 • 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

6. Return on a short sale • 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

7. Return on a short sale • 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

8. Return on a short sale • 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