1. Investment Analysis and Portfolio Management Lecture 2 Gareth Myles

2. Return The reason for holding a security is to benefit from the return it offers The holding period return is the proportional increase in value measured over the holding period Asset with no dividend Initial wealth V 0 is the purchase price p(0) Final wealth V 1 is the selling price p(1) Return is:

3. Return Example The price of Lastminute.com stock trading in London on May 29 2002 was 0.77 The price at close of trading on May 28 2003 was 1.39 No dividends were paid The return for the year of this stock is given by

4. Return Asset with dividend d is the dividend Return is Multiple dividends d is the sum of dividends Return is

5. Return Example The price of IBM stock trading in New York on May 29 2002 was $80.96 The price on May 28 2003 was $87.5. A total of $0.61 was paid in dividends over the year in four payments of $0.15, $0.15, $0.15 and $0.16 The return over the year on IBM stock was

6. Portfolio Return Two methods (i) The initial and final values of the portfolio can be determined, dividends added to the final value, and the return computed (ii) The prices and payments of the individual assets, and the holding of those assets, can be used directly

7. Portfolio Return Total value A portfolio of 200 General Motors stock and 100 IBM stock is purchased for $20,696 on May 29 2002 The value of the portfolio on May 28 2003 was $15,697 A total of $461 in dividends was received The return over the year on the portfolio was

8. Portfolio Return Individual assets Consider a portfolio of n assets The quantity of asset i in the portfolio is a i Initial price of asset i is p i (0) Final price of asset i is p i (1) Initial value of the portfolio is

9. Portfolio Return Final value of the portfolio is If there are no dividends the return is

10. Portfolio Return Example Consider the portfolio in the table The return on the portfolio is StockHoldingInitial PriceFinal Price A10023 B20032 C15012

11. Portfolio Return Including dividends The dividend payment from asset i is d i The return on the portfolio is

12. Portfolio Return Example The return on the portfolio is StockHoldingInitial PriceFinal Price Dividend per Share A5010151 B100360 C30022203

13. Short Selling Short selling means holding a negative quantity Short 100 shares of Ford stock means that the holding of Ford is given by – 100 Dividends count against the return since they are a payment that has to be made Example On June 3 2002 a portfolio is constructed of 200 Dell stocks and a short sale of 100 Ford stocks. The prices on these stocks on June 2 2003, and the dividends paid are given in the table

14. Short Selling StockInitial PriceDividendFinal Price Dell26.18030.83 Ford17.310.4011.07 The return over the year on this portfolio is r = [200 x 30.83 + (-100) x 11.47 – (200 x 26.18 + (-100) x 17.31)] (200 x 26.18 + (-100) x 17.31) = 0.43 (43%)

15. Portfolio Proportions The proportion of the portfolio invested in each asset can also be used to find the return Value of the investment in asset i is The initial value of the portfolio is Proportion invested in asset i is These proportions must sum to 1

16. Portfolio Proportions If asset i is short-sold, its proportion is negative so X i < 0 Example A portfolio consists of a purchase of 100 of stock A at $5 each, 200 of stock B at $3 each, and a short- sale of 150 of stock C at $2 each The total value of the portfolio is V 0 =100 x 5 + 200 x 3 – 150 x 2 = 800 The portfolio proportions are X A =5/8, X B = 6/8, X C = -3/8

17. Portfolio Proportions Return The return on a portfolio is the weighted average of the returns on the individual assets in the portfolio This is the standard method of calculation The scale (total value) of the portfolio does not matter

18. Portfolio Proportions Example Consider assets A, B, and C with returns The initial proportions in the portfolio are The return on the portfolio is

19. Portfolio Proportions Proportions must be recomputed at the start of each of the holding periods. The initial value of the portfolio is V 0 = 100x10 + 200x8 = 2600 The portfolio proportions are StockHolding p(0)p(1)p(2)p(3) A 10010151216 B 200891116

20. The portfolio return over the first year is At the start of the second year the value of the portfolio is V 1 =100 x 15 + 200 x 9 = 3300 Portfolio Proportions

21. This gives the new portfolio proportions as The return over the second period can be calculated to be

22. Mean Return Mean return is the average of past returns Observe the return on an asset (or portfolio) for periods 1,2,3,...,T Let r t be the observed return in period t The mean return is

23. Mean Return Example Consider the following returns observed over 10 years The mean return is r = 4 + 6 + 2 + 8 + 10 + 6 + 1 + 4 + 3 + 6 10 = 5% Year12345678910 Return (%)46281061346