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Investment Analysis and Portfolio Management

Investment Analysis and Portfolio Management. Lecture 2 Gareth Myles. Return. 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

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Investment Analysis and Portfolio Management

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  1. Investment Analysis and Portfolio Management Lecture 2 Gareth Myles

  2. Return • 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 V0is the purchase pricep(0) • Final wealth V1is the selling pricep(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 holdingof 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 ai • Initial price of asset i is pi(0) • Final price of asset i is pi(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

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

  12. Portfolio Return • Example • The return on the portfolio is

  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 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 Xi < 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 V0 =100 x 5 + 200 x 3 – 150 x 2 = 800 • The portfolio proportions are XA =5/8, XB = 6/8, XC = -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 V0 = 100x10 + 200x8 = 2600 • The portfolio proportions are

  20. Portfolio Proportions • The portfolio return over the first year is • At the start of the second year the value of the portfolio is V1 =100x15 + 200x9 = 3300

  21. Portfolio Proportions • 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 rt 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%

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