Investment Analysis and Portfolio Management

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 V0 is the purchase price p(0)
• Final wealth V1 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 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

Stock Holding Initial Price Final Price
A 100 2 3
B 200 3 2
C 150 1 2
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

Stock Holding Initial Price Final Price Dividend per Share
A 50 10 15 1
B 100 3 6 0
C 300 22 20 3
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
Stock Initial Price Dividend Final Price
Dell 26.18 0 30.83
Ford 17.31 0.40 11.07
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 Xi lt 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

Stock Holding p(0) p(1) p(2) p(3)
A 100 10 15 12 16
B 200 8 9 11 16
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

Year 1 2 3 4 5 6 7 8 9 10
Return () 4 6 2 8 10 6 1 3 4 6