1. Investments and Portfolio Management
WEEK 5 1

2. Introducing Market Indexes
Objectives :
Discuss the major uses of indexes
Determine what causes indexes to differ
Evaluate the major indexes and their characteristics
Evaluate the relationship between indexes 2

3. What is an Index?
An index tracks the value of a basket of shares (or other securities) over time. It does not actually have ownership of the shares within it.
The “basket” will typically include companies of a similar size, location or industry. E.g. FTSE100 is a large-cap index of UK listed securities.
They can also be used to track shares suggested for a particular investment strategy; growth, balanced or income.
A share can be included in more than one index. 3

4. Uses of Security-Market Indexes
To provide a benchmark for the performance of individual portfolios
The benchmark can be used to judge the performance of asset managers 1
The creation of index funds where a portfolio tracks the performance of an index over time
Index funds exist for common stock (equity) and bonds 2
To examine factors that influence aggregate market returns
This allows performance comparison of different asset classes 3
For ‘technicians’ to predict future price movements based upon past index performance
Is the past a good predictor of the future? 4
As a substitute for the market portfolio of risky assets when calculating the required return of an asset 5
ke=rf + β(rm – rf) 4

5. Factors Affecting Market Indexes
The Sample – size, breadth and source
Weighting of Sample Members
Price weighted index
Market cap weighted index
Equally weighted (or un-weighted) index
Fundamental weighted index based on operating variables, e.g. sales, ROE
Computational procedure
Arithmetic mean
Geometric mean 5

6. Price-weighted Index Simple ‘Arithmetic Mean’ of current stock prices
This means that index movements are influenced by the differential prices of the components
E.g. Dow Jones Industrial Average (DJIA)
DJIA is made up of 30 large, well known industrial stocks (blue chip stocks)
The divisor may need to be adjusted to maintain the index value after changes in the sample over time, e.g. a stock split (bonus issue in the UK) 6

7. Wall Street Journal - DJIA7
Company
Price
Change
% Change
Volume
Time (ET)
Microsoft Corp
38.16
+0.80
+2.13%
44,957,611
20:10:00
Home Depot Inc/The
77.60
+1.42
+1.86%
7,065,617
20:04:08
Walt Disney Co/The
68.97
+1.20
+1.77%
5,691,005
20:04:05
Pfizer Inc
31.87
+0.49
+1.56%
27,179,902
20:04:06
UnitedHealth Group Inc
71.01
+1.06
+1.52%
3,880,757
20:04:07
NIKE Inc
77.85
+0.98
+1.27%
2,401,072
Cisco Systems Inc
24.00
+0.27
+1.12%
75,234,897
Travelers Cos Inc/The
87.22
+0.78
+0.90%
2,081,857
Procter & Gamble Co/The
83.50
+0.70
+0.85%
7,582,173
Visa Inc
199.78
+1.51
+0.76%
2,050,456
Intel Corp
24.60
+0.17
+0.70%
22,990,316
Boeing Co/The
133.17
+0.84
+0.63%
3,578,750
Coca-Cola Co/The
40.12
+0.24
+0.60%
11,771,162
American Express Co
81.44
+0.41
+0.51%
2,828,191
McDonald's Corp
98.11
+0.45
+0.46%
4,164,823
Caterpillar Inc
84.20
+0.35
+0.42%
3,953,342
General Electric Co
27.15
+0.10
+0.37%
34,393,647
JPMorgan Chase & Co
54.14
+0.31%
22,121,852
International Business Machines Corp
183.55
+0.48
+0.26%
4,711,276
Wal-Mart Stores Inc
78.90
+0.19
+0.24%
8,289,973
3M Co
128.59
+0.23
+0.18%
2,426,280
Chevron Corp
120.09
+0.09
+0.08%
6,214,448
Goldman Sachs Group Inc/The
162.94
+0.05
+0.03%
3,398,763
United Technologies Corp
107.46
+0.01
+0.01%
2,797,564
Exxon Mobil Corp
92.59
-0.08
-0.09%
9,285,719
Johnson & Johnson
93.34
-0.22
-0.24%
8,954,791
AT&T Inc
35.07
-0.10
-0.28%
22,332,041
Verizon Communications Inc
49.99
-0.17
-0.34%
10,915,592
Merck & Co Inc
47.34
-0.25
-0.53%
14,162,665
EI du Pont de Nemours & Co
60.94
-1.11
-1.79%
6,692,518

8. What is the new index value?
The adjusted divisor
Assume the price-weighted index consists of three stocks, A, B, and C. Stock A issues a 3-for-1 stock split, i.e. if you hold 1 share you will receive an additional 2 shares to end up with 3 shares.
Stock Price Before Issue Price After Issue A B C
Index / 3 = 20
Divisor
What is the new index value? 8

9. If the divisor were not adjusted….
Stock Price Before Issue Price After Issue A B C
Index / 3 = / 3 = 13.33
Divisor
Note: Whilst the price of Stock A has reduced to a third of the original price there are now 3 times the number of shares in issue. Therefore, the total market value of the shares remains the same. Yet the value of the index has fallen from 20 to 13.33?!
This cannot be correct, therefore we need to change the divisor. 9

10. With an adjusted divisor
Note: If the total market value remains the same after a stock split then the index should not change.
Stock Price Before Issue Price After Issue A B C
Index / 3 = / X = 20
Divisor X=2
The divisor is only changed when there is a change in the sample make-up of the index: it started at 30 in 1896 but as at stands at 10
Wall Street Journal - DJIA

11. Price weighted Index – Effect of differently priced shares
The index is price weighted, therefore a stock with a high price carries more weight than one with a low price
Case A = 10% increase in share price of A
Case A
Period T (T+1 week) A B C
Sum
Divisor
Index
Percentage Change % 11

12. Price weighted Index – Impact of differently priced shares
Case B = 10% increase in share price of C
Case A Case B
Period T (T+1 week) (T+1 week) A B C
Sum
Divisor
Index
Percentage Change % 1.7%
A change in a higher priced stock will have a greater impact on a price-weighted index than a similar change in a lower priced stock 12

13. DJIA Criticism of the DJIA
30 non-randomly selected blue chip stocks not representative of the market
Stock splits reduce share price distorting weight in the index
Stock splits mean constant revisions of the divisor 13

14. Market cap weighted Index
Derive the initial total market value of all stocks used in the series
Market Cap = Number of Shares Outstanding * Current Market Price
E.g. S&P500, FTSE100
S&P uses only freely floating shares (excluding those held by insiders)
Assign a beginning index value (typically 100) and new market values are compared to the base index 14

15. Market Cap Weighted Index
where:
Index t = index value on day t
Pt = ending prices for stocks on day t
Qt = number of outstanding shares on day t
Ph = ending price for stocks on base day
Qh = number of outstanding shares on base day 15

16. Market Cap Weighted Index example
Stock
share price(£)
number of shares
Market Value
31/12/2012
(£) A 10
1,000,000
10,000,000 B 15
6,000,000
90,000,000 C 20
5,000,000
100,000,000
Base value equal to an Index of 100
200,000,000 16

17. Market Cap Weighted Index example
B – Issue a two-for-one stock split during the year
= 6,000,000 x 2 = 12,000,000
= £15 / 2 = £7.50
Stock
share price(£)
number of shares
Market Value
31/12/2013
(£) B
7.50
12,000,000
90,000,000 17

18. Market Cap Weighted Index example
After the changes:
Stock
share price(£)
number of shares
Market Value
31/12/2013
(£) A 10
1,000,000
10,000,000 B
7.50
12,000,000
90,000,000 C 20
5,000,000
100,000,000
Index remains at 100
200,000,000
In a market cap weighted index there is an automatic adjustment for stock splits as a decrease in stock price is offset by an increase in the number of shares. 18

19. Market Cap Weighted Index example 2
Now let’s assume that the stock of B remains
in demand after the capital change leading to increased prices
Stock
share price(£)
number of shares
Market Value
31/12/2013
(£) A 12
12,000,000 B 10 C 20
5,500,000
Calculate the new index as at 19

20. Market cap weighted Index example 2
After the changes:
Stock
share price(£)
number of shares
Market Value
31/12/2013
(£) A 12
1,000,000
12,000,000 B 10
120,000,000 C 20
5,000,000
100,000,000
232,000,000
New Market Cap
Market cap weighted index =
Beginning index value
Original Market Cap 20

21. Market cap weighted Index example 3
Base Value
Price A increase by 20%
Price C increase by 20%
Stock
number of shares
Price
Market Value A
1,000,000 10
10,000,000 12
12,000,000 B
6,000,000 15
90,000,000 C
5,000,000 20
100,000,000 24
120,000,000
200,000,000
202,000,000
220,000,000
100
101
110
Price changes in large market value stocks will influence the index to a greater degree than those with smaller market values. 21

22. Equally-Weighted Index (un-weighted)
All stocks carry equal weight regardless of price or market value
May be used by individuals who randomly select stocks and/or invest the same amount in each stock
Typically use arithmetic mean of the percentage price changes for the stocks in the index
The FT30 Share Index uses a geometric mean of the holding period returns 22

23. Equally-Weighted Index example
Base Value
Price increases
Stock
number of shares
Price
Market Cap
Percentage
change A
1,000,000 10
10,000,000 15
15,000,000
50.0% B
6,000,000
90,000,000 20
120,000,000
33.3% C
5,000,000
100,000,000 22
110,000,000
10.0%
200,000,000
245,000,000
93.3%
Index value
100
100x1.311 = 131.1
93.3/3 = 31.1
Market cap weighted index would be (245/200)x100 = 23

24. Global Equity Indexes
Stock market indexes found in most individual foreign markets
Local therefore difficult to compare due to different samples, weighting and computation
To overcome this some investment data firms have created consistent stock indexes to allow comparison 24

25. 25

26. FT/S&P-Actuaries World Indexes
Jointly compiled by The Financial Times Limited, Goldman Sachs & Co., and S&P’s in conjunction with the Institute of Actuaries and the Faculty of Actuaries
Measures 2,271 securities in 30 countries
Covers 70% of the total value of all listed companies in each country
Securities included must allow direct holdings of shares by foreign nationals
Index is market cap weighted with a base date of December 31, 1986 = 100
Index results are reported in U.S. dollars, U.K. pound sterling, Japanese yen, and the local currency of the country included 26

27. Morgan Stanley Capital International (MSCI) Indexes
Include over 1,500 companies listed on stock exchanges in 22 countries with a combined capitalization representing approximately 60 percent of the aggregate market value of the stock exchanges of these countries
All the indexes are market cap weighted
Reporting is in U.S. dollars and the country’s local currency 27

28. Dow Jones Wiltshire Global Indexes
Introduced in January 1993
2,200 companies worldwide
Organized into 120 industry groups
Includes 33 countries representing more than 80 percent of the combined capitalisation of these countries
Countries are grouped into three major regions: Asia/Pacific, Europe/Africa, and the Americas
Each country’s index is calculated in its own currency as well as in the U.S. dollar 28

29. Summary Indexes track the value of a basket of shares over time.
There are different ways of weighting and computing the value; price-weighted, market cap weighted and equally-weighted, using arithmetic or geometric means. The method used will determine how much influence the change in the price of one share has on an index.
Given the different methods, indexes tend to be difficult to compare. For this reason, investment companies create global indexes 29

30. Reading The slides for this week’s lecture have been based on:
Reilly, F. K. and Brown, K. C. (2012) Analysis of Investments and Management of Portfolios, 10th edition, Cengage Learning – Chapter 5
Stafford Johnson, R. (2014), Equity Markets and Portfolio Analysis, John Wiley & Sons – Chapters 1 & 5
Other sources: 30

31. Useful Bloomberg Functions
SECF <GO> and in ‘category’ select ‘index/stats’. Select whichever tab you want and can search on various fields. Clicking on the selected index will take you to a menu offering such functions as: MEMB <GO> Member weightings GP <GO> Price graph COMP <GO> comparative returns of different indexes WEI <GO> world equity indexes 31

32. Useful Bloomberg Functions
SECF <GO> ‘S&P 500’ followed by COMP <GO>, added FTSE 100 as a comparator. Note that I selected different currencies. 32

33. Useful Bloomberg Functions
Now I have included the FTSE 100 both in GBP and USD. The yellow line is in USD. i.e. the pound has weakened against the dollar so the value in USD has dropped more than the value in GBP
In GBP
In USD 33

34. Useful Bloomberg Functions
MEMB <GO> ‘UKX’ sorted by industry (one industry expanded to show data) 34
Note: UKX is FTSE 100 index