Stock Market Indexes

If we want to know how the stock
market did today, what should we look at?
The Dow Jones Industrial Average?
 The S&P 500 Index?
 The Nasdaq Composite Index?

1
What We Need to Know to
Understand an Index

The number of stocks in the index.

The types of stocks in the index.

The weighting method used to calculate
the index value.
2
Price Weighting
Start by calculating the average price (arithmetic
mean) of the stocks in the index at time t
N
Index valuet =  Pi,t divided by N
i=1
where the stocks in the index at time t go from 1 – N
3
Price Weighting: An Example
Stock
A
B
Price
Day 1
$100
$ 10
Price
Day 2
$110
$ 10
Shrs Out.
100,000
1,000,000
Note that the market cap of each stock is
$10 million on Day 1
4
Price Weighting: An Example
Index Value1 = (100 + 10)/2 = 55
Index Value2 = (110 + 10)/2 = 60
% Change Index = (60 - 55)/55 = 9.1%
A 10% increase in the price of stock A
caused a 9.1% increase in the index.
5
What if Instead...
Stock
A
B
Price Price
Day 1 Day 2
$100
$100
$ 10
$ 11
Shares Out.
100,000
1,000,000
6
Example (cont.)
Index Value1 = (100 + 10)/2 = 55
Index Value2 = (100 + 11)/2 = 55.5
% Change in Index = (55.5 - 55)/55 = .91%
A 10% increase in the price of stock B
caused a 0.91% increase in the index.
7
Price Weighting

Stock A’s Price is 10 times higher so it
gets a 10 times larger weighting.

But both companies are the same size.

Stock prices can be altered by changing
shares outstanding through splits and
repurchases
8
Price Weighting

Do any major indexes use a Price
Weighting System?
Yes
The Dow Jones Industrial Average
does
9
DJIA: History
http://www.djindexes.com
 Oldest barometer of the stock market.
 Price Weighted Index
 Started in 1896 by Charles Dow with 12
stocks. (He and Jones started Dow Jones
& Company.)
 GE is the only original stock still in the
index.

10
DJIA: Composition

Today, there are 30 Companies.

Represent about 30% of the market value
of U.S. Stocks
26 stocks trade on the NYSE
 4 stocks (MSFT, INTC, AAPL and CSCO)
trade on NASDAQ

11
DJIA: Composition
As of July 1, 2015:
3M, Nike, American Express, Apple, Merck,
Goldman Sachs, Boeing, Caterpillar,
Chevron, Cisco, Coca-Cola, DuPont,
ExxonMobil, GE,Visa, Home Depot, Intel,
IBM, Johnson & Johnson, JP Morgan Chase,
United Healthcare, McDonald’s, Microsoft,
Pfizer, Procter & Gamble, Travelers, United
Technologies,Verizon, WalMart, Disney
12
DJIA: Composition

Editors of the Dow Jones-owned WSJ
select the stocks.
◦ Dow Jones is now a subsidiary of News Corp.

What are their current prices?
◦ http://money.cnn.com/data/dow30/
13
Other Dow Jones
Price Weighted Indexes

Transportation (20 firms)
◦ Started in 1884

Utilities (15 firms)
◦ Started in 1929

Composite (65 firms)
◦ Stocks in the Industrial, Transportation and
Utilities indexes
14
DJIA: Index Value
Suppose the Dow closes at 10,589.50
How did they arrive at this value?
30
 Pi,t
i=1
DJIA Indext =
---------------------
Adj. Divisor
Note that the divisor is no longer 30. It is adjusted each
time a stock “splits” or a stock in the index is replaced
15
Market Cap Weighted Indexes
Market Capitalization = Market Value
DEFINITION:
#shares outstanding X Price per Share
16
Index Value t
n
 (P i,t ) x (#Out Shrsi,t )
i=1
Indext = ----------------------------n
X Base
Value
 ( Pi,b ) X (#Out shrsi,b )
i=1
17
Index Value t
t indexes days
 b is the base day
 i indexes stocks


Base day value needs to be arbitrarily set
to something by the firm starting the
index. 10 or 100 are common.
18
Back to Example: Case 1
Stock
A
B
Price
Price
Day 1 Day 2
$100
$110
$ 10
$ 10
Shares Out.
100,000
1,000,000
Again, note that each stock has the same
market value on day 1
19
Market Value Example – Day 1
Index Value1 =
(100)(100,000) + (10)(1,000,000)
----------------------------------------- X 100
(100)(100,000) + (10)(1,000,000)
= 100
20
Market Value Example – Day 2
Index Value2 =
(110)(100,000) + (10)(1,000,000)
----------------------------------------- X 100
(100)(100,000) + (10)(1,000,000)
= 105
21
Market Value Example
% Change =
(105 - 100)/100 = 5.0%
NOTE: a10% increase in Stock A caused a
5% increase in the index.
22
What if Instead…Case 2
Stock
A
B
Price
Day 1
$100
$ 10
Price
Day 2
$100
$ 11
Shares
Outstanding
100,000
1,000,000
Instead of stock A going up by 10%, stock B
does
23
Example (cont)
Index Value2 =
(100)(100,000) + (11)(1,000,000)
----------------------------------------- X 100
(100)(100,000) + (10)(1,000,000)
= 105
24
Market Value Example
% Change =
(105 - 100)/100 = 5.0%
Since stocks A and B have the same market
value, they receive the same weight in the
index
What indexes use this weighting system?
25
S&P 500
http://www.standardandpoors.com/home/en/us
Most famous market-value weighed index

Technically a float-weighted index

How many stocks are in the index?
26
S&P 500

1928 was S&P 90. In 1957 it became S&P
500.

Is used by 97% of U.S. money managers
and pension plan sponsors as a proxy for
the U.S. stock market.
27
S&P 500
Stocks are selected to include leading
companies in leading industries in the U.S.
 U.S. firms only, though some non- U.S.
firms are “grandfathered” into the index
 Changes are made every few weeks
 Standard and Poors (a division of
McGraw-Hill) decides which companies
to include in the index

28
Other MV Weighted Indexes

NYSE Composite: All NYSE stocks

NASDAQ Composite: All stocks listed
on NASDAQ (Roughly 3,000 stocks)

Wilshire 5000: All stocks traded in the
United States
29
Other MV Weighted Indexes

Wilshire 4500: Wilshire 5000 stocks with
the S&P 500 stocks removed.

S&P 400: A mid-cap index

S&P 600: A small-cap index
30
Other MV Weighted Indexes
Russell Indexes: U.S. Stocks from NYSE, AMEX,
and Nasdaq
http://www.russell.com/indexes
Russell 3000: 3000 largest U.S. firms
Russell 2000: 2000 smallest of Russell 3000
Russell 1000: 1000 largest of Russell 3000
31
International Indexes
International Equity Indexes:
 MSCI World Index:
1600 stocks from 23 countries
Only companies from developed
countries; market value weighted
 Global Dow: 150 stocks; both developed
and emerging countries (but 40% from
U.S.); equally-weighted
32
Implications of Skewness
Suppose there are only 4 stocks in our index:
W, X, Y & Z
W has a 300% return
 X has a 25% return
 Y has a 5% return
 Z has a - 20% return

33
Implications of Skewness

What if we have an equally-weighted index?
Index Return:
 .25(300%) + .25(25%) + .25(5%) + .25(-20%) = 77.5%

The “typical” stock in your index was not up 77.5%
 The outstanding performance of W drove the results

34
Implications of Skewness



Many indexes have skewed returns
Often get a narrow market.
Strong returns for an index may be
primarily due to one or two industries
35
Implications of Skewness
For any price-weighted or value-weighted
index, as a stock’s price goes up (relative to
other stocks) it receives a higher weighting
in the index.
 This means that if there is a “bubble” in one
sector, the index will tilt more heavily
toward the stocks in that sector.
 For those who invest in the index, it means
placing a greater weight on those stocks
which have gone up in price the most.
 Is that good or bad???

36