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: Another Example
Stock
A
B
Price
Day 1
$100
$ 10
Price
Day 2
$ 55
$ 10
Shares Out
200,000
1,000,000
Price of Stock A goes up to $110 on day 2, and at
the close of trading, it has a 2-for-1 stock split,
cutting the price in half while doubling the
shares outstanding
9
Price Weighting Index

Index Value1 = (100 + 10)/2 = 55

Index Value2 = (55 + 10)/2 = 32.5
% Change = (32.5 - 55)/55 = - 40.9%
The index is down, but stock A gained
10% and stock B was unchanged.
10
The Solution: Adjust the Divisor
Adjust the Divisor so that the index gives
us the value it would have had without
the split:
Before the Split, the index would have been:
110 + 10 = 120 and 120/2 = 60
After the Split, sum of prices Day 2 = 55 +10 = 65
65/(adjusted divisor) = 60
Adjusted Divisor = 1.083333
11
The Adjusted Divisor

From now on, we need to add the prices of the
stocks in the index and divide by the adjusted
divisor to get the index value.

We continue to use this adjusted divisor until
another stock splits, or until one of the stocks
in the index is replaced, or if there is a spin-off
or an acquisition that alters the stock’s price.
12
Price Weighting

Do any major indexes use a Price
Weighting System?
Yes
The Dow Jones Industrial Average
does
13
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.

14
DJIA: Composition

Today, there are 30 Companies.

Represent about 30% of the market value
of U.S. Stocks
27 stocks trade on the NYSE
 3 stocks (MSFT, INTC, and CSCO) trade
on NASDAQ

15
DJIA: Composition
As of Jan. 1, 2014:
3M, Nike, American Express, AT&T, Merk,
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
16
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/
17
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
18
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
19
Market Cap Weighted Indexes
Market Capitalization = Market Value
DEFINITION:
#shares outstanding X Price per Share
20
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
21
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.
22
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
23
Market Value Example – Day 1
Index Value1 =
(100)(100,000) + (10)(1,000,000)
----------------------------------------- X 100
(100)(100,000) + (10)(1,000,000)
= 100
24
Market Value Example – Day 2
Index Value2 =
(110)(100,000) + (10)(1,000,000)
----------------------------------------- X 100
(100)(100,000) + (10)(1,000,000)
= 105
25
Market Value Example
% Change =
(105 - 100)/100 = 5.0%
NOTE: a10% increase in Stock A caused a
5% increase in the index.
26
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
27
Example (cont)
Index Value2 =
(100)(100,000) + (11)(1,000,000)
----------------------------------------- X 100
(100)(100,000) + (10)(1,000,000)
= 105
28
What if a stock splits?
Stock
A
B
Price
Day 1
$100
$ 10
Price
Day 2
$ 55
$ 10
Shrs Out
200,000
1,000,000
Stock A goes up to $110 and then has a 2for-1 split at the close of Day 2
29
Market Value Example
Index Value2 =
(55)(200,000) + (10)(1,000,000)
----------------------------------------- X 100
(100)(100,000) + (10)(1,000,000)
= 105
30
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?
31
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?
32
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.
33
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

34
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
35
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
36
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
37
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
38
Equally-weighted Indexes

Each stock receives the same weight.

Indexes done either with arithmetic or
geometric averages of % changes in stock
prices.
39
Back to Example: Case 1
Stock
A
B
Price
Day 1
$100
$ 10
Price
Day 2
$110
$ 10
Shares Out.
100,000
1,000,000
40
Example

Stock A increased 10% in price and Stock
B had a price change of 0%.

Assume a starting index value of 100 on
day 1, so Index Value1 = 100
41
Example
Using Arithmetic Mean:
Average % Change = (10+0)/2 = 5%
Since the stocks in the index went up by an
average of 5%, the index must go up by
5%
Index Value2 = 100 X 1.05 = 105


Used in academic studies
42
Example
Using Geometric Mean:
Average % Change
[(1.10)(1.0)]1/2 - 1 = 4.88%
Index Value2 = 100 X 1.0488 = 104.88
Used by Value Line
43
Index Fund Formation

Price Weighted: Equal number of
shares of each stock

Market Value Weighted: Invest in
proportion to market capitalization.

Equally-weighted: Equal dollar amount
in each stock
44
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

45
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

46
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
47
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???

48