1. 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?

2. 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.

3. 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

4. Price Weighting: An Example
Price Price Stock Day 1 Day 2 Shrs Out. A $100 $ ,000 B $ 10 $ 10 1,000,000 Note that the market cap of each stock is $10 million on Day 1

5. Price Weighting: An Example
Index Value1 = ( )/2 = 55 Index Value2 = ( )/2 = 60 % Change Index = ( )/55 = 9.1% A 10% increase in the price of stock A caused a 9.1% increase in the index.

6. What if Instead...
Price Price Stock Day 1 Day 2 Shares Out. A $100 $ ,000 B $ 10 $ 11 1,000,000

7. Example (cont.) Index Value1 = (100 + 10)/2 = 55
% Change in Index = ( )/55 = .91%
A 10% increase in the price of stock B caused a 0.91% increase in the index.

8. 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

9. Price Weighting The Dow Jones Industrial Average does
Do any major indexes use a Price Weighting System?
Yes
The Dow Jones Industrial Average does

10. 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.)

11. 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

12. DJIA: Composition As of March 1, 2019:
3M, Nike, American Express, Apple, Merck, Goldman Sachs, Boeing, Caterpillar, Chevron, Cisco, Coca-Cola, DowDuPont, ExxonMobil, Visa, Home Depot, Intel, IBM, Johnson & Johnson, JP Morgan Chase, United Healthcare, McDonald’s, Microsoft, Pfizer, Procter & Gamble, Travelers, United Technologies, Verizon, WalMart, Disney, Walgreen

13. 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?

14. 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

15. DJIA: Index Value Suppose the Dow closes at 23,589.50
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

16. Market Cap Weighted Indexes
Market Capitalization = Market Value DEFINITION: #shares outstanding X Price per Share

17. Index Value t  (P i,t ) x (#Out Shrsi,t ) i = 1
Indext = X Base
n Value
 ( Pi,b ) X (#Out shrsi,b )

18. 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.

19. Back to Example: Case 1
Price Price Stock Day 1 Day 2 Shares Out. A $100 $ ,000 B $ 10 $ 10 1,000,000 Again, note that each stock has the same market value on day 1

20. Market Value Example – Day 1
Index Value1 = (100)(100,000) + (10)(1,000,000) X 100 = 100

21. Market Value Example – Day 2
Index Value2 =
(110)(100,000) + (10)(1,000,000)
X 100
(100)(100,000) + (10)(1,000,000)
= 105

22. Market Value Example
% Change = ( )/100 = 5.0% NOTE: a10% increase in Stock A caused a 5% increase in the index.

23. What if Instead…Case 2 Price Price Shares
Stock Day Day 2 Outstanding
A $ $ ,000
B $ $ ,000,000
Instead of stock A going up by 10%, stock B does

24. Example (cont) Index Value2 = (100)(100,000) + (11)(1,000,000)
(100)(100,000) + (10)(1,000,000)
= 105

25. 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?

26. 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?

27. 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.

28. 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

29. 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

30. 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

31. Other MV Weighted Indexes
Russell Indexes: U.S. Stocks from NYSE, AMEX, and Nasdaq
Russell 3000: 3000 largest U.S. firms
Russell 2000: 2000 smallest of Russell 3000
Russell 1000: 1000 largest of Russell 3000

32. 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

33. 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

34. 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

35. 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

36. 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???