1. Stock Market Indexes
How Did the Stock Market Perform Today? What should we look at?
Dow Jones Industrial Average?
S&P 500?
Nasdaq Composite?

2. What We Need to Know Regarding Stock Market Indexes
The number of stocks in the index.
The types of stocks in the index.
The weighting method used to calculate the index value.

3. Basic Idea: Price Weighting
Everyday calculate the average price (arithmetic mean price) Formula: n Indext =  Pi,t divided by n i = 1 where i indexes stocks, and there are n stocks in the index

4. Price Weighting: Example
Price Price Stock Day 1 Day 2 Shrs A $100 $ ,000 B $ 10 $ 10 1,000,000

5. 10% Increase in Stock A
Index Value1 = ( )/2 = 55 Index Value2 = ( )/2 = 60 % Change Index = ( )/55 = 9.1% 10% increase in A caused a 9.1% increase in the index.

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

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

8. Price Weighting Why is this called price weighting?
Stock A’s Price is 10 times higher so it gets a 10 times larger weighting.
Does this make Economic Sense?

9. Price Weighting: Example
Price Price Stock Day 1 Day 2 # Shrs Out A $100 $ ,000 B $ 10 $ 10 1,000,000 Stock A has a 2-for-1 split at the close of Day 2

10. Price Weighting: Example
Index Value1 = ( )/2 = 55
Index Value2 = ( )/2 = 32.5
% Change = ( )/55 = %
It appears that something bad happened when in fact, value was created.

11. Adjust the Divisor Adjust Divisor Before Split, sum of prices Day 2 =
= and 120/2 = 60
After Split, sum of prices Day 2 =
= and 65/(adj divisor) = 60
Adj Divisor =

12. Adj Divisor
From now on, add the prices of the stocks in the index and divide by the adjusted divisor to get the index value 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.

13. DJIA: History http://www.djindexes.com/mdsidx/?event= showAverages
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 only original one.
Blue Chips (leaders in their industry)

14. DJIA: Composition Today, there are 30 Companies.
Represent about 30% of the market value of U.S. Stocks
Only two stocks (MSFT and INTC) trade on NASDAQ

15. DJIA: Composition How are the firms in the index selected?
Scientifically???
(Editors of the Dow Jones owned WSJ select the stocks)

16. Other Dow Jones Price Weighted Indexes
Transportation (20 firms)
Utilities (15 firms)
Composite (65 firms)

17. DJIA: Weighting DJIA index closed at 11,589.50 This signifies what??
Is this the average price??

18. DJIA Index Value 30  Pi,t i = 1 DJIA Indext = ---------------------
Adj. Divisor

19. Market Capitalization
Market Capitalization = Market Value
DEFINITION:
#shares outstanding X Price per Share

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

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
Price Price Shares Stock Day 1 Day 2 Outstanding A $100 $ ,000 B $ 10 $ 10 1,000,000 [Designed so that each has the same mkt value]

23. Market Value Example – Day 1
Index Value1 = (100)(100,000) + (10)(1,000,000) X 100 = 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 = ( )/100 = 5.0% NOTE: 10% increase in A causes a 5% increase in the index.

26. What if Instead…Case 2 Price Price Shares
Stock Day Day 2 Outstanding
A $ $ ,000
B $ $ ,000,000

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

28. What if a stock splits? Price Price Stock Day 1 Day 2 Shrs Out
B $ $ ,000,000
Stock A has a 2-for-1 split at the close of
Day 2

29. Market Value Example Index Value2 = (55)(200,000) + (10)(1,000,000)
(100)(100,000) + (10)(1,000,000)
= 105

30. Market Value Example
% Change =
( )/100 = 5.0%

31. S&P 500
/en/us/page.topic/indices_500/2,3,2,2,0,0,0,0,0,2, 1,0,0,0,0,0.html
Most famous market-value weighed index of the U.S. stock market.
Technically a float-weighted index
How many stocks do you think 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”
Changes are made every couple of weeks or so

34. Recent Composition of S&P 500
NYSE stocks %
NASDAQ stocks 15%
AMEX stocks < 1%
Represents around 75% of market value of the U.S. stock market ($ 11 Trillion)

35. Other MV Weighted Indexes
NYSE Composite: All NYSE stocks
NASDAQ Composite: OTC stocks that meet requirements
(Roughly 5,000 stocks)
Wilshire 5000: Represents 100% of U.S. stocks with readily available price data

36. Other MV Weighted Indexes
Wilshire 5000: All U.S. headquartered firm stocks with readily available price data. Started in 1974.
From NYSE, AMEX, Most active OTC.
Originally were 5000.
Measure of overall U.S. stock market

37. Other MV Weighted Indexes
Wilshire 4500: Wilshire 5000 stocks with the S&P 500 stocks removed.

38. Other MV Weighted Indexes
Russell Indexes: U.S. Firm Stocks Only
NYSE,AMEX,OTC
Russell 3000: 3000 largest U.S. firms
Russell 2000: (2000 smallest mkt cap of Russell
3000)
Russell 1000:
(1000 largest market cap of Russell 3000)

39. Intl. Market Value Indexes
International Equity Indexes:
Morgan Stanley Capital Intl. (MSCI)
Dow Jones World Stock Index

40. Unweighted Indexes Each stock receives the same weight.
Indexes done either with arithmetic or geometric averages of % changes in stock prices.

41. Back to Example: Case 1 Price Price Shares
Stock Day Day 2 Outstanding
A $ $ ,000
B $ $ ,000,000

42. 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

43. Example Using Arithmetic Mean: Average % Change = (10+0)/2 = 5%
Index Value2 = 100 X 1.05 = 105
(Used in academic studies)

44. Example Using Geometric Mean: Average % Change
= [(1.10)(1.0)]1/2 = (1.10)1/2
= = 4.88%
Index Value2 = 100 X =

45. Unweighted Indexes (geometric mean)
Value Line: NYSE, AMEX, OTC

46. Index Funds Hold all of the stocks in an index.
Over $750 billion indexed to the S&P 500!

47. Index Fund Formation
Price Weighted: Equal number of shares of each stock
Market Value Weighted: Invest in proportion to market capitalization.
Unweighted: Equal dollar amount in each stock

48. Implications of Skewness
Suppose you have $100 to invest 
Only 4 stocks in our world (W, X, Y & Z)
W has a 300% return ($100 grows to $400)
X has a 25% return ($100 grows to $125)
Y has a 5% return ($100 grows to $105)
Z has a - 20% return ($100 shrinks to $ 80)

49. Implications of Skewness
What if put 1/4 in each??
Portfolio Return: .25(300%) + .25(25%) + .25(5%) (-20%) E(R) = 77.5% ($100 grows to $177.50)
This is more than if you put all in X, all in Y or all in Z, but less than if all in W.
The outstanding performance of W drove your results

50. Related Facts
 Over past 20 years, the S&P 500 annual return would be almost cut in half by dropping the best 50 firms in each year.
  Often get a narrow market. In the late 1990s it was the technology stocks. They had huge returns and had driven the market returns up. More recently has been energy stocks.

51. Related Facts
 For any 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???