Stock Market IndexesStock 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 What We Need to Know to Understand an IndexUnderstand an IndexThe number of stocks in the

index.

The types of stocks in the index.

The weighting method used to calculate the index value.

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Price WeightingPrice 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 Price Weighting: An ExampleExample Price Price Stock Day 1 Day 2 Shrs Out.

A $100 $110 100,000 B $ 10 $ 10 1,000,000

Note that the market cap of each stock is $10 million on Day 1

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Price Weighting: An Price Weighting: An ExampleExampleIndex 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.

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What if Instead...What if Instead...

Price PriceStock Day 1 Day 2 Shares Out.

A $100 $100 100,000

B $ 10 $ 11 1,000,000

6

Example (cont.)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.

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Price Weighting 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 Price Weighting: Another ExampleExample Price Price Stock Day 1 Day 2 Shares

Out A $100 $ 55 200,000 B $ 10 $ 10 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

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Price Weighting IndexPrice Weighting IndexIndex 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.

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The Solution: Adjust the The Solution: Adjust the DivisorDivisorAdjust 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

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The Adjusted DivisorThe 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.

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Price WeightingPrice WeightingDo any major indexes use a Price

Weighting System?

Yes

The Dow Jones Industrial Average does

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DJIA: HistoryDJIA: Historyhttp://www.djindexes.com/mdsid

x/?event=showAverages

Oldest barometer of the stock market.

Price Weighted IndexStarted 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.

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DJIA: CompositionDJIA: CompositionToday, there are 30 Companies.

Represent about 30% of the market value of U.S. Stocks

27 stocks trade on the NYSE3 stocks (MSFT, INTC, and CSCO)

trade on NASDAQ

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DJIA: CompositionDJIA: CompositionAs of Jan. 1, 2010:3M, Alcoa, American Express, AT&T,

Bank of America,Boeing, Caterpillar, Chevron, Cisco, Coca-Cola, DuPont, ExxonMobil, GE, Hewlett-Packard, Home Depot, Intel, IBM, Johnson & Johnson, JP Morgan Chase, Kraft, McDonald’s, Merk, Microsoft, Pfizer, Procter & Gamble, Travelers, United Technologies, Verizon, WalMart, Disney

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DJIA: CompositionDJIA: Composition

How are the firms in the index selected?

Editors of the Dow Jones-owned WSJ select the stocks.

Dow Jones is now a subsidiary of News Corp.

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Other Dow Jones Other Dow Jones Price Weighted IndexesPrice Weighted Indexes

Transportation (20 firms)

Utilities (15 firms)

Composite (65 firms)

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DJIA: Index ValueDJIA: 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

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Market Cap Weighted Market Cap Weighted IndexesIndexes Market Capitalization = Market

Value

DEFINITION:#shares outstanding X Price per

Share

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Index Value Index Value tt

n

(P i,t ) x (#Out Shrsi,t )

i = 1

Indext = ----------------------------- X Base

n

Value ( Pi,b ) X (#Out shrsi,b )

i = 1

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Index Value Index Value tt

t indexes daysb is the base dayi indexes stocks

Base day value needs to be arbitrarily set to something by the firm starting the index. 10 or 100 are common.

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Back to Example: Case 1Back to Example: Case 1

Price PriceStock Day 1 Day 2 Shares Out.

A $100 $110 100,000 B $ 10 $ 10 1,000,000

Again, note that each stock has the same market value on day 1

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Market Value Example – Market Value Example – Day 1Day 1Index Value1 =

(100)(100,000) + (10)(1,000,000)----------------------------------------- X

100(100)(100,000) + (10)(1,000,000)

= 100

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Market Value Example – Market Value Example – Day 2Day 2Index Value2 =

(110)(100,000) + (10)(1,000,000)----------------------------------------- X

100(100)(100,000) + (10)(1,000,000)

= 105

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Market Value ExampleMarket Value Example

% Change = (105 - 100)/100 = 5.0%

NOTE: a10% increase in Stock A caused a

5% increase in the index.

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What if Instead…Case 2What if Instead…Case 2

Price Price SharesStock Day 1 Day 2 Outstanding

A $100 $100 100,000 B $ 10 $ 11 1,000,000

Instead of stock A going up by 10%, stock B does

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Example (cont)Example (cont)

Index Value2 =

(100)(100,000) + (11)(1,000,000)----------------------------------------- X

100(100)(100,000) + (10)(1,000,000)

= 105

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What if a stock splits?What if a stock splits?

Price Price Stock Day 1 Day 2 Shrs Out

A $100 $ 55 200,000

B $ 10 $ 10 1,000,000

Stock A goes up to $110 and then has a 2-for-1 split at the close of Day 2

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Market Value Example Market Value Example

Index Value2 =

(55)(200,000) + (10)(1,000,000)----------------------------------------- X

100(100)(100,000) + (10)(1,000,000)

= 105

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Market Value ExampleMarket 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?

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S&P 500S&P 500http://www2.standardandpoors.com/portal/site/sp/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

Technically a float-weighted index

How many stocks are in the index?32

S&P 500S&P 5001928 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.

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S&P 500S&P 500Stocks 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 couple of weeks or so

Standard and Poors (a division of McGraw-Hill) decides which companies to include in the index

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Other MV Weighted Other MV Weighted IndexesIndexesNYSE Composite: All NYSE

stocks NASDAQ Composite: All stocks

listed on NASDAQ (Roughly 3,000 stocks)

Wilshire 5000: All stocks traded in the United States

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Other MV Weighted Other MV Weighted IndexesIndexes

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

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Other MV Weighted Other MV Weighted IndexesIndexesRussell Indexes: U.S. Stocks from

NYSE, AMEX, and Nasdaqhttp://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

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International IndexesInternational IndexesInternational Equity Indexes:MSCI World Index:

Maintained by Morgan Stanley1500 stocks from 23 countriesOnly companies from developed countries; market value weighted

Global Dow: 150 stocks; both developed and emerging countries (but 40% from U.S.); unweighted

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Unweighted IndexesUnweighted IndexesEach stock receives the same

weight.

Indexes done either with arithmetic or geometric averages of % changes in stock prices.

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Back to Example: Case 1 Back to Example: Case 1

Price PriceStock Day 1 Day 2 Shares Out.

A $100 $110 100,000

B $ 10 $ 10 1,000,000

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ExampleExampleStock 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

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ExampleExampleUsing 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 studies42

ExampleExample

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

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Index Fund Formation 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

44

Implications of Implications of Skewness Skewness

Suppose there are only 4 stocks in our world:

W, X, Y & Z W has a 300% return X has a 25% return Y has a 5% return Z has a - 20% return

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Implications of Implications of SkewnessSkewness

What if you invested the same amount of money in each stock?

Portfolio Return: .25(300%) + .25(25%) + .25(5%) + .25(-20%)

= 77.5%  This is more than X, Y or Z, but less than W.The outstanding performance of W drove your

results 

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Implications of Implications of SkewnessSkewness Many indexes have skewed returns   Often get a narrow market.

Strong returns for an index may be primarily due to one or two industries

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Implications of Implications of SkewnessSkewness

 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