Stock Market IndexesStock Market Indexes

How Did the Stock Market Perform Today? What should we look at?

Dow Jones Industrial Average?S&P 500?Nasdaq Composite?

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What We Need to Know What We Need to Know Regarding Stock Market Regarding Stock Market IndexesIndexesThe 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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Basic Idea: Price WeightingBasic 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

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Price Weighting: ExamplePrice Weighting: Example

Price Price Stock Day 1 Day 2 Shrs

A $100 $110 100,000

B $ 10 $ 10 1,000,000

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10% Increase in Stock A10% Increase in Stock A

Index Value1 = (100 + 10)/2 = 55

Index Value2 = (110 + 10)/2 = 60

% Change Index = (60 - 55)/55 = 9.1%

10% increase in A caused a 9.1% increase in the index.

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Example: What if Example: What if Instead...Instead...

Price Price Shares

Stock Day 1 Day 2 Outstanding

A $100 $100 100,000

B $ 10 $ 11 1,000,000

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Example (cont)Example (cont)

Index Value1 = (100 + 10)/2 = 55

Index Value2 = (100 + 11)/2 = 55.5

%Change Index = (55.5 - 55)/55

= .91%

10% increase in B caused a .91% increase in the index.

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Price Weighting 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?

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Price Weighting: ExamplePrice Weighting: Example Price Price Stock Day 1 Day 2 #

Shrs Out A $100 $ 55

200,000 B $ 10 $ 10

1,000,000

Stock A has a 2-for-1 split at the close of Day 2

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Price Weighting: ExamplePrice Weighting: ExampleIndex Value1 = (100 + 10)/2 = 55

Index Value2 = (55 + 10)/2 = 32.5

% Change = (32.5 - 55)/55 = - 40.9% It appears that something bad

happened when in fact, value was created.

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Adjust the DivisorAdjust the DivisorAdjust DivisorBefore Split, sum of prices Day 2 = 110 + 10 = 120 and 120/2 = 60

After Split, sum of prices Day 2 = 55 + 10 = 65 and 65/(adj divisor) =

60 Adj Divisor = 1.083333

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Adj DivisorAdj 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.

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DJIA: HistoryDJIA: Historyhttp://www.djindexes.com/mdsidx/?

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 only original one.

Blue Chips (leaders in their industry)

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DJIA: CompositionDJIA: CompositionToday, there are 30 Companies.

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

Only two stocks (MSFT and INTC)

trade on NASDAQ

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DJIA: CompositionDJIA: Composition

How are the firms in the index selected?

Scientifically??? (Editors of the Dow Jones owned

WSJ select the stocks)

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Other Dow Jones Other Dow Jones Price Weighted IndexesPrice Weighted IndexesTransportation (20 firms)

Utilities (15 firms)

Composite (65 firms)

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DJIA: WeightingDJIA: Weighting

DJIA index closed at 11,589.50

This signifies what??

Is this the average price??

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DJIA Index ValueDJIA Index Value

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Pi,t

i = 1

DJIA Indext = ---------------------

Adj. Divisor

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Market CapitalizationMarket Capitalization

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 Price SharesStock Day 1 Day 2

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

[Designed so that each has the same mkt value]

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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: 10% increase in A causes a 5% increase in the index.

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

Price Price Shares

Stock Day 1 Day 2 Outstanding

A $100 $100 100,000

B $ 10 $ 11 1,000,000

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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 has a 2-for-1 split at the close ofDay 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%

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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 of the U.S. stock market.

Technically a float-weighted index

How many stocks do you think are in the index?

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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”

Changes are made every couple of weeks or so

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Recent Composition of Recent Composition of S&P 500S&P 500NYSE stocks 85% NASDAQ stocks 15% AMEX stocks < 1%

Represents around 75% of market value of the U.S. stock market ($ 11 Trillion)

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Other MV Weighted Other MV Weighted IndexesIndexesNYSE 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

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Other MV Weighted Other MV Weighted IndexesIndexesWilshire 5000: All U.S. headquartered

firm stocks with readily available price data. Started in 1974.

http://www.wilshire.com/Indexes/Broad/

From NYSE, AMEX, Most active OTC.Originally were 5000.Measure of overall U.S. stock market

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Other MV Weighted Other MV Weighted IndexesIndexes

Wilshire 4500: Wilshire 5000 stocks with the S&P 500 stocks removed.

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Other MV Weighted Other MV Weighted IndexesIndexesRussell Indexes: U.S. Firm Stocks OnlyNYSE,AMEX,OTChttp://www.russell.com/indexes 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)38

Intl. Market Value IndexesIntl. Market Value Indexes

International Equity Indexes:

Morgan Stanley Capital Intl. (MSCI)

Dow Jones World Stock Index

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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 Price Shares

Stock Day 1 Day 2 Outstanding

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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ExampleExample

Using Arithmetic Mean:Average % Change = (10+0)/2 =

5%

Index Value2 = 100 X 1.05 = 105

(Used in academic studies)

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ExampleExample

Using Geometric Mean:Average % Change = [(1.10)(1.0)]1/2 =

(1.10)1/2

= 1.0488 - 1 = 4.88%

Index Value2 = 100 X 1.0488 = 104.88

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Unweighted Indexes Unweighted Indexes (geometric mean)(geometric mean)

Value Line: NYSE, AMEX, OTC

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Index FundsIndex Funds

Hold all of the stocks in an index.

Over $750 billion indexed to the S&P 500!

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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

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Implications of Implications of Skewness 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)

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Implications of Implications of SkewnessSkewness

What if put 1/4 in each??

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

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Related FactsRelated 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.

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Related FactsRelated 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???

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