Stock and Bond Market Indexes Major stock market indexes

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Stock and Bond Market Indexes Major stock market indexes

DJIA (Dow Jones Industrial Average) S&P 500 (Standard and Poor's Composite 500) NASDAQ composite index NYSE index, Wilshire 5000 index, Russell 2000

Historical data of indexes

DJIA (Dow Jones Industrial Average)

- The Dow Jones Industrial Average was founded by Charles Dow on May 26, 1896, and represented the dollar average of 12 stocks from leading American industries. See

- Current DJIA includes 30 blue chip stocks (not all are industrial companies). Changes in the list of companies is made by the editors of the Wall Street Journal.

- Historical charts of DJIA:

- How to construct the index?

Average of 30 stock prices

=

1

3=01

where 'd ' is called the Dow Divisor

- Properties

The contribution of each stock to the index is its price ? price weighted index

To replicate the DJIA index, equal number of shares of 30 firms must be included. The dollar amount of investment is determined after the number of shares is determined.

Drawbacks of price weighted index

One dollar change in prices of high and low priced stocks has the same effect on the DJIA.

One dollar change in price represents a large percentage change for a low priced stock, and vice versa. The price weighted DJIA index does not reflect this

- Dow divisor

Changes in the composition of 30 companies (some dropped and replaced by other companies)

Split of stocks: This changes the index even though the market condition has not changed.

To adjust for these changes so that index is not affected by these changes, DJIA uses the Dow Divisor.

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Example

ABC XYZ Average

initial price 30 90

(30+90)/2=60

price after split 30 45

(30+45)/1.25=60

Current prices of two stocks: $90 & $30 Index=(30+90)/2=60 divisor=2 XYZ stock is split two for one, making the price per share drop from $90 to $45 Average price (30+45)/2=37.5 Dow divisor d: find a value d such that

(30+45)/d=60 d=1.25 < 2

Portfolio tracking DJIA (Price Weighted Index) Investment fund=$12,000 Two stocks: ABC and XYZ Prices: $25 and $100 Index=(25+100)/2=62.5 (divisor=2) To track the DJIA, we need to purchase identical number of shares

Shares to buy: 12,000/(25+100)=96 shares each Amount to invest: ABC: 25x96=$2,400, XYZ: 100x96=$9,600 (1:4 ratio, the ratio of prices)

Stock split: XYZ stock is split 2 for 1 Share price of XYZ=$50 Number of shares of XYZ in portfolio: doubled to 192 Divisor: 62.5=(25+50)/d d=1.2 Portfolio has an unbalanced portfolio for the PW index

Rebalance to track the DJIA How many shares can we buy? one ABC and one XYZ cost $25+$50=$75. With $12,000, we can buy 160 shares of each. ABC: 96 to 160, need $1,600 (=25x(160-96)) XYZ: 192 to 160, need to sell 32 shares which generates 50x32=$1,600 Therefore, to rebalance, sell 32 shares of XYZ and use the proceed to buy 64 shares of ABC

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Standard and Poor's (S&P) 500 stock market index

- Standard & Poor's introduced its first value-weighted stock index of 90 firms (S&P90) in 1923.

The S&P 500 index in its present form began on March 4, 1957

- It represents the market value (market capitalization) of 500 large-cap common stocks publicly held and actively traded in the NYSE and the NASDAQ. The company must have at least 5 billion dollars of capitalization -- market value (market capitalization) weighted index

- The base year of the index is 1941-1943 and the value of base year index is 10. The market value of the S&P 500 index in the base period is the average market value of each company in 1941-1943.

- How to construct the index?

=

1

5=010

=

1

5=010

where

Ni : number of outstanding shares of firm i

Pi : share price of firm i

Vi=NiPi: market value (capitalization) of firm i

d : Divisor to adjust for the change in the member firms.

- Properties

The contribution of each stock to the index is the total market value of the firm.

Stock split does not affect the total value of the firm, and hence, does not affect the index.

To replicate the S&P500 index, you have to allocate the fund in proportion of each firm's market value

The number of shares is determined by the share price after the amount of investment id determined.

List of companies:

Historical charts of S&P 500 ^GSPC+Basic+Chart

NASDAQ Composite Index

NASDAQ = National Association of Securities Dealers Automated Quotations The Index began on February 5, 1971 at a Base Value of 100. It includes all domestic and international based common type stocks listed on the NASDAQ Stock Market. It is about 3300 stocks.

The NASDAQ Composite Index is a market capitalization-weighted index. The total value of outstanding stocks is divided by the Divisor to scale it to a lower order of magnitude

which is more desirable for reporting purposes. Historical charts of NASDAQ ^IXIC+Basic+Chart

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Portfolio tracking the value weighted index S&P 500

Investment fund = $12,000

shares Price value invest $ shares

outstanding

of firm

ABC

400 25 10000 8000 320

XYZ

50 100 5000 4000 40

Allocate fund in proportion of the fraction of each firm's market value: two to one ratio in this example.

Stock split does not affect the value of firm. No need to rebalance.

Investment strategy of mimicking the market value weighted index is equivalent to "buy and hold" strategy

Equally Weighted Indexes - allocate an equal amount of fund to each stock - the number of stock varies with the price of stock. - hold more shares of low priced stocks. buy more when price is low and buy less when price is high. - Investors desiring to continuously hold an equally-weighted index would need to readjust their portfolio in each period by selling shares in companies that had outperformed the index in the previous period and by buying shares in the companies that had under-performed the index. - NASDAQ-100 Equal Weighted Index: includes 100 of the largest non-financial securities listed on The NASDAQ Stock Market based on market capitalization - S&P also has several equally weighted indexes for various sectors - The Value Line Geometric Composite Index and the Value Line Arithmetic Composite Index

- How to compute? Invest an equal amount of fund to buy shares of stocks The equally weighted index is the ratio of the value of the portfolio at time t and the value in the base period. F: the amount of total investment fund to be allocated among n stocks F/n: equal amount invested in each stock Pti: Price of stock i at time t (F/n)/P0i: number of shares of stock i in the base period 0 Vti= Pti[(F/n)/P0i]: value of stock i at time t

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=

0

=1 =1 0

=

0

=1

0

where Index0 is the base period index value (usually 100)

Portfolio to track the EW index

company price $ invest $ shares

bought

ABC

25

6000

240

XYZ

100

6000

60

total value

12000

new portfolio invest shares expenses price value $ rebalance rebalance rebalance

30 7200 90 5400

12600

6300 6300 12600

210

900

70

-900

0

- Invest equal amounts to the two stocks.

- changes in prices - values of the two holdings become unbalanced - need to rebalance to track the EW index - sell 30 shares of ABC at a cost of $900 and use the proceed to buy 10 shares of XYZ

- stock split: value of stock stays the same - no need to rebalance

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