Appendix 4 stock market indexes

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Several issues must be dealt with in the construction of a stock market index or average. The most important involve the composition of the index or average, the weighting procedure used, and the method of calculation.

What is the composition of the market measure? Is a subsample of one exchange to be used, or a subsample from the major exchanges? If investors need a broad measure of stock performance, several markets (NYSE, AMEX, and OTC) need to be included. If investors want to know the performance of the “largest” stocks, a measure of NYSE performance may be sufficient. Some market measures use subsamples of one or more markets, whereas others use every stock on one or more markets. It is important to be aware of compositional differences among the various market measures.

A second issue involves the weighting procedure used in constructing the index or average. Does each stock receive equal weight, or is each weighted by its market value (i.e., market price multiplied by shares outstanding)? Alternatively, the measure could be price weighted, resulting in higher priced stocks carrying more weight than lower priced stocks.

The third issue is the calculation procedures used. The primary question here is whether an index or an average is being used. A market average is an arithmetic average of the prices for the sample of securities being used. It shows the arithmetic mean behavior of the prices at a given time.

A market index measures the current price behavior of the sample in relation to a base period established for a previous time. Indexes, therefore, are expressed in relative numbers, whereas averages are simply arithmetic means (weighted or unweighted). The use of an index allows for more meaningful comparisons over long periods of time because current values can be related to established base period values.

The Dow Jones Averages are arithmetic averages, but virtually all the other market measures are indices.

In principle, calculation of the DJIA involves adding up the prices of the 30 stocks and dividing by 30 to obtain the average. This is not done because of stock splits and dividends. Instead, the divisor is adjusted to reflect the stock splits and dividends that have occurred and today is much less than 1.0. As a result, a one-point change in the DJIA does not represent a change of $1 in the value of an average share; rather, the change amounts to only a few cents. You should keep this in mind the next time someone gets excited about a 50- or 60-point rise in one day in the DJIA.

The DJIA is calculated as:
DJIAj = Pit/n*
where P is the price of a stock i at time t and n* indicates an adjusted divisor.

To calculate the index, the market value of all firms is calculated (current market price times number of shares), and this total value is divided by the market value of the 500 securities for the base period. This relative value is multiplied by 10, representing the base period. In equation form, the S&P 500 is calculated as:


S&P500 = ------ (k)

P = the price of a stock i at time t

Q = number of shares of stock i at time t

b = the base period

k = the base number
A current value of 200 for the S&P 500 would indicate that the average price of the 500 stocks in the index has increased by a factor of 20 in relation to the base period. If IBM had a market value that was 10 times as great as that of Apple Computer, a 1 percent change in IBM's price would have more than 10 times the impact of a 1 percent change in Apple's price.

The NYSE Composite Index is broader still, covering all stocks listed on the NYSE. It is similar to the S&P indexes in that it is a total-market-value-weighted index. The base index value is 50 (as of year-end 1965).

The NYSE Composite Index, although comparable to the S&P indexes, is a true reflection of what is happening on the NYSE, because it covers all stocks listed. Thus, an investor who purchases a variety of NYSE stocks may find this index to be a better reflection of average performance against which to measure the performance of his or her securities.
American Stock Exchange Index

The American Stock Exchange introduced a new index in 1973, replacing the previous index based on price changes. The base period, August 31, 1973, was assigned an index number of 100. This index is similar to the S&P and NYSE indices in that it is based on market values. All common stocks, warrants, and American Depository Receipts (ADRs) listed on the AMEX are covered in this index.


The broadest of all indicators is the so-called Wilshire 5000 Index, which actually contains more than 7,000 stocks representing the dollar market value of all NYSE and AMEX stocks, as well as all actively traded OTC stocks. In effect, it is the total price for stocks for which daily quotations can be obtained. It is quoted in billions of dollars, with a base of $1.404 billion set to December 31, 1980.


The Value Line Investment Survey, perhaps the best known investment advisory service in the United States, publishes several indexes of stock prices. Since Value Line is a well-known investment advisory service, its indexes receive attention. Investors, however, should be aware of how these unique indexes differ from the others.

The Value Line Composite Index is unique in that it is an equally weighted geometric average of stock prices. It is based on the roughly 1,700 companies in the 90-plus industries that Value Line chooses to cover in its reports. June 1961 is assigned the base index of 100.

Since a daily net percentage change in price is computed for the stocks, each stock in the index has the same percentage weight. Therefore, a 20 percent movement in a stock's price has the same impact on the index, whether 10 million or 100 million shares are outstanding. Neither a stock's market value nor its price level will impact the index. The small, low-priced stocks covered by Value Line will have the same impact as the larger stocks.

In effect, the Value Line Composite is an unweighted index covering a broad cross-section of stocks. Some market observers feel that because it is unweighted, it is more reflective of general market trends.

In March 1988, Value Line introduced a new index, the Value Line Arithmetic Index (VLA). The change in this arithmetically averaged index is the sum of the price changes for all stocks in the index divided by the number of stocks. Value Line sees this index as a good estimate of the price performance of an equal dollar portfolio of stocks, whereas changes in the geometric index provide a good estimate of the median price changes of the stocks covered.

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