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A Primer on Stock-Market Averages and Indices

August 13, 2004

Tags Financial MarketsU.S. Economy

The economist Ludwig von Mises was once asked what one institution gives evidence that a society has crossed into socialism from capitalism or vice versa. He answered clearly and without hesitation: the presence of a stock market. Stock markets indicate a toleration for private ownership and exchange and provide the essential means to compare the worthiness of investment projects by a common denominator of prices. With such markets, calculation is possible and so is prosperity.

It follows that Austrians should take an interest in the various measures that track the pricing of stocks, which is why I set out to write a primer for my students. It proved more difficult than I had expected. Source after source was vague to incomplete or wrong, hence the project has proceeded only in fits and starts (and is still far from complete). Material in different sections has had to be re-written in addition to being updated. Complicating matters greatly are the constant disappearances and rearrangements of information in industry literature and on the web. 

Suggestions and updates from industry professionals are welcome, keeping in mind that this is a primer and oversimplified for the purpose of getting rough estimates and some basic points across. In today's dumbed-down textbook market, thorough and accurate discussions of indices are rare, so perhaps this can be a bumpy beginning in the recovery of useful and lost discussions.

Dow Jones Industrial Average (DJIA).  A measure of the changes in prices of common stock issues of 30 large, well-known corporations listed on either the New York Stock Exchange (NYSE) or NASDAQ stock markets.

This measure began when Charles Henry Dow, the co-founder of Dow Jones and Company in 1882, devised an average to better see broad-market movements from the daily ups and downs of individual stock prices. The first Dow average appeared July 3, 1884 in the Customer's Afternoon Letter, a two-page market letter first published by Dow Jones in November 1883.  At the time, the average was comprised of only 11 stocks, 9 of them railroad-related reflecting the relative importance of the rail industry in the economy at the time.

The DJIA first appeared on May 26, 1896 and was comprised of 12 issues.  The average increased in size to 20 issues in 1916 and reached its current size of 30 on October 1, 1928.  Of the original 12 stocks in the May 1896 average, only General Electric still remains to this day.  (Here for the current DJIA components.)

The DJIA was one of four stock averages that would eventually appear in the Wall Street Journal, a newspaper published by Dow Jones, Inc.  There are three other Dow averages besides the DJIA:  transportation (20 transportation issues), utilities (15 utility issues), and a composite (spanning all 65 issues in the industrial, transport, and utility averages).

The editors of the Journal determine which issues reside in the DJIA.  Known as "blue chips," these firms are viewed as large, well-known, consistently profitable companies.  The term blue chip was first used in 1904 in the Journal and the term derives from versions of poker where blue chips are the most valuable.

On November 1, 1999 the DJIA underwent one of its most fundamental changes in its then-103 year history.  Chevron, Goodyear, Sears Roebuck, and Union Carbide's issues were removed and replaced by those of Home Depot, Intel, Microsoft, and SBC Communications.  The unprecedented change was that for the first time, two stocks from the NASDAQ market (Intel and Microsoft) were included in the DJIA portfolio.  Up until then, DJIA stocks were only NYSE-listed.[1]  On April 8, 2004 another reconstitution of the DJIA involved the insertion of AIG, Pfizer, and Verizon and the removal of AT&T, Eastman Kodak, and International Paper. 

The DJIA computation is as follows:   

DJIA = Sum of all 30 current per-share prices in DJIA portfolio = points
                                            Current Divisor

For example, on March 29, 1999 the DJIA first reached a much-trumpeted milestone.  What was it?  It went over 10,000.  10,000 what?  When I ask that question in college classrooms a flurry of hands shoots up and I get looks of complete disdain.  "Obviously ten thousand dollars," a young man (dripping with condescension) almost always tells me.

Not So Average

Unfortunately, this is not quite correct.  The student arrives at this answer because he has heard that the DJIA is an average of stock prices.  Yet on March 29, 1999, the highest closing per-share price in the DJIA portfolio was $177.56 (IBM) and the lowest was $33.06 (Walt Disney).  The simple average of per-share prices in the DJIA portfolio that day (summing all thirty prices and dividing by thirty) gives us a closing per-share price simple average of $75.13.  That is the dollar average of stock prices in the DJIA portfolio, of course nowhere near the number 10,000. 

Using the equation above and inserting values observed on March 29, 1999 one gets:

DJIA = $2,253.75 = 10,006.78 points

In other words, the DJIA is no simple average and if it were, the divisor would be equal to 30 (as in 1928), but clearly today it is not.  Why?  The divisor is lowered whenever a DJIA component issue undergoes a split.  A stock split is typically an increase in a company's number of common shares outstanding by some proportion and a reduction in the per-share price by the reciprocal of that proportion.  For example, if a company doubles the number of its outstanding shares it then typically cuts per-share price in half.[2]

Firms are thought to split their shares to keep share prices within a certain range.  When shares are more affordable for small investors, this facilitates spreading ownership among as diverse a group of investors as possible.  A second possible reason for a split could be to signal to investors that the company expects per-share price to quickly rise again in value.

Splits are relevant to the DJIA because when they occur, its divisor is lowered to offset the artificial decline in price of the issue that has undergone the split. 

Example Stock Split on a Trading Day at 11:00 a.m.

Two stocks                   Prices before stock A         Prices after stock A
of companies                     is split 2 for 1                    is split 2 for 1
A and B                             (10:59 a.m.)                      (11:01 a.m.)
A                                              $20                                    $10
B                                                30                                     30
Average of A&B:           $50/2 = $25                       $40/divisor = 25
Divisor:                             Divisor = 2                           Divisor = 1.6 (solved for)

The divisor in this example is lowered from 2 to 1.6 to offset the artificial decline in stock A's price from $20 to $10 due to the split.  This decline is offset by lowering the divisor to keep the average locked at 25.  Notice that no units were specified with the 25 figure in the rightmost column in the table above.  At 10:59 a.m. (middle column above) we have a simple average such as the DJIA was in 1928.  By 11:01 a.m. (rightmost column) we no longer have a simple average (which would have given us an average of $20).

Because the Dow was a simple average in 1928, its divisor at that time was 30.  By 1986 the divisor had fallen to 1.044.  On March 29, 1999 it was equal to 0.22522230.  Today it is 0.13561241.  It reached this level June 21, 2004 after Proctor and Gamble's 2 for 1 split .)  So the Dow is an average of sorts but no simple one.

How useful is the DJIA for gauging the health of securities markets and the economy?  The last trading day of August 2003 (the 29th), among 3,599 companies there was a total market capitalization[3] on NYSE of approximately $11 trillion.  For AMEX on August 29, 2003 there were 790 companies listed with a total market capitalization of about $167 billion.  For NASDAQ on August 29, 2003 there were 3,374 companies listed in its composite index with a total market capitalization of roughly $3 trillion.[4]

Taking the 3,599 companies on NYSE, the 790 companies on AMEX, and the 3,374 companies in the NASDAQ composite gives us very roughly about 7,763 issues listed on the three largest U.S. markets.  This provides a very rough aggregate market capitalization of all three major markets of $14 trillion.       

In terms of the number of common issues:

DJIA = 30/3,599 = 0.8% of issues on NYSE
            30/7,763 = 0.4% of issues on the three largest markets.

In terms of market capitalization:

DJIA = $2.8 trillion
NYSE = $11 trillion[5]

Thus the DJIA is roughly only (2.8/11 = 0.25) or 25% of NYSE market capitalization.[6]

So the DJIA is a narrow measure in terms of the number of different issues traded on NYSE, NASDAQ, or all exchanges.  It is also narrow in terms of market capitalization.  For personal investing there are much larger and more diverse benchmarks.  As a measure of macroeconomic health it's not as indicative as the public is sometimes led to believe.  It is no great predictor of changes in growth, as Nobel-winning economist and Keynesian Paul Samuelson once quipped that the stock market has predicted nine of the last five recessions.

The DJIA is an odd average, not an index despite the fact that it is often referred to as an index.  Even the Wall Street Journal's Guide to Stock Markets does it several times.  Here is an example at the Motley Fool.  Here, here, and here are more examples.


An index is a formula for measuring changes in a variable that has a base (beginning) date and value.  There are two main varieties of indices:  Laspeyres and Paasche.  Laspeyres indices (e.g., CPI) involve base-period quantities as weights while Paasche indices (e.g., GDP deflator) involve current-period quantities as weights.  The following indices do not fit into either of these categories, given that they contain current prices and quantities in their numerators and base prices and quantities in their denominators.

Standard & Poor's 500 Stocks Composite Average (S&P 500).  Despite its name, this measure is an index.  It was created by Standard & Poor's, Inc., and contains 500 issues listed on the NYSE and NASDAQ markets.  (Here for the S&P 500's current components.)

Because it is an index, the S&P 500 has a base date and value of 1941–1943 = 10

S&P 500 = Sum of each company's market capitalization in the current period  X  10
                   Sum of each company's market capitalization in the base period

The S&P 500's size in terms of the number of issues:

S&P = 500/3,599 = 0.138 or 14% of the NYSE.
         = 500/7,763 = 0.064 or 6.4% of issues on the three largest markets.

In terms of capitalization, for Monday June 30, 2003, the capitalization of the S&P 500 was about $8,984,834,000 while for the NYSE (3,602 issues) it was approximately $10,683,420,671,416.30.  Thus in terms of market capitalization, the S&P 500 last June 30 was roughly 84% of the NYSE's capitalization value (keeping in mind that the S&P contains NASDAQ issues as well).

National Association of Securities Dealers Automated Quotation system (NASDAQ) Composite Index.  This index today tracks over 3,000 domestic and foreign common issues listed on the NASDAQ stock market.  This market has no central, physical location like NYSE.  It was phone-based when it began in 1971 and today is computer-based.  In 1998 it merged with the American Stock Exchange (AMEX) in Chicago to form NASDAQ-AMEX.  (Here for NASDAQ's components.) 

The base date and value for this measure is February 5, 1971 = 100.

Using the August 2003 numbers from above, the NASDAQ composite tracks roughly only about (3,374/7,763 = 0.435) or 44% of issues on the three largest markets.  In terms of capitalization it is about (3/14 = 0.214) or 21% of the three largest markets.   

Russell 2000.  This index was created by the Frank Russell Company of Tacoma, Washington.  It measures the performance of 2,000 stocks of small-capitalization[7] ("small cap") companies in the U.S. and its territories.

Contrary to one reported misconception, this index does not contain the 2000 smallest of the small-cap companies.  Instead Russell begins with its Russell 3000 (containing the 3000 largest companies) and splits it into two smaller components, the Russell 1000 (containing the 1000 largest companies), and the Russell 2000 (small-cap companies).

All of Russell's 21 indices are subsets of its Russell 3000 index which, according to Russell, "represents approximately 98% of the investable U.S. equity market."  (Russell 2000 components are here in .pdf format.)

The base date and value of the Russell 2000 is December 31, 1978 = 100 for daily calculations by Russell.  The problem is that in the Wall Street Journal, Barron's, Investors' Business Daily, and many newspapers and Web sites (besides Russell's), Russell 2000 quotes are calculated by Bridge with a base date and value of December 31, 1986 = 135.

In terms of the number of different issues, the Russell 2000 measures only about (2,000/7,763 = 0.258) or 26% of issues listed on the three largest markets. As of July 9, 2003 the market capitalization of the Russell 2000 was $712.7 billion (or 7.6% of the Russell 3000 which, again, is said by Russell to represent roughly 98% of the U.S. equity market).

Dow Jones Wilshire 5000 Composite Index. This index, first known as the Wilshire 5000, was created by Wilshire Associates, Inc. of Santa Monica, California in 1974. It tracks the performance of over 5,000 issues (5,079 as of June 30, 2004) of U.S.-headquartered firms and is one of the broadest indices available. Despite its broadness, in terms of numbers of issues it tracks roughly about (5,000/7,764 = 0.644) or 64% of all issues on the three largest markets.

The base date and capitalization value are December 31, 1980 = $1,404.596 billion.

The Wilshire 5000 is named as such because at its 1974 creation it contained almost 5,000 stock issues.  At one point in 1999 it tracked about 7,300 issues.  Since the dot-com bust and recession that number has understandably fallen.  As of June 30, 2004 this index's issues had a total market value of $12.7 trillion.

Yahoo! Finance did not even have a chart of this index's performance in 1999 but by September 2001 had 1- and 5-day charts on it.  Today a 6-month chart is available.  Detailed information about this index is much more available than 5 years ago.

And so there we have it: the essential tools of trade that Mises said gives evidence of the existence of the factor markets that are the bare minimum requirement for advanced civilization. Use it profitably.


Dale Steinreich, Ph.D., is an adjunct scholar of the Mises Institute and contributor to AgainstTheCrowd.comdsteinreich@msn.com.  Comment on the blog

[1] The three largest U.S. exchanges are the NYSE, NASDAQ, and American Stock Exchange (AMEX), which merged with NASDAQ in 1998.

[2] Of course there are other possibilities just as there are reverse splits.

[3] Market capitalization for an individual company is the current or closing per-share price times the number of shares outstanding.  Example: $10 per-share price times 1,000,000 shares outstanding = $10 million market capitalization.  Market capitalization for an entire stock market would involve the summation of all individual capitalizations.

[4] In its usual effort to be ever more helpful in providing information [sarcasm], NASD no longer includes firm-capitalization data in its composite spreadsheet downloads.  Hence for reasons of consistency I am using August 2003 data that I luckily happened to have for the three major American markets.  No, NASD has not responded to my inquiries as to why this change was made and I haven't yet found another Web source of daily information.  Any assistance would be greatly appreciated. 

[5] Domestic companies only.

[6] I have not forgotten that DJIA now contains two NASDAQ issues (Intel and Microsoft).  For simplicity I'm ignoring that consideration to get some very rough approximations for now.  Also postponed for the future is discussion of pink-sheet and OTC bulletin-board issues. 

[7] The definition of capitalization depends on the source.  According to one source, small-capitalization companies have market values in the range of $300 million to $2 billion.  The average market capitalization for the Russell 2000 as of June 30, 2004 was $900 million, with the largest company valued at $1.9 billion and the smallest at $117 million.  So the Russell 2000 companies seem to fit into this particular definition well.

Note: The views expressed on Mises.org are not necessarily those of the Mises Institute.

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