*For this week's post, Dr. Oscar Varela, a professor at the UTEP College of Business’ Economics and Finance department, explains some of the history and workings of the Dow Jones industrial average.*

With the stock market showing high volatility, here is a brief discussion of the Dow Jones Industrial Average and the way to financially interpret current changes in it.

First, a little history on the DJIA.

This average was created by Charles Dow and Edward Jones. These are the same duo that began the Wall Street Journal, which commenced publication on July 8, 1889. The DJIA commenced 7 years later, on May 26, 1896, and it began its existence as a stock price average for 12 industrial companies. It took until October 1, 1928 for the DJIA to expand to an average of 30 industrial companies, the same number as it has today, except that not all firms listed in it now are industrial firms – such as Bank of America, American Express, McDonald’s, Wal Mart, Verizon..

For a little historical perspective, the New York Stock Exchange (NYSE) dates to May 1792, was founded as the Buttonwood Agreement by 24 Brokers, was organized in 1817 as the New York Stock and Exchange Board, and finally changes its name in 1863 to the New York Stock Exchange. The NYSE is not the oldest exchange in the U.S. – that honor belongs to the Philadelphia Stock Exchange which began its existence a few months before NYSE.

On the other hand, the American Stock Exchange (AMEX) was founded in 1910 as the New York Curb Market Association (before this it was called the Outdoor Curb Market trading unlisted shares on Wall and Hanover Streets in New York). In 1953 it changed its name to the American Stock Exchange. The NASDAQ market started in 1976.

Back to the DJIA. The idea behind the calculation of it is as follows:

Imagine we have only three stocks (stocks A, B and C) in the DJIA. Let’s say stock A has a $20 price, stock B a $25 price and stock C $30. When the DJIA was first started, the DJIA average for the hypothetical example above would have been equal to the arithmetic average of the prices, that is:

DJIA = 25 = ($20 price for A + $25 price for B + $30 price for C) / 3.

Now, a problem occurs when one of these stocks splits – let’s say stock C splits 3 to 1, so that now the price per share will equal $10. What happens if we calculate the DJIA now? Let’s try to redo the calculations, such that

DJIA = 18.33 = ($20 price for A + $25 price for B + $10 price for C) / 3.

Having substituted $10 for $30 for stock C, the DJIA would fall from 25 to 18.33 – about a 28% market fall. The problem is that this decline in the market is not a real decline, because nothing happened except that stock C split 3 to 1. Thus, the DJIA should remain unchanged from its initial value of 25, and now the only way to accomplish this is to change the denominator so that the ratio stays at 25.

So this is what we have to do – solve for the denominator’s value x below, such that

DJIA = 25 = ($20 price for A + $25 price for B + $10 price for C) / x.

If x equals 2.2, then the DJIA remains unchanged at 25, as it should. It follows that the DJIA divisor will change when we have stock splits in any of the 30 companies (subject to some exceptions).

Now, the value of this divisor as shown in the Wall Street Journal on August 10, 2011 (page C4, Dow Jones Industrial Average table) was 0.132129493.

To obtain a financial interpretation, use the divisor in combination with the value of the DJIA index. For example, the DJIA index closed at 11239.77 on August 9, 2011 and 10719.94 on August 10, 2011, down 519.83 points. So, based on how the index is calculated using a 30 stock portfolio, we have on August 10, 2011:

DJIA = 10719.94 = (price for 1+price for stock 2+price for stock 3+ …+price for stock 30) / (0.132129493)

We can then solve for the combined prices of all its 30 stocks, since

(10719.94) (0.132129493) = $1,416.42 =

= (price for 1+price for stock 2+price for stock 3+ …+price for stock 30)

Thus, the value of a portfolio consisting of one share for each of the 30 Dow stocks on August 10, 2011 was $1,416.42 (with a little error because not all stock splits cause the divisor to be adjusted).

As a result, the price per share on the average for each of the 30 Dow stocks on August 10, 2011 was:

$47.21 = $1,416.42 / 30

And the average per share dollar value of a point in the DJIA is

$ 0.0044 = $47.21 / 10719.94

so that each point change in the DJIA is worth about 4/10 of U.S. penny in terms of the average price per share.

Thus, when the DJIA declined by 519.83 points on August 10, 2011, the average decrease in the price per share for each of its 30 stocks was $2.28.