A Hoax or Not a Hoax, That’s the Question

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Editor’s note: You might want to read another of this author’s articles about the Dow Jones titled, “The DIJA Is a Hoax“. The history of the Dow Jones in this article is interesting and written so you can understand it. It’s worthwhile reading though the Dow index is not changing in 2015, that’s an April Fool’s Day hoax. I issue this spoiler alert  because I don’t like April Fool’s jokes.

Dow

by Wim Grommen

After intensive consultation with his advisors, President Obama has decided to modify the formula used for calculating the Dow Jones Index. On January 1, 2015 the Dow Divisor will be changed to 30. The result of this change will be that the Dow Jones Index drops from the current 16532 points to about 85.8 points. The underlying value of the 30 component stocks of course remains unchanged. With this modification to the formula Obama aims to make the large Dow fluctuations of recent decennia a thing of the past, and hopes that this will bring stability to the stock market. Banks, major investors and pension funds welcome this change in the Dow Jones Index formula.

To understand Obama’s proposal we must go back in Dow Jones history. The Dow was first published in 1896. The Dow was calculated by dividing the sum of the 12 component company stocks by 12:

Dow-index_1896 = (x1 + x2+ ……….+x12) / 12

In 1916 the Dow was enlarged to 20 companies; 4 were removed and 12 added:

Dow-index_1916 = (x1 + x2+ ……….+x20) / 20

The shares of a number of companies were split in 1927, and for those shares a weighting factor was introduced in the calculation. The formula is now as follows:
(x1 = American Can is multiplied by 6, x2 = General Electric by 4 etc. )

Dow-index_1927 = (6.x1 + 4.x2+ ……….+x20) / 20

On 1 October 1928 the Dow was further enlarged to 30 stocks. Because everything had to be calculated by hand, the index calculation was simplified. The Dow Divisor was introduced. The index was calculated by dividing the sum of the share values by the Dow Divisor. In order to give the index an uninterrupted graph the Dow Divisor was given the value 16.67.

Dow-index_Oct_1928 = (x1 + x2+ ……….+x30) / Dow Divisor
Dow-index_Oct_1928 = (x1 + x2+ ……….+x30) / 16.67

Since then the Dow Divisor has acquired a new value every time there has been a change in the component stocks, with a consequent change in the formula used to calculate the index. This is because at the moment of change the results of two formulas based on two different share baskets must give the same result. When stocks are split the Dow Divisor is changed for the same reason.

In autumn 1928 and spring 1929 there were 8 stock splits, causing the Dow Divisor to drop to 10.47.

Dow-index_Sep_1929 = (x1 + x2+ ……….+x30) / 10.47

After the stock market crash of 1929, 18 companies were replaced in the Dow and the Dow Divisor got the value 15.1.

 


Table: Changes in the Dow, stock splits and Dow Divisor
 

The table above makes it clear that the Dow Jones formula has been changed many times and that the Dow Divisor in the period 1980-2010 has actually become a Dow Multiplier, due to the large number of stock splits in that period. Where in the past the sum of the share values was divided by the number of shares, nowadays the sum of the share values multiplied by 6.4 . Dividing by 0.15571590501117 is after all the same as multiplying by 6.4 . (1 / 0,1557 = 6.4). This partly explains the behaviour of the Dow graph since 1980.

 


Figure: the Dow Jones since 1896
 

The proposed change on 1 January 2015 restores the formula to what it originally was: the sum of the share values divided by the number of component shares.

Dow-index_Jan_2015 = (x1 + x2+ ……….+x30) / 30

The aggregate current value of the 30 component stocks is 2574 dollars. By changing the Dow Divisor from 0.15571590501117 to 30 (a factor 192 larger) the index will, at current values, change from 15658 to 85.8 points (a factor 192 smaller).

The emotional factor in the current formula, the nervousness or euphoria of investors resulting from large fluctuations in the Dow, will be greatly reduced by this change (192 times) and so rationality should gain the upper hand in investor’s decisions.

Obama’s proposed change must still be approved by House and Senate. Both Republicans and Democrats have told Obama they support his proposal. Politicians, irrespective of political colour, desire stability in the stock markets. For the investor however it will take some getting used to: the Dow Jones at 85.8 points.

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About the Author

Wim Grommen was teacher in mathematics and physics for ten years at secondary schools. The last twenty years he trained programmers in Oracle-software. He worked almost five years as trainer for Oracle and the last 17 years as trainer for Transfer Solutions in the Netherlands. The last 15 years he has studied transitions, social transformation processes, the S-curve and transitions in relation to market indices. Articles about these topics have been published in various magazines and sites in The Netherlands and Belgium. 

 

HOW THE DOW WORKS, INVESTOPEDIA (This is real)

The Dow is up, the Dow is down … the daily news just wouldn’t be complete without a report about the open and close of this market index. But although you’ve certainly heard reports about the Dow Jones Industrial Average (DJIA) being up or down a certain number of points, do you know what these points represent? Read on to find out how the Dow works and what changes mean for investors and the market.

The Dow and the Market
In the United States there are three major indicators, or indexes, of market movements: the Nasdaq Composite, Dow Jones Industrial Average (DJIA or “the Dow”) and the Standard & Poor’s 500. As a collective, these market indexes are referred to as the Security Market Indicator Series (SMIS). They provide a basic signal of how specific markets perform during the day. Of these three, the DJIA is the most widely publicized and discussed. Fortunately for us, it is also the easiest to calculate and explain.

History of the DJIA
Dow Jones & Co. was founded in 1882 by Charles Dow, Edward Jones and Charles Bergstresser. Despite popular belief, the first averages were not published in the Wall Street Journal but in its precursor, called the Customer’s Afternoon Letter. The first averages didn’t even include any industrial stocks. The focus was on the growth stocks of the time, mainly transportation companies. This means that the first Dow Jones Index included nine railroad stocks, a steamship line and a communications company. This average eventually evolved into the transportation Average. It wasn’t until May 26, 1896, that Dow split transportation and industrials into two different averages, creating what we know now as the Dow Jones Industrial Average.

Charles Dow had the vision to create a benchmark that would project general market conditions and therefore help investors bewildered by fractional dollar changes. It was a revolutionary idea at the time, but its implementation was simple. The averages were, well, plain old averages. To calculate the first average, Dow added up the stock prices and divided by 11 – the number of stocks included in the index.

Today, the DJIA is a benchmark that tracks American stocks that are considered to be the leaders of the economy and are on the Nasdaq and NYSE. The DJIA covers 30 large-cap companies, which are subjectively picked by the editors of the Wall Street Journal. Over the years, companies in the index have been changed to ensure the index stays current in its measure of the U.S. economy. In fact, of the initial companies included in the average, only General Electric remains as part of the modern-day average.

DJIA Complications
As you might have guessed, calculating the DJIA today isn’t as simple as adding up the stocks and dividing by 30. Dow lived in times when stock splits and stock dividendsweren’t commonplace, so he didn’t foresee how these corporate actions would affect the average.

For example, if a company trading at $100 implements a 2-for-1 split, the number of its shares doubles, and the price of each share becomes $50. This change in price brings down the average even though there is no fundamental change in the stock. To absorb the effects of price changes from splits, those calculating the DJIA developed the Dow divisor, a number adjusted to account for events like splits that is used as the divisor in the calculation of the average.

How Does the Dow Divisor Work?
To calculate the DJIA, the current prices of the 30 stocks that make up the index are added and then divided by the Dow divisor, which is constantly modified. To demonstrate how this use of the divisor works, we will create a mock index, the Investopedia Mock Average (IMA). The IMA is composed of 10 stocks, which total $1,000 when their stock prices are added together. The IMA quoted in the media is therefore 100 ($1,000/10). Note that the divisor in our example is 10.

Now, let’s say that one of the stocks in the IMA average trades at $100 but undergoes a 2-for-1 split, reducing its stock price to $50. If our divisor remains unchanged, the calculation for the average would give us 95 ($950/10). This would not be accurate because the stock split merely changed the price, not the value of the company. To compensate for the effects of the split, we have to adjust the divisor downward to 9.5. This way, the index remains at 100 ($950/9.5) and more accurately reflects the value of the stock in the average. If you are interested in finding the current Dow divisor, you can find it at the website of the Dow Jones Indexes and the Chicago Board of Trade.

And How Does the DJIA Number Translate into a Dollar Value?
To figure out how a change in any particular stock affects the index, divide the stock’s price change by the current divisor. For example, if General Electric is up $5, divide five by 0.14418073, which equals 34.68. Thus, if the DJIA was up 100 points on the day, GE was responsible for 34.68 points of the move.

Weighing the Index
The DJIA’s methodology of calculating an index is known as the price-weighted method. On top of having to deal with stock splits, the downside to this method is that it does not reflect the fact that a $1 change for a $10 stock is much more significant (percentage wise) than a $1 change for a $100 stock. Because of price-weighting’s associated problems, most other major indexes, such as the S&P 500, are market-capitalization weighted.

The Bottom Line
Despite all its shortcomings, the Dow is still one of the most-watched indicators for stock market performance. After 110 years as a marker of major market developments, the DJIA is still one of the most recognized and cited of all market indexes.

 

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