Key takeaway
- Originally, the Dow Jones Industrial Average was the average dollar value of the 12 stocks this index fund contained.
- As time went on, the calculations got more complicated. Stocks have been added and removed. Companies have engaged in stock splits or spinoffs. These situations all call for the denominator to be recalculated to reflect an accurate picture of the index value.
- Today, the Dow Jones Industrial Average contains 30 stocks and has a divisor of 0.1517.
The Dow Jones Industrial Average (often abbreviated to the Dow Jones or DJIA) is an index of 30 large, American companies. At its origin in the 1890s, the index held only 12 stocks and was a simple average of these 12 stocks’ values in terms of dollars.
As the market – and the index – have evolved, the calculations have become far more complicated. Here’s how to understand some of the different mathematical functions that produce the DJIA and how they are applied.
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Establishing index value
To make things simple, let’s keep our example index to just two stocks. To establish an original index value, we would simply take the average value of the two stocks.
Say Alpha Corp. (A) was valued at $48 per share. Beta, Inc. (B) is valued at $90 per share.
The value of A + B divided by the number of stocks in the index (two) would give us our initial index value.
In this case, that would be:
(48 + 90) / 2 = 69
So our index value would be 69.
Calculating dollar-based changes
The next step to understanding Dow Jones Industrial Average calculations is understanding net sum price changes.
Let’s say the price of A went up by $4 to $52 the next day. B came down by $2, now valued at $88. The new index value calculation would be:
(52 + 88) / 2 = 70
The difference between today’s value – 70 – and yesterday’s value – 69 – is one. So we would say, “The index is +1.”
On the news you might hear that “The Dow is up by 500,” or “The Dow was down by 50 today.” That’s where these numbers come from – they’re a measurement of real-dollar changes in the index’s value over a given period of time.
Divisors for index expansions
Adding new stocks to the index gets tricky. You can’t just use the total number of stocks as your divisor anymore. It skews the overall index value too much. For example, if you added Gamma Corp. (G) to our example index with a value of $22 per share, simply adding the stock to the index would make the formula look like this:
(52 + 88 + 22) / 3 = 54
This makes it look like the entire index experienced a fall of -16, when really all that happened was one company was added.
So instead of using the number of stocks as the denominator in your equation, you have to come up with a new divisor. To calculate your divisor in cases of index expansions, you first need to find the new price summation, which is simply the combined value of all stocks in the index:
(52 + 88 + 22) = 162
Then, you would take 162 and divide it by the last reliable index value, which was 70.
162 / 70 = 2.3143
That would make your new divisor 2.3143. You’d then plug the divisor in as the denominator in your original equation:
(52 + 88 + 22) / 2.3143 = 70
This stabilizes the value of the index. You would use the same divisor moving forward until there was a need to modify it.
Divisors in cases of stock splits
Let’s say we’re looking at a situation where A, B and G are all still in the equation. B is sitting at $88, and Beta, Inc. executives decide on a 4-for-1 stock split. This decreases the value of each B share to $22.
But the valuation for Beta, Inc. hasn’t changed – it just has a larger number of total shares.
To accommodate for the stock split, you’d recalculate the divisor, otherwise your calculation will show a massive loss in index value where there was none. First, you’d calculate the new price summation:
(52 + 22 + 22) = 96
Then, you’d divide the new price summation by the last reliable index value, which was 70.
96 / 70 = 1.3714
Then, you’d plug the new divisor in as the denominator in your original equation:
(52 + 22 + 22) / 1.3714 = 70
This way, you can see that while the value of each share has changed, the overall index value has not.
Divisors for index contractions
Let’s say Beta, Inc. was bought and absorbed by another company, and as a result B is no longer on the market. You would need to remove B from your index.
To find your new divisor, you would need to first calculate the new price summation, or the value of A + G:
(52 + 22) = 74
You would then divide the price summation by the last reliable index value, which in this case is 70.
74 / 70 = 1.0571
Your new divisor would be 1.0571. You would use this number moving forward. So let’s say the next day A rose to $58, while G rose to $30. To find the new index value, your equation would look like this:
(58 + 30) / 1.0571 = 83
This shows that the index rose +13, whereas if you had incorrectly kept the old divisor it would have looked like the index sank simply because you removed B from the equation.
Current Dow Jones Industrial average divisor
The current divisor on the Dow Jones Industrial Average is 0.1517. It most recently changed on Nov. 4, 2021 when IBM completed a spinoff.
Essentially, IBM parted ways with Kyndryl – which is now an independent business trading under KD – which manages information technology infrastructure. For every five shares of IBM owned, stockholders were issued one share of KD.
This spinoff caused the Dow Jones Industrial Average divisor to fall from about 0.1518 to its current amount of about 0.1517.
Limitations of Dow Jones Industrial average calculations
The Dow Jones Industrial Average is based on dollar value. That does impose some limitations.
Because it is tied to dollars and not percentages of gains or loss, it cannot account for industry size or market capitalization.
Other indices, like the S&P 500, are market-weighted. That means each company’s market cap is figured into the equation, which weights the calculations for overall impact rather than calculating raw dollar value.
Another issue with the DJIA is that if a singular stock experiences significant gains or losses in terms of dollar value per share, it can throw the entire index for a loop – even if just one stock was affected.
The bottom line
This math can be a little confusing, and while it’s interesting, it’s the kind of under-the-hood information that isn’t ultimately essential to the everyday investor.
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