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Dow's daily active weightings not what you think

Workers prepare for the opening of an Apple store in China.
Chance Chan | Reuters

Yes, the news is out. Apple is joining the Dow Jones industrial average. Finally. And it's only because Visa is undergoing a stock split, allowing the index membership bosses to kick AT&T out to bring Apple in.

And yes, it's a price-weighted index, meaning that the stocks with the largest per-share prices will have the biggest weight. That means a $1 move in Goldman Sachs stock is worth the same as a $1 move in Coca-Cola, even though it's four times as different when measured in percent.

But here's the thing: Not every stock is equally volatile. Some stocks just move a lot more than others. So when considering which stocks will have the biggest impact on how the Dow changes each day, it's not just the price that matters, but also the volatility. A $20 stock that moves $10 per day will move the Dow more than a $100 stock that only moves $1 per day.

With that in mind, let's consider the true ranking of stocks that will impact the Dow. By considering BOTH the price and volatility, we see that Goldman Sachs and Apple will be responsible for more than 26 percent of the index's daily price changes.

In the case of Goldman Sachs, one share's price is around $190. The stock has averaged 55 percent volatility in the past year. On a daily basis, that leads to an approximate move of $6 per day. Goldman's stock is both the highest priced in the Dow, and the most volatile. It would then make sense that it should have the biggest impact in daily moves of the index.

Apple, when it enters the index, will have the fifth-biggest weighting due to price alone. But it's the second-most volatile stock, so on a volatility-adjusted basis, it will be the second-most impactful stock in the Dow.

The three stocks with higher share prices than Apple are IBM, Boeing and 3M. Each of them have very low volatility, hence their impact on the index will be quite muted, despite the nominal value of their high price leading to a heavy weight in the index.

So this new Dow 30 will really just be Goldman Sachs, Apple and 28 other stocks.