The stocks were rallying Tuesday, but their gains could be short-lived, analysts say. The changes to the index, effective Sept. 23, include the exit of Alcoa, Hewlett-Packard and Bank of America. Only Bank of America was trading higher Tuesday.
The triple expiration of equity options and futures takes place the Friday before the index changes are to be made.
"The week after triple witching is the worst of all four" weeks of September directionally, said Jeff Hirsch, editor-in-chief of Stock Trader's Almanac. The Dow was lower in 19 of the last 25 years, with an average decline of 1.1 percent, he said.
Even without the calendar impact, the euphoria could wear off.
"One thing they have going against them is they were announced today, and the change is in two weeks. All the stocks that were added today got a spike," said Paul Hickey, co-founder of Bespoke Investment Group. The stocks could be overbought at the point they go into the index and could sell off, he added.
That could trigger a negative effect on the overall stock market, as the three stocks will have much more weight in the Dow than the three they are replacing.
"What's notable is the three stocks that are being added are much higher-priced, so while the divisor of the Dow will go up, making the index technically less volatile, the names being added have larger dollar moves on a daily basis," Hickey said. "In theory, it will be less volatile, but Goldman can move $5 in a day. That isn't out of the question. Goldman is going to be between a 30- and 35-point move in the Dow. It helps to take some of the weight out of IBM."
Goldman stock has moved $5 or more 10 times in the past six months.
David Blitzer, chairman of the index committee at S&P Dow Jones Indices, said he did not give much thought to the triple-witching timing. He also does not see the index becoming more volatile, as some analysts suggest.
"These are all big, liquid stocks," he said. "I don't think it has any impact."
S&P Dow Jones Indices said in a press release that the changes will not cause any "disruption in the level of the index. The divisor used to calculate the DJIA from its components' prices on their respective home exchanges will be changed prior to the opening on September 23. This procedure prevents any distortion in the DJIA's reflection of the U.S. stock market."
But analysts expect to see slightly more volatility, even though in theory there should be less. The Dow's divisor will increase to the point where a $1 move in the price of any index component will cause a change in the index of about 6.5 points instead of the current 7.7 points, according to Bespoke.
(Read more: Big changes on the way for the Dow)
"I think the most important part is you're taking out the three lowest-weighted stocks and replacing them with two that will be two of the three highest-weighted stocks," said Daniel Greenhaus, chief global strategist at BTIG. The stocks they are replacing make up about 2.3 percent of the Dow.
After IBM, Visa will have the second-highest weighting, and Goldman will have the third. Alcoa, an $8 stock, has a weighting of 0.4 percent; Bank of America is 0.74. Bank of America, one of the best Dow performers this year, is just a $14 stock. HP trades at about $22.
Visa was trading Thursday at about $183, and Goldman was about $165. Nike was about $65. All three have outperformed the Dow's 16 percent year-to-date move. Visa, which Greenhaus owns, is up 24 percent year-to-date, and Goldman is up almost 30 percent.
"By definition then, the Dow is going to look and act very differently going forward. Leaving aside Nike and Hewlett-Packard, you've replaced two stocks that essentially don't matter in Alcoa and Bank of America with two that do," Greenhaus said.
IBM has a 9.4 percent weighting, followed by Chevron and 3M. Together, he said, they represent 22 percent of the Dow.
The three stocks leaving the Dow should not see much impact, as the industrials average is not widely used for indexing, like the S&P 500 or Russell 2000.
"A name like Alcoa is not really reflective of what's going on," Hickey said. "Maybe Alcoa loses something. ... Alcoa is basically known for being in the Dow and for being the symbolic start of the earnings season. It's losing one thing people were following it for. Typically when they're removed from the indexes, they're typically out of favor. So when stocks are out of favor, you tend to see a rebound in them. I don't think them being booted from the Dow is going to lead to underperformance in these names."
—By CNBC's Patti Domm. Follow here on Twitter @pattidomm.