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.
(Read more: Here's what you need to know about the Dow index changes)
"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)