United Technologies (UTX) shares fell today, two days after CEO Gregory Hayes said his board is considering breaking up the sprawling industrial conglomerate.

Shares fell 0.3% to $133.16 after rising for two days following Hayes's presentation at the Barclays Industrial Select Conference in Miami.

"Is UTC better off in three separate businesses?," Hayes asked. "One being an aerospace business, which would have significant scale, $45 billion to $50 billion. And then an Otis business of $12 billion to $13 billion and then a Climate Control business of $17 billion or $18 billion. That's the question for the Board. That's a question we continue to study."

Company spokeswoman Maureen Fitzgerald said Hayes was referring to the revenue of United Technologies' three main businesses, which the case of the aerospace business now consists of two units, Pratt & Whitney and UTC Aerospace Systems, which together had about $30 billion of sales in 2017. Fitzgerald said Hayes was reckoning on the additional sales the unit could generate once United Technologies completes its $30 billion purchase of Rockwell Collins, an avionics business that's now in a regulatory approval process.

--Updates and corrects a story published Feb. 22 to say Hayes was referring to the revenues of the units that might be sold, not the purchase price those units could attract.