GE shares closed down 0.1 percent at $9.28 a share, falling past Friday's close by one cent. The stock had risen as much as 2.1 percent to $9.53 a share in midday trading.

Culp bought 225,000 shares at an average price of $9.73 a share on Thursday, a day before the stock closed at the lowest price in nearly a decade, an SEC filing disclosed Monday. The purchase brings his total GE holdings to 416,000 shares. Culp bought 191,000 shares on July 24 at $13.04 a share while he served on GE's board, the filing said.

CEOs buying back shares can indicate a bottom for a struggling company. J.P. Morgan CEO Jamie Dimon bought back shares three times between January 2009 and February 2016, each time adding 500,000 shares near the stock's lowest point of the year. Dimon's investment proved to be shrewd, as J.P. Morgan stock has surged 330 percent since his first of the three buybacks.

Culp took over at GE on Oct. 1. In one of his first actions, he slashed the quarterly dividend last week to just a penny a share starting in 2019. The move frees up some cash for the beleaguered conglomerate, but it is expected to be the first of many from Culp to turn the company around. Culp is facing multiple predicaments, including the company's ailing power business and ongoing accounting investigations by the Justice Department and the SEC.

Culp also singed a stock-heavy compensation plan when he signed with GE. The company is set to pay Culp as much as $317 million in annual pay and awards if he boosts GE shares dramatically over the next four years.