PensionIssste, which manages about 195 billion pesos ($10.5 billion) of mostly government workers' retirement money, became the largest shareholder in ICA, with a stake of almost 10 percent, said three people with knowledge of the investment who spoke on condition of anonymity.

Many details of the transaction are not publicly available and none of the parties involved were willing to comment.

Half-way through 2015, ICA shares had sunk more than 50 percent from the year earlier as a crash in the peso had increased its heavy dollar-denominated debt load and lower government infrastructure spending led to a cash crunch.

Despite that PensionIssste began to buy up ICA shares and spent around 400 million pesos ($21.5 million) at an average price of around 7 pesos per share, one source said.

ICA, formally known as Empresas ICA SAB de CV, finally stopped making debt payments in December 2015, a fall from grace for what had once been Mexico's largest construction company.

Tapen Sinha, a professor at Mexico's ITAM University who specializes in risk management and pension funds, said funds should avoid such volatile stocks right off the bat.

"It's not for no reason something drops 50 percent," he said. "There should be alarm bells (going) off in risk management inside PensionIssste."

Pensions regulator Consar examined the purchases, its president, Carlos Ramirez, said, adding that the deal complied with existing rules.

Details on the holdings of Mexican pension funds are not public. PensionIssste did not respond to emailed questions or a call for comment.

ICA and four subsidiaries filed a prepackaged bankruptcy agreement in August 2017, leading to the suspension of trading in the shares at 1.48 pesos.

Last Monday, ICA said a judge had approved its creditors agreement, which was accepted by a majority of debtholders.

Unlike PensionIssste, one investor who opted for debt over equity is set to benefit from ICA's restructuring plan.

Mexican financier David Martinez's vehicle Fintech lent ICA $215 million in 2016 and under the restructuring plan, will be the largest shareholder in the company that emerges from bankruptcy, according to documents on ICA's website.

PensionIssste and other ICA shareholders will see their holdings diluted to 0.01 percent of the company, according to the documents.

The fund has asked banking and securities regulator CNBV to investigate whether ICA violated Mexican securities law, two of the sources said. PensionIssste is seeking to determine whether ICA failed to disclose important information to the market during its bankruptcy process, one source said.

ICA declined to comment on a list of questions submitted by Reuters. The CNBV said under law it could not comment.

It was not clear what PensionIssste, which changed its management team last year, could achieve with its claims, especially since ICA's restructuring plan has been approved.

Sinha, the ITAM professor, said it was unlikely the fund would recover anything in the process.

"Too bad. That's the risk you take when you buy stocks," Sinha said.

(Reporting by Christine Murray; Editing by Frank Jack Daniel and Jeffrey Benkoe)

By Christine Murray