– The biggest U.S. public pension system may have set off a race among funds to disclose the amount of profit it has shared with private-equity firms.

The California Public Employees' Retirement System last week released a much-anticipated report saying its private-equity managers, such as Blackstone Group LP and Apollo Global Management LLC., reaped $3.4 billion since 1990 under profit-sharing agreements. Calpers earned $24 billion on those investments during that time.

Such profits have become a flash point in the debate over whether taxpayer-financed pension funds should take on the risks and complexity common in private-equity deals, and whether investors are getting their money's worth. Increasingly, pensions have turned to alternative investments rather than traditional stocks and bonds to boost returns needed to match lifetime benefits promised to government workers.

"Because Calpers is going through this exercise, it's going to mean that other large institutional investors are going to be asking their private-equity firms the same questions," said Reena Aggarwal, a finance professor at Georgetown University in Washington.

Private-equity managers typically charge investors a 1 percent to 2 percent annual management fee on committed capital that is taxed as income. They generally also keep 20 percent of investment profits as carried interest.

Over time, the Calpers disclosure "will raise questions about whether the total amount of compensation paid to private- equity managers is more than is necessary," said Michael Flaherman, a former Calpers board member.

Other retirement systems are taking notice. New Jersey's public pension already reports carried interest, and disclosed that it paid about $600 million in private-equity fees and incentives in 2014 with $334.8 million going to carried interest.