It's one of the big mysteries in Harrisburg: How many billions of dollars in unreported profits have BlackRock, Apollo Global, and more than 100 private-equity investment firms made on investments for Pennsylvania's two giant pension funds — profits that are in addition to money management fees these firms earn?

About $3.8 billion over the last 10 years, estimated Ludovic Phalippou, professor of finance at Oxford University, testifying Thursday before the five-member Public Pension Management and Asset Investment Review Commission, which is charged with recommending ways to cut pension costs in the future.

While the sum would help the poorly funded pensions, Phalippou and other experts didn't suggest that managers return this money or that the state stop investing in private equity.

They did suggest the pension funds should be more transparent and disclose all their expenses, which would enable state officials to negotiate lower fees.

Still, the number shocked some observers, and suggests that the pension funds may come under increasing pressure to disclose all the money that fund managers make.

Democratic State Treasurer Joe Torsella called the $3.8 billion in unreported gains by pension management firms "a staggering number."

Pennsylvania's main pension funds have less than 60 cents set aside for every dollar of pensions they expect to have to pay when today's public workers retire. The state worker (SERS) and school employee (PSERS) pension funds blame the shortfall on inadequate past state "employer contributions," mostly during the administrations of Republican Tom Ridge and Democrat Ed Rendell.

To make up the shortfall, Pennsylvania taxpayers now have to pay a pension premium of more than 30 cents for every dollar of wages and salaries paid to public employees in the pension systems.

"I expect the commission will find substantive measures to reduce fees to Wall Street and that the pension systems will take action to implement them," said Gov. Wolf in a statement. Wolf signed Act 5, the law passed by the Republican-run General Assembly which set up the commission.

Chaired by State Rep. Mike Tobash (R., Schuylkill) with Torsella as vice chair, the commission has been grilling experts about whether the state funds have gotten good value for their investment contracts and the management fees that they pay private firms.

Phalippou and other witnesses, including Tim Jenkinson, Phalippou's colleague at Oxford, told commission members that Pennsylvania's private equity funds — a slice of its total portfolio — had performed as well as those in California and other states even after firms siphoned off those $3.8 billion in profits.

But both professors urged Pennsylvanians to demand more transparency and accountability from SERS and PSERS, which have boasted of lower direct money-management fees in recent years. Those fees represent a second way that firms make money. The funds have previously disclosed they paid $2.2 billion in fees to private fund managers over the last decade, while mostly failing to say how much they let those firms keep in profits.

Those profits are popular among professional money managers, in part because they are taxed by the federal government at lower capital-gains rates, not as regular income. Successful private managers have become billionaires, investing in luxury yachts and NBA teams.

In his testimony, Stanford University pensions scholar Ashby Monk accused SERS and PSERS of sometimes cherry-picking the benchmarks they use to compare their past performance.

He estimates the Pennsylvania systems' long-term performance is among the worst in the country for similarly situated funds. The funds have claimed above-average performance.

He also noted that SERS and PSERS have declined to share manager fee agreements, claiming exemptions from public reporting because disclosure could make it harder to strike more deals.

That's outdated thinking, Monk said. More and more, investors are demanding fuller disclosure of the incentives that private money managers enjoy when they put the people's billions to work on behalf of state and local government pensioners.