But CEM was only able to benchmark about half of the investment costs reported in South Carolina's pension plan.

At the time, 30 percent of the plan's assets were allocated to alternatives—private equity, hedge funds and real estate investments–compared to an average of 19 percent alternative allocation in the rest of the public fund universe.

Those alternative assets, particularly private equity, tend to be more expensive and have complex cost structures relative to publicly traded assets.

"This makes cost disclosure and cost benchmarking difficult at best," wrote CEM's analysts.

South Carolina subsequently took a good amount of heat in the national press, with stories in the trade and mainstream media alleging the payments to alternative asset managers were unjustifiably high.

But South Carolina's pension fund may have been victim of greater transparency, according to CEM's report, which found that the fund wasn't incurring more costs than other pensions, but was "simply reporting more costs than other funds."

That is evidence of a need for improved cost reporting standards in pensions funds, particularly with private equity investments, according to the paper.

Though the Government Accounting Standards Board has implemented a new rule, GASB 67, which attempts to improve upon and clarify previous fee disclosure requirements, the new language is still too ambiguous, says the paper.

"In practice, the amended guidelines have not led to more transparent cost disclosure, especially for private equity," write the analysts.

Private equity funds charge pensions a management fee, a fee for performance on the investment, and other fees incurred from managing the companies in equity portfolio. Pension funds also incur cost of monitoring their private equity investments.

That complexity means that pension funds are substantially underreporting the cost of private equity. For a $3 billion private equity portfolio, the average difference between what pension funds report in fees and the actual costs is $61 million, according to CEM's estimates.

In 2014, the Securities and Exchange Commission found "material weaknesses" in how private equity managers disclosed fees to pension funds on over half of the cases investigated.

The paper does not suggest that private equity is inappropriate for pensions funds, but says that improved transparency in accounting can give pension funds greater negotiating power with fund managers.

It also can lead to more efficient selecting of funds, as higher costs ultimately affect the return paid to pension fund investors.

"Higher costs are justified if they produce higher returns," write the analysts. "Private equity has been a strong performing asset class for some pension funds."

Still, other pension funds have not fared as well with private equity investments, as pension funds around the country reconsider allocations to private equity and other alternative investments.

Christopher Ailman, chief investment officer of California State Teachers' Retirement System, has called for new standardized cost reporting, as the fund has been reviewing its $31 billion allocation to private equity.

"We need someone to propose an industry standard," he said, that can become "something we need to follow."