Both Mr. Bennet, whom the White House has praised for his innovative approach to education, and Mr. Boasberg defend the deal they recommended in Denver back in 2008. They say that it has saved the school district $20 million it would have otherwise had to pay to cover the pension shortfall, and they maintain that no one could have predicted the credit crisis of 2008 that elevated the deal’s costs.

But the savings cited by the two men do not take into account termination fees associated with the complex deal. And had the school district issued fixed-rate debt, Wall Street would not have received the cornucopia of fees embedded in the more complex deal.

While the expenses associated with more complex transactions vary depending on the terms of the deal, Denver offers an example of the additional costs they can impose. So far, Denver has paid about $9.7 million more in fees for its deal than it would have had it chosen a simpler transaction.

Joseph S. Fichera, chief executive of Saber Partners, a financial advisory firm that specializes in structured finance, said that the type of transaction pursued by the Denver schools was a false solution for what the issuers want to achieve — lower long-term costs — because the banks selling the deals rarely quantified all of the potential risks involved.

“The issuer made a simple financing highly complex and took on substantial risk without knowing how large its downside could be,” he said, referring to the Denver deal. “The advisers and bankers may have disclosed that there were risks, but apparently did not help the issuer truly understand them. They typically present economic outcomes to the issuer only on projected savings and assume away any chance of the risks happening.”

THE PROBLEM

$400 Million Gap

In a Pension Fund

The Denver public schools needed to do financial contortions because, like many other public agencies nationwide, its pension plan did not have enough funds to meet the payments due to retirees. And for years, the school system had not met its required annual pension payments to ensure a fully funded plan; by 2007, the school system faced a $400 million gap.

The school system solicited advice from several banks on how to handle this problem and ultimately decided to issue bonds that allowed it to refinance its existing debt of $300 million, which had a fixed interest rate. It also raised an additional $450 million, most of which went into the pension to fill the gap in that plan. Together, $750 million was raised using the riskier pension certificates.