The FHA was more accepting of arguments raised by Caplin and others, who say its actuary wasn't correctly estimating risk for so-called streamline refinancing. The program moves borrowers from one FHA loan to another and doesn't require updated property appraisals.

Caplin and six other researchers estimated that as many as 71 percent of FHA borrowers who streamline-refinanced in Los Angeles County, California, in 2009 owed more than their houses were worth, according to a February 2010 paper. Using the FHA actuary's methodology, only 1.5 percent of the streamline refinanced borrowers would have had negative equity, Caplin said.

Capturing Values

For its 2011 estimates, the FHA's actuary, Integrated Financial Engineering Inc. of Rockville, Maryland, changed its approach to try to capture home values after the refinancings, said Barry Dennis, the firm's president. The change was one of several that increased the insurance fund's potential payouts as of Sept. 30 by about $6 billion.

"Some borrowers have streamline-refinanced 10 times," Dennis said.

Caplin said the change didn't go far enough. The actuary counts each refinancing as a "successfully terminated mortgage," he said. If a borrower refinances three times, the FHA counts that as three successful payoffs, Caplin said. That makes the agency's performance look better -- and that history helps shape estimates of future losses, he said.

"The refinance is just a rate reduction, it's not a successfully terminated mortgage," Caplin said. "Ask yourself if we're creating sustainable homeownership. How many borrowers are ending their reliance on FHA?"

Handling Risk

Dennis said his firm's approach uses FHA performance data to determine whether loans have had trouble in the past. While a refinancing removes risk from one year's projections -- the year in which the original loan was made -- it adds risk in the year of the new loan, he said.

"It's the same risk in the portfolio; it's just in a different year," Dennis said. "We've continued to improve our modeling."

Caplin, Gyourko and others also question how the FHA gauges the condition of the housing market. The agency uses the Federal Housing Finance Agency index, which shows that home prices have declined 15 percent from a March 2007 peak. Another measure, the S&P Case-Shiller Home Price Index, shows that values have declined 34 percent since a July 2006 peak.

The FHFA index is more appropriate because the properties it tracks tend to be in the same geographic areas where the FHA insures mortgages, according to the agency's annual report to Congress. Also, it said the Case-Shiller index "includes concentrations of properties subjected to subprime loans, and those sold in distress sales," which aren't in the FHFA index.

'Appear Better'