The mortgage settlement may assist underwater borrowers with principal reductions, but how many remains a mystery.

There were quite a few features in the $26 billion mortgage settlement in February between the nation’s five largest banks and 49 state attorneys general, but one of the more notable details involved a $10 billion commitment to principal reductions for underwater borrowers.

Like those other features, though, specific details on the reductions plan were hazy at best, and Ted Gayer of the Brookings Institute has taken a detailed look at the plan and attempted to estimate how many distressed homeowners would be aided by its funds.

Describing his analysis as more “back of the envelope” than scholarly, Gayer began by assessing how many loans are actually eligible for the settlement’s principal reduction plan. To qualify, homeowners must be underwater on their mortgage, which, according to CoreLogic’s latest data, would count 11.1 million borrowers. Mortgages guaranteed by Fannie Mae and Freddie Mac, though, would not qualify, and among the 26 million Fannie/Freddie loans, 14.1 percent of Freddie and 11.3 percent of Fannie loans are underwater, meaning roughly 3.3 million borrowers would not have access to the program.

So, subtracting 3.3 million from 11.1 million, we’re left with 7.8 million loans – except, there are stipulations for those loans, as well, Gayer writes. Borrowers must be either delinquent or facing imminent default, and according to the Federal Reserve, 28 percent of underwater borrowers, or 2.2 million, are at that stage. Then, we have to look at borrowers with mortgages from the five largest banks (Bank of America Corporation, JP Morgan Chase & Co., Wells Fargo & Co., Citigroup Inc., and Ally Financial Inc.), who service 55 percent of all loans, which brings the total down further to 1.2 million. And finally, the properties must be owner-occupied, and CoreLogic has reported that 82 percent of underwater mortgages are such, so the number falls further to 1 million.

As if that were not enough, there is one last step – only loans on the banks’ balance sheets are likely to receive reductions (other loans, owned by investors in the form of mortgage-backed securities, are unlikely to receive reductions to honor investor-portfolios), and according to CoreLogic, roughly 50 percent of homeowners have such loans. So we’re left, in the end, with 500,000 qualifying mortgages.

Gayer said that though his estimation is far from fact, if correct, it represents a very small percentage of underwater borrowers who would, nonetheless, still receive a considerable amount of aid.

“If the estimate is correct of 500,000 eligible loans, then this represents less than five percent of the universe of underwater borrowers,” Gayer wrote. “If each of these eligible borrowers were to apply for and receive a principal reduction, then the $10 billion allotted for principal reduction in the settlement agreement would amount to an average of $20,000 per eligible underwater borrower. This would be a significant amount of principal reduction, but only about 30 percent of the average amount of underwater equity.”

Given the small numbers deduced by Gayer, is this just another superfluous plan that helps too few borrowers, or is the nature of the aid itself more important than the numbers it services?