One thing that I’ve been pointing out is that the best estimate by HUD and other federal and state boosters of the foreclosure fraud settlement is that it will help 1 million underwater borrowers get principal reductions. That represents a little less than 10% of the total underwater borrowers in the country. The latest data on negative equity from CoreLogic shows 11.1 million borrowers underwater at the end of 2011, which represents a whopping 22.8% of all residential properties with a mortgage. By the way, that’s up from 10.7 million at the end of the third quarter of 2011.

So even under HUD’s own terms, the settlement won’t put much of a dent in negative equity. But what if HUD’s estimates are too high? What if only half as many borrowers as HUD claims will see relief? That’s the opinion of Ted Gayer of the Brookings Institution, which he came to by running the numbers.

First, the borrower must be underwater, meaning owing more in mortgage debt than the house is worth. According to CoreLogic, there are 11.1 million underwater borrowers. Second, loans backed by Fannie Mae or Freddie Mac are not eligible for the principal reduction. According to analysis by the Federal Reserve of data from LPS Applied Analytics and CoreLogic, as of December, 14.1 percent of Freddie Mae loans were underwater and 11.3 percent of Fannie Mae loans were underwater. Taking the midpoint, and assuming there are 26 million Fannie or Freddie loans (about half of the number of existing loans), then there are approximately 3.3 million Fannie and Freddie underwater loans, bringing us to 7.8 million remaining borrowers eligible for the principal reduction. Third, the borrower must be delinquent or facing imminent default to qualify for the principal reduction. According to the Federal Reserve (PDF), approximately 28 percent of underwater borrowers are not current on their payments, bringing us to 2.2 million remaining borrowers. Third, the agreement is with the five largest mortgage servicing banks. According to Inside Mortgage Finance, the five banks service 55 percent of all loans, bringing us to 1.2 million remaining borrowers. Fourth, only owner-occupied homes are eligible. According to CoreLogic, 82 percent of underwater borrowers are owner occupied, bringing us to 1 million remaining borrowers.

There is another complication, in that some of these loans are held on the banks’ balance sheets, and others are part of mortgage-backed securities owned by outside investors. For the latter, the banks are contractually obligated to minimize losses to the investors, meaning it is unlikely they can reduce principal on these loans without facing the ire (and possible lawsuits) from the investors. Department of Housing and Urban Development Secretary Donovan acknowledged this problem by suggesting that the banks will target the principal reductions to the loans that they hold on their balance sheets. According to CoreLogic, about 41 percent of underwater borrowers had home equity loans, which typically are held on banks balance sheets. So even if these borrowers’ first loans do not qualify for a principal reduction, their second loans – which represent the bulk of their negative equity – do. Also according to CoreLogic, about 9 percent of underwater borrowers had no second loan and had their first loan held on banks’ balance sheets. Applying this 50 percent leaves us an estimate of 500,000 loans eligible for the principal reduction.

In other words, Gayer’s winnowing process means that, in order for HUD’s boast to be true, every single home eligible within the criteria would get a principal reduction. I don’t think that anyone expects the servicers to be that efficient.

Shaun Donovan has elsewhere said that he expects 15% of the principal reductions to come from private-label mortgage-backed securities loans. It’s based on the idea that investors would either somehow agree to that or that the principal write-down would be NPV-positive so there’s an implied consent there. I don’t think that’s a guarantee. But let’s for the moment take HUD at their word. So I would bulk up Gayer’s analysis slightly, by adding that 15% into the mix. So maybe you get 600,000, at the maximum, eligible for principal reductions.

And then you have to make the caveat that, as Gayer says, this is just a description of eligibility. Assuming that these numbers are correct does not mean that you can assume that servicers will carry out the principal reductions, especially because they can also obtain credit on the settlement for things like short sales, anti-blight actions (like donating homes), and even waiving deficiency judgments. So I would knock off more just based on the fact that servicers will employ all those strategies, and even then I don’t think you can say with any certitude that the servicers will abide by their obligations. Put it this way, they never have before.

If you’re extremely generous and you say that everyone eligible for a principal reduction under the settlement will get one, then you’re talking about, using Gayer’s numbers, 5% of total underwater borrowers, getting an average of $20,000 of principal reduction apiece, which represents about 30% of the average underwater equity. Gayer doesn’t even favor principal reduction, and he’s basically calling that inadequate.

HUD would no doubt add that there are refi programs for current underwater borrowers, and plans to get Fannie and Freddie to do principal reductions and refis. But the inescapable facts are that the settlement’s principal reduction demands are a drop in the ocean. And that’s if they get done at all.