Dealing with Adverse Selection in the Mortgage Market

Suppose that a bank calculates that the net value of the mortgage to the bank as a fraction of its principal is equal to four years' interest minus the chance of default:

π = 4r - d

And suppose that the homeowners and homebuyers who come to the bank have a chance of default which is:

d = 15% + 20r²

Then bank profits expected from a typical homeowner and home buyer are:

π = 4r - 20r² - 15%

Which means that a bank can make profits as long as:

5% ≤ r ≤ 15%

And if there are a bunch of competitive banks, and if homeowners can comparison shop, competition will push the interest rate down to 5% and a bit more. And the observed default probability will be 20%.

Now suppose that there is bad economic news: the default probability rises by 5% to:

d = 20% + 20r²

Then, the way I have rigged this scenario, interest rates rise to 10%: no bank can make money charging less than 10%, given the new, higher default probability--and the observed default probability will rise not by 5% but by 20%, to 40%. The big increase in default, you see, comes not from the bad economic news but from the fact that a lot of people who could still make their mortgage payments at the old interest rate cannot make them at the new one.

And if the default probability rises even more, to:

d = 21% + 20r²

then the market collapses. There is no interest rate at which any bank--even a monopoly bank--wishes to be in this business. No loans are made at all.

Suppose that at this stage the government steps in. "We," the government says, "are going to cap your default losses at 20%." Then banks look at the situation and once again discover that it is profitable to make loans at any interest rate above 5%. Competition chases the market interest rate back down to 5% again. There is a problem--at a 5% interest rate default losses are not 20% but rather 26%--and so the government has to kick in money. But maybe a 26% default rate with the government having to kick in some money is better than a 40% default rate from a cultural, sociological, political, and in the presence of aggregate demand externalities economic point of view. And surely it is better than a complete collapse of the mortgage market.

That is the logic behind Frank, Dodd-Obama, the Barr-Tyson plan being pushed by Hillary Rodham Clinton, and the other variants: that when the major cause of large-scale defaults is not the fecklessness of the borrowers but rather the fact that the market equilibrium has high interest rates that are themselves both the consequence and cause of high default rates, that the government has a market-making role to play by providing guarantees. This seems to me to be a good logic.

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Here is Alan Blinder on this issue:

How to Cast a Mortgage Lifeline?: THE financial markets are downright scary. And it seems unlikely that we can extricate ourselves from the current series of rolling financial crises without improving the situation in three related markets: those for houses, mortgages and securities based on mortgages. In a previous column for Sunday Business, I advocated one possible approach: creating a modern version of the Home Owners' Loan Corporation.... How would it work in practice? Let's concentrate on six major design issues:

STRUCTURE The original HOLC bought mortgages outright. But Representative Barney Frank, the Massachusetts Democrat, and Senator Christopher J. Dodd, Democrat of Connecticut, the chairmen of the two banking committees of Congress... would use a beefed-up Federal Housing Administration to guarantee new mortgages -- issued, say, by banks -- instead of buying up old ones. The effects would be much the same: old, unaffordable mortgages would be replaced by new, affordable ones; and the government would then assume the risk of default. But in the Frank-Dodd proposal, the federal government would be a big insurer rather than a big bank. Because the approach actually has a chance of becoming law, let's adopt its structure.

BAILOUTS The Frank-Dodd plan for a Super F.H.A. is intended to make a bad situation better. But it must not be too generous in shielding people and businesses from the consequences of their own bad decisions -- both for economic reasons (to minimize moral hazard) and for political reasons (to gain voter support)... existing mortgages would be bought below face value, forcing investors to, as they say in the trade, "take a haircut"... [and] the proposal would make homeowners relinquish part of any price appreciation on their houses for as long as their Super F.H.A. mortgages remain in effect....

LEGAL SAFE HARBOR The Super F.H.A. would have to deal with legal complexities.... Servicers are petrified of lawsuits if they sell individual mortgages... at a loss.... Congress must pass legislation shielding servicers from legal liability when (as now) market conditions depress prices....

SETTING PRICES The HOLC bought pre-existing mortgages at a discount. The Super F.H.A. would use government guarantees to induce private businesses to do so. In either case, we need prices for the old mortgages.... My suggestion is that the Super F.H.A. categorize the mortgages it might refinance into, say, "high," "medium," and "low" qualities... adjust those prices according to whether mortgage owners rush in to sell (meaning that the prices were set too high) or stay away (meaning that the prices were set too low)....

SUNSET Emergency measures must not outlast emergencies....

ELIGIBILITY AND SCALE How large should the mop-up operation be? Mr. Frank and Mr. Dodd are thinking about one million to two million mortgages, but they understand that a larger number might be necessary to stem the downward spiral....

The urgency of creating something like the HOLC or a Super F.H.A. has grown, not shrunk, since I wrote my previous column.... [T]he Frank-Dodd proposal... offers a smart approach to a knotty set of problems.... Their design is not flawless. But do you know of any perfect solutions? It deserves our support.

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Figures:

Comments

[a]

""We," the government says, "are going to cap your default losses at 20%." Then banks look at the situation and once again discover that it is profitable to make loans at any interest rate above 5%."

And then what happens is: foreigners look at all the bad assets (all those foreclosed homes) that the U.S. government is holding on its books and decide that they don't want to hold Treasuries or the U.S. dollar any more.

[Matt]

When the mortgage market slows the borrowers tend toward the highly qualified and there is a quit shut off valve for defaults. It won't collapse, but it will leave the marginal buyers out, the ones Barney thinks he will save.

[Slocum]

"This seems to me to be a good logic."

But the default rate only rises with interest increases for borrowers with adjustable mortgages -- which is only about a third of homeowners. And for new purchases, if interest rates rise, then housing prices fall and/or purchasers don't qualify for the same size mortgage they would have before -- and their default risk is not elevated (if interest rates rise from 5% to 10%, and I'm house shopping -- either the houses I'm shopping for become cheaper, which compensates for the higher interest or I buy a smaller house than I would have or don't buy at all -- but my risk of default is not higher than if I'd bought when rates were 5%).

And, in any case, nothing like this seems to be happening now --bankrate.com lists 30-year fixed mortgages at 5.75% today. And one has to assume that the fraction of homeowners taking out ARMs rather than fixed mortgages much be declining rapidly and that many of the homeowners with ARMs now are going to be converting to fixed rate loans (which, at 5.75 are not exactly exorbitant now).

[Dean Baker]

suppose, alternatively that the default rate is related to the gap between the purchase price and the equilibrium or trend price of a house. Suppose that the homeowners took out loans to purchase homes at bubble inflated prices and that the prices are now being pushed back by market forces to their trend price.

In this case, the Blinder intervention will at best temporarily reduce the default rate (it will not keep the bubble from deflating, it will only slow it), it will end up costing the government lots of money and it will cause homeowners to blow lots more money in interest payments and other ownership costs than they ever would have paid renting a comparable unit. Furthermore, the homeowners will end up with no equity, because house prices are falling.

This ends up being a good way to get some taxpayer money to troubled banks, but a really bad policy otherwise. Get the full story here [http://www.cepr.net/index.php/publications/reports/subprime-rescue-plans-backdoor-bank-bailouts/].

[halbhh]

I think almost everyone would agree that it's good to have government guarantee mortgages to subsidize home buying by first-time buyers or even all buyers up to a certain price limit. After that is when we have more diverse opinions.

Probably almost all of us would say we'd like the rules to be set up so that speculative run-ups in home prices would be moderated and reduced in amplitude. And perhaps even most of us would recognize the simple effective way to do that: capital requirements or reducing leverage.

But supposing we didn't control leverage and house prices ran up in a big speculative fever, as they have at the moment.

What to do?

Well, if the source of home loans ultimately backed by the government continue to offer mortages, then we'd not have to worry about lending dissappearing.

Indeed this is the case, as Fannie Mae and Freddie Mac, and the FHLB are all functioning as intended and mortages are contining to be available at reasonable rates. With implicit governmet guarantee. And most of us are pleased at that most likely.

So.....this begs the question....what is the Frank-Dodd bill *acutally* for?

It's strictly to help keep some people in homes that would lose them and cannot get GSE type re-fis. Right? That's good enough.

Some of us (not most perhaps) will accept we are going to rob Peter to pay Paul, and we'll justify it as best we can, and hope Peter doesn't really understand.

Why suggest that mortage lending in general though requires the Frank-Dodd Bill?

It is so stiking this disconnect that it provokes questions. Is more going on here?

[a]

"I think almost everyone would agree that it's good to have government guarantee mortgages to subsidize home buying by first-time buyers or even all buyers up to a certain price limit."

False, not "almost everyone". And the idea proposed (subsidizing all buyers up to a certain price limit) is ridiculous, basically having 1/3 of the country subsidize the other 2/3 (the other 2/3 who are already receiving one big gigantic tax break). Since the 1/3 are on the whole poorer, those in this section just couldn't do it, even if they wanted to.

[Kaleberg]

One interesting side effect, is that interest rates are kept low. In our current cash rich age, this means that there is lots of money slopping around looking for a return higher than the inflation rate. It is showing up in commodities speculation, if nowhere else. As soon as all that money aligns again, we are on to the next big bubble. (Check out yesterday's New York Times article on Odd Crop Prices).

If incomes were rising, there would be more investment opportunities, but that hasn't happened since the late seventies.

[bigTom]

Brad's example didn't look at the way things can change over time. Given that most mortagages run for a long enough length of time that market risk (of not knowing about the economy 5 10 or 20 years in the future) is substantial. His example is about making a new loan profitable according to an up do date model. But is that really the main problem? Isn't todays problem more the value of loans that were made with an assumption that conditions would be such that the default rate was grossly underestimated, and hence the crop of existing loans must now be heavily discounted. And after discounting the loans on their books, the banks have no money to loan, making the issue of whether a loan would be profitable moot. Of course putting some reasonable floor under the price of the existing loans might help with this aspect as well. But I suppose that talking about the proposal in terms of existing debt just highlights the inherent moral hazard, so we would rather talk about future loans, than the crop of bad ones.

[Matt]

Well, in the absence of a shock, everyone would ultimately buy the housing that sets their probability of default to the same level. That assumes we operate in a linear region of housing utility.

So, if there is bad news, and the news is absorbed while we are still in the linear utility region, then, from initial equilibrium, (equal probability of default across price ranges, then all mortgages should have the same percentage change in default probability, stationary process conditions hold.

The real problem arises because low end housing, which is so numerous in the market, it is quantized in price for lower end buyers, that is, it is difficult to buy down or up in small linear increments for them.

Hence, any shock change in housing prices over all have a more strongly adverse affect on linear utility for these lower end buyers.

[TIV]

Excellent summary. But more importantly, how is this picture of the infamous event where the heads of the FDIC, OCC, OTS, Federal Reserve Board, and NCUA used tree shears and a chainsaw to cut those annoying banking regulations, not the poster for the current crisis?

http://www.egrpra.gov/images/photo0603.jpg

[kharris]

Um, guys? I think the perfesser has done what perfessers do with simple models. He has clarified a single issue. That's what simple models do. Slocum's points seem generally correct, but the model still applies to a significant fraction of the market, a big enough fraction that the model - assuming it correctly identifies the dynamics in that franction of the market - is useful in understanding what happened. There is a feedback through the default rate that makes the system unstable - a market failure? Knowing that helps.

We also need to think about the divergence from trend in home prices, divergence from trend in residential construction as a share of GDP, winners-and-losers stuff that results from efforts to aid any particular class. There is, however, enough bad thinking going on (just ask Tanta over at CalculatedRisk), that we probably need to start with a lot of simple models.

And no, we don't want to go spending a bunch of money based on a single, simple model.

[Jules]

This is an elegant argument. Does it, however, pass the "real-world" test to link default rates to interest rates alone? Doesn't "jingle mail" also have an effect on default rates? In other words, won't the overvaluation of housing stock in the US, and the consequent mkt correction of that overvaluation, make it difficult for the gvt to facilitate a new equilibrium in the mortgage market? Even if the govt succeeds in scotching the real estate market's fall (and that's a BIG if), won't the high level of asset prices continue to be a problem? If I understand correctly, the Frank-Dodd proposal will present home owners with a choice of either defaulting or "taking a haircut" on their principle. That seems like an efficient way to get home prices down fast (if that's what you want.)

[kharris]

a,

There are published data on default rates by mortgage class, published data on shares of outstanding mortgages by class and by year. Feel free to look them up.

[Charles]

Dean Baker says, "In this case, the Blinder intervention will at best temporarily reduce the default rate (it will not keep the bubble from deflating, it will only slow it), it will end up costing the government lots of money and it will cause homeowners to blow lots more money in interest payments and other ownership costs than they ever would have paid renting a comparable unit."

Dean, you need to do the calculation to arrive at a precise value of the amount "lots" and compare that to the alternative. My own SWAGs suggest that "lots" = $50 - $100B, while the alternative cost *to the government* of doing nothing is substantially higher (like, say, up to $500B over 5r years).

Homeowners who took on mortgages they couldn't afford should (absent fraud) be stuck with some of the pain, just as banks who turned a blind eye to questionable (but non-fraudulent) lending should be stuck with some of the pain. And the people who committed actual fraud should go to jail.

As for the banks benefiting, well, that's part of the deal. Having banks go down is bad for all of us.

Looking at your report, the main reason that you reach the conclusion that homeowners will achieve no equity is because you only allow four years. While that's the average time of residence at present, if people had an incentive to stay, they might well stay longer. As they stay longer, the percentage points of income they are paying above 30% diminishes. I also don't think you are accounting for re-negotiation of mortgages. Once mortgages obtain guarantees, they are much more attractive for refinancing.

A much better way to achieve fairness for subprime borrowers is by raising wages.

[ottnott]

Let's save Brad's model for some future situation where an external shock is the source of the problem.

A simple model based on default rates and interest rates is simply the wrong model for the current problem.

The current problem for housing and mortgages is that lenders and borrowers both decided to dismiss or deny the fact that housing prices were rising far above historical norms. Large numbers of mortgages were made to people who couldn't afford those mortgages.

It was not a combination of competition and external shock that did the lenders in. It was fee-driven greed.

Large numbers of borrowers are defaulting even though there has been no increase in the rates established or expected at the time the loan was made. There has been no shock to their rates, as LIBOR remains low and the spread over LIBOR was set at the time of the loan.

[PQuincy]

A site-technical issue: any particular reason I'm seeing a grey square overlaying the top half of the first graph (and also one on top a graph in a subsequent post). Is this site not Mac/Firefox compatible?

[a]

"There are published data on default rates by mortgage class, published data on shares of outstanding mortgages by class and by year. Feel free to look them up."

Are you saying that they confirm the model? Or are you saying you don't know, and I'm supposed to look and hope that by some chance they do?

[anon]

My initial reaction (guess) was that the default rate does not shift up as much as modeled, but that prices on other things (stocks, labor) go down because people start selling more to pay off debts (increase in supply) and people redirect discretionary 401k and other investment to pay debt (lower demand for stocks), and other changes -- there are interactive variables in all of this

Do you penalize debtors (crush inflation with high interest rates and deflation) or do you penalize creditors (inflate your way out of questionable borrowing and lending) or can you find some sort of happy medium?

[Mark]

My first problem with the model is your discription of "d". If d is being used in a calculation of expected return to the bank, then d has to have at least 2 components: (a) the magnitude of the default and (b) the probability of default. Because this model is disconnected from housing prices, it misses the fact that a "default" which impacts the value of the mortgage loan only occurs when (i) the current mortgagee no longer has the desire or the ability to pay and (ii) the mortgagee cannot timely sell or otherwise turn their equity in the property in cash to satisfy their current mortgage. In other words, if the borrower can turn around and sell the property for more than the value of the underlying loan, there will be no default or the magnitude of the default should be very, very small.

In order for d above to be a default rate in your calculation of profitability, the implication is that the bank recovers nothing in the event of a default other than collecting the capitalized interest and fees from the 4r term in your profitability equation. This is clearly not the case. In practice, the amount and likelihood of recovery from the pledged asset can be estimated from an appropriate housing pricing model over time and the allowed initial leverage on the loan. In other words, if the bank was only willing to lend 50% of the current appraised value of the property, in the absence of fraud, the bank should be able to recover 100% of its money in the event of a default, even if it has to take the property through foreclosure. If you use a historically based time series model of housing appreciation, even 75% loan to value results in a minimal difference in expected cash flow between a recourse and nonrecourse mortgage.

My next major problem is your default rates appear to me to be way too high. Even in subprime mortgages, a 15% default rate would be considered fairly horrendous.

"Mortgage loan delinquency (the percentage of mortgage borrowers 60 or more days past due) hit a national average of 2.99 percent in the fourth quarter, up almost 17 percent over the previous quarter. It was highest in Nevada (4.68 percent), followed closely by Florida (4.49 percent). The lowest mortgage delinquency rates were found in North Dakota (1.13 percent), Alaska (1.23 percent) and Montana (1.34 percent)."
Source: http://sev.prnewswire.com/banking-financial-services/20080429/AQTU50929042008-1.html

As you can see, deliquency nationally is well under 5% ... so I'm not sure how you can justify starting your analysis with a 15% base default rate. Also, just because someone is 60+ days delinquent, it does not necessarily mean they are going to default. Some of those 60+ folks manage to come current. Some of them manage to work a deal with their lender whereby their missed payments get tacked onto the end of the loan, they pay a modification fee, and go on making payments. Some of them manage to sell their house for sufficient money to repay the bank in full, including late fees and interest at default rates. And yes, some of them will default and either be foreclosed upon or hand their keys to the bank ... either in person or through "jingle mail". But even those houses can be sold at some price for some recovery (excluding fraud cases).

Ultimately, looking at more complete models which include such things as allowed leverage in purchasing a house, I cannot justify providing a guaranty to lenders who took insufficient collateral to protect their position unless the guarantor is being paid appropriately to take that risk. This is true whethe the guarantor is a public entity or a private insurance company.

It is also ironic that the recent changes in the Bankruptcy Code favoring credit cards has had an unanticipated impact on the housing mortgage market. For those of you who did not know, after the latest changes, for the most part, it is now harder to discharge credit card debt than it is to discharge mortgage debt in a bankruptcy. The predictable result is that people have started paying the credit card companies prior to paying their mortgages under certain circumstances.

Just my 2 cents.