Tuesday, January 29, 2008

Options Theory and Mortgage Pricing

by Tanta on 1/29/2008 11:02:00 AM

One of the hot topics of conversation lately is the idea of a mortgage “put option.” There seem to be more than a few people—including those who don’t exactly use the language of options contracts, like that weird couple featured recently on 60 Minutes—who are slightly confused about what the “optionality” of a mortgage contract is. There are also lots of folks who are wondering what will happen to mortgage pricing in general should a substantial number of folks decide to “exercise the put” on their mortgages. It seems wise to me to try to tease out what’s going on here.

First, mortgage contracts in the U.S. are not, actually, options contracts. You may peruse your note and mortgage at length now, if you didn’t do so when you signed them, and you will not find any “put” or “call” in there. Your note is a promise to pay money you have borrowed, and your mortgage or deed of trust is a pledge of real estate you own (or are buying with the borrowed money) as security for that note. That means, in short, that if you fail to keep your promise to pay the loan in cash, the lender can force you to sell your property at auction (to produce cash with which to pay the loan in full). Because the mortgage instrument gives your lender a “lien,” any sales proceeds are first applied to the mortgage debt before you get any of it.

People get very confused about this because it is often the lender who ends up buying the property at the forced auction. When that happens, it is basically because the lender simply wants to put a “floor” bid in the auction: the lender bids an amount based on what it is willing to lose (if any). Typically, the lender bids its “make whole amount” or the loan amount plus accrued interest and expenses. If someone else bids more than that, the lender is happy to let the property go to the higher bidder.

The lender might bid less than its make-whole amount; it might bid its “probable loss” amount. If the lender is owed $300,000 and doesn’t think it could ever end up recovering more than $200,000, it might bid $200,000 at the FC auction. The lender doesn’t actually want to win the auction; lenders are not really in the business of real estate investment or property management. However, the lender would rather buy the home at the auction and pay itself back eventually by re-selling the property later (as a listed property in a private sale instead of a courthouse auction) than let the property go for $50,000 (meaning the lender would recover only $50,000 on a $300,000 loan instead of $200,000). Nothing ever stops any third party from bidding $1 more than the lender’s bid and winning the auction (except, of course, any third party’s own inclinations).

We need to remember, then, right away, when anyone talks about “giving the house back to the bank” or “mailing in the keys,” we are already in the land of metaphorical language. The only situation in which “giving the house back to the bank” would literally be possible is if you bought the house from the bank (say, it was REO) and the contract explicitly gave you an option to sell it back to the bank, whenever you wanted to, at a price equal to your loan balance. Nobody writes REO sales contracts that way. In most cases, of course, you bought the house from someone other than a bank. You have no option to “put the house back” to the seller. You win only if it's "heads."

A “put option,” in the financial world, is a contract that gives the buyer of the put the right, but not the obligation, to sell something (a commodity, a stock, a bond, etc.) in the future at a predetermined price. On the other side of the deal, the “writer” of the put is obligated to buy the thing in question if the put buyer exercises the option. Some of you may already be a bit confused about “buyer” and “seller” here, but that’s an important point. You don’t get “free puts.” You buy puts. There is a fee or a “premium” that you pay for the option contract. If you do not exercise the option, the put-writer pockets that fee. If you do exercise your option, the put-writer pockets that fee (to offset his loss on the deal) and your gains on the ultimate sale of the thing are net of the option premium.

The point of a put is that you buy them when you want to be protected from falling prices: if you think there is a good chance that the value of something will fall in the future, buying a put that allows you the option of selling it next month at this month’s price might well be worth paying that option premium. But you do always pay an option premium and you do not get it back.

The opposite of the put option is the call option: it is the option to buy something in the future at a predetermined price. You buy calls when you think the value of the thing is likely to rise. You also always pay some premium or fee for a call.

Residential real estate sales and mortgage loans do not, actually, literally, have puts and calls in them. If you buy a home today, you assume the risk that its price may fall in the future. Your contract does not include an option for you to sell the house at the price you paid for it. Nor does the seller of the house have a “call”; the seller cannot force you to sell the house back to him at the original price if its value rises.

Your mortgage loan contract does not give you the right to simply substitute the current value of the house for the current balance of the loan: you do, in fact, risk being “upside down.” (The only time this isn’t true in the U.S. is with a reverse mortgage; those are written explicitly to have this kind of a feature, where the balance due on the loan can never exceed the current market value of the property. But of course reverse mortgages aren’t purchase-money loans.) Nor does the mortgage contract give your lender the right to buy your house from you for the “price” of the loan amount when that is less than its value. Mortgage lenders never do better than paid back. If the real estate securing your loan increases in value, that appreciation belongs to you (as long as you make your loan payments).

So why is it that people keep talking about “puts” and “calls” in terms of mortgage loans? That’s because mortgage contracts have features that can affect their value to the writer of the contract (the lender or investor) in a way that is analytically comparable, in some ways, to classic options. Options theory is applied to mortgages in order to price them as investments. (Strictly speaking, this is a matter of analyzing them so that a price can be determined.) The interest rate, then, that you get on a mortgage loan will depend, in part, on how the lender/investor “priced” the implied options in the contract.

The “implied put” in a mortgage contract is the borrower’s ability to default (walk away, send jingle mail, whatever you want to call it). We do not, generally, consider “distress” (that’s actually the formal term in the literature, for you Googlers) as an “implied put.” Some borrowers will fall on hard times and be unable to fulfill their mortgage contracts. This is a matter of “credit risk” and it is, analytically, a different matter of mortgage contract valuation. The “implied put” analysis is trying to capture the possible cost to the lender/investor of what we call the “ruthless” borrower. “Ruthless” isn’t really intended to be a casual insult; it is in fact the term we use to describe borrowers who can pay their debts but choose not to, because there is a greater financial return to that borrower in defaulting as opposed to not defaulting. It is “ruthless” precisely because there is not a contractual option to do this: the only way you can exercise the “implied put” is to default on your contract.

Many many people are very confused about this. When we talk about the “social acceptability” of jingle mail, what we are talking about is at some level the extent to which there is or ought to be some rhetorical or social “fig leaf” over ruthlessness. It seems to be true, after all, that most people are more likely to behave ruthlessly if they can call it something other than ruthlessness. (There are always people who have no trouble with ruthlessness; they often get the CEO job. Most of us have at least moderately strong inhibitions about ruthless behavior.) There is, therefore, a process in which the ruthless put is re-described in various alternative terms, or has alternative narrative contexts built up around it, such that it no longer “feels” ruthless. The borrower was victimized (by the lender, the original property seller, the media, the Man). The put premium was actually paid (“they charge me so much they can afford this”). The ruthless borrower is actually the distressed borrower (redefining what one can “afford” or what is necessary expense so that a payment you can make becomes a payment you “can’t” make).

Before anyone starts in on me, let me note that these fig leaf mechanisms are effective precisely because victimization, predatory interest rates, and truly distressed household budgets do really exist. They wouldn’t be very convincing otherwise. (Very few ruthless borrowers will claim it’s because of, say, alien abduction or something equally implausible.) I am not, therefore, asserting that all claims of predation or distress are “false.” I am simply pointing out that it is, after all, a hallmark of the not-usually-ruthless person who is nonetheless acting ruthlessly to rationalize his conduct.

I don’t offer that as some startling insight into human psychology. I offer it as an attempt to get some analytic clarity. When CR talks about lenders fearing that jingle mail will become socially acceptable, he’s not exactly saying that lenders fear that society will no longer stigmatize financial failure (“distress”). They are afraid that rationalization mechanisms will become so effective that true ruthlessness (which is historically pretty rare in home mortgage lending) will become a significant additional problem (in addition to true distress). And they fear this because, delusions to the contrary, those loans did not have enough of a “put premium” priced into them to cover widespread “ruthless default.”

In fact, the very language of options theory can function, for a certain class of ruthless borrowers, as the fig leaf. To say “Hey, I’m just exercising my put” is a retroactive reinterpretation of your mortgage contract to “formalize” the “implied put” so that you do not have to describe what you’re doing as “defaulting.” This strategy is apparently popular with folks who have some modest exposure to financial markets jargon and an unwillingness to lump themselves in with the “riffraff”—victims of predators and financially failing households and other “weaklings.” (Sadly, a lot of people who have a very high degree of exposure to financial markets jargon don’t need no steenkin’ rationalization. Like most sociopaths, they don’t understand why “ruthless” would be considered insulting or what this term “social acceptability” might mean. So if you’re hearing the “put” excuse, you are probably in the presence of a relative amateur.)

The other side of the problem in valuation of mortgage loans and mortgage securities is the “implied call.” The “call-like feature” in a mortgage contract is the right to prepay. In the U.S., all mortgage contracts have the right to prepay. (Some, but not all, have a “prepayment penalty” in the early years of the loan, but “penalty” here means a prepayment fee, not an actual legal prohibition on prepayment.) The reason the right to prepay functions like an implied call is that it gives the borrower the right to “buy” the loan from the lender at “par,” even if the value of the loan is much higher than “par.” If you refinance your mortgage, you are required only to pay the unpaid principal balance (plus accrued interest to the payoff date) to the old lender in order to get the old lien released. Unless the loan specifically has a prepayment penalty, you are not required to further compensate the old lender for the loss of a profitable loan. So a loan with a prepayment penalty has an implied call and a real call exercise price. A loan without a prepayment penalty, or past the term of its prepayment penalty, has a “free call.” (In the original lender’s point of view. There is always some price to be paid to get a new refinance loan; the borrower’s calculation of the value of refinancing always has to take that into account. Among other things, this fact results in mortgage “call exercise” being much less “efficient” than it is on actual call contracts, which makes the call much more difficult to value, analytically, for mortgages.)

While ruthless default might, historically, be rare, refinancing has been ubiquitous for decades now. It wasn’t always so easily available; your grandparents might never have refinanced a loan not because their existing interest rates were never above market, but just because there weren’t lenders around offering inexpensive refinances. In fact, refinances have been so ubiquitous for so long now that many people have come to think of the availability of refinancing money as somehow guaranteed. This isn’t just a naïveté about interest rate cycles, although it is that too. It is a belief that credit standards and operating costs of lenders never change, so that if someone thought you were “creditworthy” once, they’ll automatically think of you as creditworthy again, and that lenders can always afford to refinance you without charging you upfront fees.

People who price mortgage-backed securities have always known that the prepayment behavior of mortgage loans is impacted not just by prevailing interest rates, but also by the borrower’s creditworthiness, the lenders’ risk appetites, and the cost (time and money) of the refinance transaction. We were talking the other day about the prepayment characteristics of jumbo loans in comparison to conforming loans; the fact is that people who have the largest loans are the most likely to refinance at any given reduction in interest rate, since a reduction in interest rate produces more dollars-per-month in savings on a larger loan than it does on a smaller loan. Considering these types of things is very important to people who price MBS, because in fact prepayment behavior is both hard to “price” and absolutely critical to “pricing” mortgages as an investment.

MBS, unlike other kinds of bonds, are “negatively convex.” I have been threatening to talk about convexity for a while and I keep chickening out. It’s actually useful to understand it if you want to understand why mortgage rates (and the value of servicing portfolios) behave the way they do. The trouble is that convexity involves a whole bunch of seriously geeky math and computer models and normal people probably don’t want to go there. (I don’t even want to go there.) So as a compromise, this is a very quick and simple explanation of convexity.

The convexity of mortgages is a result of the “implied options” in them. Most people understand intuitively that the higher the interest rate on a loan, the more an investor would pay for that loan: if you had the choice today of buying a bond that paid you 6.00% and one that paid you 6.50%, you would probably not offer the same price for each of them. With a classic “vanilla” bond, the price you would offer would be a matter of looking at the term to maturity, the frequency of payments, the interest rate, and some appropriate discount rate.

The trouble with mortgages is that while they have a maximum legal term to maturity, they have an unpredictable actual loan life, because they have the prepayment “calls” implied in the contracts. The return on a mortgage is uncertain, because you might get repaid early, forcing you to reinvest your funds at a lower rate. On the other hand, the loans might just stay there until legal maturity, at an interest rate that is now below the market rate on a new investment. The problem, obviously, is that borrowers refinance most often when prevailing market rates have dropped (right when the investor might want the loans to be long-lived) and don’t refinance when prevailing rates have risen (right when the investor would like to see you go away). “Vanilla” bonds don’t behave this way. Vanilla bonds, like Treasury bonds and notes, are “positively convex.” Mortgages are “negatively convex.”

Here’s a comparative convexity graph prepared by Mark Adelman of Nomura (do pursue the link if you want more detailed information about MBS valuation). This graph plots three example instruments all with a face value of $1,000 and a price of par ($1,000) at 6.00%. The vertical axis reflects the change in price of the bond. The horizontal axis reflects the change in prevailing market yields. As you move to the left of 6.00%, you see that the price of the bond increases (it has an above-market yield); as you move to the right it decreases.



However, the three instruments do not increase or decrease in price in the same way. The 30-year bond has a steeper curve than the 10-year note, which is a function of the difference in maturities of the two instruments. The MBS isn’t just not as steep; it is a different shape. The 30-year bond and the 10-year note price functions create an upward-curving slope when you plot them against price/yield changes like this, and the MBS price functions create a downward-curving slope. The term “negative convexity” means, exactly, that downward curving slope.

What’s going on here is that when market yields fall (moving to the left in the graph), average loan life in an MBS pool will shorten markedly, as borrowers are “in the money” to refinance. At a relatively modest fall in market yields, the price of the MBS does increase (but the increase is much less than the increase in the other bonds). At a larger drop in market yields, the MBS price gets as high as it will ever get and then stops increasing at all. What happens here is that the underlying mortgage loans have become so “rate sensitive” that any additional decrease in market yield (increase in the spread between the bond’s coupon of 6.00% and current market coupons) is entirely offset by shortened loan life: loans will pay off so fast at this point that this “officially” 30-year bond really returns principal to the investor the way a 1-year or even 6-month Treasury bill would. No investor is going to pay more for the MBS at this point than it would for the very shortest-term alternative.

On the other side of the graph, you see that the MBS price declines more slowly than the vanilla bonds, although its curvature at this point is very like the 10-year. At this side of the chart, average loan life is increasing. (Mortgage bonds never go to zero prepayments or actual average loan life = 30 years.)

What all this implies is that, analytically, mortgages do have some sort of “option price” built in. (There is actually a name for this, the OAS or Option Adjusted Spread, a method of comparing cash flows of a mortgage bond across multiple interest rate and prepayment scenarios. It’s heavy math and modeling.) In the case of voluntary prepayment (refinancing or selling your home, basically), your “call” option has, in fact, been priced—it’s in the interest rate/fees you pay to get a refinanceable mortgage loan. Investors accept the uncertainty of mortgage duration by (attempting to) price it in.

All that, however, is about trying to price the full return of principal (which, in the case of a mortgage loan, is also the point at which interest payments cease). It isn’t trying to model the return of less than outstanding principal, which is what the “put” or ruthless default is. A refinancing borrower pays you back early at par. A defaulting borrower pays you back early at less than par. Standard MBS valuation models that were developed for GSE or Ginnie Mae securities (that are guaranteed against credit loss) do not “worry” about ruthless puts in terms of principal loss, since that loss is covered by the guarantor. What is causing some trouble these days with the “ruthless put” in the prepayment models is simply that this is an unexpected source of prepayment that isn’t correlating with “typical” interest rate scenarios. (We are seeing increased defaults in a very low-rate environment, because of the house price problem, which isn’t built into the prepayment models for guaranteed securities. Historically, prepayment models “expect” non-negligible numbers of ruthless puts only in higher-rate environments.)

It may help you to understand that we have been talking about how an investor might price an MBS coupon, which isn’t the same thing as the interest rate on a loan. In a Fannie Mae or Freddie Mac MBS, the “coupon” or interest rate paid to the investor might be, say, 6.00%. That means that the weighted average interest rate on the underlying loans in the pool is substantially more than 6.00%. There is the bit that has to go to the servicer, and there’s the bit that has to go to the GSE to offset the credit risk. The mortgages must pay a high enough rate of interest to provide 6.00% to the investor after the servicing and guarantee fees come off the top. In essence, then, MBS traders set the “current coupon” or the coupon that trades at par, the GSEs set the guarantee fee and/or loan-level settlement fees that cover the credit risk, the servicer sets the required servicing fee, and all that adds up to the “market rate” for conforming mortgage loans (plus mortgage insurance, if applicable, which is conceptually an offset to the guarantee fee).

One way of describing the situation we’re currently in is that borrowers are continuing the short loan life of the boom (which was made possible by easy refi money and hot RE markets) by substituting jingle mail for refinancing. That increases credit losses to whoever takes the credit loss (the GSEs and the mortgage insurers), decreases servicer cash flow (a refi substitutes a new fee-paying loan for the old loan; a default substitutes a no-fee-paying problem for the old loan), and makes everyone’s prepayment models go whacky-looking. This is one reason why it obviously wasn’t a good time for MBS traders to be told they’d be suddenly getting jumbos in their conforming pools; at some level the response to that could be summed up as “we don’t need one more thing that defies analysis.”



Ultimately, there is no way anyone can mobilize “social acceptability” as a defense against the ruthless put (even if you wanted to). The industry has, in fact, created the conditions in which it’s rational, and as long as it’s rational it will go on. Just as it was rational to buy at 100% LTV. The only possible way to get back to an environment in which ruthless default is rare is to abandon the “innovations” that give rise to them: no-down financing, wish-fulfillment appraisals, underpriced investment property loans, etc. The administration is currently pushing for increasing the FHA loan amounts and the FHA maximum LTV up to 100%. This is not likely to remove the incentive to take another reckless loan on a still-too-high-priced house. If we aren’t going to ration credit with tighter guidelines and loan limits, then it will have to be rationed with pricing: eventually the models will “solve” the problem by increasing the costs of mortgage credit. You cannot simply keep writing “free puts.”

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