## Saturday, March 17, 2007

### Tanta: Negative Amortization for UberNerds

by Calculated Risk on 3/17/2007 06:44:00 PM

Confusion about Option ARMs and other kinds of negative amortization keep coming up in the comments. If you really want to know how this stuff works, you should know up front that it’s a long story. If you’re not up for the long story, skip to the next post. I would never dream of holding it against you; the following is hard-core UberNerdism, and there’s nothing wrong with just being a normal reader of the blog. In fact, I envy you. Someday the rest of us will get help for our UberNerdism; until then . . .

With a regularly amortizing ARM, the rate adjusts on some schedule that is laid out in the original contract (the note). Take a 5/1: the rate adjusts after five years, and then every year thereafter. But because it is a regularly amortizing ARM, the payment adjusts after the rate adjusts, so that the payment is always enough to cover the interest due plus sufficient principal to retire the debt at maturity (that's the definition of "amortization"). With this loan, there are no "payment caps." There are "rate caps." This means some limitation on how high or low the rate can go at any given adjustment, or over the life of the loan. The lack of “payment caps” means that the payment must go as high (or low) as it needs to in order to satisfy the rate increase (decrease). If there’s “rate shock” in this loan, you feel it immediately, because you immediately begin making payments at the “shocking” interest rate.

Negative amortization loans can work by calculating two "rates": the actual accrual rate (the real interest charged) and the payment rate (a kind of "artificial rate" used to set the minimum payment). The payment rate might also be an “introductory rate.” Here’s an example of a neg am variant on the old 5/1 ARM. (Important: this is just an example. There are jillions of unique neg am ARMs out there, and the Option ARM is even more complicated than the following. Do not assume that the following example is how they all work in exact terms; it’s just how they work in overall concept.)

In our example loan, the introductory accrual rate is 1.95% for three months. This means that the first three payments are based on an actual rate of 1.95%, and so for three months the loan amortizes (the payment due is equal to the payment required to satisfy all interest and a portion of principal.) Let’s assume a loan with an original balance of \$90,000 used to purchase a property with a sales price of \$100,000. For the first three payments, you get this:

 # Beginning Balance PMT Rate Minimum PMT Accrual Rate Accrued Interest Scheduled principal Short- fall Ending Balance Original Prop Value LTV 1 90,000.00 1.95% (\$330.41) 1.95% (\$146.25) (\$184.16) 0.00 89,815.84 100.000.00 0.9000 2 89,815.84 1.95% (\$330.41) 1.95% (\$145.95) (\$184.46) 0.00 89,631.38 100,000.00 0.8982 3 89,631.38 1.95% (\$330.41) 1.95% (\$145.65) (\$184.76) 0.00 89,446.62 100.000.00 0.8963

After three months, the accrual rate changes to 6.50% for the remaining 57 months of the initial 5-year period. However, the minimum payment remains fixed for the remaining 57 months.* What this means is that the minimum payment required is calculated at a lower rate than the actual accrual, and so if the borrower makes the minimum payment, the loan negatively amortizes, meaning that the difference between interest accrued at 6.50% but paid at 1.95% is added to the loan balance. The borrower is not forced to make the minimum payment, although of course we’re seeing people take these loans precisely because they can’t afford the amortizing payment. You can see right here that the borrower already got “rate-shocked” in real terms, going from 1.95% to 6.50%. The borrower just doesn’t feel rate-shocked, because by making the minimum payment, the borrower is in essence borrowing enough money each month to subsidize the debt service.

Here’s what the loan looks like (condensed) for the remaining 57 months. I have broken out the “fully amortizing” payment at the accrual rate into its principal and interest components; the required payment from the borrower to actually amortize the loan (satisfy all interest due plus retire some principal) would be the total of the two. If the loan were an Option ARM with the choice of making an interest only payment rather than a fully-amortizing or negatively-amortizing (minimum) payment, the required IO payment would be the portion shown below as “accrued interest.” This chart shows the “shortfall” as the total difference between the amortizing payment and the minimum payment; the ending balance, however, is equal to the beginning balance less the difference between “accrued interest” and “minimum payment” (because “scheduled principal reduction” does not happen with a minimum payment). An alternative way to calculate that is to subtract the scheduled principal from the beginning balance, then add back the entire shortfall (not just the interest shortfall) to get the ending balance. (You may wish to have a drink before continuing.)

 # Beginning Balance PMT Rate Minimum PMT Accrual Rate Accrued Interest Scheduled principal Short- fall Ending Balance Original Prop Value LTV 4 90,000.00 1.95% (\$330.41) 6.50% (\$484.50) (\$82.41) (236.50) 89,600.71 100.000.00 0.8945 5 89,600.71 1.95% (\$330.41) 6.50% (\$485.34) (\$83.07) (238.00) 89,755.63 100,000.00 0.8960 6 89,755.63 1.95% (\$330.41) 6.50% (\$486.18) (\$83.74) (239.51) 89,911.40 100.000.00 0.8976 ... 56 98,673.00 1.95% (\$330.41) 6.50% (\$534.48) (\$127.42) (331.49) 98,877.07 100.000.00 0.9867 57 98,877.07 1.95% (\$330.41) 6.50% (\$535.58) (\$128.54) (333.71) 99,082.24 100,000.00 0.9888 58 99,082.24 1.95% (\$330.41) 6.50% (\$536.70) (\$129.67) (335.96) 99,288.52 100.000.00 0.9908 59 99,288,52 1.95% (\$330.41) 6.50% (\$537.81) (\$130.82) (338.22) 99,495.92 100,000.00 0.9929 60 99,495.92 1.95% (\$330.41) 6.50% (\$538.94) (\$131.98) (340.50) 99,704.45 100.000.00 0.9950

You notice here that the ending balance of the loan after 60 payments is \$99,704.45, or just over 110% of its original balance. This will become important below. Also notice that the LTV here is based on a constant original appraised value. You can make any changes you want to that original value and get a better or worse looking current LTV. But the contractual limitations on a neg am loan have to do with the relationship of current balance to original balance, not LTV. In the real world, of course, a borrower who is negatively amortizing at the same time that the appraised value of the property is dropping is getting much further underwater than this example indicates; I’m just trying to show effect on LTV if value stays constant.

After 60 months, the accrual rate adjusts to the formula of index plus margin, just like any other 5/1 ARM. However, the required payment after the first adjustment (at 60 months) is capped at 7.50% of the prior payment. If the adjustment to the new accrual rate would require a new payment greater than 107.5% of the old payment in order to fully amortize the loan, and the borrower makes the minimum payment instead, the loan negatively amortizes. The 7.50% payment cap is different from the rate cap. On a 5/1 ARM, the rate cap could be 5.00% at the first adjustment and 2.00% at each subsequent adjustment. What that means is that the rate will not increase more than five points at the first adjustment or more than two points at subsequent adjustments. If the initial accrual rate is 6.50%, at the first adjustment the rate will never be higher than 11.50% (6.50% plus five points). The payment cap, on the other hand, is a percent limitation, not points. In other words, to calculate the new minimum payment, you take the old payment and multiply by 1.075.

Using our example above, and assuming that the accrual rate increases only by 2.00% to 8.50%, the new fully amortizing payment is \$802.85 (\$706.24 interest plus \$96.61 principal). However, the payment cap of 7.50% would limit the new minimum payment to \$355.19 (\$330.41 times 1.075%). On this example loan, that won’t actually happen, though. Keep reading; it just gets more complicated.

At each point, the amortizing payment is calculated on the actual loan balance outstanding. This is how neg am becomes turbo-charged ugly: if you make only the minimum payment each month, the difference between accrued and paid interest is added to your balance. Therefore, next month, your accrued interest is charged on a higher balance than last month—you are paying interest on interest. So neg am becomes “exponential” instead of “arithmetical.” It’s the reverse of compounding interest in a savings account.

So, in order to keep this exponential growth of the loan balance under control, the neg am ARM has “recast” mechanisms. These are separate from rate and payment caps and adjustments. One of the big problems with understanding all this is that too many people (including our fine media) use the terms “reset” and “recast” as if they were synonyms. You’ll never understand a neg am ARM if you do that. What we went through above was “resets” of the rate and payment. What we’re about to go through now is “recast.”

To understand recast, think of it as a process that is concurrent with but not on the same schedule as the reset process. Resets (adjustments to rates and therefore required and minimum payments) happen according to the pre-arranged terms laid out in the original note (such as every year after the first five years). But, contractually, the borrower is not required to negatively amortize; one can make the full payment, not just the minimum payment. (On an Option ARM, one can also make a full interest only payment; that doesn’t lower the balance, but it doesn’t increase it because all interest due is paid for the month.) One can also make occasional curtailments (lump sum payments of principal that don’t pay off the loan in full but that reduce its balance substantially). So for any given neg am loan, you can’t know ahead of time whether and at what point and how fast it will negatively amortize. By “how fast,” we are also referring to the magnitude of the interest rate adjustments. With any ARM, you cannot know in advance how much the rate might change at the first adjustment or any subsequent adjustment, because the new rate is determined by the formula margin (constant, spelled out in the note) plus index value (variable; the index chosen is in the note, but the actual value of it in the future is unknown). The higher the future accrual rate increases, the faster the loan will (potentially) negatively amortize.

So the “recast” provisions are a separate process of monitoring and forcing the restructure of the loan, over time, to make sure that any negative amortization doesn’t get too far out of hand. Recast provisions can be as complicated as resets, but here’s a common setup:

First, there is a provision to reamortize the loan every 60 months. What this means is that every five years, the servicer has to recalculate the minimum payment by ignoring those 7.50% payment caps. This may or may not produce huge payment shock to the borrower; it will depend on how significant the rate resets were in the preceding 60-month period, or, for the very first recast, how deep the discount was between the accrual rate (6.50% in our example) and the payment rate (1.95%). Remember that it is possible at any rate change date that the rate adjustment was small enough that the new required payment was less than 1.075% of the old payment. It is of course possible that it wasn’t, and this can hurt. In any case, this 60-month recast brings the minimum payment up to fully amortizing, but it doesn’t cancel out the regular rate and payment resets that can happen in the next five years as outlined above. So, with an ARM with annual accrual rate adjustments, the 60-month rolling recast keeps the loan amortizing for the following year; after that, neg am could start happening again (until the next 60-month recast). Think of it as a way of “catching the borrower up” every five years, but allowing them to start “getting behind again” eventually. So that is one reason why our example loan above is not going to get a new payment of \$335.19, even though that’s what it would be just using the 7.50% increase limitation. The issue is that the first rate adjustment date happens to coincide with the first 60-month recast date. If the example loan didn’t have an initial fixed period of five years—say it was a 3/1 type structure—then the 7.50% payment cap might have come into play after 36 or 48 payments. (Have another drink; we’re not done yet.)

Second, there is a provision to force the loan to amortize whenever the balance hits 110% of the original balance. This is not “scheduled” like the 60-month rolling recast above; it is triggered only for a given loan if and when it has hit the 110% mark, and thus will not necessarily happen on a rate or payment change date; for some loans, it might never happen at all, if the borrower only occasionally makes the minimum payment, or makes a periodic curtailment that brings the balance down. If it does happen, the loan must become a fully amortizing loan—no more minimum payment allowed, all payments must be sufficient to pay all interest due and sufficient principal to amortize the loan over the remaining term. The percent of original balance limitation, in other words, marks the day that neg am is no longer an option for the borrower, and the loan has to start paying down principal from here on out—the borrower is “caught up,” and never again allowed to “get behind.” In our example above, the loan hit the 110% limit after the application of payment 57. So even though this loan was not scheduled for a rate increase or rolling recast until month 60, the servicer would have sent notice to the borrower that as of payment 58, the required payment is the fully-amortizing payment. Note that the loan remains an ARM, even though it is now no longer a neg am ARM. That means that the borrower’s payment can still increase or decrease at future rate change dates. It will simply be, from here on out, an increase or decrease from one fully-amortizing payment to a new fully-amortizing payment.

Neg am ARMs are structured such that the minimum payment will always satisfy at least some interest due. This is true because with a neg am loan, like any mortgage loan, payments are applied to interest before principal. I have noticed that this confuses a lot of people, undoubtedly because we all tend to think in terms of “regular” amortization, which assumes that some portion of a loan payment always goes to principal, and so people imagine that the “principal portion” of the scheduled payment could be larger than the minimum payment, which would result in no cash interest paid in a month. That cannot, however, happen. It doesn’t matter what the “scheduled principal” part of a payment might be; if the borrower’s minimum payment isn’t enough to satisfy both scheduled principal and accrued interest, the payment is applied to the interest, the unpaid interest amount is added to the balance, and no “scheduled” principal reduction occurs. (Compare that to an interest only loan, where the full interest amount is paid by the borrower in cash, but no principal, so the loan balance neither increases nor decreases.) To a borrower in hock, that’s probably a distinction without a difference, but for accounting and regulatory purposes, it’s important (see below under “noncash income” to the lender).