Watch that Prepayment Model Risk!

Teri Geske, vice president of product development at Capital Management Sciences, Inc., warns what can happen to your portfolio when your model's prepayment assumptions go awry.

Predicting human behavior is one of the toughest challenges around. Take mortgage pre-payment as a pretty arcane but good example. Whether or not a mortgage-holder chooses to refinance should be based on some clear, obvious financial criteria, such as interest rates, no? Well, no. It turns out that interest rates are only a small piece of the puzzle. Sometimes people just don't get around to refinancing when rates are favorable. Or a householder anticipating an upcoming sale and relocation might actually pre-pay the mortgage at an unfavorable rate. Even the seasons-and the weather-seem sometimes to have bizarre effects on mortgage pre-payment patterns.

Consequently, it is almost impossible to develop a model that accurately predicts mortage pre-payment. The best we can do is analyze data from the past-and simply hope that it be a guide to the future. Sometimes that hope is foolish. History is littered with cases where mortgage portfolios have gone underwater with a seemingly capricious change in pre-payment rates. Thus any sound valuation of a portfolio of mortgage-backed securities must take into account; 1) the model's prepayment assumptions; and 2) the portfolio's likely behavior should those assumptions turn out to be flawed.

This article will discuss pre-payment risk in the mortgage market, and how it factors into models. We shall also discuss a method for identifying portfolios' sensitivity to pre-payment uncertainty.

MBS 101

Most of us learned in Securities Analysis 101 that a bond's price is equal to the present value of its expected future cashflows. This is a straightforward exercise in discounting when bonds have no embedded options. However securities with call or put options require some type of option model to determine expected future cashflows under different interest rate environments. For corporate bonds with embedded call options, valuation models typically assume that a corporation will make a rational decision about whether or not to call-i.e., if interest rates fall and the bond's price rises above its call price, the company will call the issue.

Financial models typically assume that an investor will exercise an embedded put option only when it is optimal to do so, and will never put the bond back to the issuer at par if the bond's price is greater than 100. However, although mortgages by nature are optional, since the homeowner has the option to prepay, one cannot make the same assumptions about rational economic behavior. Homeowners will sometimes fail to exercise a call which is in-the-money, or exercise a put which is out-of-the-money.

When valuing mortgage-backed securities (both pass-through mortgage pools and CMOs), model designers face the problem of forecasting the amount and timing of prepayments in order to find the present value of expected future cashflows. They often handle the problem differently. Each of various mortgage research departments on Wall Street have their own prepayment models on the assumptions they find credible. The result is that there often is a huge difference in these firms' price quotes for a given CMO tranche.

Most models incorporate mounds of historic data about the average number of months to maturity and average loan rate of various mortgage pools which prepaid in the past, the time of year in which the prepayments occurred, and other variables. Therefore prepayment models implicitly expect homeowners to behave in the future as they have in the past-not necessarily a bad assumption, but not always an accurate one. Last December, for example, statistics showed an acceleration of prepayments, contrary to conventional wisdom which states that prepayments slow down in the winter and speed up in the summer.

The impact of revised prepayment expectations on the valuation of mortgage-backed securities constitutes an additional source of risk to investors which is not captured by standard valuation measures. Since the theoretical price that a model will compute for a mortgage-backed security depends heavily upon the prepayment model used to forecast future cashflows, an investor should be aware of how sensitive the valuation is to a change in the model's prepayment forecasts. Put differently, investors should ask themselves how the price would be affected if homeowners' current behavior turns out to differ from the data used to build the prepayment model.

Considering Prepayment Uncertainty

Prepayment uncertainty measures address these questions by gauging the sensitivity of a mortgage-backed security's price to a change in a model's prepayment estimates. Such measures operates on the assumption that risk analysis must go beyond interest rate risk measurement to other sources of risk which impact mortgage-backed securities. While prepayment uncertainty has been discussed in academia, and also by some Wall Street mortgage analysts, as yet there are few analytical tools of this type used by investors.

My firm, Capital Management Sciences(CMS) has developed a BondEdge system, in which prepayment uncertainty is defined as the sensitivity of a mortgage-backed security's price to a 10 percent change in the level of those prepayment speeds projected by a prepayment model. To calculate this measure, alternative sets of cashflows for the mortgage-backed security are created by shifting each standard monthly mortality rate generated by our prepayment model, either upward and downward by 10 percent. Based on the original option-adjusted spread that has been calculated for the security, two new prices are then computed using the slower and faster prepayment estimates.

The average percentage change in these prices, when compared to the starting price is our prepayment uncertainty measure. For example, if a prepayment model predicts that FNMA 8.00 percent moderately seasoned collateral will exhibit a weighted average remaining lifetime prepayment speed of 220 percent PSA, it is useful to know what would happen to the price of a CMO tranche backed by this collateral if prepayment estimates were revised downward or upward by 22 percent PSA. An overall prepayment uncertainty of +0.20 indicates that a security's price will increase (decrease) by 0.2 percent if all projected prepayment rates are revised downward (upward) by 10 percent.

In many situations, investors might be less concerned with the possibility of an overall change in prepayment patterns and more concerned at a change in homeowners' refinancing behavior. As homeowners become more savvy about refinancing opportunities and mortgage lenders become more aggressive in offering low-fee and no-fee loans, a mortgage-backed securities investor should want to know how sensitive the price of a CMO is to a change in the refinancing component of a prepayment model.

Our model also derives a partial prepayment uncertainty measure based on a +/- 10 percent scaling of the refinancing incentive component of each standard monthly mortality rate predicted by the prepayment model. The calculation is otherwise analogous to the overall prepayment uncertainty.

To complete the picture, we also compute a partial prepayment uncertainty measure (to address householders who will prepay in anticipation of a move) which quantifies the exposure to revisions of the projected baseline prepayment rate-the number which expresses the fact that regardless of the interest rate environment a certain number of mortgages will be prepaid each year.

Risky CMO Tranches

While almost all types of mortgage-backed securities have some degree of sensitivity to a change in prepayment estimates, the prepayment uncertainty measures for some risky CMO tranches can attain much higher positive and negative values than for straight pass-throughs. Alternatively, VADMs and well-structured PACs may exhibit much less prepayment uncertainty than pass-throughs of the same collateral type. The following table shows the prepayment uncertainty measures for different CMO tranche types:

The benefits

Prepayment uncertainty measures provide an additional dimension to investment analysis. They complement other measures such as effective duration and convexity, the primary measures of interest rate risk. Prepayment uncertainty can assist investors with trading decisions on a single security basis, since differences in prepayment uncertainty may explain why two securities with seemingly similar characteristics have different option adjusted spreads and offer different risk/return profiles. At the portfolio level prepayment uncertainty measures allow managers to manage exposure to the unavoidable uncertainty embedded in all prepayment models. So even if we can't predict the behavior of those consistently inconsistent householders, we can at least minimize exposure to their perplexing behavior.