Part 2-The New CMS Prepayment Model Framework: 
Analysis and Assumptions

Wesley Phoa, Ph.D.
President of Research

Prepayments, past and future
Prepayment modeling has traditionally been treated as a branch of econometrics. In this approach, prepayment speeds are taken as a dependent econometric variable, related to various independent variables such as Treasury yields via a set of response functions. Prepayment modeling then consists of specifying the mathematical form of these functions and estimating their parameters using statistical techniques applied to historical prepayment and market data.

In a dynamically evolving mortgage market, this approach is obviously flawed. If prepayments are influenced by factors which are not dynamically modeled, and not incorporated in the statistical estimation process, and if these factors change over time, then a model fitted to historical data will be unsuitable for predicting the future. Examples of such factors include fixed and variable costs of refinancing, convenience of refinancing, borrower attitudes towards refinancing, mortgage product innovation and marketing, and the underlying state of the housing market. These are all sources of model risk.

However, the econometric approach – perhaps more accurately referred to as the response function approach – has a number of strengths that should make one reluctant to abandon it. It is simple, it is robust, and it is familiar. CMS has therefore taken the following approach in developing its new prepayment model framework. First, we have retained the basic response function framework, but considerably enriched the way in which response functions are specified in order to make assumptions about the mortgage market completely explicit. Second, in determining parameters for the new model, we have incorporated forward-looking mortgage market research and judgments about future prepayment behavior as well as the results of a detailed analysis of historical prepayments.

More details about the model appear in the previous article; in the present article, we first present initial results from the new model, and we then explain the underlying prepayment assumptions currently used in the new model.

New model results
Exhibit 1 shows the results of the new prepayment model with the proposed BE 4.0g parameter set, as applied to a range of conventional and GNMA TBA mortgages. The first three columns compare new, old and empirical effective durations. Because of the volatility of empirical durations, a band is shown, representing varying estimates based on data drawn from the period 10/98–4/99. (Bands are omitted for coupons in the range 8%–9%, since it was extremely difficult to estimate meaningful empirical durations, with estimates frequently being negative.) Interestingly, broker estimates tend to be consistently longer than empirical durations.

The new model durations are noticeably shorter than those estimated by the current model, and more consistent with empirical durations, particularly for higher coupons. The next columns show the convexity and OAS of each TBA security, as estimated using the new model. These also seem reasonable, forming a consistent pattern.

The final two columns show the lifetime CPR estimated by the new model, compared to recent historical CPRs; for the latter, 3/99 and 4/99 speeds are shown. One would not expect future lifetime speeds to coincide with recent historical speeds, because of the influence of seasoning and burnout; however, it is reassuring that the predicted CPRs are consistent with recently observed trends.

Exhibit 1:  Analysis of TBA mortgages as of 4/30/1999

Model features
The new prepayment model framework allows for considerable subtlety in modeling prepayments. For example, different seasoning profiles can be specified for relocations, defaults and refinancings, and there are several different parameters which control interest rate responsiveness and burnout.

Note, however, that certain features have been implemented in the new model, but have not been activated in the initial parameter set. For example the new model allows for "cure", where the impact of burnout will gradually decline over time, and a "media effect", where burnout becomes less significant when mortgage rates decline to new lows. In the initial calibration process, it was discovered that satisfactory results could be obtained without enabling these features. However, as research progresses, it may be desirable to incorporate cure and media effect settings in future versions of the model parameters.

Users are also reminded that BondEdge version 4.1 will allow them to adjust CMS prepayment assumptions and to create new parameter sets corresponding to collateral types not currently modeled by CMS.

Analysis of historical prepayments
We now discuss some specific model assumptions in the context of historical prepayments. Exhibits 2, 3, and 4 compare observed historical CPRs for FHLMC 30-year pass-throughs, aggregated across pools, with the CPR vectors that would have been generated using the new model assumptions applied to historical data. In other words, they compare actual historical prepayments with predictions generated by feeding historical interest rates through the new model.

Note that one must be careful when interpreting these comparisons: if one believes that structural prepayment patterns have changed over time in such a way as to influence future prepayment behavior, the model must not fit the historical data, since this would imply that the model assumptions do not incorporate these structural changes. Or, to be more precise: the situations in which the model does or does not fit the historical data should correspond to the structural factors which, in the judgment of the prepayment analyst, have remained the same or have changed.

Prepayment data is notoriously noisy. In the graphs, a mild degree of exponential smoothing has been applied to the data to make the underlying trends more visible.

Relocations and seasoning profile
Exhibit 2 illustrates some basic assumptions about non interest rate sensitive prepayments. The level of relocations assumed for fully seasoned mortgages is consistent with that observed over the past couple of years. However, relocations are assumed to season somewhat more rapidly than the actual seasoning profile observed in 1994-95. This is because seasoning is partly a function of the strength of the economy, insofar as this influences both housing prices and real wages, and thus the ability to trade up.

Exhibit 2:  FHLMC30 5.5% 1993-relocations
and seasoning profile

Improving housing market and cash-out refis
Exhibit 3 illustrates some model assumptions about cash-out refis. Research suggests that these occur when (a) current mortgages rates are no higher than the rate currently being paid by the borrower, (b) property values have risen, creating borrower equity, and (c) borrowers have an incentive to release equity, e.g. because of high personal debt.

Model prepayment estimates for early 1996 are higher than those actually experienced. This is because the model calculations assume that, because of rising prices, LTVs are and will remain much lower than they were in 1996. For example, actual 1996 prepayments in California and New England were very slow because of the large number of underwater loans, whereas most of those same borrowers now have significant equity. Thus, if one "replayed" 1996, one would now expect much higher speeds.

Exhibit 3:  FHLMC 6.5% 1993 - improving housing market and cash-out refis

By contrast, model prepayments for 1998 and early 1999 are lower than those actually experienced. It is our assessment that the spurt in housing prices in 1998, combined with prevailing high personal debt ratios, caused the release of pent-up demand for equity release to fund debt consolidation or deferred expenditure. In other words, the surge in cash-out refis with no or negligible interest rate saving was partly a one-off effect: the future rate of equity release will decline, and borrowers will also increasingly make use of second mortgages to release equity as these become more efficiently priced and marketed. This is already suggested by the most recent prepayment data, as shown in Exhibit 1. However, this judgment is obviously subject to revision – which is a good reason to make it explicit.

Refinancings, burnout and efficiency
Exhibit 4 illustrates some assumptions about the propensity to refinance, and about burnout. There are two main observations. First, the model assumes a higher degree of interest rate sensitivity than that observed historically. This is because (a) borrowers are now better informed about refinancing opportunities, (b) refinancing itself has become a more convenient process, (c) costs of refinancing have fallen, and (d) with the advent of no point/no fee deals, refinancing no longer requires a cash injection.

Exhibit 4:  FHLMC 30 8% 1991- refinancings, burnout and efficiency

Second, actual prepayments in early 1996 were much lower than would have been predicted by the new model, with burnout being much more significant than the new model would suggest. This is again due to the different economic environment in early 1996 compared to today: many borrowers’ LTVs have dropped from over 100% to 80% or below, making refinancing newly feasible. Note that, unlike the case of cash-out refis, second mortgages do not provide an alternative to refinancing the first mortgage, because the motive for refinancing is the interest rate saving itself.

FHA mortgages
Recent prepayments on FHA mortgages have been more rapid and exhibited more interest rate sensitivity than data from the 1980s and early 1990s. Our GNMA prepayment assumptions were last revised in early 1998, but the continued strength in the job market, in real wages for lower income borrowers, and in prices at the lower end of the housing market suggest that some further adjustment is appropriate.

To summarize: baseline relocation rate assumptions have been increased to approximately 100% PSA (remember, this is exclusive of curtailments and defaults); the refinancing threshold has been set only ¼% wider than the threshold assumed for conventional mortgages; interest rate sensitivity beyond the threshold is about 80% that of conventional mortgages; and, importantly, burnout is now assumed to be less significant. All these changes reflect a general assumption that broad economic strength will continue, and will continue to be a positive influence on the prospects for lower income homeowners.

Seasoned mortgages and burnout
A subtle change has been made in the way burnout is modeled. The former procedure estimated the degree of burnout applicable to a pool by observing its actual factor. In the new model framework, burnout is instead a function of the estimated factor of a generic pool with the same characteristics. In other words, burnout now depends on the extent of past refinancing opportunities rather than refinancings experienced by a specific pool. This change seems justified by empirical data, and it also ensures more consistency between pools with similar characteristics but different factors.

Note that pool-specific adjustments to prepayment forecasts are still possible. Actually, the optimal approach to burnout modeling would be to make use of pool-specific data (on LTV profiles, etc.), but the relevant data is nearly always unavailable.

Implications for portfolio management
With the shift to the new prepayment model, and to updated prepayment assumptions as listed above, users will notice changes in mortgage durations and other risk measures. As noted earlier, results for seasoned and high coupon collateral will be noticeably more accurate. Both portfolio and index calculations will be affected. Clients whose portfolio composition differs significantly from that of the index may find that their estimated duration relative to the index has changed; if this is a potential concern, your consultant may be able to arrange test runs of the new model on your MBS portfolio in advance of the BE 4.0g release.

Return components computed by PART are prepayment model dependent. More specifically, the sector/quality effect for MBS makes use of generic OAS calculations, while the Treasury curve effect makes use of estimated effective durations. PART results will be stable as long as frequent, large adjustments to the model are avoided; and they will be meaningful as long as the assumptions made by the model are updated to reflect structural changes in prepayment behavior, so that the model remains realistic. As with portfolio analytics in general, the robustness of PART thus requires the implementation of a policy which provides for appropriate model revisions in response to such structural changes.

Future model revisions
As we emphasized at the beginning of this article, the mortgage market is continually changing. We have tried to recognize this in calibrating the model parameters, by making judgments about the future as well as analyzing the past. But it is inevitable that some of these judgments will need to be revised as time passes.

CMS has been conservative about making model revisions, recognizing that this causes potential disruption to clients. There is a trade-off between stability and consistency with recent data, and the best approach seems to be based on the following two principles: (a) only revise the model when recent short term data gives strong evidence about a change in long term behavior, corroborated by additional analysis of the mortgage market; and (b) ensure that clients are informed, well in advance, of what model changes will be made, why these changes are necessary, when these changes will occur, and what impact they will have on clients’ portfolio analytics.

As well as ongoing review of existing model assumptions, we are actively working on extending the model to new collateral types. Work has begun on modeling whole loan prepayments within the new framework – including both jumbo and alternative-A loans – and, to aid in future work, the model has been specifically designed to take account of atypical loan features such as prepayment penalties.