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The following article is reprinted from the January, 1998 issue
of On the Edge, the Interactive Data Fixed Income Analytics bimonthly newsletter.

Prepayment Uncertainty-Prepayment Model Risk

Teri Geske
Senior Vice President, Product Development


Prepayment modeling is a critical component of mortgage-backed security valuation, portfolio analysis and risk management. A prepayment model is typically developed using empirical data of homeowners’ mortgage prepayment patterns over time; the goal of the model is to predict future behavior on the basis of this historical data. For a variety of reasons, no two prepayment models will produce the same prepayment forecast, even with the same information about the interest rate environment and the mortgage collateral pools pertaining to the securities of interest. For example, different models are calibrated to different historical data sets - some may use five, seven or even ten years of data, others may use data from only the past three years; some models attach greater weight to more recent data, others attach equal weight to all time periods; the variables used to explain and forecast prepayment behavior differ across models, and so on. Therefore, differences in prepayment modeling across well-respected and capable providers is to be
expected1.

In addition to differences in the way models are calibrated and specified, there is some likelihood that the historical data used to fit the model no longer reflects current prepayment behavior. For example, over the past few years mortgage lenders became more aggressive in offering low-cost or no-cost refinancing. As a result, a smaller decline in interest rates is now sufficient to entice homeowners to refinance their mortgages compared to five years ago. Further developments in the marketplace (e.g. internet-based mortgage lending, the impact on relocations of Gen-X’ers displacing Baby Boomers, etc.) will undoubtedly affect future prepayment patterns in ways that the historical data used to fit today’s prepayment models does not reflect.

Since modeling future prepayment behavior is an inexact science, any analysis is subject to some error due to mis-estimates of future prepayments used in valuing mortgage-backed and asset-backed securities. We can quantify this risk by computing a Prepayment Uncertainty measure that describes the sensitivity of an asset’s price to a change in the level of prepayments predicted by a model. (Rather than describing this as a modeling “error”, we can think of it as measuring the sensitivity to a change in a modeling parameter that is impossible to measure precisely). To derive this Prepayment Uncertainty measure, we first decrease, then increase the predicted prepayment speeds generated by the model by 10%, and derive a new price under the slower and faster versions of the model (holding the security’s option-adjusted spread constant). Computed this way, mortgage-backed securities priced below par show a negative Prepayment Uncertainty. This makes intuitive sense, as a slowdown in prepayment speeds means the investor must wait longer to be repaid at par. Conversely, mortgage-backed securities priced above par show a positive Prepayment Uncertainty, because a decline in prepayment speeds allows the investor to receive the above-market coupon rate on the mortgage for a longer period of time than originally forecast.

The Overall Prepayment Uncertainty measure is the percentage price change that would occur if actual prepayments deviated from the prepayment model’s forecast by 10%. Although the values appear to be small in many cases, we should keep in mind that prepayment estimates from Wall Street firms often differ from each other by much more than 10%. Therefore, even a 20% change in prepayment speeds (e.g. from 6% per year to 7.2% per year) would not be unreasonable to contemplate, which would be equivalent to doubling the Prepayment Uncertainty values. The following graph shows Prepayment Uncertainty for mortgage pass-throughs; CMOs with complicated deal structures can display extremely large Prepayment Uncertainty values, two or three times larger than the Prepayment Uncertainty of the underlying collateral.

The magnitude of the Overall Prepayment Uncertainty is related to the WAC (weighted average coupon), time to maturity (loan age) and current price of the collateral. The absolute value of the Prepayment Uncertainty increases as the price moves away from par; premium mortgages tend to display the largest positive Prepayment Uncertainty. This means that a slowdown in prepayments compared to the model’s predicted prepayment pattern would cause the largest percentage change in the price of mortgages with high weighted average coupons (WACs). While a risk analysis typically focuses on price sensitivity to changes interest rates (i.e. duration and convexity), some high coupon mortgages have Prepayment Uncertainty measures which are more than half the size of their effective durations. In essence, this means that a 10% mis-estimate in prepayment modeling can produce as much (or more) of a change in price as a 50bp shift in interest rates. It is interesting to note that in general, the magnitude of a mortgage pass-through’s Prepayment Uncertainty is negatively correlated with its effective; therefore, although the interest rate risk associated with your mortgage holdings may be relatively low (as measured by duration), the prepayment uncertainty may be fairly high.

One of the most important variables in a prepayment model is the assumed level of financial incentive homeowners require to refinance their mortgages when interest rates drop. The minimum incentive required to trigger a wave of refinancings has certainly dropped over the past decade; in the early days of prepayment modeling, it was not unusual to assume that new mortgage rates had to be 150 or 200 bps lower than a homeowner’s mortgage rate before refinancings would occur. Today, a prepayment model may assume that a 75bp incentive is sufficient to entice a certain percentage of homeowners in a pool to refinance their mortgages. Therefore, we may wish to examine how sensitive our valuation is to a mis-estimate in the minimum refinancing incentive the prepayment model assumes.

To do so, we dissect the overall Prepayment Uncertainty measure into two components: Refinancing Uncertainty and Relocation Uncertainty. The “Refi” measure describes the sensitivity of a valuation to changes in the aforementioned refinancing incentive, and the “Relo” measure shows the sensitivity to a change in the level of prepayments that occur independent of the level of interest rates (i.e., due to demographic factors such as a change in job status or location, growing family, divorce, retirement, etc.).

As one would expect, the “Refinancing” component of the Prepayment Uncertainty measure is largest for collateral pools with high WACs. If homeowners with above-market mortgage rates begin to refinance at a faster rate than a prepayment model predicts, investors who purchase high WAC pools face the greatest risk. The “Relocation” component is negative for discount collateral; if the level of housing turnover declines below the model’s predicted amount, investors in discount mortgages must wait longer to be repaid. Therefore, prices of discount mortgages would decline. The opposite is true for premiums, where a lower rate of turnover would allow the investor to collect the high mortgage coupon for a longer period of time. The absolute magnitude of the Refinancing Uncertainty measure tends to be larger than the Relocation Uncertainty number (except for deep discount collateral). This is a reminder that the projected cashflows for a mortgage-backed security can be highly sensitive to the refinancing incentive component of a prepayment model.

In BondEdge, we compute Prepayment Uncertainty at the individual security level (in Security Valuation) and at the portfolio level (under the Portfolio Simulation menu). The Prepayment Uncertainty measure can be used to assess relative value across investment alternatives (for example, a higher OAS may be justified if a security has a greater amount of prepayment uncertainty), and should be measured at the portfolio level, as there is a diversification effect in prepayment uncertainty by holding discount and premium collateral. We hope this discussion of Prepayment Uncertainty has been useful, and we welcome your comments.

1For a discussion of how one can assess the accuracy of a prepayment model, see the Interactive Data Fixed Income Analytics research paper titled “Evaluating a Fixed Rate Prepayment Model” by Wesley K. Phoa, Ph.D. and Terrence Nercessian.