Welcome to The S-Curve
Now you will be able to receive the latest announcements, product updates, and our insights on the mortgage market in real time.
The name of the blog, the S-Curve, is a reflection of our logo and the central feature of our prepayment model. S-curves are seen in nature in many phenomenon, from population growth to prepayment and default models. Our first S-curve, in the early 1990s, used the arctangent function, then piece-wise linear functions, and evolved over time to be more complex and vary by FICO, loan size and LTV. This evolution encapsulates both the timeless nature of fundamental relationships and constant innovation to describe them better over time.
We hope you find the information useful and we look forward to your feedback.
-
Drivers of Discount PrepaymentsThoughts
As interest rates rise and fewer loans with refinancing incentive remain, other factors are primed to play a larger role in determining prepayment speeds in the coming months (and perhaps years). Turnover, the rate at which people move, is the most cited of these factors. In this blog post, we’ll consider two other potential drivers: curtailments, or partial prepayments, and mortgage payoffs that don’t involve taking out a new loan.
The charts below the rates of curtailment and payoffs in a sample of Fannie Mae loan level data[1].

Curtailments involve borrowers making additional payments beyond their amortization schedule yet short of paying off the full amount, i.e., people making an extra payment each month. In the charts we can see the rate rising slightly over time (which is mainly attributed to age; this data only has loans originated after Jan 1999, so the earlier months are limited to younger loans) and settling into a rate around 1.5-2.5 CPR. However, there was also a bit of a jump during the pandemic, which can perhaps be attributed to borrowers having extra cash from stimulus payments.

Full payoffs involve paying off a mortgage completely without moving or taking out a new mortgage, which tend to occur if borrowers find themselves with enough cash to cover the outstanding balance. While this can’t be known with 100% certainty, we’ve estimated the rate by looking at payoffs with a remaining term of 36 months of less. These are unlikely to be refinances and while we can’t rule out the possibility of the borrowers moving, we observe payoff rates loans with short remaining terms to be dramatically above the baseline turnover level. In essence, this chart shows the percentage of loans with short remaining terms (low) multiplied by their payoff rate (high) to get the overall contribution to CPR. Like curtailment, the data takes a while to ramp up, but then settles into 1-3 CPR range.
Both series represent a small percentage of prepayments in normal environments, but a greater percentage of the overall level in a world without refinancing. While it’s not a given that these numbers will remain constant in the face of rising rates, it is likely that these factors won’t have quite the same sensitivity to rates as refinancing (this study found payoffs to be relatively flat at negative incentive[1]). If rates stay high, it may be useful to keep these factors in mind moving forward.
[1] https://www.philadelphiafed.org/-/media/frbp/assets/working-papers/2019/wp19-39.pdf
[1] https://capitalmarkets.fanniemae.com/credit-risk-transfer/single-family-credit-risk-transfer/fannie-mae-single-family-loan-performance-data
-
Ability-To-Repay Benchmark UpdateThoughts
Summary
In 2021, Andrew Davidson & Co. Inc. (AD&Co) proposed a benchmark cohort approach to setting Ability-to-Repay (ATR) Qualified Mortgages (QM) standards. Successful benchmarks based on data are model-free and transparent, and the cohorts must perform consistently in comparison to one another and across time. Our original work used data through the early stages of the pandemic when non-performing loan percentages skyrocketed. This update shows that the cohorts continue to perform consistently.
To review; the metric is 60+ DQ (delinquency) rates at 24 months old for loans guaranteed by GSEs, FHA, VA, and non-QM securitizations. We update performance through late 2021 or early 2022 depending on the data source. The update turned out to be six to nine months past the peak non- performance rates (60+ DQ + Forbearance) of the pandemic. One of the best tests of reliability are cohorts that perform consistently at significant turning points. We show two different examples of cohort performance which all pass with flying colors.
Figure 1 extends the original time-series delinquency graph by cohort across combined federal segments (GSE, FHA, VA) and shows consistent performance through the two sharp turning points in delinquencies from the lows before the pandemic and the peak thereafter.
Figure 1. Delinquency Rates by Cohort

Figure 2 extends the time-series graph that compares the ‘FHA Average’ cohort for each of the three federal segments, GSE, VA, FHA, and non-QM. The ‘FHA Average’ cohort is roughly 95 LTV, 680 FICO, 40 DTI for government lending, and about 90 LTV, 680 FICO for non-QM. The results continue to illustrate that the benchmark cohorts perform consistently across market segments.
Figure 2. Delinquency Rates for ‘FHA Average’

Conclusion
The pandemic and the federal response to it are unprecedented in modern times for their impact on the US economy and housing market. Nevertheless, mortgage cohorts performed consistently over the last several years across federal and non-QM segments, increasing confidence in this approach. This stability contrasts with the vastly higher non-performance rates of the subprime and reduced documentation era that resulted from poor lending practices, as we reported in the original study.
This highlights that conscientiously measuring income is essential to consistency.
-
How Lowering Capital Costs Affects Higher Risk LoansThoughtsHow Lowering Capital Costs Affects Higher-Risk Loans
Government-sponsored enterprises (or GSEs) are companies that provide guarantees and financing to originators through the mortgage secondary market. The size and resilience of the GSE secondary market maximizes diversification and liquidity which reduces financial risk and cost of capital. This benefit accrues to conforming borrowers through lower mortgage rates and resiliently available financing.
Capital Safe Investments
One hundred years of the stock price performance of public utilities shows higher dividends, combined with lower returns and capital costs than an index of large companies. Theory indeed predicts that companies in protected markets would have lower income volatility that translates into lower stock price volatility and lower required returns.
This can be seen empirically by comparing two ETFs (exchange traded funds), XLU, the largest and oldest utility ETF, launched in 1998, versus SPY, the S&P 500 index. Since inception, XLU’s price return is about 130% (compared to SPY’s 280%), and its 10-year annualized return is 11% (compared to SPY’s 16%). However XLU pays a persistently higher dividend yield of 2.9% compared to 1.2% for SPY, and shows lower price volatility with a beta of 60%, compared to SPY’s beta of 100%. This is evidence that protected markets are safer havens to beat inflation with lower risk. Firms generally price to a 12%-15% return on equity, while regulated utilities generally price to 5-10% ROE. Even though ETFs are not individual companies, XLU and SPY’s performance have implications about GSE capital cost, which is the largest component of guarantee fees.
The Benefits of Lowering GSE Capital Costs
Fannie Mae and Freddie Mac (the GSEs) charge guarantee fees to compensate for the risk of guaranteeing and securitizing mortgages. These fees are included in the mortgage rate. The GSE guarantee conveys the lowest possible rate on mortgage backed securities through to borrowers. Lowering guarantee fees on higher-risk loans would lower mortgage rates and cumulatively, could save borrowers up to $3,000.
For example, for a $300,000 mortgage at 4%, the monthly P&I payment would be $1432. However, lowering the guarantee fee (and the mortgage rate) by 25 basis points lowers the payment $43 per month. This saves borrowers more than $3000 over seven years.
Lowering GSE capital costs to 6%-8% from 12%, could reduce guarantee fees by 25 bps for loans that require more capital without sacrificing financial resiliency. These borrowers are more likely to be lower-income, first-time homeowners or minority households. So, allowing the GSEs to retain federal backing as regulated utilities, and thus recognizing that GSE capital costs are lower than for fully private firms, can lower mortgage rates for higher risk loans which are more likely to be underserved populations.
Making Homeownership More Accessible to Lower-Income Families and Underserved Groups
Homeownership is the largest source of inter-generational wealth for working- and middle-class families, and the gateway is access to a mortgage. Especially for those whose access to homeownership has historically been hindered, financial security is enhanced by affordable credit. This regulated utility framework shows that the right public-private combination can focus enduring benefits on underserved communities to help build credit and long-term financial stability. National standards and lower mortgage rates help avoid predatory lending and never-ending debt — so that these households have a better chance to thrive in the financial marketplace.
Building wealth in underserved communities can begin by boosting individual wealth and lead to more local commercial activity. This can start the flywheel of positive economic community feedback that middle class and white neighborhoods are accustomed to.
As the largest mortgage financing provider, the GSEs have repeatedly shown resilient presence in the market in sharp contrast to mortgage segments that are not federally backed. They now operate more like regulated utilities and intermediate most risk into the public capital markets with an effective regulator setting standards for capital, credit and returns. The final component is to recognize their lower cost of capital and thus allow guarantee fees and mortgage rates to reduce accordingly.
-
On the Road Away from LIBORProductsThe release of Andrew Davidson & Co., Inc.’s (AD&Co) new generation of financial engineering tools marks a shift to a new reality; when the traditional benchmark for MBS valuation, the LIBOR/ Swap yield curve, becomes unavailable. Our recent Product Release email informed our readers about the change. In short, our users can:
- Conduct valuation relative to one of three benchmark rate curves: Treasury, LIBOR or SOFR.
- Provide either an absolute rate volatility matrix or the traditional relative volatility matrix.
- Apply a negative shift (floor) to otherwise positive-rate models (Squared Gaussian or Black-Karasinski).
The 3-benchmark valuation option provides analytical flexibility within the transitional period of LIBOR availability and well beyond; hence, this is both a "transitional" and "permanent" solution. Regardless of the benchmark chosen, SOFR-indexed ARMs and CMO/CRT floaters will use a SOFR term structure of rates (if provided) for the index projection. If a SOFR term structure isn’t provided, we will project SOFR indices off the chosen benchmark plus the initial spread.
The absolute volatility quotation has grown as a popular format. It represents the best practical choice when a valuation benchmark (e.g. Treasury) is different from a volatility source (e.g. options of SOFR swaps).
Which yield-curve benchmark should practitioners use for valuation? About 30-40 years ago, MBS were priced off Treasury bonds, a close investment alternative. However, Treasury rates have never been borrowing rates; this honor belonged to the LIBOR market. A pricing spread to a borrowing curve can be easily translated into return on equity (given the leverage) and, unsurprisingly, the LIBOR/Swap curve became the dominant benchmark.
With the upcoming demise of LIBOR, the current market trend suggests a return to Treasuries. Most dealers now report exclusively Treasury OAS on TBAs. The Security Finance Association (SFA) established a task force that recommended one of the Treasury-based spreads. The so-called I-curve (interpolated-WAL curve) was voted the best quotation option according to the SFA by “a supermajority of investors, traders and syndicate desks…across all structured finance products” whereas “issuers and bankers are split on the benchmark they favor with a slight majority preferring a Treasury-based curve over the SOFR swap curve.” To reiterate, our tools are ready for a change in prevailing practice.
What about the preferred source of volatility? With the Treasury curve returning to the benchmark role, which market volatility would we recommend of using? The only Treasury-related options – options on Treasury futures – represent a thin layer of information, which, at best can be interpreted as volatility on long bonds. While they may help decipher the value of the embedded prepayment option, they are less relevant to caps and floors found in CMO/CRT floaters and ARMs. It is also impossible to calibrate the mean reversion parameter of a term structure model without observing volatility quotes on differing tenors.
Our recommendation, which may be unexpected at a first glance, is to consider options on SOFR-based swaps that have developed in a way similar to LIBOR-based swaps. Since Treasury rates differ from SOFR-swap rates, we recommend using absolute (aka “normal”), rather than traditional relative (aka “lognormal” or Black), volatility inputs. Essentially, we posit that, given a tenor, various US rate benchmarks tend to exhibit similar volatilities. Our review of the SOFR/Swap volatility and LIBOR/Swap volatility confirms this assumption – despite the difference in rate’s levels.
Are we changing the Current-Coupon Yield (CCY) model? The existing CCY model is a linear regression calibrated to a multi-year historical movements against the 2-year and the 10-year points of either Treasury or swap rates. The SOFR term rates are relatively short in history and at the point of writing, there is no immediate reason to change the model’s coefficients when the SOFR curve is chosen as a benchmark. Going forward, this statement merits a review; the entire approach to projecting CCY from benchmark rates may also need to be reassessed.
Are we changing the LoanDynamics Model (LDM) at all? Borrower behavior for SOFR-indexed ARMs is likely to be unaffected by the index’s name, as long as we control for the current and projected loan rate. At this time, we have no history of SOFR-ARM prepayments or defaults that warrants any revisions of LDM.
-
Insights on Updating GSE Credit Score PolicyThoughtsFHFA held a listening session for interested parties on its proposed rule on the GSE process for credit scores. The objective is making mortgage underwriting and pricing more accurate and more fair while balancing practical implementation by firms in the mortgage ecosystem. Along with many others, I had the opportunity to provide insights on this proposed rulemaking.
Insights
-
The mortgage credit score market is better served by 2 providers rather than 1, or 10. Other consumer credit markets have had two major providers for years and the main reason only one score is used for mortgages is regulatory restriction. Why two? The credit score market has core characteristics of a regulated utility. Providers are commercial enterprises that have barriers to entry and large externalities; negative if run poorly, positive if run well, and large information asymmetries. Their mission is profitable but not profit maximizing. Two regulated actors provide innovation and service to market while limiting confusion or destructive competition.
-
Credit providers set the rules for which score, not the credit requesters. There is concern that with a choice of credit scores, originators will pick off the GSEs. This is a false concern since FNMA (soon FRE) hasn’t used credit scores for years. As a major investor in credit risk, FNMA uses core consumer data and doesn’t rely on third party metrics. Estimates are that a dual score model could cost $500 M over three years. Since several thousand originators in other markets already use two scores this seems unlikely. Even if true, this amounts to 1 basis point on mortgage origination volume over this time.
-
Important consumer data is not included in classic credit scores today, and some may never be because they’re not credit data, such as Trended Data, Telecom Utility data, and rental data. Regulators should ensure that all card companies report Trended Data. Even if it’s possible to combine into one score, it may not benefit consumers to have an even broader opaque metric of their financial lives controlled by private companies.
-
It’s likely that expanding consumer financial data in mortgage underwriting and pricing will benefit first-time buyers and under-banked populations that have been historically discriminated. Since digital availability is widespread, transition expenses should not be a reason to avoid improving lending fairness.
-
The data necessary to build a quantitative bridge from old scores based on limited data to new scores based on expanded data should eventually be generally available so the broader market can make their own risk decisions as well as the GSEs (MIs, servicers, investors, researchers, etc.).
It’s clear that important consumer credit data is available outside classic credit scores and that perhaps should not be embedded into single consumer credit metrics. This extra data is quite likely to benefit first time homebuyers and underserved populations. Finally, it’s quite likely that this highly regulated, private market will provide larger benefits to consumers with two actors rather than one, or ten.
-
The S-Curve Archives
-
EventsSeveral AD&Co employees attended SFVegas 2025. This post shares their unique perspectives from attending the conference and key takeaways from the sessions.
-
ThoughtsWe’re excited to announce our latest Quantitative Perspectives providing in-depth insights into current market trends and advanced valuation techniques. This publication offers valuable information for mortgage market participants and those involved in credit risk transfer transactions.
-
PodcastTune in to Laura Silberg's interview with Andrew Davidson, Eknath Belbase and Alex Levin as they discuss their latest Quantitative Perspectives, our independent commentary series, titled
-
ThoughtsAs providers of mortgage models for financial institutions, Andrew Davidson & Co., Inc. (AD&Co) enables clients to validate their use of our models and offers documentation describing the conceptual framework of the models, back-testing results, and sample forecasts under a variety of economic conditions. We also work with analytics providers who have incorporated our models to ensure that the models works as intended.
-
ThoughtsWe’re excited to announce two new Quantitative Perspectives that provide in-depth insights into current market trends and advanced valuation techniques. These papers offer valuable information for mortgage market participants and those involved in credit risk transfer transactions.
-
EventsAndrew Davidson & Co. Inc. (AD&Co) proudly sponsored the Information Management Network (IMN)’s 10th Annual Mortgage Servicing Rights (MSR) Forum, held November 21 - 22, 2024 at the New York Marriott at Brooklyn Bridge.
-
PodcastTune in to Michelle Stepien Breier's interview with Alex Levin & Matteo Caracciolo-King as they discuss their latest Pipeline article “AD&Co Updates its Home Price Index Model.” The interview highlights key points from the article as they share recent updates to the HPI3 model.
-
ThoughtsWith the increasing volumes of Synthetic Risk Transfer (SRT) and Credit Risk Transfer (CRT) along with the discussion of BASEL III, we thought it would be useful to re-issue our comment letter to FHFA on the capital treatment of Credit Risk Transfer.
-
PodcastRecently, senior credit modeler, Daniel Swanson had the pleasure of speaking with Rob Kessel from the Panoramic Capital Academy podcast titled, “Modeler’s Perspective on Prepayment Modeling.” T
-
ThoughtsThe earliest paper we found examining the impact of climate risks on house prices was from 2017, which found a relationship between elevation/sea level rise and house price differences.[1]
We built our climate-conditioned HPA model in 2022 based on the idea that an increase in insurance costs would impact house prices (something we had not studied yet) in the same way that an increase of the same size in mortgage rates would impact house prices (something that we were quite familiar with).