The S-Curve

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.

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Blog - Latest
  • How Lowering Capital Costs Affects Higher Risk Loans

    Richard Cooperstein

    Thoughts

    How 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 LIBOR

    Alex Levin

    Products

    The 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 Policy

    Richard Cooperstein

    Thoughts

    FHFA 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

    1. 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.

    2. 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.

    3. 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.

    4. 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.

    5. 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.

  • Overcoming a Legacy of Bias in the Housing Industry: The Discussion Continues

    Andrew Davidson

    Thoughts

    In our January 19th blog entitled, A More Equitable Lending System Will Not Be Created by Accident, we described the efforts it will take to overcome not just bias in lending today, but the systemic factors that have limited access to credit in the past and have created an unjust system. 

    We have received much positive feedback on this blog and our earlier blog: In the Mortgage Industry, Who Qualifies as a ‘Good’ Homeowner? However, just as a more equitable lending system will not be created by accident, or even using seemly neutral analytical techniques, a more equitable lending system will not be created by a single individual or organization. Therefore, we believe it is important to highlight recently released research and analysis that can help advance a more equitable lending system.

    First, Bankrate published a piece describing some of the sources of the racial wealth gap and several ways that people of color are Combating The Racial Wealth Gap: 9 Money Moves For Individuals of Color”.  While many of the recommendations are applicable to anyone looking to engage with the financial system, they are especially important in communities that have not had full access to the financial system.

    Second, the politics and sports analytics website, FiveThirtyEight, published a detailed study of the extensive residual impact of redlining, more than 50 years after the practice was banned, The Lasting Impact of Redlining.  The study presents a disturbing portrait of how the legacy of redlining has remained imbedded in the structure of homeownership in America.

    Finally, bringing many of these threads together, the National Fair Housing Alliance has released a framework for developing and accessing analytical systems used for making credit determinations.  Their framework is consistent with the model development and risk management guidelines of the banking regulators and focuses on what steps are necessary during the Purpose, Process and Monitoring phases of model development and implementation.

    The confluence of these and other studies and reports on improving access and fairness in the housing finance system are a welcome sign of potential progress, but are just the beginning of what will need to sustained effort to overcome a legacy of bias.

     

  • Fixing Flood Insurance

    Eknath Belbase

    Thoughts

    In this short blog post I discuss some developments taking place in the flood insurance landscape in the US and look ahead at a few potential directions things could go. I suggest that universal catastrophic flood insurance coverage with a continuation of the introduction of risk-based pricing would be a significant improvement.

    Background

    FEMA’s NFIP, which is required by lenders on at-risk properties, has a cap of $250,000 per property on residential properties and has recently evolved. This evolution has introduced risk-based pricing and will result in drops in many policy premiums (about 1.1 million properties) but also large increases (which will be phased in over years) in those of higher risk properties (about 200,000). FEMA is in the process of transitioning from using lagging flood zone maps to using commercial software similar to that used by the reinsurance industry for the purposes of pricing this risk. This has been covered in multiple articles recently in the media, as well as the topic of rising homeowner’s insurance policy premiums, which have been growing faster than inflation (since homeowner’s policies cover replacement value of homes, any increase in the cost of building materials would naturally show up in replacement cost, so inflation could be expected to pass through to homeowner’s premiums).

    Somewhat less known is that FEMA has also been purchasing reinsurance since 2016. In 2021, the NFIP bought $1.15 billion in coverage from 32 private insurers. Additionally, in 2018 FEMA began to use the catastrophe bond market to also tap the capital markets for reinsurance, with the FloodSmart Re shelf. Including 2021 issuance, total coverage in place through catastrophe bonds is $2.9 billion.

    Private flood insurance is also growing. In 2021, 58 private firms were writing flood insurance, with 2020 total gross premiums collected over $730 million. Between NFIP and private firms, the percent of homeowners surveyed by the Insurance Information Institute stating that they had some form of flood coverage has risen from 12-14% to a recent high of 27%.

    Looking Ahead

    To observers familiar with the mortgage market, the early moves made by NFIP appear similar to the introduction of loan-level pricing adjustments to differentiate borrower-level credit risk, and the creation of the CRT market to lay off portfolio credit risk using a combination of reinsurance and capital markets. However, the largest concern at this point in time is that there is no requirement to have coverage – unless the lender has identified the subject property as at-risk (the GSEs, for example, currently only require it for properties defined as at-risk based on the legacy FEMA flood map system, which means that at best the information used to make this determination is a decade old). This also means that as climate change increases inland flooding patterns and frequency, which is much less covered by legacy maps, a lot more homeowners are potentially at risk. It is worth taking a look at what other countries do.

    Two basic approaches appear to exist in other developed countries. Under the first, homeowner’s have the option of extending their regular homeowner’s policy to cover flood. This approach is taken, for example, in Germany and Italy. Drawbacks of this approach are that because it is optional, only homeowners at higher risk take it up, and therefore it tends to be rather expensive. It also means that homeowners who underestimated their risk (which is more likely going forward due to the changing climate) are likely to find themselves self-insuring when they need it.

    The second approach, taken by Spain, Japan and the UK, requires home insurance to include wind, fire and flood. The upside of this approach is that everyone is covered. While it increases everyone’s premiums, the increase is small for most homeowner’s and spreads the risk over the entire population. This approach doesn’t preclude the use of risk-based pricing, but instead sets a minimum level of flood coverage premium for every home – even those in areas that have never recorded flooding, but may in the future (given that rainfall patterns as well as the built environment is changing, future flooding may be less predictable using past flooding data).

    Our system in the US shares a similarity with this second system, but it is hidden. NFIP has been operating at losses for a significant length of time and has been subsidized by Congressional appropriations, which are ultimately owed by the taxpayer. This means that losses beyond premiums collected is already socialized. Additionally, the lack of extensive coverage means that there are two sorts of uncovered losses. A typical low-grade flood event seems to result in losses in the $10-20,000 range, which one can imagine many homeowner’s managing to cover from personal resources (though many might also struggle). However, the largest disasters, such as hurricanes, result in average losses over $100,000. At this point the Federal government usually appropriates disaster funds. This is why, so far at least, these disasters have resulted in rebuilding and house price recovery more often than they have resulted in house price declines. This is the second form of socialization of losses.

    It is important to point out that under this hidden system of universal coverage, both efficiency and equity suffer. In economics there is usually a trade-off between efficiency (which comes from allowing price signals to reach buyers to disincentivize risky behavior) and equity (subsidizing those who have the least). In this case, everyone is subsidizing those in flood-prone areas, many of which are higher-income vacation and second homes.

    We can compare this approach to socialization of losses with a policy of universal flood insurance as a requirement towards obtaining a mortgage. Every homeowner would pay some minimum level of flood insurance premium. This could be for a catastrophic policy, meaning with a sufficiently high deductible that the policy would only payout when something truly disastrous happens, that a typical homeowner would be very likely to struggle with on their own. In contrast to the hidden universal system, higher risk properties would have substantially higher premiums, in some cases high enough to impact affordability. This would create an important price signal, indicating to a potential buyer that there is something to pay attention to in this location. Better yet would be a system similar to equipping a potential adjustable-rate mortgage (ARM) buyer with both a payment schedule based on current interest rates and one based on hitting periodic and life caps – disclosing not just current insurance premiums but the projected path of future insurance costs if they were to acquire that property. This would address the considerable informational asymmetry that exists in real estate markets, between developers and sellers, who know the area well, and buyers, who may be new to the area.

    Right now, there is very little transparency with regard to future costs in owning a home beyond the mortgage payment schedule. The lack of insight into future insurance premiums is compounded by the potential for rising property tax assessments in the very places that also have high exposure to climate-driven natural risks. This is because the highest risk locations also face significant risk to their public infrastructure, which is funded by state and local taxes, often heavily reliant on property taxes. A universal requirement for flood insurance and risk-based pricing of that insurance would be an important step to improving this transparency.

     

    Further Reading: https://www.iii.org/article/spotlight-on-flood-insurance

Blog - Archives

The S-Curve Archives

  • Alex Levin

    News

    AD&Co US Mortgage High Yield Indices

    The Federal Reserve Economic Data (FRED) portal, housed by the Federal Reserve Bank of St. Louis, has been publishing AD&Co’s CRT indices since 2019. These series posted under the overall name of “US Mortgage High-Yield” include total return rates and credit and option-adjusted spreads (crOAS) – a projected return’s spread over Treasury (in the past, Libor). These series are available going back to 2014-end and tiered by CRT initial supports.

  • Joni Baker, Sanjeeban Chatterjee, Richard Cooperstein, Andrew Davidson

    Thoughts

    In July 2025, the US Federal Housing Finance Agency (FHFA) announced that the government-sponsored entities (the Enterprises or GSEs), Fannie Mae and Freddie Mac, would permit lenders to choose between Classic FICO and VantageScore 4.0 credit score models for loans sold to the GSEs. FHFA also stated in a social media post that the tri-merge standard would be maintained for mortgage underwriting. Nevertheless, some mortgage industry stakeholders recommend moving away from the tri-merge standard for GSE mortgages in favor of a single or bi-merge report standard.

  • Joann Gollette

    News

    As housing faces more climate threats that result in more losses, the insurance program that it sits on is teetering on the brink of collapse. Yet, the home insurance market has three distinct stakeholders that have competing priorities, and today, there is no motivation for a collaborative solution.

    Understanding how to strengthen and protect the current structure requires looking at the cost burdens along with the risk for each of those parties.

  • Sanjeeban Chatterjee

    Thoughts

    There has been a flurry of activity in the mortgage markets since the 2018 passage of the Economic Growth, Regulatory Relief, and Consumer Protection Act. This act requires the Federal Housing Finance Agency (FHFA, now known as US Federal Housing) to validate and modernize the credit score models used in the housing finance system. It should be noted that so far, the discourse has been around mortgages sold to the Enterprises (Fannie Mae and Freddie Mac). Ginnie Mae has not provided any guidance on their plans to start using new credit score models.

  • Vivian Li, Rob Landauer

    Events

    Andrew Davidson & Co., Inc (AD&Co) proudly sponsored IMN’s 11th Annual Mortgage Servicing Rights (MSR) Forum by Informa at the New York Hilton Midtown. Senior modeler Daniel Swanson joined the “Managing Delinquencies & Forbearance Value” panel in discussing how servicers are adapting to today’s market and the evolving delinquency trends.

  • Kevin Lin, Eknath Belbase

    Podcast

    Tune in to our fourth episode of AD&Conversations with Kevin Lin and Eknath Belbase, our product lead for our Climate model. In this episode, they discuss the new Climate Impact Suite (CIS) pilot project, and Belbase outlines several challenges the team is navigating, including:

  • Kevin Lin, Eknath Belbase

    Podcast

    Tune in to our fourth episode of AD&Conversations with Kevin Lin and Eknath Belbase, our product lead for our Climate model. In this episode, they discuss the new Climate Impact Suite (CIS) pilot project, and Belbase outlines several challenges the team is navigating, including:

  • Andrew Davidson

    Podcast

    Andrew Davidson was invited to speak on Equifax's Market Pulse Podcast titled, "Driving Efficiency and Resilience in the Mortgage Industry" live at the 2025 MBA Annual Convention in Las Vegas. 

    Andy explains how variations in data files can distort risk assessment, creating a dual risk for lenders: extending credit to borrowers more likely to default while overcharging customers whose risk is overstated. 

  • Richard Cooperstein

    Thoughts

    Our latest Policy Perspective written by Richard Cooperstein offers an analysis of the U.S. housing and mortgage finance markets, focusing on key trends and forward-looking risks. While housing markets are not fully efficient, they do respond to economic imbalances which create opportunities and vulnerabilities. This article explores how demographic shifts, credit access, interest rates, and climate risks shape both housing demand and supply.

    Key findings include:

  • Kevin Lin, Richard Cooperstein

    Podcast

    Join Kevin Lin in a conversation with Richard Cooperstein as they dive into Kinetics, AD&Co's modular platform designed to deliver the full power of our models and analytics; with the flexibility to license only the tools you need.