Welcome to The S-Curve
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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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Takeaways from Lessons Learned: Insights for Managing the Interest Rate Risk of BanksEventsAndrew Davidson & Co., Inc. (AD&Co) held a webinar on June 8th entitled “Lessons Learned: Insights for Managing the Interest Rate Risk of Banks.” Mickey Storms from our Alliances and Policies team, Alex Levin from our Financial Engineering team and Andrew Davidson were featured speakers.
Mickey revisited interest rate changes since the onset of the pandemic and showed how these led to changes in appetite for yield curve risk at banks as interest rate declines compressed their Net Interest Margins (NIM) as depicted in the slid below. He went on to show how this appetite conveyed a questionable sense of comfort by banks that the Assets and Liabilities (A/L) duration gap would not be problematic in the future. The example presented was the strategy of increased short funding of MBS with deposits as rates fell during the pandemic, the success of which depended on an implied long duration of deposits to conceive of a manageable duration gap between A/L. He went on to show the significant duration that exists on the asset side of bank balance sheets and that in the absence of hedging, the success of short funding strategies relies critically on the behavior and duration of deposits whose behavior has changed recently. Mickey closed by pointing out that there has been a lack of regulatory focus on Interest Rate Risk (IRR) in recent years that accommodated banks taking interest rate and duration risk at U.S. Banks.

Alex considered several important methodological challenges in measuring IRR and the A/L duration gap. He began with the asset side and explained why an empirically developed prepayment model is not sufficient to fully capture AFS assets’ market sensitivities. For the purpose of replicating those sensitivities, a prepayment model needs to be “risk-neutralized” with faster refinancing and slower housing turnover – the main feared directions of the prepay-model risks. A risk-neutral model would better track market sensitivities of premium and discount assets, as illustrated by the dynamics of different duration measures during 2022 (a similar pattern observed across the TBA coupon stack).
As a risk-neutral turnover rate is slower than an actually observed one, the currently outstanding MBS portfolios (and most banks’ assets) are longer (duration-wise) than many people think.

Comparative Duration Measures
OAD – Option-adjusted duration utilizing empirically developed prepay model
prOAD – Option-adjusted duration utilizing risk-neutralized prepay model
EmpDur – Empirical 60-day sensitivity measured from the daily moves of TBA price and 10-yr rate (model-free)Alex discussed the role of Non-Maturing Deposits (NMD). While an empirically defensible model of retention and paid rate is a good start, many external factors are typically not evident from historical data. Those include possible changes in the deposit base or media/bad press effects that could shorten the duration of NMDs. Therefore, A/L duration gaps are likely to be wider than ones measured.
Alex demonstrated a Net Present Value (NPV) analysis of a hypothetical bank with assets, term liabilities, and NMDs. He constructed a TBA-13-type of NPV of equity profile for two cases:
- NMDs are intact (chart on the left below)
- NMDs are replaced with par-valued liabilities having no intangible value to the bank (chart on the right below).

This exclusion of the economic value of NMDs from the NPV consideration is a useful stress-test we recommend banks conduct.
A bank’s hesitation to hedge IRR is commonly linked to a loss of NIM under the commonly steep yield curve. Under the current inversion, swaps have a positive carry that would improve NIM while closing (or even inverting) the duration gap. Alex demonstrated the use of a 3-year SOFR swap that would make the same bank duration-neutral while adding 50 bps of NIM or even inverting the IRR exposure while adding 100 bps of NIM.
Andy closed by dimensioning the two-way risks that exist with respect to future interest rates and the shape of the yield curve and pointed out how this may impact the dynamics of other assets and businesses that banks maintain. Among these were mortgage servicing and origination. He addressed bank risk management board roles, policies, procedures and controls and discussed the critical importance of an open culture with respect to risk insights and tactics. The review of models and scenarios used to manage IRR was also presented, as was the importance of asset diversification and capital allocation processes that include risk limits. He closed by talking about Basel 2 IRR analytical methods and how focusing on economic value, earnings and market are essential to effective IRR management.
Click here to view the presentation and webinar recording.
The S-Curve Archives
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EventsAt Andrew Davidson & Co., Inc. (AD&Co), our dedication to Diversity, Equity, and Inclusion (DEI) has been a cornerstone of our values. We established our DEI Committee in 2020, following the tragic murder of George Floyd. Despite the evolving landscape, including the recent U.S. Supreme Court decision impacting affirmative action in higher education, we remain steadfast in our commitment to fostering an inclusive environment that strengthens both our employees and the company.
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PodcastTune in to Eknath Belbase's interview with Michelle Stepien Breier & Richard Cooperstein as they discuss their latest Pipeline article “Improving Mortgage Data: A Data Exchange for the Mortgage Ecosystem.” -
EventsAndy and I recently attended AmeriCatalyst ‘Going to Extremes’ Climate, Housing and Finance Leadership Summit in Washington, D.C., a fantastic conference on all things related to climate risk and the housing ecosystem. While going over all the great speakers and broad expertise represented there would take a novella, I want to connect a few key ideas discussed there to our ongoing efforts in this area.
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EventsAt the recent AmeriCatalyst ‘Going to Extremes’ Climate, Housing and Finance Leadership Summit, I presented a session on how risks related to weather-related losses impact the housing finance system.
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ProductsAndrew Davidson & Co., Inc (AD&Co) is thrilled to announce an expanding relationship with a Third-Party Vendor! AD&Co enjoys working with countless analytical providers to offer our clients seamless solutions and we would like to welcome Milliman M-PIRe™ to the team!
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EventsThe Federal Home Loan Bank of San Francisco directed the Urban Institute to develop innovative and actionable ideas to close the gap between white and black homeownership rates, which is as wide today as before the Fair Housing Act, enacted 60 years ago. Homeownership is crucial to a fairer society because working and middle-class families most commonly create inter-generational wealth by owning homes with amortizing mortgages.
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EventsThe Data Foundation of Mortgage Finance
Homeownership is the largest source of wealth accumulation and inter-generational wealth transfer for the working and middle class. However, the non-interest cost of financing is always an obstacle for first-time and low-wealth buyers, and underserved populations.
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ThoughtsIn this blog post, we used the recently updated Mortgage Market Statistical Annual to examine the dynamics of residential loan origination by state and by market segments and highlight important trends.
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ProductsAndrew Davidson & Co., Inc. (AD&Co) is pleased to announce the official release of Kinetics v1.10, the latest update to AD&Co’s modular platform for running the AD&Co suite of analytics. This update introduces the Multifamily LoanDynamics Module, the newest way to run Multifamily LoanDynamics Model (LDM). Investors, servicers, insurers and lenders can leverage this new module to better understand the prepayment and credit risk of their multifamily mortgage portfolio.
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EventsAndrew Davidson & Co., Inc. (AD&Co) held a webinar on June 8th entitled “Lessons Learned: Insights for Managing the Interest Rate Risk of Banks.” Mickey Storms from our Alliances and Policies team, Alex Levin from our Financial Engineering team and Andrew Davidson were featured speakers.