Assumptions around nonmaturity deposits (NMDs) are key drivers of a bank’s interest rate risk profile. I’ve looked at a host of models over the course of my career. These include market models, credit models, prepayment models, and stress testing models. But NMD modeling presents the most challenges. What makes NMD risk modeling so difficult?
Modeling NMDs
Banks model NMDs, like savings and checking accounts, for both earnings-at-risk (EAR) and economic value of equity (EVE) purposes. This post will focus on the use of NMDs in EVE estimates. We can leave their use in EAR for another time.
EVE relies on a series of present value calculations for assets and liabilities. Remember that:
A lower present value of your liabilities will, all else being equal, produce a higher EVE. The PV calculation for deposits will project their cash flows and then apply a discount rate. The cash flows reflect principal and interest payments on the deposits over some time horizon along with some cost to administer the deposits. The discount rate typically reflects rates for alternative funding sources, such as FHLB advances with comparable maturities.
The most critical assumptions here are how much deposit rates change in response to overall market rate changes and how fast deposits run off (attrition). A typical approach is to look at the retention of cohorts of deposit accounts over time. (Attrition Rate = 1 – Retention Rate) For example, you could track deposits opened in 2020 by looking at their remaining balances in 2021, 2022 and so on. You repeat this process for other cohorts. You then apply those retention rates to current balances, by cohort.
Challenges with NMD Modeling
The math behind these calculations isn’t especially complex, but certain aspects of NMDs can complicate the analysis. They include the following:
NMDs vary across banks and products. It’s easiest to model financial instruments that are close to uniform. Treasuries are super easy. Just plug in the note rate, the maturity, and the current market rate and a 1980s vintage financial calculator can spit out the market price and price sensitivity. MBS are more complicated, but one 30-year, 4% Fannie Mae usually doesn’t differ much from another. NMDs are a whole different story. Customer behavior can be very specific to a bank, depending on their size, market area, and business strategy. A “savings account” at Synchrony (currently paying 4.30%) is a lot different from a “savings account” at Wells Fargo (paying 0.05%). They have similar names but little else in common.
Customers move between accounts. Depositors don’t just terminate their accounts. They can also move money between accounts. For example, if rates go up, depositors may jump from low-paying transaction accounts to higher rate CDs. This may not be a big deal from a liquidity standpoint, since the money stays in the bank. But moving from low to high-rate accounts increases overall funding costs. Banks can struggle tracking these within-bank moves.
U.S. banks went through a prolonged period of near-zero interest rates. Near-zero interest rates made it hard to estimate the rate sensitivity of deposits. There was little opportunity cost for holding a low-rate deposit. Forecasting how the deposits might behave in a higher rate environment was at best speculative. The rise in rates starting in 2022 made this less of a concern but the problem has not gone away. Modelers usually like to work from a more extensive history. Longer-term histories can help separate the signal from the noise. But it can also lead to a misleading picture of current conditions.
Consider the following hypothetical example (see graph below). Suppose a bank has deposits like checking accounts that pay little or no interest. Short-term market interest rates were near zero from 2010 through 2021. Low market rates meant that deposit attrition was low, say 3% annually. With the rise in rates in 2022 and 2023, attrition rates shoot up, first to 15% then to 20%. (I’m not describing a run here, just a movement to higher rate accounts.) However, the average 14-year attrition rate is still only 5%, which could provide a misleading picture of deposit retention. Varying attrition rates by rate scenario can paint a more realistic picture but also makes for a more complex model.
When Bad Things Happen to Good Modeling Practices. The example above is one illustration of how some usually sound modeling practices can go awry. It’s better to build models based on more rather than fewer data points. But some data points may be more relevant to your analysis. If you are concerned about the behavior of deposits under rising rates, then customer behavior in 2022 and 2023 tells you a lot more than what happened in 2010-2021.
Outcomes analysis is another example. How well did the model’s forecast square with reality? Unfortunately, a model that performs well during benign periods can fall apart under more stressed conditions. Using our earlier example, a deposit model that assumed a very low attrition rate would have performed fabulously from 2010-2021 but disastrously in 2022 and 2023, when it mattered the most.
Models assign a value to NMDs, but withdrawals and many liquidations are at par. EVE calculations usually assume a value to NMDs (in this case PV<face value) under both baseline and rising rate scenarios. But customer withdrawals are redeemed at par. This is often the case with liquidations as well. The FDIC received zero deposit premium for SVB, Signature, and First Republic. It recently received a 6.67% premium for First National Bank of Lindsay, OK, but that deal excluded uninsured deposits. Overall, nine of the past 20 FDIC resolutions resulted in zero premiums and the average premium was just 1.32%.
There is little market data to tether deposit models to reality. Modeling other financial instruments can also be challenging. Banks have worked for years developing mortgage prepayment models, but those models still fail on occasion. However, developers can look at market prices to see whether the model is working or at least in line with the market. There’s not a visible trading market for NMDs. Valuations derived from deposit models are strictly mark-to-model, which often paint an overly optimistic picture. Mark to model approaches remind me of the old Windows 7 ads where ordinary people in their own imaginations are inevitably younger, slimmer, and better looking.
The information that is available does not necessarily support current model assumptions. According to the OCC, bank ALM models assumed a median average life of 5.0 years for both savings and non-interest-bearing accounts. But if we look at FDIC resolutions, the average deposit premium during a higher rate period (2023-2024) was just 1.85%, not much higher than the average 1.32% premium when rates were near zero (2017-2020). Considering that short-term rates rose at least 300 bps during that period, it suggests an effective duration of well under a year. The data is way too sparse and noisy to infer very much but the observed relationship between deposit premiums and market interest rates is weak, at best.
It was usually considered bad form for examiners to bring up liquidation values. We would not expect liquidation to be the focus of a going concern. However, the potential impact on resolution costs does seem an appropriate consideration for regulators.
What’s the Solution?
Modeling NMDs, especially for EVE purposes, is very difficult. That doesn’t mean model developers and risk managers should just throw up their hands. They can take certain actions to mitigate the model risk.
Stress test assumptions. NMD models make assumptions about attrition, rate sensitivity, and a host of other factors. Risk managers should evaluate the sensitivity of overall values and durations to these assumptions. This practice has become more common in recent years, at least among larger banks. However, the sensitivity analyses need to show meaningful stress to the assumptions. For example, if you start with an annual attrition rate of 5%, stressing that assumption by 10% only increases the attrition rate to 5.5%, barely a rounding error. The stress should assume a large but still plausible model miss. Stressing the assumptions won’t get you to the “right” answer but can better inform bank managers on the range of plausible outcomes. Also remember that “plausible” is often worse than you think.
Constrain the Model. Attrition models can run over an infinite time horizon. To make the models more tractable and to reduce model risk, model developers often truncate cash flows after five, ten, or even thirty years. The model will assume that customers redeem remaining balances at the truncation point. The impact can be quite large. A deposit with a 5% attrition rate has a terminal weighted average life of about twenty years. The table below shows WALs at the same attrition rate but also assuming 30, 10, and 5-year truncation points. These calculations still understate WALs since they only look at principal balances but not interest credited, which is payable at withdrawal.
Truncation approaches recognize two key limitations of deposit modeling. First, deposit models make assumptions about not just the current environment but also about what could happen ten, twenty, or thirty years down the road. This is especially important since NMD cash flows primarily reflect customer behavior rather than contractual obligations. A lot can change over ten or twenty years. The second relates to overall asset-liability management. Assume your model produces a WAL of 15 years. Is it prudent to match those deposits with 15-year investments? If rates go up, the value of the investment portfolio goes down significantly. They may even involve a capital hit if the securities are available-for-sale. The model may say you have offsets on the deposit side, but there is no realistic way to monetize those offsets.
Conclusions
Model risk isn’t just about the math. While some deposit models can get quite complex, uncertainty plays a much more important role. The bespoke nature of NMDs, the prolonged period of near-zero market interest rates, and the inability to calibrate model output to market data all present huge challenges to model developers, bank risk managers, and regulators.