Behavioral Models for NMD Deposits: Beta, Decay, and Why They Matter
Non-maturity deposits (NMDs) — demand deposits, savings accounts, money market accounts — are typically the largest funding source on a bank's balance sheet. They have no contractual maturity date, which means their IRRBB treatment depends entirely on behavioral assumptions. Get these assumptions wrong, and your ΔEVE number is fiction.
The Problem
Consider a bank with $15 billion in demand deposits. These deposits can be withdrawn at any time — tomorrow, next month, or never. From a contractual perspective, their maturity is overnight and their duration is zero.
But that can't be right. In practice, demand deposit balances are remarkably stable. Customers keep balances for years, even decades. If you treat $15B of deposits as overnight funding, you're dramatically overstating the bank's duration gap and ΔEVE loss.
The solution is to model two behavioral characteristics:
- Rate sensitivity (beta): How much does the deposit rate change when market rates change?
- Volume stability (decay): How quickly do depositors withdraw their balances over time?
Together, these two models transform a deposit with zero contractual maturity into an instrument with a behavioral maturity profile — and this transformation is the single most consequential modeling choice in all of IRRBB.
Deposit Beta
The deposit beta measures how much the deposit rate moves in response to a 1% change in market rates. It is defined as:
Deposit Beta
β = Δ(deposit rate) / Δ(market rate)
A beta of 0.40 means that when market rates rise by 100bp, the bank raises the deposit rate by only 40bp. The remaining 60bp accrues to the bank as increased margin.
Beta varies significantly by deposit type:
| Deposit Segment | Typical Beta (Up) | Rationale |
|---|---|---|
| Demand Deposits (DDA) | 0.10 – 0.25 | Primarily transactional; rate is not the reason customers hold the account |
| Savings Accounts | 0.30 – 0.50 | Partially rate-sensitive; competition forces some pass-through |
| Money Market (MMDA) | 0.50 – 0.70 | Rate-sensitive; customers compare with money market funds |
| Institutional/Corporate | 0.70 – 0.90 | Sophisticated treasurers; high rate awareness; large balances with low switching costs |
Beta drives the ΔNII calculation. When rates rise by 200bp and the deposit beta is 0.40, the bank's deposit cost rises by only 80bp — the remaining 120bp goes straight to NII. Lower betas mean more NII protection in rising rate environments.
Asymmetric Betas and Franchise Value
One of the most important empirical findings in deposit modeling is that betas are asymmetric:
Key Idea
Banks are slow to raise deposit rates when market rates rise (low βup), but faster to cut deposit rates when market rates fall (higher βdown). This asymmetry is the deposit franchise value — the bank captures more of the rate movement in both directions.
Consider a savings account with βup = 0.40 and βdown = 0.65:
- Rates rise 200bp: Deposit rate rises by only 80bp. Bank keeps 120bp of margin improvement.
- Rates fall 200bp: Deposit rate falls by 130bp. Bank's cost reduction is larger than the rate pass-through to customers.
In both scenarios, the bank benefits. This asymmetry is a core source of bank profitability — and it exists because retail depositors are relatively insensitive to rate changes, face switching costs, and value the convenience of their primary banking relationship over marginal yield.
For IRRBB modeling, asymmetric betas mean you need separate models for rising and falling rate scenarios. Using a symmetric average beta underestimates the franchise value and can lead to over-hedging.
Deposit Decay
While beta determines rate sensitivity, decay determines how long the deposits stay. The decay rate is the speed at which depositors withdraw their balances over time.
Decay matters primarily for ΔEVE. If deposits are modeled as overnight (zero decay, immediate withdrawal), they have zero duration and don't offset the duration of the asset side. If modeled with multi-year behavioral stability, they acquire meaningful duration — significantly reducing the duration gap and ΔEVE.
The simplest decay model is exponential:
Exponential Decay
Balance(t) = Balance(0) × e−λt
Where λ is the decay rate. The average life is 1/λ. A decay rate of 0.20/year gives an average life of 5 years.
But a single exponential is often too simple. Empirical data shows that deposit portfolios have a bimodal structure: a portion of balances is very stable (core), while the rest is rate-sensitive and volatile.
Core vs Volatile
The core/volatile decomposition is the standard industry approach to NMD decay modeling, and is explicitly required by the BCBS IRRBB framework.
Two-Component Decay Model
- Core Deposits
- The stable portion of NMD balances that remains even under stress. Decays slowly (average life 3–10 years). Represents customers with strong banking relationships, transactional needs, and low rate sensitivity.
- Volatile Deposits
- The rate-sensitive portion that can leave quickly. Decays rapidly (average life 0.5–2 years). Represents hot money, rate-chasing balances, and institutional deposits with low loyalty.
The total deposit balance at time t is:
Balance(t) = α × B₀ × e−λcoret + (1 − α) × B₀ × e−λvolt
Where α is the core fraction (e.g., 70% for retail DDA), λcore is the core decay rate (e.g., 0.10/yr → 10-year average life), and λvol is the volatile decay rate (e.g., 0.67/yr → 1.5-year average life).
Typical core fractions by segment:
| Segment | Core Fraction | Core Avg Life | Volatile Avg Life |
|---|---|---|---|
| Retail DDA | 70–80% | 7–10 years | 1–2 years |
| Retail Savings | 60–70% | 5–8 years | 1–1.5 years |
| MMDA | 50–60% | 4–6 years | 0.5–1 year |
| Corporate/Institutional | 30–50% | 2–4 years | 0.25–0.5 years |
BCBS Caps
To prevent banks from assuming excessively long behavioral maturities (which would reduce ΔEVE and potentially mask risk), the BCBS imposes explicit caps:
Regulatory Constraints
- Average repricing maturity: ≤ 5 years for non-retail NMDs, ≤ 10 years for retail NMDs (for the core portion under the standardized framework)
- Core deposit share: Many jurisdictions cap the core fraction (e.g., at 70-90% depending on segment and regulatory regime)
- Maximum behavioral maturity of any single cashflow: Typically capped at the average life limit
These caps create a tension: a bank's internal models may show — based on genuine historical data — that retail DDA deposits have 12-year average lives. But the regulatory framework may cap them at 10 years. Banks must manage this gap between internal economics and regulatory measurement.
The Impact on ΔEVE
The magnitude of the ΔEVE impact from NMD assumptions is often staggering.
Example: NMD Assumption Sensitivity
A bank with $15B in NMD deposits, under a +200bp parallel shock:
| NMD Assumption | Avg Life | NMD Duration | ΔEVE Impact |
|---|---|---|---|
| Contractual (overnight) | 0 years | ~0 | $0 offset |
| Conservative behavioral | 2 years | ~1.9 | −$570M offset |
| Moderate behavioral | 5 years | ~4.5 | −$1,350M offset |
| Aggressive behavioral | 8 years | ~7.0 | −$2,100M offset |
The "offset" is the ΔEVE benefit: longer-duration deposits absorb more of the rate shock, reducing the net ΔEVE loss. The difference between "contractual" and "moderate behavioral" is $1.35 billion — often larger than the bank's entire ΔEVE budget.
This is why NMD assumptions are the most debated topic in every IRRBB model validation. A $1.35B swing from a single modeling choice makes these assumptions genuinely consequential for capital adequacy, hedging strategy, and regulatory outcomes.
Model Risk Considerations
Given the impact, it's worth being explicit about the model risks embedded in NMD behavioral assumptions:
1. Regime dependence. Deposit behavior estimated during a low-rate environment (2010–2021) may not hold in a rising-rate environment. Betas tend to increase with the level of rates, and decay rates tend to accelerate when depositors can earn meaningful yields elsewhere (money market funds, Treasury bills).
2. Sample bias. Banks often estimate betas and decay from their own historical data, but this data reflects a specific competitive environment, customer mix, and rate regime that may not persist. A new fintech competitor offering 5%+ savings yields can permanently shift your deposit behavior.
3. Circularity in beta estimation. The deposit rate is a management decision, not purely a market-driven outcome. When you estimate beta from historical data, you're partially estimating your own pricing strategy — which could change.
4. Aggregation effects. Segment-level betas and decay rates mask heterogeneity within segments. The "average" retail savings customer may be a mixture of a large core that never moves and a small tail that is extremely rate-sensitive. The mixture model (core/volatile) partially addresses this, but the allocation between components is itself uncertain.
5. Tail behavior under stress. The most important question — how will deposits behave under a severe rate shock? — is precisely the question for which we have the least data. Historical observations typically cover ±200bp of gradual rate movements, not the ±400bp shocks that occurred in 2022.
The Bigger Picture
NMD deposits are a paradox: they are the bank's cheapest and most stable funding source, yet they are the most uncertain element in its IRRBB measurement. The gap between contractual maturity (overnight) and behavioral maturity (years) is wider for NMDs than for any other instrument on the balance sheet.
The Most Consequential Assumption
If you had to audit only one assumption in a bank's IRRBB model, make it the NMD behavioral maturity. It is the single input that can move ΔEVE by billions of dollars, and it is the one with the widest range of defensible values. Understanding how beta and decay interact, how they are estimated, and what their limitations are is essential for anyone involved in ALM, risk management, or regulatory review.
Banks that invest in granular deposit modeling — using account-level data, multi-driver hazard models for decay, and regime-dependent beta estimation — gain not just better IRRBB numbers but a deeper understanding of their franchise value and its vulnerability to rate regime changes.
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