Deposit Behavioral Maturity

From overnight contract to real duration — finding the number that changes everything about the cost of funds

A demand deposit has no contractual maturity. Its repricing tenor is overnight. The customer can withdraw every cent tomorrow morning, and the contract says the bank must hand it over. Yet the balance sits for years. Sometimes for decades. And if you price loans as though deposits fund at the overnight rate — rolling daily, never locking in a term — you kill the franchise. The funding cost jumps by 100 basis points or more, every loan looks uncompetitive, and the treasury desk wonders why the bank bothers collecting deposits at all. But if you price as though those deposits fund at five years — stable, locked, permanent — you are lying about the risk. Somewhere between overnight and forever is the deposit's real duration. Finding it changes everything about the cost of funds.

The question is not academic. This single number — the behavioral maturity of the deposit pool — determines the franchise credit that subsidizes every loan on the book. Overstate it, and you build on sand. Understate it, and you throw away the bank's most valuable asset. So how do you find it?

The two clocks on every deposit

Every deposit account carries two clocks, and they tick independently.

The repricing clock

How fast does the deposit's rate adjust when the central bank moves? A savings account might take six months to pass through half a rate hike. A money market account might adjust within weeks. The speed of this adjustment is measured by a single parameter called deposit beta — the fraction of policy rate movements that the bank passes along to depositors. A beta of 0.4 means 40% passthrough: when the policy rate rises 100 basis points, the depositor sees only 40 of them. The bank keeps the other 60.

Low beta means cheap funding. High beta means expensive funding. And the repricing clock tells you how long the bank gets to enjoy the gap between what the market charges and what the depositor receives.

The attrition clock

How long does the balance survive before the customer leaves? Not the contractual term — that is overnight, and it tells you nothing. The behavioral life. Measured by survival analysis on historical balance data: of every dollar deposited today, how much is still here in one year? In three? In five? The attrition clock measures the pace at which the deposit pool decays, customer by customer, dollar by dollar.

Here is what matters: these two clocks are independent. A deposit can reprice quickly — high beta, short repricing clock — but stay for years because the customer never bothers to move. Or it can reprice slowly — low beta, the bank keeps most of every rate hike — but leave the moment a competitor offers 20 basis points more. The two clocks together, not either one alone, determine the deposit's economic value to the bank.

Why does this matter? Because the combination of both clocks determines what fixed-income instrument the deposit economically resembles. A checking account with a beta of 0.15 and a behavioral life of seven years looks nothing like an overnight instrument. It looks like a medium-term fixed-rate bond — cheap, stable, long-lived. A money market account with a beta of 0.80 and a behavioral life of eighteen months looks almost like wholesale funding: expensive, rate-sensitive, ready to leave.

Why contractual maturity is useless

Contractually, a demand deposit matures overnight. Every single one of them. The savings account, the checking account, the money market account — all overnight. If you took the contract at face value, every deposit on the book would be modeled as rolling overnight funding.

What does that imply for loan pricing? It means funding the five-year corporate loan at the overnight rate, rolled daily for five years. The term premium is zero. The franchise credit is zero. The cost of funds equals the wholesale overnight rate. And the loan price comes out 100 basis points higher than any competitor who bothers to look at how deposits actually behave.

But deposits do not behave like overnight instruments. They sit. They earn below-market rates. They do not leave when rates rise. They do not reprice to market. The contractual view throws away all of this information — the very information that makes deposits valuable in the first place.

The behavioral view asks a different question: if I held a pool of these deposits, how would the balance evolve over time? How would the rate evolve? And what fixed-income instrument has the same cash-flow pattern?

That question leads to the replicating portfolio.

The replicating portfolio approach

The concept is straightforward, even if the calibration is not. Take the deposit pool's behavioral cash flows — the path of balances over time, adjusted for attrition and repricing — and find a portfolio of fixed-term instruments whose weighted cash flows match that path. The instruments might be 1-month, 3-month, 6-month, 1-year, 2-year, 3-year, and 5-year wholesale borrowings. The weights on each tenor tell you the behavioral maturity profile of the deposit pool.

If the replicating portfolio comes out as 20% at 1 year, 30% at 2 years, 25% at 3 years, 15% at 4 years, and 10% at 5 years, the deposit pool has a weighted average behavioral maturity of about 2.5 years. Not overnight. Not five years. 2.5 years — the duration that explains how the balance and its cost actually evolve.

Avelmont's replicating portfolio

Consider Avelmont's deposit pool, broken into three segments:

The blended pool has a behavioral maturity of approximately 2.3 years. That is the number that enters the cost-of-funds calculation. Not overnight. Not the contractual term. The behavioral maturity, derived from the replicating portfolio, reflecting both clocks — how fast the rate moves and how long the money stays.

Deposit beta — the most consequential single parameter

Of all the numbers in the deposit model, beta is the one that does the most work. It determines how much of every rate move the bank keeps versus how much it gives away. It drives the franchise credit. It shapes the replicating portfolio. And it is, in practice, the hardest number to pin down.

Beta measures rate passthrough. If the central bank raises rates by 100 basis points and the bank raises its deposit rate by 40 basis points, the beta is 0.40. The bank keeps 60 basis points. That 60 basis points, applied to the entire deposit pool, is the raw material of the franchise credit.

Low beta means cheap funding and a large franchise credit. High beta means expensive funding and a small one. The distinction across products is dramatic:

But beta and behavioral life are not independent in practice, even though the two clocks are conceptually distinct. They are linked by customer behavior. A low-beta deposit — one where the bank passes very little to the customer — is cheap and sticky in calm markets, because customers are inattentive. It behaves like longer-term funding. A high-beta deposit — one that reprices to market — behaves like shorter-term funding, because the customers holding it are rate-sensitive and will leave if they find something better.

The beta-life trade-off

Here is the trade-off the bank navigates. If you raise beta — pass more to customers — deposits stay longer. Attrition falls. The behavioral maturity extends. But the cost rises. If you lower beta — keep more for the bank — deposits leave faster. Attrition rises. The behavioral maturity shrinks. But each dollar that stays is cheaper.

The bank optimizes inside this trade-off. Push beta too low and the pool shrinks until the franchise credit, though large per dollar, applies to so few dollars that total value falls. Push beta too high and the pool grows but the franchise credit per dollar collapses. Somewhere in the middle is the point where total franchise value — credit per dollar times dollars — is maximized.

The SVB trap — extending life in a crisis

Silicon Valley Bank assumed deposits had long behavioral life. The models were calibrated on a decade of calm data — low rates, stable balances, minimal attrition. The replicating portfolio extended far out the curve. The franchise credit was large. And the bank invested accordingly, locking funds into long-duration securities that would deliver handsome returns as long as the deposits stayed.

When rates rose 500 basis points in eighteen months, the deposits did not stay. They left faster than the model predicted. The behavioral maturity that had looked like three or four years in calm markets turned out to be six months in a rate shock. The long-duration assets could not be unwound without massive losses. The franchise credit that had subsidized the entire investment portfolio evaporated in a quarter.

What is the defense? Do not assume stability you have not tested. Stress the beta: what happens if passthrough doubles? Stress the attrition: what happens if quarterly outflows triple? Run the replicating portfolio under the stressed parameters and report both the base case and the stressed case. If a 300-basis-point rate hike cuts your deposit pool by 20% in the stress scenario, the behavioral maturity you report to the board should carry that caveat in bold.

Honest practice means acknowledging that the two clocks can accelerate simultaneously. In calm markets, beta is low and attrition is low — deposits are cheap and sticky. In a rate shock, both clocks speed up at once. Beta rises because customers wake up and demand higher rates. Attrition rises because the customers who do not get higher rates leave. The franchise credit compresses from both directions at the same time.

How the franchise credit reaches the loan price

The deposit's behavioral maturity determines which point on the funding curve it reads. A behavioral maturity of 2.5 years reads the 2.5-year wholesale funding spread — the rate at which the bank could borrow unsecured term money in the market for that tenor. The difference between that wholesale rate and what the bank actually pays the depositor, after accounting for beta, is the franchise credit.

Avelmont's franchise credit

For Avelmont, the numbers look like this:

That 99 basis points is not a rounding error. It is the single largest subsidy in the bank's cost structure. It is subtracted from the wholesale cost of funds in the blended funding calculation, which is why Avelmont's blended cost of funds (305 bps) sits well below the risk-free rate (438 bps). Without the franchise credit, the bank's funding cost would look like a wholesale borrower's — and every loan on the book would need to be repriced upward by nearly a full percentage point.

Think about what this means for competitive positioning. A bank that correctly measures its franchise credit can price loans 99 basis points below a wholesale-funded competitor and still break even. A bank that ignores the franchise credit — pricing as if all funding is wholesale — quotes higher than it needs to and loses market share to competitors who know their own deposits better. A bank that overstates the franchise credit — assuming deposits are stickier and cheaper than they really are — quotes lower than it should and bleeds value when the deposits reprice or leave.

The number that lives between two clocks

The deposit's real duration is not a number you can read off a contract. It is not printed on the account agreement. It does not appear in the general ledger. It lives in the intersection of two clocks — how fast the rate moves and how long the money stays — and extracting it requires a model that respects both dimensions.

Get it right and the franchise credit flows through to every loan on the book. The cost of funds falls below wholesale. The pricing engine produces rates that are competitive and profitable. The ALM desk knows the true interest rate risk of the deposit portfolio, not the contractual fiction.

Get it wrong in one direction — too short, too conservative — and you kill the competitive advantage. Every loan is overpriced by the franchise credit you refused to recognize. The bank funds itself as though it were a wholesale borrower, even though it sits on billions of cheap, stable deposits.

Get it wrong in the other direction — too long, too optimistic — and you are building on sand. The franchise credit you booked is larger than reality. The loans are underpriced. And when the deposits reprice or leave — as they will in any significant rate shock — the gap between what you assumed and what actually happened shows up as a loss, all at once, with no time to adjust.

The honest answer is always a range, not a point. The base case says 2.3 years. The stress case says 1.4 years. The board sees both. The pricing engine uses the base case but the risk limit uses the stress case. And the difference between the two — that uncomfortable gap — is the measure of how much franchise credit the bank is earning today that it might not earn tomorrow.

That is the discipline. Not a formula, but a habit of mind: two clocks, two cases, and the intellectual honesty to report the gap between them.

The illustrative numbers use Avelmont, a fictional institution, with parameters calibrated to public data. Deposit betas and behavioral maturities are institution-specific and vary with the rate environment, competitive landscape, and customer demographics. The replicating portfolio approach follows the methodology described by Castagna and Fede, among others. The SVB example draws on widely reported public information.