What Does It Actually Cost to Keep the Funding in Place?

Structural liquidity, the term liquidity premium, and the chain of reasoning that turns a maturity mismatch into a basis-point charge on the loan

A bank writes a five-year loan to an SME. The money leaves the balance sheet today. But who, exactly, is keeping that money in place for five years? Not the depositor — she can walk out in thirty days. Not the bondholder who bought a six-month note. The maturity mismatch is the business model, and everyone knows it. What fewer people can answer precisely is: what does that mismatch cost?

Not in vague terms. Not "something north of the deposit rate." In basis points, traceable to their source, decomposed into what is expected and what is tail risk. That is the question this article tries to answer — step by step, from the shape of the bank's cash-flow shortfall all the way to the price that should reach the loan.

To make every idea concrete, the numbers here come from a single illustrative institution — call it Avelmont — with a simple balance sheet and a five-year SME loan sitting at the center of the problem.

The starting point: where does the shortfall live?

Before pricing anything, you need to see the gap. Think of the bank's cash flows laid out on a timeline: on one side, the needs — contractual outflows (maturing debt, scheduled repayments) and behavioral outflows (deposits walking out, credit lines drawn). On the other, the capacity — what the bank can actually mobilize to meet those needs.

Each flow has two dimensions that matter: when it arrives and how certain it is. A bond coupon on a fixed date is known. Deposit runoff under stress is not. The gap exists because the two sides refuse to match at every horizon.

But here is the subtlety that trips many practitioners: the gap is not a single number. It is a term structure — one quantity (the shortfall) quoted at each horizon. And it has two landmarks worth naming: the first breach (when cumulated need first exceeds usable capacity) and the deepest point (where the shortfall is largest).

Notice the word usable. A bank may hold 2,150M in bonds, cash, and committed facilities. But once you subtract what is encumbered as collateral, locked in the wrong currency, or subject to haircuts, the figure that actually plugs the gap is smaller — 1,500M in Avelmont's case. One asset, one route: a bond already pledged for a repo cannot also count as a liquidity buffer. The waterfall from gross to usable is severe, and any analysis that skips it overstates resilience.

One gap, two very different questions

Here is where a subtle but consequential fork appears. The same gap curve can be read in two entirely different ways, depending on what you assume about funding access.

The planning read assumes business as usual: deposits roll at their behavioral maturity, wholesale tranches refund on schedule, markets remain open. Its question is straightforward — what must I refinance, and when? The output is a price, in basis points, that enters the cost of funds.

The survival read applies stressed weights. Deposits run first. Wholesale dries up. Markets close. Its question is different — how long can I pay without new external funding? The output is a quantity, in dollars, not basis points. It sizes the liquidity buffer.

So who fills the gap — and with what?

Once the planning read shows the shortfall profile, the natural next question is: from where will the money come? This is the forward funding mix — and it hides a trap that catches even experienced practitioners.

Consider Avelmont. On any given day, wholesale funding represents 23% of the standing balance that funds the new book. But if you ask Treasury what share of its gross issuance is wholesale, the answer is 40%. How can both be true?

Because wholesale turns over faster. A three-month tranche rolls four times a year; a five-year deposit sits still. So wholesale appears in the issuance schedule far more often than its weight in the balance. The bank issues wholesale at 40% of gross raises but holds it at 23% of the standing book. Both numbers are correct. They answer different questions. And the cost of funds must price on the standing balance share (23%), not the issuance share (40%) — because that is what actually funds the loan at any given moment.

That drift is worth pausing on. If the loan book grows at 8% and deposits grow at 5%, wholesale fills the widening gap. In Avelmont's plan, the wholesale share of the new book rises from 23% to 32% over five years. This is not a policy failure — it is arithmetic. But it is arithmetic that the cost of funds must reflect, because the loan being priced today will be funded on the mix that prevails during its life, not the mix that prevails at origination.

How often does the wholesale money roll?

Knowing the wholesale share tells you how much of the funding is market-dependent. The next question is how often that money comes up for repricing. This is where the concept of turnover enters — and where a common shortcut leads to the wrong answer.

Avelmont's wholesale ladder looks like this:

The temptation is to compute a "weighted average maturity" first and then read the spread at that point on the curve. But that buries the short money. Three-month paper turns over four times a year; two-year paper turns over half a time. The correct approach is to sum the refunding rates first, weighted by each tranche's share. Avelmont's ladder turns 2.35 times per year — meaning Treasury accesses the market roughly every five months on average.

Why does this number matter so much? Because every market-access event is a moment where spreads might have moved. The ladder does three things at once: it sizes the raise, picks the point on the curve for each tranche, and — crucially — sets how often the bank is exposed to the market's mood. More turns, more chances for a crisis to bite.

The term liquidity premium: pay upfront, or take the ride?

Now we arrive at the core question. The bank needs funding for five years. What does that commitment cost, over and above the risk-free rate?

There are two routes to an answer, and they apply in different situations.

The first route is straightforward: if the bank can issue a five-year unsecured bond at 66 bps over the risk-free rate, then 66 bps is the term liquidity premium. Case closed. But can every bank actually print at five years, at size, at that spread? Many cannot — they fund short and roll, either by necessity or by choice.

For those banks, the premium must be built from the rollover itself. And building it means answering a harder question: when the three-month tranche comes up for renewal, what spread will the market demand? On a calm day, perhaps 9 bps. In a crisis, perhaps 90. Over the five-year life of the loan, the expected average is 26 bps — but the tail average, the one that matters for risk pricing, is 42 bps. The difference — 16 bps — is funding cost risk: the price of not knowing what spread the next roll will carry.

Which route should the bank use? It depends on what it can actually do. If it can print term debt at the quoted spread, that is a cleaner input. If it funds short, the built route is the honest one. Either way, the premium is real, and it must reach the loan.

A brief detour through stochastic thinking

The "built" route requires machinery. Before diving into the model, it helps to lay out five plain-language ideas that underpin everything that follows — because the mathematics is only useful if the intuition is clear.

First: what is a path? Think of recording your commute time every day for a month. That month is one path — one realized history. Replay the month with different weather, different accidents, and you get another path. Neither is "the truth." The distribution across thousands of replayed months is where the statistics live.

Second: mean reversion. Funding spreads wander, but they do not wander forever. Four decades of credit-spread data show them pulled back toward a long-run level. Two parameters govern this: a speed of return and a home level. Shocks push spreads away; the pull drags them back. On average, the pull wins. This is not a modeling assumption — it is an empirical fact visible in the data since 1986.

Third: fat tails. A Gaussian bell curve would price the 2008 spread spike as a once-in-many-lifetimes event. It happened again in 2020. Real funding-spread distributions have heavier tails than the Gaussian admits: extreme moves happen more often than the textbook predicts. Any model that ignores this will systematically underprice the tail.

Fourth: Monte Carlo. Run 20,000 replayed paths from the same starting point, each with fresh randomness. Collapse each path to a single number: its life-average funding cost. Stack 20,000 averages into a distribution. That distribution — not any individual path — is what the risk statistics read.

Fifth: why Expected Shortfall, not Value at Risk? VaR tells you where bad begins (the 97.5th percentile threshold). Expected Shortfall tells you what bad actually costs — the average of everything beyond that threshold. VaR says "here is the door to the tail." ES walks through the door and measures the room. It is coherent (merging two books cannot create risk from nothing), and it charges the severity of the tail, not merely its boundary.

What process should drive the spreads?

With the framework in place, the question becomes practical: what stochastic model should generate the 20,000 spread paths? The choice matters, because the wrong process will misprice the tail — and the tail is exactly what we are trying to charge.

A natural candidate is the Cox-Ingersoll-Ross (CIR) process:

Why CIR, and not a simpler Gaussian (Vasicek-style) model? Three reasons, all practical:

1. Mean reversion (κ pulls S back toward θ): spreads wander but return. This matches the data.
2. Non-negativity: the √S term keeps the spread positive. Funding spreads do not go below zero — a constraint the Gaussian model violates.
3. Level-scaled volatility: when spreads are high (crisis), swings are proportionally larger; when low (calm), swings are smaller. This single feature generates fat tails without bolting on a separate tail parameter. A Gaussian model keeps volatility constant and therefore cannot produce 2008-scale moves without extreme contortions.

What data, and how much?

A model is only as honest as its calibration. The approach that works well in practice uses a principle of intellectual transparency: take the stress from long history and the cross-tenor shape from recent data.

Four decades of Moody's data contain both 2008 and 2020 in-sample — crises that the model must reproduce, not explain away. The cross-tenor shape (how the 3-month, 6-month, 1-year, and 2-year rungs move relative to each other) comes from a principal component analysis on more recent spread data. One factor, fanned across the ladder by its loadings: when wholesale funding gets expensive, all tenors get expensive, but the 2-year rung loads about 17% more heavily than average.

A sanity check worth memorizing

The CIR stays above zero only if the Feller condition holds: 2κθ ≥ σ². For the illustrative calibration:

The process never touches zero. If this inequality failed, the simulation would produce negative spreads on some paths — a clear sign that something in the calibration went wrong.

From simulation to a number on the loan

With the CIR fitted and fanned across the ladder, the simulation pipeline is mechanical:

1. Draw random shocks for 20 quarters (the five-year life of the loan).
2. Each quarter, compute the spread for each tranche on the ladder, weighted by its share.
3. Collapse the entire five-year path to a single number: its life-average funding spread.
4. Repeat 20,000 times.
5. Sort the 20,000 life averages. Take the mean of the worst 2.5%.
6. That mean is the Expected Shortfall: 42 bps — the charged spread.

The expected path averages 26 bps. The charged path averages 42 bps. The difference — 16 bps — is funding cost risk: the price of the possibility that when the bank next accesses the market, 2008 is happening again.

Now the cost of funds stack can be assembled:

Is 437 the final answer? No — deliberately not. It prices one funding source only: wholesale, with the full tail undiluted. Deposits, which carry no rollover tail, are not yet blended in. But the wholesale-only figure is valuable precisely because of what it reveals: it is the ceiling (no blended cost can exceed it), it isolates the rollover mechanism cleanly for sensitivity analysis, and it makes the deposit franchise value visible by contrast — the gap between 437 and the final blended cost is exactly what the deposit franchise is worth to the bank.

A paradox inside the ladder

One more subtlety deserves attention, because it creates a genuine paradox that is easy to overlook.

Should each tranche's spread be read at today's factor level, or at the level that prevailed when the tranche was originally issued? The first approach (mark to current) is market-consistent. The second (hold to strike) reflects what the bank actually agreed to pay. Both are defensible, and they produce different numbers.

But the deeper puzzle is this: longer money costs more per unit (bigger base spread), yet it rolls less often (fewer repricing events). Which effect dominates?

The all-3-month ladder has the smallest tail — but sixteen market-access events per year, each one a chance for spreads to spike. The all-2-year ladder has the largest tail — but only two refunding dates per year. Neither extreme is optimal. The ladder is a policy choice, and different banks will land in different places depending on their risk appetite, their market access, and the curve shape at the time. What matters for pricing is that the choice is made explicit, its consequences are measured, and the cost reaches the loan.

Choosing how to represent uncertainty

Before any of this machinery runs, someone must decide how to represent the uncertainty in the gap and the spreads. This is not a technical afterthought — it is one of the most consequential modeling decisions in the entire chain, and it deserves scrutiny.

Not every liquidity question needs a probability distribution. Four methods require none at all: scenario analysis (committee picks a story), reverse stress testing (find the conditions that break the bank), historical replay (use another institution's crisis), and sensitivity grids (which parameter moves the number most). These are valuable, practical, and carry no distributional baggage.

But when should a full stochastic model be brought in? Three conditions must hold simultaneously:

1. The data must be long enough to have seen a genuinely bad month — not just volatility, but a crisis.
2. The decision must actually turn on the tail. If the answer is the same at the 50th and the 99th percentile, the distribution adds cost without insight.
3. The governance must own the premises. If the board cannot explain why the model assumes a given correlation structure, the number is an orphan.

And here is where correlation proves treacherous. Consider three flows: deposit runoff, credit-line drawdowns, and wholesale rollover. Modeled independently, the 97.5% tail of the combined gap might be 892M. At 50% correlation, it jumps to 1,114M. At 75%, to 1,222M. The range is 450M — driven entirely by one assumption that no regression can settle. This is not a reason to avoid the model; it is a reason to report the range and let governance choose where in that range to anchor the policy.

Putting the chain together

Start with the gap. Read it for planning. That tells you the forward funding mix. The mix tells you how much is wholesale, and the ladder tells you how often it rolls. The rollover frequency, combined with a stochastic spread model calibrated to decades of data, produces a distribution of life-average costs. The Expected Shortfall of that distribution is the charged spread. Add it to the risk-free rate. The result is the cost of funds.

Every link matters. Get the gap wrong, and the mix is wrong. Get the mix wrong, and the wholesale share is wrong. Get the turnover wrong, and the tail is wrong. Get the model wrong, and the tail is either too fat or too thin. The chain is sequential and unforgiving.

Structural liquidity is not a compliance exercise. It is a pricing engine. The gap tells you how much you need. The mix tells you from where. The ladder tells you how often. And the term premium tells you what it costs — including the tail risk that calm markets hide. Get every link right, and the transfer price reflects reality. Get any one wrong, and the loan is mispriced — in a direction you may not discover until the next crisis.

There is still work to do beyond this point. Deposits have their own cost and their own franchise value. The liquidity buffer has a carry cost. Credit risk, capital requirements, and embedded options all add layers. But the structural liquidity leg — the chain from gap to term premium to cost of funds — is the foundation. Everything else builds on top of it.

And the foundation, as we have seen, rests on a question that sounds simple but has taken us through gaps, ladders, CIR processes, and Monte Carlo tails to answer:

What does it actually cost to keep the funding in place?

For Avelmont's five-year SME loan, funded entirely on wholesale: 437 basis points. Every one of them traceable.

The worked example uses Avelmont, a fictional institution, with illustrative parameters calibrated to public data (Moody's credit spreads, U.S. Treasury curves). The approach described is one way — not the only way — to build the term liquidity premium from first principles.