Three Numbers for the Same Spread — and Only One Belongs in the Price

Locked at 66 basis points. Expected at 26. Charged at 42. The term liquidity premium looks simple until three defensible answers land on the same desk — and only one of them should reach the loan.

Ask a treasurer what the term liquidity premium is, and you may get three different numbers — all defensible, all derived from the same underlying data. The first is locked: 66 basis points, read directly from the bank's own issuance curve. The second is expected: 26 basis points, the statistical mean of a simulated rollover strategy. The third is charged: 42 basis points, the risk-adjusted figure that accounts for what happens when rollovers coincide with a market seizure. One of these three numbers belongs in the transfer price. Picking the wrong one misprices every loan on the book — and the error compounds silently, because all three look reasonable on paper.

How can a single bank, looking at its own funding, produce three answers that differ by a factor of more than two? And how should anyone decide which one carries the weight of a pricing decision? These are the questions this article works through — step by step, with numbers attached to each claim.

To keep the arithmetic grounded, the worked example here belongs to Avelmont, a fictional mid-sized institution with a real-enough balance sheet and a five-year SME loan sitting at the center of the problem.

The quoted route — reading the curve

Start with the simplest version of the question. Avelmont can issue a five-year unsecured bond. The market clears that bond at 66 basis points over the risk-free rate. If the bank can print at that spread, at that tenor, at the size it needs — then 66 basis points is the term liquidity premium. Full stop. There is nothing to model, nothing to simulate. The market has spoken, and the number is observable, certain, and locked in for the life of the bond.

This is the cleanest input any pricing desk could wish for. But how many banks can actually use it? The five-year unsecured market is not open to everyone. Some institutions cannot issue at that tenor. Others can issue, but not at size — their name carries a liquidity discount that widens with volume. Still others find the market open one quarter and shut the next. The quoted route is pristine in theory and patchy in practice.

For a bank that can print across the curve, the term structure of funding spreads tells a story of its own. Avelmont's indicative levels look roughly like this:

Why does the curve steepen so sharply? Because issuing long removes optionality. A bank that funds at three months can refinance in ninety days — if spreads tighten, it captures the improvement. A bank that locks in five years surrenders that option. The market charges for the surrender, and the charge grows with tenor. The 66 bps at five years is not just a credit spread — it is a credit spread plus the price of giving up every future refinancing opportunity over the life of the bond.

But what if the bank cannot print at five years? What if the market is closed, or the size is too small to justify the issuance cost, or the bank's policy is to fund short and roll? Then the quoted route offers no answer, and the premium must be built from something else entirely.

The built route — simulating the roll

Avelmont funds short and rolls. Its wholesale ladder is split across four tenors: roughly a third at three months, a third at six months, a fifth at one year, and a tenth at two years. Each tranche matures, and the bank goes back to market to replace it. Every replacement is a repricing event — the market decides, in that moment, what spread to demand.

On a calm day, that spread might be 9 basis points for the three-month tranche, 14 for the six-month, 22 for the one-year, 34 for the two-year. On a day like September 2008 or March 2020, it could be 90 or more across the board — if the market is open at all.

The question the built route tries to answer is this: over the full five-year life of the loan, what will the bank actually pay in aggregate funding spreads, given that each rollover is a coin toss weighted by the state of the credit market?

The machinery to answer that question is Monte Carlo simulation. Run 20,000 paths. Each path covers 20 quarters — the five-year life of Avelmont's SME loan. At each quarter, draw a spread from a calibrated stochastic process (one that mean-reverts, stays positive, and produces fat tails). Apply that spread to whichever tranches happen to be rolling in that quarter. Record the cost. Move to the next quarter. When the path ends, collapse all 20 quarterly costs into a single number: the life-average funding spread for that path.

Do this 20,000 times, and you have 20,000 life-averages. Stack them into a distribution. That distribution is the raw material from which both the "expected" and the "charged" numbers emerge.

What "expected" actually averages over

This is where a subtle but important distinction earns its keep. The expected value of the simulation — the 26 basis points — is not the average of 20,000 quarterly snapshots. That would be a cross-sectional average: take one quarter, look at all 20,000 paths, average their spreads. Useful, but not what we want.

What we want is a life-average for each path. Each of the 20,000 paths produces one number: the sum of all its quarterly funding costs divided by 20 quarters. Path number 1 might average 24 bps over its five years. Path number 2 might average 31. Path number 7,412 might average 19. Each path distills its entire history — calm quarters and crisis quarters together — into a single figure.

Now stack those 20,000 life-averages into a histogram. The mean of that histogram is 26 basis points. That is the "expected" roll cost: the funding spread a bank would pay on a typical journey through time, averaging over everything that might happen along the way. It is a useful number. It is the statistician's best guess. And it is not the number that belongs in the price, because it ignores the question every risk manager must ask: what happens on the paths where the journey goes badly?

VaR vs Expected Shortfall — and why it matters here

To read the tail of those 20,000 life-averages, two statistics compete for the job: Value at Risk and Expected Shortfall. Both are measures of tail severity, but they answer different questions — and the difference is not academic.

Value at Risk at 97.5% finds the threshold where the worst 2.5% of outcomes begins. Sort all 20,000 life-averages from lowest to highest. Walk up from the bottom. When you reach the 500th-worst outcome, you are standing at the VaR line. For Avelmont's simulation, that threshold is roughly 38 basis points. VaR tells you: "Below this point, you are fine 97.5% of the time." It is a doorstep — the boundary where bad starts.

Expected Shortfall walks through that doorstep and measures the room behind the door. It takes those 500 worst outcomes — the ones past the VaR threshold — and averages them. Some of those 500 paths averaged 39 bps over their life. Others averaged 52. A handful averaged 70 or more. The mean of those 500 tail paths is 42 basis points. ES tells you: "When things go wrong, this is what they actually cost."

So the charged spread is 42 basis points. Not because it is the worst case — some paths are far worse. Not because it is the expected case — 26 covers that. It is the average cost conditional on being in the tail: the number that ensures the bank charges enough to cover its funding costs even when the rollovers land in hostile territory.

The whale chart decomposed

The distribution of 20,000 life-averages has a shape worth studying, because it reveals the anatomy of funding cost risk more clearly than any single number can.

The shape tells you several things at once. The lean body — the tall, narrow part of the distribution — clusters tightly around 26 bps. Most paths through time look fairly similar: spreads wander a bit, mean-revert, and the five-year average lands in a familiar neighborhood. This is the quiet bulk of the simulation where nothing dramatic happens.

The blubber — the right skew, the fat tail pushing out toward 50, 60, even 70 bps — is what makes the whale a whale. It comes from the stochastic spread process itself: funding spreads are not Gaussian, they are fat-tailed, and paths that stumble into a crisis quarter or two get dragged rightward. The tail is not symmetric. Nobody worries about funding costs being too low.

But here is the feature that many practitioners miss on first encounter: the tail in life-averages is much narrower than the tail in quarterly snapshots. Why? Because a five-year life-average smears one crisis quarter across 19 other quarters. A funding spread that spikes to 90 bps for a single quarter gets diluted to an increment of only 4.5 bps (90 / 20) in the life-average. That dilution is why the ES of the life-average distribution is 42 bps, not 90.

What the averaging horizon does to the tail

This is the averaging-horizon effect, and it has real pricing consequences. A one-quarter loan — funded once, no rollover — faces the full quarterly spread distribution. Its tail is essentially the quarterly VaR: 90+ bps. A five-year loan averages over 20 quarters, compressing the tail to 42 bps. A twenty-year loan averages over 80 quarters, squeezing the tail further until it approaches the long-run mean of the spread process itself.

Shorter loans carry wider funding cost risk. Longer loans carry narrower funding cost risk. This is not a paradox — it is the law of large numbers applied to a time series of rollovers. And it means the term liquidity premium is not a flat charge. It is a function of loan life, even when the underlying spread process is the same.

The 16 basis points of funding cost risk

Take the charged spread and subtract the expected spread: 42 minus 26 equals 16 basis points. That difference is the risk premium embedded in the transfer price — the price of the possibility that when Avelmont next rolls its wholesale funding, the market is in the grip of something like 2008.

Where does this risk premium live? Only on the wholesale leg. Deposits do not roll at market spreads — they reprice according to the bank's own rate-setting, behavioral patterns, and competitive dynamics. A deposit that re-prices is not a market-access event in the same sense. The funding cost risk of 16 bps applies specifically to the portion of the book that must go to market for renewal.

Three dials move this number, and understanding them is essential for any bank that wants to manage its term liquidity premium rather than merely observe it.

Wholesale share. The higher the fraction of the loan book funded by wholesale, the more of the book is exposed to market repricing on rollover. A bank that funds 40% wholesale has more funding cost risk than one that funds 15%, all else equal. The 16 bps figure assumes Avelmont's current mix. Change the mix, and the number changes with it.

Turnover frequency. A ladder that rolls four times a year creates four repricing events — four moments where spreads might have moved. A ladder that rolls twice a year creates two. More rolls mean more opportunities for a crisis to bite. The three-month tranche turns over sixteen times during the five-year loan life; the two-year tranche turns over only twice. The blend of turnover rates across the ladder determines how many dice-rolls the bank takes against the spread process.

Spread volatility. Fatter tails in the underlying spread process produce fatter tails in the life-average distribution. If funding spreads are historically calm (low volatility, fast mean reversion), the 16 bps might shrink to 10. If the spread process carries the weight of multiple crises in its calibration data, the 16 bps might widen to 22. The model is only as honest as the history it consumes.

The 24 basis points between the routes

Now step back and look at the two routes side by side. The quoted route says 66. The built route says 42. The gap is 24 basis points. Is that an arbitrage? Can the bank fund short at 42 and pocket the 24 that the term market would have charged?

No. The gap is not an arbitrage. It is the price of certainty.

The quoted route — issuing a five-year bond at 66 bps — locks the spread for the entire life of the loan. No rollover risk. No tail. No repricing events. The bank pays more per basis point, but it pays the same basis points for five years, regardless of what the market does. That is worth something, and the market prices it.

The built route — funding short and rolling — accepts rollover risk and charges for it at the Expected Shortfall level. The expected cost is lower (26 vs. 66), and even the risk-adjusted cost is lower (42 vs. 66). But the built route is model-dependent: change the calibration, the confidence level, or the spread process, and the 42 moves. The 66 does not move. It is a market print.

The bank's choice between routes depends on two things: issuance capacity and risk appetite. A bank that can print at 66 and charges 66 is safe — overfunded, perhaps, relative to the expected cost, but immune to rollover surprise. A bank that funds short and charges 42 is accepting model risk in exchange for a lower cost of funds. Both positions are defensible.

What is not defensible is a bank that funds short and charges only 26 — the expected cost, with no tail loading. That bank is underpricing risk by 16 basis points on every loan. The 16 bps will not show up in any single quarter. It will show up all at once, in the quarter when the wholesale market freezes and every rollover comes at 90+ bps. By then, the mispricing is baked into a portfolio of loans that cannot be re-priced.

Three numbers, one loan, one answer

Three numbers. Same data. Same loan. Same balance sheet.

The first — 66 — is the market price of certainty. It buys five years of locked funding and removes rollover risk entirely. For a bank with reliable term-issuance capacity, this is the cleanest and most defensible transfer price input.

The second — 26 — is the statistician's best guess. It is the average cost of rolling short over the life of the loan, computed across 20,000 simulated paths. It is useful for understanding the central tendency of funding costs and for benchmarking against the quoted route. It is dangerous for pricing, because it systematically ignores the tail — the very region where funding costs can destroy the margin on a loan portfolio.

The third — 42 — is the risk-adjusted charge. It takes the same simulation, walks into the tail, and averages the worst 2.5% of outcomes. It is the Expected Shortfall: the number that answers the question "what does funding cost when things go wrong?" It carries model risk (the 42 depends on calibration choices), but it carries the right kind of model risk — risk that can be governed, stress-tested, and explained to a board.

Only the last one — 42, or 66 if the bank can lock it — belongs in the transfer price. The other two are useful for understanding. They are dangerous for pricing.

A bank that charges 66 and funds at 66 is safe. A bank that charges 42 and funds short is taking a measured risk with eyes open. A bank that charges 26 and funds short is underpricing every loan by 16 basis points — and will not discover the error until the market delivers the crisis that the expected value pretended would not come.

The question was never "what is the term liquidity premium?" The question was always "which term liquidity premium?" Three numbers. One answer. And the distance between them is the difference between a transfer price that holds under stress and one that quietly bleeds basis points until the stress arrives.

The worked example uses Avelmont, a fictional institution, with illustrative parameters calibrated to public data (Moody's credit spreads, U.S. Treasury curves). The three numbers — 66, 26, and 42 — are specific to Avelmont's assumptions and should not be read as benchmarks for any real institution.