Yesterday's Rate on Tomorrow's Roll

The subscript that separates what the bank locked in from what the market now demands — and why every ladder, convention, and refunding calendar moves the cost of funds by dozens of basis points

A two-year tranche issued eighteen months ago is still paying the spread it agreed to at issuance. Thirty-four basis points over the benchmark — that was the number on the term sheet, and that is the number leaving the bank's account every quarter. But the risk model reads today's spread, and today's two-year wholesale paper trades at fifty-one basis points. The accounting system, meanwhile, faithfully records thirty-four. When the treasurer asks "what does our wholesale funding cost?", which number answers? And does the answer change if the question is about pricing a new loan versus measuring the cost of the existing book?

This is not a philosophical distinction. The gap between those two numbers can be twenty, thirty, sometimes fifty basis points wide. It depends on how many tranches are outstanding, when they were issued, and what the market has done since. Get the subscript wrong and the entire transfer-pricing chain inherits the error — silently, persistently, and in a direction that flatters the business when spreads are widening and punishes it when they tighten.

To make this concrete, the numbers here come from a single illustrative institution — call it Avelmont — with a wholesale funding ladder and a simple question: what does the next loan actually cost to fund?

The subscript problem: S_t versus S_s

Every funding-cost model contains a spread variable, and every spread variable carries a subscript. The subscript determines which spread the model reads. There are two plausible choices, and they answer different questions.

S_t — the current factor

Mark every outstanding tranche to today's market level. If spreads have widened since issuance, the model says funding is expensive — regardless of whether the bank locked in a lower rate months or years ago. S_t treats the entire book as though it were being re-issued this morning. The logic is forward-looking: what would it cost to replace this funding if it matured today?

S_s — the historical strike

Each tranche keeps the spread agreed at issuance. The eighteen-month-old two-year tranche holds its thirty-four basis points until it matures. The six-month note issued last quarter holds whatever the market charged last quarter. S_s is backward-looking: it reflects what the bank actually pays, not what the market would charge if the bank went back today.

The paradox: longer money costs more but rolls less

The term structure of wholesale spreads slopes upward. Three-month paper trades at 9 basis points over the benchmark. Two-year paper trades at 34. The longer the tenor, the more the bank pays per unit of time. This is the level effect: it says longer money is dearer.

But there is a second force pulling in the opposite direction. A two-year tranche refunds 0.5 times per year. A three-month tranche refunds four times. Every refunding event is a repricing event — a moment when the bank returns to the market and discovers whatever spread the market is now charging. More rolls mean more chances to catch a crisis. This is the frequency effect: it says longer money is cheaper, because the bank faces fewer moments of exposure to market conditions.

Which dominates? Consider a tail scenario where spreads spike. The short tranche has a smaller base spread, so the absolute increase in cost per roll is smaller. But the short tranche rolls so often that it catches the spike multiple times — while the long tranche, if it happens to mature during the calm period, misses the crisis entirely. Multiply a small shock by sixteen annual market-access events and compare it to a large shock multiplied by half an event. The answer depends on the curve shape and the volatility structure, and it is not obvious in advance which way it goes.

Four ladders, same premises, different answers

To see how these forces play out in practice, consider four funding strategies for Avelmont, all starting from the same balance sheet, the same spread curve, and the same volatility parameters. The only thing that changes is the ladder — the mix of tenors in the wholesale funding book.

The cost of funds ranges from 419 to 486 — a sixty-seven basis-point spread — from the ladder choice alone. Same bank, same assets, same market. The only variable is how often the wholesale book turns over and at what tenor.

But the table tells an incomplete story if you read only the cost column. The all-three-month ladder wins on expected cost — but it requires sixteen market-access events per year. Every single one is a chance for spreads to spike, for the market to shut, for an operational failure to cascade into a liquidity event. The all-two-year ladder costs sixty-seven basis points more but refunds only twice per year. It buys stability at a price.

Building the refunding schedule by hand

The numbers in the previous table emerged from a model. But the model rests on a physical reality: at any point in time, the bank has tranches outstanding at different tenors, issued on different dates, each carrying the spread agreed at issuance. This is the refunding schedule, and it is worth building by hand at least once to see what the model is actually doing.

Consider Avelmont's wholesale book at month 18. The mixed ladder has the following tranches outstanding:

The blended cost of the standing book is the weighted average of these strikes. If each tranche funds an equal share of the balance sheet, the blended strike at month 18 is somewhere around 17 basis points — well below today's market of 51. The bank is, in effect, still benefiting from spreads it locked in months ago.

But the cost for pricing a new loan is not 17. It is whatever the market charges today for the tenor the bank will issue to fund that loan. The new loan must earn today's spread, not yesterday's. This is exactly the S_t versus S_s distinction, made tangible in a single snapshot of the book.

What the reset convention is worth

When a tranche matures and the bank returns to the market, the new tranche picks up whatever spread the market is charging. This is a clean roll — full repricing at each refunding event. The bank bears the entire curve at each turn of the ladder.

But not all funding behaves this way. Some structured facilities reset on a different schedule — annually, regardless of the tranche's maturity. A two-year facility with annual resets reprices once at the one-year mark, locking the second year's spread at that point. This is contractual reset: partial repricing, decoupled from the maturity calendar.

The difference between these two conventions is not trivial. Depending on the ladder and the volatility environment, the gap can be five to fifteen basis points. In Avelmont's mixed ladder, the clean-roll convention produces a marginal cost of funds about eight basis points higher than the contractual-reset convention, because the clean roll exposes every refunding event to current market conditions, while the contractual reset locks spreads at intervals that may not coincide with market stress.

Most wholesale funding operates on clean rolls. But the moment a bank taps structured facilities, bilateral lines, or private placements with non-standard reset features, the convention becomes a pricing decision that deserves explicit documentation and governance — not an assumption buried in a spreadsheet.

Two-thirds of the effect is structural

Here is an experiment worth running. Take the spread model and remove the drift: set the mean-reversion target equal to the current level so that spreads have no expected direction. In this flat-spread world, is the gap between S_t and S_s still there?

It is. The gap shrinks by about one-third, but two-thirds of the effect survives. The surviving piece is structural — it comes from the simple fact that a tranche issued eighteen months ago was issued in a different market, and its price is frozen there. Even if the market has not trended in any direction, random fluctuations since issuance mean that the average strike on the standing book will differ from today's spot. The only way to eliminate the gap entirely is to have all tranches issued at exactly today's spread — which requires either instantaneous rollover or zero volatility. Neither exists.

The structural component does not require a trending market. It requires only that time has passed and spreads have moved — in any direction, by any amount. The subscript choice matters even when the market is going nowhere.

The implication is practical: a bank that dismisses the S_t/S_s distinction because "spreads are stable right now" is still making a choice worth tens of basis points. The distinction does not disappear in calm markets. It only shrinks by a third.

Policy implications: the ladder as a governance choice

The ladder is not a market outcome. Nobody forces a bank to fund at three months or two years. The tenor mix is a policy decision, made by the ALCO or the treasury committee, and it reflects a set of trade-offs that deserve explicit articulation:

• Cost tolerance: how much is the bank willing to pay in basis points to avoid refunding risk? The all-two-year ladder costs 67 bps more than the all-three-month ladder. Is that gap worth the stability?
• Market-access frequency: can the bank reliably access wholesale markets sixteen times per year? Four times? Twice? The answer depends on the bank's credit standing, its market relationships, and the depth of its investor base.
• Operational capacity: every roll requires documentation, settlement, counterparty management. A bank with a lean treasury operation may not be able to sustain sixteen annual issuances without error.
• Risk appetite: the short ladder concentrates repricing risk in frequent rolls. The long ladder spreads it over fewer events but locks in higher base costs. Neither extreme is right for every institution.

What matters for governance is not which ladder the bank picks. It is that the bank names the convention — S_t or S_s — measures the gap between them, reports it to the appropriate committee, and owns the choice. A treasury that cannot state which subscript its transfer-pricing model uses is a treasury that does not know what its funding costs.

A bank that loads on short money saves on expected cost but concentrates repricing risk in frequent rolls. A bank that extends tenor pays a higher base but smooths the repricing over fewer events. The right answer depends on the institution's risk appetite, its market access, and the shape of its balance sheet. What is never the right answer is picking a ladder by inertia and never examining what it implies for the cost of funds.

The subscript is a single letter in the model's notation. S_t or S_s — one character of difference. But the gap between reading today's spread and yesterday's strike can move the cost of funds by twenty or more basis points. Most transfer-pricing implementations do not even name the choice. They pick one subscript and never revisit it. The ladder gets inherited from a predecessor. The reset convention gets buried in a system configuration. And the bank goes on pricing loans against a cost-of-funds number whose provenance nobody can trace.

The ladder and the convention deserve the same governance attention as the spread model itself. They are not ancillary inputs. They are structural choices that determine what the model sees when it looks at the book. A model that reads the wrong spread with perfect precision is still reading the wrong spread.

Because a model that prices the wrong spread precisely is still pricing the wrong spread.

The worked example uses Avelmont, a fictional institution, with illustrative parameters calibrated to public data. The approach described is one way — not the only way — to think about the relationship between the funding ladder, the reset convention, and the transfer price. Practitioners should adapt the framework to their own balance sheets and market conditions.