I recently saw a copy of a 2023 ECB workshop presentation on deposit modelling being circulated on LinkedIn. It fascinated me for a few reasons.

  1. The upper bound of the range is significantly over the Basel and EBA deposit caps. The model doesn’t split core from non-core, so its 14.4-year output applies to the whole NMD base, nearly three times the EBA aggregate cap. Against Basel, the implied core duration is further still.
  2. The twelve-year range itself, 14.4 years down to 2.5, felt intuitively odd. It seems unlikely that a typical retail base contains enough rate-sensitive depositors to create that kind of swing.
  3. The model is wildly rate-sensitive. I recently wrote an article showing a one-year shift in deposit duration is enough to consume the EVE SOT limit. The twelve-year swing this model generates is therefore an immediate SOT buster. It would be difficult to adopt without significantly dampening the rate sensitivity first.

A few caveats. The presentation was prepared by Peter Hoffmann, Sebastian Frontczak and Federico Pierobon for the 2023 EBA Policy Research Workshop, with the standard disclaimer that the views are the authors’ alone and not necessarily those of the ECB. The slides are noted as not intended for circulation, so the authors are clearly not advocating its use at this point. That said, they are publicly available on the EBA website and I have seen them floating around in other LinkedIn posts. It’s an interesting case study on the impact of models on IRRBB metrics.

The main thing I wanted to understand was what is driving the duration range. This is what I found.

What the model does

The presentation states:

On average, a 100 bps increase in the difference between deposit and market rates implies a monthly increase (decrease) of 0.4% (or 5% per year) in deposit volumes.

In a low-rate world, the gap between market and deposit rate is small. Outflows are small. Deposits look sticky. The model returns 14.4 years.

In a high-rate world, the gap widens sharply. The 5% rule gets applied to a much bigger gap, year after year, and the deposit base is modelled as melting away. Duration collapses to 2.5 years.

What’s driving the range

Two problems, the second following from the first.

Problem 1: Everyone behaves the same

The model applies one behavioural response across the deposit base. There is no distinction between the customers who chase rate and the ones who don’t. One elasticity, one response function, and every euro is assumed to have the same probability of leaving regardless of who holds it.

This is wrong in a specific and obvious way. Depositors come in flavours. Some people obsessively chase rate. Most don’t. Salary lands, direct debits go out, and the balance sits there.

The aggregate 5% number is a mass-weighted average of these populations. Applied uniformly to every euro of deposits, it overestimates how much of the base will move when rates rise. The hot money has already been priced in.

The authors have probably skipped the split between rate-sensitive and non-rate-sensitive deposits because the alternative requires judgement and isn’t directly observable in aggregate data. That’s a defensible choice for a workshop presentation, you estimate what you can estimate. But the absence of that split is itself an assumption, and in this case it materially changes the duration. By treating all customers as behaviourally uniform, the model implicitly assumes the sticky cohort is zero. That is the choice driving the twelve-year range.

This is the assumption doing all the work. The other problem is what happens when you carry it through the maths.

Problem 2: Outflows compound forever

The model says a 1% gap causes 5% of deposits to leave this year. And another 5% next year. And another the year after, indefinitely, for as long as the gap stays open.

In reality, a rate gap opens, the price-sensitive depositors notice, they move, and they’re gone. The runoff is front-loaded. After the movers have left, the remaining base is the cohort that didn’t move when they had the chance, so by revealed preference they aren’t going to move in year two or year three either. Outflows should spike and then tail off.

The model can’t see this, because it doesn’t know the population has two types. It just keeps applying the same percentage to whatever balance is left, as if a fresh cohort of rate-sensitive customers showed up every January. In the high-rate scenarios, this is what drives duration to collapse. The model is exhausting a finite pool of movers indefinitely.

The fix

Split the depositor base into a sticky cohort and a rate-sensitive cohort. Apply two different outflow elasticities, a low one for the inert customers and a much higher one for the rate-chasers. Cap the rate-sensitive cohort’s outflows so they can’t run beyond the size of that cohort.

Make that single change and the range narrows dramatically. As an illustration, on a 50% sticky / 50% sensitive split, the 14.4-year to 2.5-year range becomes something more like 7 years to 5 years. This is purely an example. The actual split will be bank-specific and needs to be calibrated to each franchise. Still a real rate sensitivity. Not a model that flips its mind every time the policy rate moves a hundred basis points.

I’m not sure this fix in isolation will make the model adoptable in the IRRBB EVE use case. There will still likely be problems with the model output producing ranges outside the regulatory caps and bank risk appetite. But it will make the rate-dynamic element more plausible.

The takeaway

The model applies the same rate-sensitivity to every customer, then lets that single assumption compound year after year against the whole deposit base.

A single uniform-elasticity assumption, run through standard methodology, produces an IRRBB duration range twelve years wide. Most of that range falls outside the regulatory perimeter on one side or the other.