Monitoring Static Behavioural Assumptions Without Pretending They’re Models

In ALM and IRRBB, behavioural assumptions are the quiet workhorses of the model. An annual prepayment rate of 8%, an early-redemption rate of 12%, a deposit attrition curve — these are often treated as fixed inputs rather than outputs of a live parametric model.

Why? Because sometimes the data simply isn’t rich enough for a reliable logit or survival model. Covariates lack significance. Granular loan-level history is patchy. Or the governance committee prefers a transparent, auditable number over a black-box equation. So teams do the pragmatic thing: they calculate a historical average (simple mean or balance-weighted) from 2015–2020 and lock it in as the static assumption for cash-flow projections, EVE, and NII.

But “static” does not mean “set and forget.” Borrower behaviour drifts — interest-rate cycles, policy changes, generational shifts, economic shocks. The question is: how do you know when the assumption has drifted far enough that it needs recalibration, without pretending you have a full dynamic model?

The Practical Middle Ground: Wilson Confidence Intervals

Most teams either (a) jump straight to complex parametric models or (b) eyeball the latest observed rate against the assumption. Both are suboptimal.

The elegant solution sits right in the middle: use Wilson score intervals to create a statistically defensible monitoring band around the observed behaviour. If your static assumption falls inside the band, it remains consistent with recent data — no action required. If it falls outside, you have objective evidence to escalate to the ALM committee.

This is governance-friendly, auditable, and works with any behavioural proportion (prepayments, defaults, attrition, utilisation, etc.).

The Wilson interval is not a model of behaviour. It is a monitoring tool that tells you when your pragmatic static number has become inconsistent with what you are actually seeing.

The Real-World Story (2020 → 2021 and Beyond)

December 2020. Your mortgage portfolio has 5,000 loans. Over five years you’ve calculated a balance-weighted average prepayment rate of 8.0%. No fancy model with LTV, credit score, and rate incentive showed statistical significance beyond this mean. The assumption is locked.

Q1 2021. You begin quarterly monitoring. Each quarter you calculate the recent observed prepayment rate (rolling 12-month or period-specific) and the corresponding sample size (number of mortgages, or effective sample size if balance-weighted).

You plug the numbers into a 95% Wilson confidence interval.

If the interval is, say, [6.2%, 11.8%] and your 8% assumption sits comfortably inside → green light. Behaviour is statistically consistent. Keep the assumption.
If observed rate rises to 12% and the interval becomes [10.5%, 13.8%] → 8% is now outside. Red flag. Time to investigate and potentially recalibrate.

You repeat this every quarter or semi-annually. The rule is objective, transparent, and defensible to auditors and regulators.

The Wilson Formula (Everything You Need)

For a simple observed proportion

\hat{p} = \frac{x}{n}

(where

x

= number of prepayments,

n

= number of mortgages):

Let

z

be the critical value:

90% → $z = 1.645$
95% → $z = 1.96$ (most common)
99% → $z = 2.576$

The Wilson lower and upper bounds are:

\text{Lower} = \frac{\hat{p} + \frac{z^2}{2n} - z \sqrt{\frac{\hat{p}(1-\hat{p})}{n} + \frac{z^2}{4n^2}}}{1 + \frac{z^2}{n}}

\text{Upper} = \frac{\hat{p} + \frac{z^2}{2n} + z \sqrt{\frac{\hat{p}(1-\hat{p})}{n} + \frac{z^2}{4n^2}}}{1 + \frac{z^2}{n}}

(Equivalently, compute the centre

\tilde{p} = \frac{\hat{p} + \frac{z^2}{2n}}{1 + \frac{z^2}{n}}

and margin, then subtract/add.)

This formula has excellent coverage properties, stays inside [0,1], and performs far better than the normal approximation for small n or extreme rates.

Extension: When You Use a Balance-Weighted Average

Many teams use volume-weighted (balance-weighted) rates rather than simple counts. The observed rate becomes:

\hat{p}_w = \frac{\sum b_i \cdot r_i}{\sum b_i}

where

b_i

= balance of loan

i

r_i

= 1 if prepaid.

To adjust the Wilson interval for weighting, compute the effective sample size:

n_{\text{eff}} = \frac{\left( \sum b_i \right)^2}{\sum b_i^2}

Then plug

\hat{p}_w

and

n = n_{\text{eff}}

directly into the standard Wilson formulas above.

This is the standard survey-sampling correction (design effect). When balances are equal, n_eff = n. When one or two loans dominate the book, n_eff drops dramatically — correctly reflecting that you have less independent information.

The same logic applies whether you are monitoring a single quarter or a rolling window.

Beyond Finance: This Works Anywhere You Track Static Proportions

The same technique applies far outside banking and IRRBB.

SaaS / Product: monitoring whether your assumed monthly churn rate of 2.8% still holds against recent observed cancellations.
Digital marketing: checking if click-through or conversion assumptions used in media-mix models remain consistent with live campaign data.
Manufacturing / Quality: tracking defect or failure proportions against the fixed rate you use in reliability or warranty models.
Survey research & polling: deciding when a historical “likely voter” turnout assumption needs updating.
Healthcare operations: monitoring readmission or no-show rates used in capacity planning.

Whenever you have a pragmatic static proportion that drives decisions or forecasts, Wilson monitoring gives you an objective, low-drama trigger for “time to revisit the number” without requiring you to build a full predictive model first.

Try It Yourself — Interactive Monitor

Here is a fully self-contained interactive tool. Adjust the observed rate, sample size, confidence level, and your current assumed rate. The visualisation and status box update instantly.

The interactive uses the count-based version for clarity. When you work with balance-weighted data, calculate the effective sample size n_eff as shown above and use that as your “sample size” input.

Practical Takeaway

Static assumptions are often the right engineering choice. The governance problem is not that they are static — it is that teams have no disciplined way to know when they have stopped being reasonable.

Wilson score intervals give you exactly that: a transparent, statistically grounded, regulator-friendly monitoring band that works with the data you actually have.

Use it. Your future self (and your auditors) will thank you.

If you are in risk, treasury, ALM, or any function that lives or dies by behavioural proportions, this is worth running quarterly.

The Practical Middle Ground: Wilson Confidence Intervals#

The Real-World Story (2020 → 2021 and Beyond)#

The Wilson Formula (Everything You Need)#

Extension: When You Use a Balance-Weighted Average#

Beyond Finance: This Works Anywhere You Track Static Proportions#

Try It Yourself — Interactive Monitor#

Practical Takeaway#