Credit Risk 103: Expected Loss Isn't a Formula, It's a Bet Lenders Don't Realize They're Making

When the Model Was Right But the Money Was Still Lost

Priced a book three years ago where the PD was spot on. Borrower segment defaulted at 7.8%, model said 8.1%. Victory lap, right?

The book still lost money.

Because while PD held, exposure at default came in 60% higher than underwriting assumed. Borrowers drew down their full credit lines in the months before they defaulted, behavior the model didn't predict because no one had ever asked it to.

A shorter version of this piece appears on LinkedIn.

That portfolio was a $180 million book of revolving credit facilities to small business borrowers. Clean model, reasonable spreads, diversified geographies. The credit committee had spent three meetings debating the probability of default estimate—was 8% too high? Should we use 7.5%? What about industry stress scenarios from 2008?

They settled on 8.1%. The model performed. The portfolio delivered 7.8% defaults over the three-year window, well within acceptable variance.

But that $180 million book became a $247 million book right before the defaults hit. Not because of portfolio growth or new originations, but because the borrowers who were about to default drew their lines to the maximum in the six months preceding their default date. Average utilization at default: 91%. Underwriting assumption: 57%.

The loss wasn't wrong because the model was poorly calibrated. It was wrong because it was modeling only one dimension of a three-dimensional problem.

The Formula That Isn't Just a Formula

Expected Loss looks like a formula:

Where:

- **PD** = Probability of Default

- **LGD** = Loss Given Default

- **EAD** = Exposure at Default

Three inputs. One multiplication operation. Clean, tidy, ready for a spreadsheet.

But it's not arithmetic. It's a system, and the components don't sit still while you multiply them.

PD tells you how often borrowers default. EAD tells you how much they owe when they do. Get PD right and EAD wrong, and the loss lands exactly as hard as if you'd modeled neither. Most lenders calibrate PD obsessively and treat EAD like a static input, a percentage of committed exposure locked in at origination. But exposure moves. Borrowers in distress don't pay down, they draw down. The ones who default aren't randomly sampled from your book, they're the ones who maximized their exposure right before they stopped paying.

Here's what most lenders miss: these three components aren't independent variables you can estimate separately and then combine. They're interdependent measurements of borrower behavior under financial stress, and they correlate in predictable but widely ignored ways.

When a borrower starts to experience distress, they don't just become more likely to default (increasing PD). They simultaneously change their behavior in ways that affect both how much they owe (EAD) and how much you'll recover (LGD). A struggling business doesn't make its normal payments while maintaining normal operations. It draws its line to fund operations, stops paying vendors, lets collateral deteriorate, and begins the slow dissolution of enterprise value that tanks your recovery rate.

A Worked Example: The Math Lenders Actually Use vs. The Math That Actually Happens

Let's use real numbers from a hypothetical revolving credit book to show how this plays out.

**What the model assumed:**

- Portfolio of 1,000 borrowers

- Average committed line: $500,000

- Assumed utilization at default: 60%

- Probability of default: 8%

- Loss given default: 45%

Expected loss calculation:

The pricing desk adds a credit spread sufficient to cover $10.8M in expected losses plus a buffer for unexpected losses and a return hurdle. Loan committee approves. Book gets funded.

**What actually happened:**

- 78 borrowers defaulted (7.8% default rate—model was right!)

- Average utilization at default: 92%

- Loss given default: 51% (collateral had deteriorated pre-default)

Actual loss calculation:

Expected loss: $10.8M. Actual loss: $18.3M. Difference: 69% higher than modeled.

The PD was nearly perfect. The book still lost $7.5 million more than anticipated, completely overwhelming the risk buffer and turning a theoretically profitable portfolio into a loss-maker.

Why Lenders Miss This: The Calibration Trap

Most credit teams operate in a world where PD gets all the attention. There are entire conferences dedicated to PD modeling. Consultants specialize in PD calibration. Regulatory guidance focuses overwhelmingly on ensuring PD estimates are robust, back-tested, and stress-tested.

EAD? It gets a paragraph in the model documentation and a static assumption in the pricing tool.

This happens for three reasons:

**First, data availability.** Every lender tracks defaults. It's a binary, observable event. You know exactly who defaulted and when. Building a PD model requires historical default data, and every lender has it. But how many lenders track monthly utilization patterns segmented by borrowers who eventually defaulted versus those who didn't? How many can tell you the draw-down behavior in the six months pre-default versus the six months prior to that? The data exists in the servicing system, but it's rarely extracted, structured, or analyzed with the same rigor as default outcomes.

**Second, regulatory focus.** Basel II and III frameworks require extensive PD modeling and validation but provide far less prescriptive guidance on EAD for non-retail exposures. The regulatory floor is lower, so lenders do less. The irony is that regulatory capital calculations use the same EL formula, meaning underpredicted EAD flows directly into underpredicted capital requirements.

**Third, organizational structure.** PD modeling typically lives in a centralized credit risk team with quants, statisticians, and dedicated resources. EAD assumptions often get set by product teams or underwriting, based on "industry standards" or historical portfolio averages, without the statistical apparatus that surrounds PD. No one owns EAD modeling the way someone owns PD modeling.

The result: lenders spend months calibrating a PD model to the second decimal point, then multiply it by an EAD assumption someone pulled from a dropdown menu.

What This Means in Practice

That behavior isn't random. It's modelable.

Borrowers in distress exhibit predictable patterns:

- They draw revolving lines more aggressively (higher utilization)

- They delay payments on term facilities (higher current exposure)

- They divert cash from operations to owners (lower recovery values)

- They stop maintaining collateral (higher LGD)

None of this is mysterious. It's all observable in historical data if you structure the analysis correctly.

Here's what that looks like operationally:

**For revolving credit:** Track utilization rates by cohort and time-to-default. Borrowers 6-12 months from default typically show utilization 20-40 percentage points higher than performing borrowers. That's not noise; that's signal. Model it.

**For term loans:** Exposure doesn't grow, but it doesn't amortize as expected either. Distressed borrowers miss payments or negotiate modifications that defer principal. Your EAD assumption of 80% of original balance (assuming some amortization) becomes 95% because the borrowers who default are the ones who haven't paid down.

**For letters of credit and commitments:** Distressed borrowers draw unfunded commitments at rates 3-4x higher than performing borrowers. If your EAD model assumes 20% conversion of unfunded commitments, you'll see 60%+ for the cohort that actually defaults.

All of this affects the formula:

Not as three separate inputs, but as three correlated behaviors that all spike simultaneously when a borrower enters distress.

The Dangerous Comfort of Accurate PD

There's something particularly insidious about getting PD right while missing EAD. It creates false confidence.

When defaults come in close to forecast, risk teams feel validated. The model worked. The process held. The quarterly risk report shows actuals within confidence intervals, and everyone moves on.

Meanwhile, the portfolio bleeds from a wound no one's measuring. Loss dollars come in high, but it's attributed to "elevated loss severity" or "tough recovery environment"—qualitative explanations that don't trigger model recalibration because the default rate, the thing everyone watches, performed fine.

This is how portfolios drift into unprofitability while the credit models show green lights. The measurement system is optimized for one component of risk and nearly blind to another component with equal impact on outcomes.

The fix isn't complicated in concept: apply the same rigor to EAD that you already apply to PD. Segment by behavior, track pre-default patterns, build statistical models that predict utilization conditional on borrower characteristics and stress indicators.

But it requires acknowledging that the formula isn't three independent variables you can estimate in isolation. It's a system where borrower behavior under stress affects all three components simultaneously, and where getting one right while ignoring the others produces losses that feel like they came from nowhere.

They didn't come from nowhere. They came from exactly where the model wasn't looking.

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Next week: how these three components interact under stress, and why your loss forecast breaks in a downturn even when your PD model holds.

If this gap exists in your book, let's look at it together: calendly.com/muhammed-adediran/30min