Credit Risk 201: The Stress Test That Told the Truth

The Stress Test That Told the Truth

I ran a stress test for a commercial lender last month. The scenario was severe but plausible: unemployment up four points, property values down eighteen percent, base rate held high for another year. Their model ran clean. PD ticked up as expected. LGD moved in line with historical recovery rates under stress. EAD stayed within tolerance.

Reserves looked adequate.

Six weeks into the actual downturn, they weren't.

The model wasn't wrong about any single component. PD did rise. LGD did worsen. EAD did expand. But the three moved together, and the interaction was worse than the sum. Borrowers who were marginal at origination defaulted faster under rate pressure. Collateral liquidation took longer in a weak property market, raising collection costs and eroding time-adjusted recovery. Undrawn credit lines got pulled hard exactly when cash flow tightened.

Each input was stress-tested in isolation. The system wasn't.

This is what happens when you understand the components but miss the structure. You already know PD, LGD, and EAD as separate metrics. This series is about what happens when they move together, and why a model that passes component-level stress can still understate loss when the components interact. A shorter version of this post appears on [LinkedIn](LINKEDIN_POST_URL), but the full depth lives here.

The Three Components You Think You Know

Start with the definitions, not because they're hard, but because most lenders stop here and assume understanding follows.

Probability of Default (PD) is the likelihood a borrower fails to meet their contractual obligations over a defined time horizon, typically twelve months. It's a probability, not a verdict. A borrower with a PD of 0.08 isn't safe, they're eight-in-a-hundred likely to default under the conditions the model was trained on. Change the conditions and that number moves, whether your credit score updates or not.

Loss Given Default (LGD) is the proportion of exposure you lose once a default occurs, net of recoveries. It's expressed as a percentage of Exposure at Default. If you lend £100,000, the borrower defaults, and you recover £40,000 after costs, your LGD is 60%. The formula is:

LGD is where loan books quietly bleed, because recovery is a function of collateral quality, legal enforceability, collection costs, and time. All of those degrade under stress.

Exposure at Default (EAD) is how much you're owed when the borrower defaults. For a term loan, it's the outstanding balance. For a revolving facility, it's the drawn amount plus some estimate of what might be drawn before you can cut the line. EAD is the one component lenders consistently underestimate, because borrowers draw down credit lines hard exactly when financial stress hits.

Most credit risk models treat these as independent inputs. They're not. They're parts of a system, and the system behaves differently under stress than the components do in isolation.

Expected Loss: The Formula Everyone Uses

Expected Loss is the product of the three components:

This is the baseline. If you have a portfolio of 1,000 loans, each with £50,000 outstanding, a PD of 0.05, and an LGD of 0.50, your expected loss over twelve months is:

That's the number you provision for under normal conditions. The model assumes that 5% of borrowers default, you lose half of what's owed when they do, and the exposure stays at £50,000. The formula is clean. The assumptions are fragile.

What Stress Does to the Components

The lender I worked with last month understood what stress does to each component individually. They ran their PD model under the unemployment shock and saw defaults rise from 5% to 8%. They adjusted LGD upward from 50% to 58% to reflect weaker collateral values and longer recovery timelines. They modeled EAD creep, estimating that undrawn commitments would be pulled at a higher rate, lifting average exposure by 12%.

Component by component, the model was defensible. PD moved in line with historical recession behavior. LGD reflected the property market stress. EAD captured the liquidity squeeze. Plug the stressed inputs into the expected loss formula and reserves looked adequate.

But the three components don't move independently. They move together, and the interaction amplifies the loss.

The Interaction Nobody Modeled

Here's what actually happened when the downturn hit.

Borrowers who were marginal at origination, the ones sitting just above the approval threshold, defaulted faster than the model predicted. Not because the PD model was wrong, but because the stress hit multiple risk factors at once. A borrower with tight debt service coverage loses their job in a high-unemployment scenario. Their property value drops, eliminating any equity buffer. The rate stays high, so refinancing isn't an option. They default not at the historical 8% rate the stressed PD suggested, but at 11%, because the stresses compounded.

That's the first interaction: PD and macroeconomic stress aren't independent. A borrower's probability of default under a single shock (unemployment alone) is lower than their probability under multiple simultaneous shocks (unemployment plus falling property values plus sustained high rates). The model tested each shock separately and missed the joint effect.

The second interaction was between LGD and the property market. Collateral liquidation took longer in a weak market. Longer timelines mean higher holding costs, higher legal fees, and greater time-adjusted erosion of recovery value. The model had stressed LGD to 58% based on historical recovery rates during past downturns, but those historical periods didn't feature the same illiquidity in the property market. Actual LGD came in at 64%, not because collateral values fell further than expected, but because the time to liquidate stretched from an average of nine months to fourteen. Time is a cost, and the model hadn't priced it into the stressed scenario.

The third interaction was between EAD and borrower behavior under financial stress. Undrawn credit lines got pulled hard exactly when cash flow tightened. The model had estimated a 12% increase in drawn balances, based on historical drawdown rates during prior stress periods. But this time, borrowers were more aggressive. They drew lines faster and fuller, because they saw the stress coming and wanted liquidity before the lender could cut access. Actual EAD came in 19% higher than the stressed estimate, not because the model was wrong about behavior in general, but because it didn't account for the speed and intensity of drawdowns when multiple stress signals hit at once.

Each component moved worse than expected, but the real problem was that they moved together. The borrowers who defaulted faster were the same ones whose collateral was hardest to liquidate, and they were the same ones who had drawn their lines heaviest before default. The model had stress-tested PD, LGD, and EAD as separate variables. It hadn't stress-tested the portfolio of borrowers where all three were elevated simultaneously.

The Reserve Gap

Run the numbers with the actual outcomes. The portfolio had 1,000 loans, average drawn balance of £50,000 at the start. Under the original stress scenario:

That's what they provisioned for. Under the actual conditions:

The gap between the stressed reserve and the actual loss was £1.6 million on a £50 million book. Not catastrophic, but not immaterial either. More importantly, it was a gap that didn't come from a modeling error in any single component. It came from testing the components in isolation and missing the interaction.

Why Component-Level Stress Isn't Enough

The standard approach to credit risk stress testing is to shock each input, hold the others constant, and measure the sensitivity. Increase PD by two standard deviations, see what happens to expected loss. Increase LGD by 20%, see what happens. Increase EAD by 15%, see what happens. Add up the effects, apply some judgmental overlay for conservatism, and call it a stressed scenario.

That approach works when the components are genuinely independent. They're not.

PD, LGD, and EAD are all functions of the same underlying economic conditions. A recession doesn't just increase the probability that borrowers default. It increases the probability that the borrowers who default are the ones with weaker collateral, longer recovery timelines, and higher drawn balances at the point of default. The components are correlated, and the correlation is strongest exactly when you need your stress test to be accurate.

This isn't a statistical nicety. It's the thing your capital model is quietly betting against. When you stress-test components in isolation, you're implicitly assuming that the worst-case PD happens with average LGD and average EAD. That's not how stress works. The worst-case PD happens with worse-than-average LGD and worse-than-average EAD, because the same conditions that drive defaults also drive recovery losses and exposure expansion.

What a System-Level Stress Test Looks Like

A system-level stress test doesn't shock the components independently. It shocks the underlying economic drivers and lets the components respond jointly.

Start with the macroeconomic scenario: unemployment up four points, property values down eighteen percent, base rate held high for another year. Don't feed those shocks into separate PD, LGD, and EAD models. Feed them into a single model that estimates the joint distribution of outcomes.

That means modeling not just the marginal probability that PD rises to 8%, but the conditional probability that PD rises to 8% and LGD rises to 64% and EAD rises by 19%, all in the same cohort of borrowers. It means recognizing that the borrowers who default under stress are not a random sample of the portfolio. They're the ones who were already marginal, and marginality is correlated with collateral weakness and liquidity pressure.

The math gets harder. You need to estimate the correlation structure between PD, LGD, and EAD under stress, and that requires data from prior stress periods where you observed all three moving together. Most lenders don't have that data, or don't have it in a form that's usable for modeling. But the alternative is to keep stress-testing components in isolation and hope the interactions don't matter. They do.

The Practical Edge Case: Undrawn Commitments

The hardest part of system-level stress testing is modeling EAD, because EAD is partly under the borrower's control. A term loan has a fixed exposure. A revolving credit facility has an exposure that can change daily, and it changes most when the borrower is under stress.

The standard approach is to apply a Credit Conversion Factor (CCF) to undrawn commitments. If a borrower has £20,000 drawn and £30,000 undrawn on a £50,000 facility, you assume they'll draw some portion of that undrawn amount before default. The CCF is typically estimated from historical data, something like 40% for corporate revolvers, meaning you'd model EAD as:

That works under normal conditions. Under stress, borrowers don't draw at the historical average rate. They draw faster, and they draw more, because they see the stress coming and want liquidity before the bank cuts access. The CCF that holds under normal conditions understates EAD under stress, and the understatement is largest for the borrowers most likely to default.

The lender I worked with had modeled a stressed CCF of 50%, up from 40% under normal conditions. Actual drawdowns came in closer to 60%, because borrowers were more aggressive than the historical data suggested. That's the edge case: when borrower behavior under stress is different in kind, not just in degree, from behavior under normal conditions. The model can't catch that unless it's built to recognize that stress changes incentives, not just probabilities.

Why This Matters for Capital

The reserve gap I described earlier wasn't just an accounting problem. It was a capital problem.

Banks hold capital against expected loss and unexpected loss. Expected loss is what you provision for. Unexpected loss is what you hold capital for, the tail risk that your actual losses exceed your provisions. The size of the capital buffer you need depends on how much uncertainty there is around your expected loss estimate.

If you stress-test components in isolation, you understate both expected loss and the uncertainty around it. You think your stressed expected loss is £2.6 million when it's actually £4.2 million, and you think the uncertainty band around that estimate is narrower than it is, because you haven't modeled the correlation that makes the tail fatter.

That means your capital buffer is too small, not just relative to the actual expected loss, but relative to the actual unexpected loss. You're undercapitalized for the scenario you stress-tested, and you don't know it until the scenario happens.

Regulators know this. That's why the capital frameworks (Basel II, Basel III, IFRS 9) all require institutions to model not just the components of credit risk, but the interactions between them. The language is usually buried in technical annexes about correlation assumptions and joint probability distributions, but the requirement is there. A stress test that shocks PD, LGD, and EAD independently doesn't meet the standard, even if each component is modeled correctly.

What to Do About It

If you're running credit risk models, the first step is to stop treating PD, LGD, and EAD as independent inputs. They're not. They're outputs of the same underlying economic process, and they move together under stress.

The second step is to build or buy a model that estimates the joint distribution of outcomes, not just the marginal distributions. That means modeling the correlation structure between the components, using data from prior stress periods where you observed all three moving together. If you don't have that data, use proxy data from comparable institutions or markets, or use scenario analysis to estimate the correlations under different stress conditions.

The third step is to test the model against historical stress events and see whether it would have predicted the reserve gap that actually occurred. If your model would have understated losses during the last recession, it will understate losses during the next one. Fix it before the next one happens.

The fourth step is to communicate the results clearly to the people who set capital policy. The interaction between PD, LGD, and EAD isn't a technical modeling detail. It's a driver of capital adequacy, and it needs to be part of the conversation about how much buffer the institution needs to hold.

Next Week

This is Part 1 of a four-part series on system-level credit risk. Next week: why correlation isn't just a statistical nicety, it's the thing your capital model is quietly betting against, and how to estimate it when your data is thin.

If you're running credit risk models and need to stress-test the interaction before the scenario surfaces it, the calendar link is calendly.com/muhammed-adediran/30min.