Risk: From Market Risk to Expected Credit Loss, Part 4. Previously: Stress Testing.
Probability of default is the first of three numbers that every credit risk model in every bank reduces to. The other two are loss given default and exposure at default. Together they answer one question: if this borrower fails, how much do we actually lose?
The equation
Expected Loss = PD × LGD × EAD
Three factors, one multiplication. A loan with a 2% probability of default, 40% loss given default, and 10 billion VND of exposure carries an expected loss of 2% × 40% × 10bn = 80 million VND.
That number is not a prediction about this loan. This loan will either default or not; it will not lose exactly 80 million. The figure is what the loan costs on average across many similar loans, which is precisely what a bank needs in order to price credit and set provisions.
Note the structure: expected loss is a cost of doing business, priced into the interest rate. Unexpected loss — the variation around that average — is what capital exists to absorb. Confusing the two is the most common conceptual error in credit risk.
Probability of default
PD is the likelihood that a borrower fails to meet obligations over a defined horizon, usually one year.
The definition of “fails” matters more than it sounds. Basel’s reference definition is 90 days past due, or an assessment that the borrower is unlikely to pay without recourse to collateral. Vietnamese regulation reaches a similar place through loan classification: under Circular 31/2024/TT-NHNN loans are classified into five groups by deterioration, with groups 3 to 5 constituting non-performing debt.
Estimation runs through one of three routes:
- Internal rating models. Score borrowers on financial ratios and qualitative factors, group them into rating grades, and observe the historical default rate of each grade.
- External ratings. Map agency ratings to published default statistics. Usable for large corporates, irrelevant for the SME and retail book where most Vietnamese lending sits.
- Market-implied. Back out default probability from bond spreads or CDS. Requires liquid traded credit, which rules it out in most of the region.
One subtlety that the next post is devoted to: a PD can be estimated as a long-run average across the cycle, or as a current best estimate for today’s conditions. Those two numbers differ substantially, and using the wrong one is a live problem in practice.
Loss given default
LGD is the fraction of exposure not recovered after default, expressed as a percentage. Recover 60% of a defaulted loan and LGD is 40%.
It is harder to estimate than PD for reasons that are operational rather than statistical. Recovery takes years, so the data arrives late. Recovery depends on collateral quality, legal enforcement speed, and the state of the market when the collateral is sold. And it is correlated with PD — defaults cluster in downturns, which is exactly when collateral values are depressed and buyers are scarce.
That correlation is why supervisors require downturn LGD rather than a simple historical average. An LGD estimated across good years understates losses in the year it matters.
For secured lending the main drivers are the loan-to-value ratio at origination, how quickly collateral can be legally seized and sold, and the depth of the secondary market for that asset type. In Vietnam the second factor dominates — enforcement timelines move LGD more than valuation haircuts do.
Exposure at default
EAD is the amount outstanding when default occurs. For a term loan with a fixed amortisation schedule this is nearly trivial.
For anything with an undrawn commitment, it is the hardest of the three. A borrower approaching distress draws down available credit lines, so exposure at default routinely exceeds exposure today. A credit card or revolving facility that appears half-utilised in normal conditions may be fully drawn by the time of default.
The standard treatment uses a credit conversion factor applied to the undrawn portion:
EAD = drawn amount + CCF × undrawn amount
Estimating CCF requires data on utilisation paths in the run-up to default, which most banks have in poor shape because the historical systems were built to record balances rather than trajectories.
How the three compare
| PD | LGD | EAD | |
|---|---|---|---|
| Measures | Likelihood of failure | Severity of failure | Size at failure |
| Horizon | Usually 1 year | Resolution period | Point of default |
| Driven mainly by | Borrower quality | Collateral and enforcement | Facility structure |
| Data available | Reasonable | Sparse and lagged | Often poor |
| Hardest part | Few defaults to observe | Downturn adjustment | Utilisation behaviour |
The practical conclusion surprises people new to the field: PD gets most of the modelling attention, but LGD and EAD are where estimates are weakest. A precise PD multiplied by a guessed LGD is still a guess.
Frequently asked questions
What is probability of default?
It is the likelihood a borrower fails to meet obligations within a set horizon, usually one year, where failure is typically defined as 90 days past due or unlikeliness to pay.
Why is LGD harder to estimate than PD?
Because recovery data arrives years late, depends on legal enforcement and market conditions, and correlates with PD — losses are deepest precisely when defaults are most frequent.
What is a credit conversion factor?
It is the fraction of an undrawn commitment assumed to be drawn by the time of default. Borrowers in distress typically draw down available lines, so exposure grows as credit quality falls.
What is the difference between expected and unexpected loss?
Expected loss is the average cost, priced into the lending rate and covered by provisions. Unexpected loss is the variation around it, and that is what capital absorbs.
Try it yourself
Build an expected loss calculation, in this order:
- Take a portfolio of ten hypothetical loans with different sizes and ratings.
- Assign each a PD from a rating grade, an LGD by collateral type, and an EAD including any undrawn amount.
- Compute expected loss per loan and sum across the portfolio.
- Raise every LGD by ten percentage points and recompute.
- Compare that change against a ten-percentage-point increase in PD instead.
The two shifts move the total by the same proportion, which makes the point of the last section concrete: a well-estimated PD paired with a weak LGD gives you a well-estimated fraction of a bad answer.
Next in this series: through-the-cycle versus point-in-time PD — the distinction that changes everything.