P6. Low Default Portfolios: Rating Models With No Data

Risk: From Market Risk to Expected Credit Loss, Part 6. Previously: Through-the-Cycle vs Point-in-Time PD.

A low default portfolio is one where defaults are too rare to estimate default probability reliably by counting them. Sovereign exposures, large corporates, project finance, specialised lending — and, in many emerging-market banks, entire segments where the portfolio is simply young.

The textbook answer assumes thousands of observed defaults. Here you might have four.

Why counting fails

Suppose a grade contains 200 borrowers and recorded one default last year. The naive estimate is 0.5%.

Now consider the uncertainty. With one event in 200 trials, the 95% confidence interval runs from roughly 0.01% to 2.8%. The point estimate is nearly meaningless — the true rate could plausibly be fifty times smaller or five times larger.

Worse is the case that occurs constantly in practice: zero observed defaults. The naive estimate is 0%, which is obviously wrong. No exposure has zero default probability, and a model that says otherwise will be rejected the moment anyone looks at it.

Five approaches that work

None of these conjures data that does not exist. Each trades a different assumption for stability.

1. Pooling. Combine grades or segments with genuinely similar risk characteristics to increase the observation count.
2. The confidence-bound method. Rather than using the point estimate, use the upper bound of a confidence interval as the PD.
3. External benchmarking. Map internal grades to rating-agency grades and borrow their long-run default statistics.
4. Shadow rating. Build a model that replicates external ratings, then apply it to unrated borrowers and inherit the associated default rates.
5. Expert judgement with structure. Document a defensible rationale for the assigned PD, subjected to challenge and periodic review.

The confidence-bound method in practice

This is the most widely accepted technique and the one supervisors expect to see, so it is worth stating concretely.

Take the zero-default case: a grade with 100 borrowers and no defaults observed. Ask what the highest true PD could be that would still make zero defaults a plausible outcome. At a 95% confidence level the answer is approximately 3%. That figure, not 0%, becomes the PD.

The logic is conservative by construction, and the conservatism scales correctly: a grade with 1,000 clean observations yields a bound near 0.3%, ten times lower. More evidence earns a lower number.

What goes wrong with pooling

Pooling is the first instinct and the easiest to abuse. Combining two grades because it produces a workable number, rather than because the borrowers are genuinely comparable, destroys the rating model’s discriminatory power while appearing to solve the problem.

Three tests before pooling. Do the segments share economic drivers? Does the rating model assign them similar scores for similar reasons? Would a credit officer consider them equivalent risks? If any answer is no, pooling is hiding the problem rather than addressing it.

The emerging-market version

In a Vietnamese bank the low-default problem is rarely confined to exotic exposures. It appears across ordinary segments, for three reasons.

The portfolio is young. Rapid loan growth means much of the book has not yet lived through a full cycle. Default rates on recent vintages understate lifetime experience simply because the loans have not aged.

Data predates the systems. Default history from before a core banking migration is often incomplete or inconsistently defined, so the usable series is shorter than the bank’s actual operating history.

Restructuring masks defaults. Loans restructured under forbearance programmes may not appear as defaults in the historical record even where the underlying credit deteriorated. This matters specifically in Vietnam, where restructuring circulars have repeatedly permitted retaining existing loan groups — meaning the recorded classification understates true migration.

The last point deserves explicit treatment in any model documentation. A PD estimated from a period covering a forbearance programme, without adjustment, embeds a downward bias that is invisible to anyone reading only the output.

Making it defensible

With thin data, the model cannot be validated on statistical power alone. What carries the weight is documentation.

• State the data limitation explicitly. A validator who discovers it independently will treat everything else with suspicion.
• Show the uncertainty. Report confidence intervals alongside point estimates rather than presenting a single figure.
• Justify every conservative adjustment. Including why that confidence level, and not a different one.
• Benchmark externally. Comparison against agency statistics or peer-bank disclosures is evidence even when it is imperfect.
• Define the review trigger. Specify how many additional observations would prompt re-estimation, and when.

The goal is not a model that looks precise. It is a model whose limitations are stated more clearly by its owner than by its critics.

Frequently asked questions

What is a low default portfolio?

It is a portfolio where observed defaults are too few to estimate PD reliably by counting — sovereigns, large corporates, specialised lending, and young or fast-growing books.

What PD do you assign when zero defaults are observed?

Not zero. The standard method uses the upper bound of a confidence interval, which for 100 clean observations gives roughly 3% at 95% confidence.

Is pooling segments acceptable?

Only when the segments share economic drivers and comparable credit characteristics. Pooling purely to obtain a workable sample destroys discriminatory power while appearing to fix the problem.

How does loan restructuring affect PD estimates?

Forbearance can keep deteriorating loans in their existing classification, so recorded defaults understate true migration. Estimates covering such periods need explicit adjustment.

Try it yourself

Quantify how thin your evidence really is, in this order:

1. Take a rating grade and record its borrower count and observed defaults.
2. Compute the naive default rate.
3. Compute the 95% upper confidence bound for that count.
4. Compare the two figures and note the ratio.
5. Repeat for your largest and smallest grades.

The grades where the ratio is largest are where your model is weakest — and they are rarely the ones receiving the most attention.

Next in this series: IFRS 9 expected credit loss, applied to Vietnamese banks.