Lesson 1.4: Defining default and the observation window
Learn how lenders define default, why the threshold and the time window change the default rate, and how to label loans good, bad or indeterminate.
By the end of this lesson you will be able to write a precise definition of default, choose an observation point and a performance window, label each loan as good, bad or indeterminate, and explain why the same portfolio can show a default rate of 3 per cent or 9 per cent depending on two choices that look like small details. You will see why loans that are too young must be left out of a 12-month default rate, and you will learn the checks that keep a definition honest. You need Lessons 1.1 to 1.3: probability of default, the loan ledger and days past due. The arithmetic is only percentages.
Lesson 1.1 said that the probability of default is a percentage of borrowers who default within a period. That sentence hides two questions. What counts as a default? And over what period? Neither has a single right answer. Yet every model, every provision and every regulatory number in this track depends on the answers. Two analysts at the same lender who use different definitions will produce different PDs from the same data, and both will be right about their own definition. A credit risk team therefore writes its definition down, signs it off and applies it everywhere.
What is a default?
In plain words, a default is the point at which the lender concludes that the borrower is not going to repay as agreed. The practical question is what evidence is enough to say so. Lenders use several tests, alone or together.
Days past due. The loan is more than a set number of days late. The commonest threshold is 90 days past due. Many regulators and international standards use it, and in India the regulator's rule for classifying a loan as non-performing is also based on a 90-day overdue test. Always check the current rule for your product and your regulator.
Unlikely to pay. The lender judges, before the 90 days, that the borrower will not repay in full without action such as selling collateral. Examples are a borrower's bankruptcy, a fraud finding or a restructuring on distressed terms.
Write-off or settlement. The lender wrote off part of the balance or agreed to accept less than owed.
Materiality. A tiny overdue amount, such as ₹50 left on a ₹2 lakh loan, may be ignored. Definitions often set a minimum amount so that a trivial shortfall does not trigger default.
Predict first: two loans of the same size are overdue. The first has missed two instalments and is 75 days past due. The second is 100 days past due on a single small instalment worth 0.5 per cent of the loan. Under a plain 90-day rule, which is in default? Would a materiality rule change your answer?
Under the plain rule, only the second is in default, because it has passed 90 days. A materiality rule could change that. If the rules ignore overdue amounts below, say, 1 per cent of the balance, the second loan would not count, and the first would be the one to watch. This is why the exact wording of the definition matters, and why the same data can produce two different default counts.
Two ways to apply the same threshold
Suppose the agreed test is 90 days past due. A second choice remains: do you look at whether a loan ever reached that point during a period, or whether it is at that point on a given date? The two answers differ, and the difference is large.
Ever 90+ in the window. A loan is bad if, at any month-end in the 12 months after the observation date, its DPD reached 90 or more. It is a measure of how many loans went through serious delinquency.
90+ at the end of the window. A loan is bad only if it is 90 or more days past due at the end of month 12. Loans that went bad earlier and were later cured, or were written off and removed, would not show.
Here are four illustrative measures from one portfolio of 10,000 loans, observed for 12 months.
The same loans give a default rate of 3.1 per cent, 4.2 per cent, 6.0 per cent or 9.5 per cent. None is wrong. They answer different questions. Ever-90 asks how many loans ever became seriously delinquent. 90-at-month-12 asks how many were still seriously delinquent on one date. A lender that compares its own PD with a peer's, or with a regulator's figure, without checking the definitions is comparing different things.
Try changing the threshold.
A shorter threshold such as 30 days gives more bad loans, which helps a model learn because it has more events to study, but many of those loans cure and never lose money. A longer threshold gives fewer, cleaner events that are closer to actual loss, but there are fewer of them. Choosing is a trade-off between having enough bad loans to model and having bad loans that really are bad. Most retail scorecards settle on 90 days.
The observation point and the performance window
A default definition needs a clock. Lesson 1.2 introduced two windows around an observation date: the lead-up, from which features are taken, and the performance window, in which the outcome is watched. Now we set them properly.
For an application scorecard, the observation date is the date of application. Everything the model uses must be known by then. The outcome is whether the loan, if approved and disbursed, reaches the default definition within, say, 12 months of disbursal.
For a behaviour scorecard, used on existing customers, the observation date is a month-end snapshot. Features come from the customer's history up to that date, such as DPD, utilisation and payment ratios. The outcome is whether the account defaults within the next 12 months.
The length of the performance window is a choice. Look at how the cumulative default rate builds over the life of a group of loans.
The curve rises quickly through the first year and then flattens. A window should be long enough for most defaults to have shown up, which is called maturity, and short enough that the data is recent and a good number of loans have had that much time. Twelve months is the usual compromise for retail loans. For long loans such as home loans, lenders often need longer windows, because defaults appear later.
Loans that are too young
A subtle error spoils many first-time analyses. Take the 10,000 loans disbursed over the last 12 months. The loan disbursed in the last month has been observed for one month. It cannot yet have had 12 months to default, because 12 months have not passed. If you count it as a "good" loan, since it has not defaulted, you understate the default rate. This is called censoring: the loan's outcome is not fully observed.
How big is the effect? Suppose the eventual 12-month default rate is 4.2 per cent, and defaults build as in the curve above. A group of loans observed for only 6 months will show about a third of the eventual defaults.
At 6 months the loans show about 1.5 per cent against an eventual 4.2 per cent, which is only 35 per cent of the final default rate. A report built on all the loans, regardless of age, would blend mature and immature loans and give an average that is too low and keeps changing as loans age. The rule is simple. A 12-month default rate includes only loans that have had 12 full months. Everything else is excluded, or handled by a method that accounts for partial observation, such as the survival methods and vintage curves you will meet in Module 4.
Good, bad and indeterminate
For scorecard building, each loan in the sample is labelled by its behaviour in the performance window. Three groups are common.
Bad: reached the default definition, for example 90 or more days past due at any time in 12 months.
Good: stayed clean enough, for example never more than 30 days past due.
Indeterminate: in between. The loan was late, but not enough to count as default, and not clean enough to count as good.
With the 10,000-loan portfolio from the chart, 4.2 per cent are bad (420 loans), 9.5 per cent ever reached 30 days past due, and so 5.3 per cent (530 loans) reached 30 to 89 days past due but never 90. The rest, 90.5 per cent or 9,050 loans, were never more than 30 days late.
Label · Rule in the 12-month window · Loans · ShareBad · Ever 90 or more days past due · 420 · 4.2%
Indeterminate · Ever 30 to 89, never 90 · 530 · 5.3%
Good · Never more than 30 days past due · 9,050 · 90.5%
Total · · 10,000 · 100%
The check at the bottom, 420 + 530 + 9,050 = 10,000, is the habit to keep. Many teams leave the indeterminates out when training a model, because their behaviour is ambiguous, and the model then learns from a sharp contrast between clearly good and clearly bad loans. The bad rate for modelling is then 420 ÷ (420 + 9,050) = 4.4 per cent, a little above the 4.2 per cent of the whole group. Remember when reporting that the model's training bad rate and the portfolio's true default rate are two different numbers.
More details a definition must settle
A written default definition answers a longer list of questions than days past due.
Cure and re-ageing. If a defaulted borrower pays the overdue amount, is the loan back to normal? Many policies require a probation period of consecutive on-time payments before treating a loan as cured, to stop loans from flickering in and out of default.
Restructuring. A loan restructured because the borrower cannot pay is usually flagged as distressed even if it is current on the new terms. Treat it as a bad outcome or track it separately.
Cross-default. If a customer has several loans with the lender, does default on one make all of them default? At retail level, definitions can work either per loan or per customer, and the choice changes the counts.
Fraud and first-payment default. A loan that misses its very first instalment is often fraud or misrepresentation and behaves differently from a loan that goes bad after a year. Some teams label these separately.
Write-offs. A loan written off must be flagged as bad even though it disappears from the active book, or the bad rate will be understated as bad loans leave the data.
Recoveries. The end of the story, the money recovered after default, belongs to LGD in Lesson 1.1, and the definition should say when a defaulted account is considered closed.
A worked example: labelling five loans
Apply the rules we have chosen, ever 90 or more days past due for bad, never more than 30 for good, a 12-month window and a requirement of 12 full months, to five loans.
Loan · Months observed · Highest DPD in window · DPD at last month · Label · ReasonL1 · 12 · 0 · 0 · Good · Never late
L2 · 12 · 28 · 0 · Good · Late once, within 30 days
L3 · 12 · 45 · 12 · Indeterminate · Reached 45 days, not 90
L4 · 12 · 92 · 0 · Bad · Reached 90 days, later cured
L5 · 5 · 0 · 0 · Excluded · Window not complete
Three things are worth noticing. L4 is bad under the "ever" test even though it is clean at month 12. Under the "at month 12" test it would count as good, which is exactly how the two definitions give different rates. L3 is neither good nor bad, so it is left out of a model sample but still counts as a loan in the portfolio. And L5 looks perfect, but it has only five months of history. It might default in month 8, so it cannot be called good yet.
On this sample of four mature loans, the bad rate under "ever 90" is 1 in 4, or 25 per cent. A real portfolio would show a rate near 4 per cent, but the counting rule is exactly the same.
One definition for models, another for regulation
A lender usually carries more than one default definition, each serving a different purpose. The regulatory definition is set by the supervisor, drives how loans are classified and provisioned, and is applied to every loan in the book. The modelling definition is chosen by the data science team to build the most useful scorecard, and may use a different threshold or window. A scorecard can be built on "ever 60 days past due" to have more events, while provisions follow the 90-day rule. The two should be linked and the gap explained. When a model's output is used for a regulatory number, such as an expected loss figure for provisions, the PD must be adjusted to match the regulatory definition. Failing to do so is a common cause of findings in model reviews.
Building the flag in Python
Given a monthly snapshot table with one row per loan per month and a column of days past due, the 12-month bad flag takes a few lines.
python
import pandas as pd
snap = pd.readcsv("snapshots.csv", parsedates=["disbursaldate", "snapshotdate"])
months since disbursal at each snapshot
snap["mob"] = ((snap["snapshotdate"].dt.year - snap["disbursaldate"].dt.year) 12
+ snap["snapshotdate"].dt.month - snap["disbursaldate"].dt.month)
window = snap[(snap["mob"] >= 1) & (snap["mob"] <= 12)]
flags = window.groupby("loanid").agg(
maxdpd=("dpd", "max"),
monthsseen=("mob", "max"),
)
flags["bad"] = (flags["maxdpd"] >= 90).astype(int)
flags["good"] = (flags["maxdpd"] <= 30).astype(int)
mature = flags[flags["monthsseen"] >= 12] # only loans with a full window
mature["bad"].mean() # 12-month ever-90 default rate
The line selecting monthsseen >= 12 is the most important one. Without it, immature loans pull the bad rate down. Also confirm that written-off loans stay in the snapshots with a bad DPD or a write-off flag, because dropping them would hide the worst outcomes.
Common mistakes
Not writing the definition down. Two analysts with different definitions get different PDs. Record the threshold, the window, the cure rule and the exclusions.
Including loans that are too young. A 12-month rate needs 12 full months. Immature loans understate it.
Mixing "ever" and "at" measures. State which one you used before comparing with any other figure.
Letting written-off loans disappear. Bad loans removed from the data make the bad rate look better than it is.
Using a threshold chosen to get a nice number. Pick the threshold for business and regulatory reasons, and not to hit a target bad rate.
Forgetting the model's bad rate differs from the portfolio's. Dropping indeterminates changes the rate, so report both.
Key takeaways
A default definition combines a days-past-due threshold, often 90, with tests such as unlikely to pay, write-off and materiality, and it must be written down.
"Ever reached 90 days" and "at 90 or more on a given date" give different rates from the same data, and so do different thresholds.
A performance window of about 12 months is common for retail loans, because the default curve flattens by then, but the right window depends on the product.
Loans that have not completed the window must be excluded from a 12-month default rate. Otherwise the rate is understated, as the simulator showed.
Loans are labelled good, bad or indeterminate. The groups must add up to the whole sample, and the model's training bad rate differs from the true rate if indeterminates are left out.
Cure, restructuring, cross-default and write-offs all need rules in the definition.
Check yourself
1. In a portfolio of 10,000 loans, 4.2 per cent ever reach 90 days past due. How many bad loans is that, and what would the 60-day definition give if 6 per cent reach that level?
420 loans under the 90-day definition. At 60 days, 6 per cent is 600 loans.
2. Loans have been observed for six months and the eventual 12-month rate is 4.2 per cent. What rate would a careless analyst report, roughly?
About 1.5 per cent, or about 35 per cent of the eventual rate, because many defaults have not yet happened.
3. Why might a lender leave indeterminate loans out of a scorecard sample?
Their behaviour is ambiguous. Removing them gives the model a clearer contrast between good and bad loans.
4. A loan was written off in month 7 and then disappeared from the data. What happens to the bad rate if it is dropped?
The bad rate is understated, because a clear bad outcome has been removed.
5. Why is the first-instalment default often treated separately?
It often reflects fraud or misrepresentation, not the slow deterioration behind most defaults, so it behaves differently.
Try this
Write a default definition for a loan product you know, and test it on a small made-up portfolio. Set aside forty to forty-five minutes.
1. Choose the product, such as a personal loan or a two-wheeler loan. Write the default threshold in days past due, the materiality rule, the unlikely-to-pay triggers and the cure rule in one short paragraph.
2. Choose a performance window and give two reasons, one about the speed at which defaults appear and one about data availability.
3. Invent a portfolio of 20 loans, each with a maximum days past due in its first 12 months. Label every loan good, bad or indeterminate, and check that the three groups add up to 20.
4. Compute the bad rate with all loans, and with the indeterminates removed. Note the difference.
5. Add three loans that have been open only 4 months. Say how you would treat them in a 12-month default rate and why.
6. Use the threshold simulator with your own assumed rates to see how the bad rate changes between 30, 60 and 90 days.
7. Write a short note explaining what would change if the regulator moved the default threshold from 90 to 60 days.
A good result is a half-page definition that another analyst could apply without asking you questions, and a table of 20 labelled loans. That definition is the foundation for the next modules, which turn loans into datasets and study how delinquency moves through the portfolio. With Module 1 complete, you now have the vocabulary of the whole track: PD, LGD, EAD, the ledger, the schedule and the definition of the event we are trying to predict.
Tags: Credit Risk Analytics Default definition Performance window Good and bad Beginner