Loan Horizons

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A smaller cumulative missed-payment count can reflect a shorter observation window. This fictional record exercise compares equal payment ages instead.

Fix the event and the clock

Take ten invented loans at a June 30, 2026 extraction. The five A loans first had a scheduled monthly payment in January 2025; the five B loans started in January 2026. Each monthly payment is due by month-end. Count only whether the first missed scheduled payment has occurred, not the number of missed payments or the unpaid balance. Select six-period and twelve-period questions before inspecting outcomes.

At extraction, A supplies eighteen observed payment periods and B six. Table entries are payment-month positions; “None” means no observed miss.

Loan	First miss	Observed through
A1	3	18
A2	10	18
A3	15	18
A4	None	18
A5	None	18
B1	3	6
B2	None	6
B3	None	6
B4	None	6
B5	None	6

Change the horizon, not the records

At extraction, A has three first misses among five loans, while B has one among five. Those are 60% and 20%, but the windows are eighteen and six periods. At the common six-period horizon, only A1 and B1 count: both groups have one first miss among five, or 20%.

At twelve periods, A1 and A2 count, producing 2/5. A3’s month-15 miss is known at extraction but lies outside that target. B1 already supplies a positive twelve-period outcome because its first miss occurred at month 3. B2–B5 do not supply negative twelve-period outcomes: each has only six observed periods.

Elapsed age does not replace observation

Separately, suppose A5 becomes unobservable after month 5 with no recorded miss. Its calendar age remains eighteen periods, but it no longer establishes an event-free six-period outcome.

NIST’s reliability handbook distinguishes event times from observation ending without an event.

Recognize the age label in published data

A November 24, 2025 FEDS Note presents cumulative auto-loan delinquency by origination vintage. Its accessible Figure 4 labels rows “quarters since origination.” That is a real example of an elapsed-age axis, not the source of our invented observations. Our first-missed-payment event is not that publication’s delinquency measure.

Equal six-period fractions answer this stipulated record question. They do not establish equal borrower quality or predict either group’s future performance.