Loss Development Factor Stability Calculator
Enter six cumulative-loss pairs from one development interval to examine the consistency of their age-to-age factors. The results compare common averages and show variation, trend, possible outliers, and the effect of omitting each cohort.
Volume-weighted factor1.44
- Cohort age-to-age factors
- Cohort 1: 1.4500; Cohort 2: 1.4000; Cohort 3: 1.5000; Cohort 4: 1.4000; Cohort 5: 1.4500; Cohort 6: 1.4500
- Simple-average factor
- 1.44
- Geometric-average factor
- 1.44
- Factor coefficient of variation
- 2.61%
- Recent-versus-prior shift
- -1.15%
- Factor trend per cohort
- 0
- Potential outlier cohorts
- None are flagged.
- Leave-one-out factor range
- 1.4326 to 1.4518
- Most influential cohort
- Cohort 3 (0.69% change when omitted)
Cohort age-to-age factors
| Cohort | Starting cumulative loss | Ending cumulative loss | Factor |
|---|---|---|---|
| 1 | $100,000.00 | $145,000.00 | 1.45 |
| 2 | $120,000.00 | $168,000.00 | 1.4 |
| 3 | $150,000.00 | $225,000.00 | 1.5 |
| 4 | $180,000.00 | $252,000.00 | 1.4 |
| 5 | $210,000.00 | $304,500.00 | 1.45 |
| 6 | $250,000.00 | $362,500.00 | 1.45 |
Compare cohorts only when they use the same loss basis, valuation interval, and monetary units.
How to use this calculator
- Enter the starting-age and ending-age cumulative losses for each cohort, ordered from oldest to newest.
- Use the same loss basis, valuation interval, and monetary units for all six pairs.
- Review the individual factors and compare the volume-weighted, simple, and geometric averages.
- Use the variation, shift, trend, outlier, and leave-one-out results to decide what needs investigation.
How the factor diagnostics are calculated
An age-to-age loss development factor, also called a link ratio, compares a cohort’s cumulative loss at two development ages. For each cohort i, the calculator divides ending cumulative loss Ei by starting cumulative loss Si:
fi = Ei ÷ Si
The volume-weighted factor gives larger cohorts more influence: W = ΣEi ÷ ΣSi. The simple average instead gives every cohort equal weight: A = Σfi ÷ 6. The geometric average is G = (Πfi)^(1/6) when every factor is positive. Different averages can be useful comparison points; they are not competing prescriptions for selecting a factor.
What the stability measures show
The coefficient of variation is the sample standard deviation of the six factors divided by their simple mean: CV = 100 × s ÷ A. A larger CV means the observed factors are more dispersed relative to their level. The recent-versus-prior shift compares the average of cohorts 4 through 6 with the average of cohorts 1 through 3: 100 × (recent ÷ prior − 1). The trend is an ordinary least-squares slope of factor against cohort order, from oldest to newest.
For a robust outlier screen, the calculator finds the median factor M and median absolute deviation MAD, then uses zi = 0.6745 × (fi − M) ÷ MAD. A cohort is flagged when the absolute modified z-score exceeds 3.5. A flag is not a reason to remove a cohort: it is a prompt to check operations, mix, catastrophes, reserving changes, or data quality. If MAD is zero, robust scoring is indeterminate rather than forced through a division by zero.
Why leave-one-out sensitivity matters
The calculator recomputes the volume-weighted factor six times, omitting one cohort each time. The resulting range and largest percentage change identify how much a single cohort can move the all-cohort result. It also warns when one cohort contributes more than 80% of starting loss, because that concentration can dominate a volume-weighted view even without an unusual individual factor.
What this calculator does not do
This is an exploratory historical diagnostic. It does not select a loss development factor, estimate ultimate losses, calculate an insurance reserve, or adjust for claim-handling changes, case-reserving practices, coverage mix, limits, inflation, catastrophes, or data-quality issues. Six cohorts are limited evidence and should be considered with broader actuarial review.
Worked example
Suppose the six starting losses are $100,000, $120,000, $150,000, $180,000, $210,000, and $250,000, while ending losses are $145,000, $168,000, $225,000, $252,000, $304,500, and $362,500. The six factors are 1.4500, 1.4000, 1.5000, 1.4000, 1.4500, and 1.4500.
Total ending loss is $1,457,000 and total starting loss is $1,010,000, so the volume-weighted factor is 1.4426 before display rounding. The simple average is 1.4417. The relatively narrow leave-one-out range shows that no one of these six cohorts changes the volume-weighted result much, while the table makes the higher third-cohort factor visible for review.
Common questions
What is an age-to-age loss development factor?
It is the ratio of cumulative loss at a later development age to cumulative loss at an earlier age for the same cohort. For example, cumulative incurred loss growing from $100,000 to $145,000 has an age-to-age factor of 1.45. It describes observed historical development over that interval.
Why do simple and volume-weighted factors differ?
The simple average gives each cohort equal influence, regardless of size. The volume-weighted factor combines all ending losses and all starting losses, so a large cohort has more effect. A material difference between them can signal that factor level varies with cohort size or that one large cohort deserves closer review.
What does a high coefficient of variation mean?
A high coefficient of variation means the individual factors are spread widely relative to their average. It does not identify the cause or prove that a factor is unsuitable. Review claim operations, loss mix, unusual events, case reserves, and data consistency before drawing a conclusion.
Can an incurred-loss development factor be below 1?
Yes. Cumulative incurred loss can fall when case reserves are reduced, claims close for less than expected, recoveries are recognized, or corrections are made. A factor below 1 should be checked in context; this calculator permits it rather than treating it as an error.
How does leave-one-out sensitivity identify influential cohorts?
Each leave-one-out result recalculates the volume-weighted factor after omitting one cohort. The cohort whose omission causes the largest percentage change is the most influential under this measure. It may be influential because of its size, its factor, or both.
Does this calculator select an LDF or calculate an insurance reserve?
No. It reports descriptive diagnostics for six observed factors and does not produce an ultimate-loss estimate or booked reserve. Selecting an LDF requires actuarial judgment and usually additional triangles, segmentation, adjustment work, and diagnostics.