[[Actuarial Notes Wiki|Wiki]] / [[Exam 5 (CAS)]] / **Tail Factor**
## Definition
==Tail Factor== The tail factor represents the development expected to occur beyond the last age shown in the development triangle.
## Purpose
- Account for long-term development
- Estimate ultimate losses
- Complete the development pattern
- Critical for long-tail lines
## Estimation Methods
### Industry Data
Use published tail factors from industry studies:
- ISO data
- Rating bureau factors
- Reinsurance studies
### Curve Fitting
Fit mathematical curve to development pattern:
```
Common functions:
- Exponential decay
- Power curve: y = a × x^b
- Inverse power: y = a + b/x
```
### Judgment
Based on:
- Line of business characteristics
- Historical settlement patterns
- Claim department experience
- Legal environment
## Example by Line of Business
```
Workers Compensation:
60-ultimate tail: 1.030-1.050
Long development, medical inflation
General Liability:
60-ultimate tail: 1.050-1.100
Very long tail, legal uncertainty
Medical Malpractice:
60-ultimate tail: 1.100-1.200
Extremely long tail
Auto Physical Damage:
60-ultimate tail: 1.000-1.005
Minimal tail, fast settlement
```
## Impact on Reserves
```
Example:
Reported @ 60 months: $1,000,000
60-Ultimate CDF without tail: 1.020
With tail factor: 1.030
Without tail:
Ultimate = $1,000,000 × 1.020 = $1,020,000
With tail:
Ultimate = $1,000,000 × 1.020 × 1.030 = $1,050,600
Difference: $30,600 (3.0% of reported)
```
## Related Concepts
- [[Development Factor]]
- [[Cumulative Development Factor]]
- [[Long Tail Insurance]]
## References
- Friedland, Chapter 4