The Claim Staffing Method for the ULAE Reserve - the Third Way

1. The Claim Staffing Method for the ULAE Reserve - the Third Way 1999 Casualty Loss Reserve Seminar Speaker: Craig A. Allen, FCAS, FCIA

2. The Issue • Two traditional methods available • Paid-to-paid (PTP) • Johnson • The results of one method vary widely from those of the other - which one is correct? • If neither is correct, propose a third way

3. Paid-to-paid biased upward Johnson biased downward, unless properly parameterized (very difficult to do) Comparison

4. What’s Wrong with Paid-to-Paid? • Standard caveats • inflation • change in size of book • and so on, and so on • It is upward biased,even in a steady state portfolio

5. Source of Bias • Average Claim Size in the paid-to-paid ratio is less than Average Size of Unpaid Claims on the balance sheet • Ratio of ULAE to claims is greater for smaller claims than for larger claims => Ratio in paid-to-paid ratio is too large to apply to unpaid claims

6. Claims in PTP Ratio are Smaller than Open Claims at Period End • All claims handled by company make an appearance in the paid-to-paid ratio • But, there are claims that never appear on a balance sheet - those that are both incurred and settled between accounting dates • Adler & Kline: Those claims that are settled earlier tend to be smaller than those settled later

7. Ratio of ULAE / (Loss + ALAE) is larger for smaller claims • Compare internal expense of settling • 10 claims of $100,000 each • 1 claim of $1 million • Ratio is infinite for claims closed with no payment

8. Example of PTP’s Bias • Every year, 2 claims incurred, both reported in the year incurred, and closed according to the following pattern AYAY+1 Claim $1000 $2500 ULAE $ 375 $ 500 • ULAE incurred 100% at time claim closed • Financial statements produced annually

9. Example (cont’d) Calendar Year 19992000 Acc 1998 $2,500 Claims Year $ 500 ULAE 1999 $1,000 $2,500 Claims $ 375 $ 500 ULAE

10. Example (cont’d) True Value < PTP Estimate

11. Example (Cont’d) • Paid-to-paid ratio 375 + 500 = 25% 1000 + 2500 • True ratio of unpaid ULAE to unpaid claims 500 = 20% 2500

12. Johnson Method • More flexible - user can fine-tune the parameters • But, Johnson’s paper doesn’t explicitly deal with transition from steady state to runoff • Ratio of (Paid ULAE)/(Weighted Open Claims) is taken from calendar years with a mix of new and old claims • Method applies ratio to a run-off of increasingly old claims - ratio not likely high enough for older claims

13. How to Capture and Quantify the Run-off Effect • Need to measure the increased expense of disposing of older claims • Use Claims Department’s management information • workload of claims staff • ULAE cost per staff

14. Example - Johnson Method

15. Example - Claim Staffing Method

16. Workload of Claims Staff • Optimal situation: unit of claims staff dedicated to dealing with older claims • workload can be determined directly • Otherwise: interview claims staff to determine share of time taken by older claims

17. Example - Workload Estimation • Interview claims staff • Current workload: 300 claims • 30 claims are at least 5 years old • take 20% of claims staff’s time • Workload after 5 years of run-off = 30 claims = 150 claims 20%

18. Average ULAE per Staff • 3 considerations • higher salaries for more skilled staff - needed for more complex claims • increasing share of costs for overhead as portfolio is run off • pure economic inflation

19. Higher Salaries for More-Skilled Staff • For first year of run-off, use current average salary, benefits, other variable costs • e.g. $60,000 • For last year of run-off, use salary, benefits, etc. from mid-point of highest salary range for claims staff • e.g. $100,000 • Interpolate for years in between, e.g.linearly

20. Increasing Share of Overhead • Determine overhead from Claims Department Budget • Divide by implied staff count for each year of the run-off • Add to salary to determine ULAE per Staff

21. Pure Economic Inflation • Use CPI or other measure of inflation

22. Example - ULAE per Staff