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

2. 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. 3 Comparison Paid-to-paid –biased upward Johnson –biased downward, unless properly parameterized (very difficult to do)

4. 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. 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. 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. 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. 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. 9 Example (cont’d) Calendar Year 19992000 Acc1998$2,500Claims Year$ 500ULAE 1999$1,000$2,500Claims $ 375$ 500ULAE

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

11. 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. 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. 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. 14 Example - Johnson Method

15. 15 Example - Claim Staffing Method

16. 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. 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. 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. 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. 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. 21 Pure Economic Inflation Use CPI or other measure of inflation

22. 22 Example - ULAE per Staff