1 the claim staffing method for the ulae reserve - the third way 1999 casualty loss reserve seminar...
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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
Comparison
• Paid-to-paid– biased upward
• Johnson– biased downward,
unless properly parameterized (very difficult to do)
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
AY AY+1
Claim $1000 $2500
ULAE $ 375 $ 500
• ULAE incurred 100% at time claim closed
• Financial statements produced annually
9
Example (cont’d)
Calendar Year
1999 2000
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 MethodYear (1)
ProjdNumber
ofClaimsin Play
(2)Trend
- could includerunoff effects,
but how toquantify?
(3)TrendedExpense
per Claim
(4)Projected
ULAE= (1) x (3)
1999 1000 2% 700 700,000
2000 800 2% 714 571,200
2001 600 2% 728 436,800
2002 400 2% 743 297,200
2003 200 2% 758 151,600
Total 2,156,800
15
Example - Claim Staffing Method
Year (1)Projd
Numberof
Claimsin Play
(2)Work-load
(3)Implied
StaffCount
= (1) / (2)
(4)Avg
ULAE perStaff(from
Slide 22)
(5)Projected
ULAE= (3) x (4)
1999 1000 100 10 71,400 714,000
2000 800 90 9 84,388 759,492
2001 600 80 8 98,162 785,296
2002 400 70 6 115,460 692,760
2003 200 60 3 147,210 441,630
Total 3,393,178
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 Year (1)
Salary(2)
Over-head
(3)Implied
StaffCount(from
Slide 15)
(4)ULAE per
Staff= (1)
+[(2) / (3)]
(5)Econ.
Inflation
(6)TrendedULAE
per Staff
1999 60,000 100,000 10 70,000 2% 71,400
2000 70,000 100,000 9 81,111 2% 84,388
2001 80,000 100,000 8 92,500 2% 98,162
2002 90,000 100,000 6 106,667 2% 115,460
2003 100,000 100,000 3 133,333 2% 147,210
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