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

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

1999 Casualty Loss Reserve Seminar

Speaker:

Craig A. Allen, FCAS, FCIA

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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

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Comparison

• Paid-to-paid– biased upward

• Johnson– biased downward,

unless properly parameterized (very difficult to do)

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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

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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

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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

•

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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

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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

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Example (cont’d)

Calendar Year

1999 2000

Acc 1998 $2,500 Claims

Year $ 500 ULAE

1999 $1,000 $2,500 Claims

$ 375 $ 500 ULAE

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Example (cont’d)

True Value < PTP Estimate

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Example (Cont’d)

• Paid-to-paid ratio

375 + 500 = 25%

1000 + 2500

• True ratio of unpaid ULAE to unpaid claims

500 = 20%

2500

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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

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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

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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

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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

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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

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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%

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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

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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

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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

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Pure Economic Inflation

• Use CPI or other measure of inflation

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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