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

The Claim Staffing Method for
the ULAE Reserve
- the Third Way
2000 Casualty Loss Reserve Seminar
Speaker:
Craig A. Allen, FCAS, FCIA
1
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
2
Comparison
• Paid-to-paid
– biased upward
• Johnson
– biased downward,
unless properly
parameterized (very
difficult to do)
3
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
4
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
5
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
6
•
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
7
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
8
Example (cont’d)
Acc 1998
Year
1999
Calendar Year
1999
2000
$2,500
$ 500
Claims
ULAE
$1,000
$ 375
Claims
ULAE
$2,500
$ 500
9
Example (cont’d)
True Value < PTP Estimate
10
Example (Cont’d)
• Paid-to-paid ratio
375 + 500 =
1000 + 2500
25%
• True ratio of unpaid ULAE to unpaid claims
500
=
20%
2500
11
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
12
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
13
Example - Johnson Method
Year
(1)
(2)
(3)
Projd
Trend
Trended
Number - could include Expense
of
runoff effects, per Claim
Claims
but how to
in Play
quantify?
(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
14
Example - Claim Staffing
Method
Year
(1)
Projd
Number
of
Claims
in Play
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
(2)
Workload
(3)
(4)
(5)
Implied
Avg
Projected
Staff
ULAE per ULAE
Count
Staff
= (3) x (4)
= (1) / (2)
(from
Slide 22)
3,393,178
15
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
16
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%
17
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
18
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
19
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
20
Pure Economic Inflation
• Use CPI or other measure of inflation
21
Example - ULAE per Staff
Year
(1)
Salary
(2)
Overhead
(3)
(4)
(5)
(6)
Implied ULAE per Econ. Trended
Staff
Staff
Inflation ULAE
Count
= (1)
per Staff
(from
+
Slide 15) [(2) / (3)]
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
22