Richard Sherman
&
Gordon Diss


Extensive data for 160,000 permanent disability claims.

Accident years 1926-2002.

77 years of development experience.

Medical & indemnity payments separated.

Separate data by injury type.

Paid Loss Development Factors

Age to Age MPD Paid LDFs
Years of Development
2 3 4 5 6 7 8 9 10 11 12 13 14 15
6.624 1.525 1.140 1.072 1.041 1.027 1.019 1.020 1.015 1.013 1.012 1.013 1.012 1.010
Your guess of a tail factor at 15 years? ______

16
Age to Age MPD Paid LDFs
Years of Development
17 18 19 20 21 22 23 24 25
1.011 1.013 1.011 1.011 1.012 1.012 1.014 1.012 1.015 1.015
Your guess of a tail factor at 25 years? ______

Age to Age MPD Paid LDFs
Years of Development
26 27 28 29 30 31 32 33 34 35
1.016 1.020 1.023 1.027 1.026 1.022 1.018 1.015 1.017 1.018
Your guess of a tail factor at 35 years? ______

Comparison of Your Guesses to SAIF’s Indicated Paid Tail Factors
Maturity Your
(Years)
15
25
Guess
_______
_______
SAIF’s MPD
Tail Factor
______
______

C
OMMON
I
NTUITIVE
A
SSUMPTION

MPD TAIL FACTORS
BEHAVE LIKE TAIL FACTORS
CIA-1
IN OTHER CASUALTY LINES.
COMMON TAIL METHODS
ARE APPLICABLE.


REPEAT THE LAST FACTOR

LINEAR DECAY

EXPONENTIAL DECAY

INVERSE POWER CURVE

LATEST INCURRED TO PAID RATIO

CIA-2
Since there are relatively few MPD claims and since they represent a small portion of current calendar year payments,
MPD reserves should be relatively small

SAIF’s Indicated Paid Tail Factors
Maturity
(Years) MPD Other WC Total WC
10
15
25
35
2.469
2.328
2.054
1.680
1.263
1.234
1.129
1.052
1.671
1.613
1.457
1.294

Medical Permanent Disability
CIA-3
Paid Loss Development Factors
Decrease
Monotonically

Model v. Actual SAIF PLDFs Less 1.0
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0.00
6
10 14 18 22 26 30 34 38 42 46 50 54 58
Year of Development
Model
SAIF
S

OPPOSITE INFLUENCES
FORCE OF MORTALITY
VERSUS
FORCE OF MEDICAL COST ESCALATION

A) Incremental Paid Losses ($000’s)
AY 12 24 36 48 60 72
1997 2,823 15,936 9,182 4,282 2,064 1,411
1998 2,638 14,250 9,096 2,936 3,214
1999 3,331 15,806 9,735 4,309
2000 3,170 18,602 12,462
2001 3,143 20,306
2002 4,263
B) Open Counts
AY 12 24 36 48 60 72
1997 362 1,112 793 490 375 324
1998 338 888 628 431 352
1999 343 840 664 492
2000 268 867 731
2001 276 897
2002 333
C) Incremental Paid per Prior Open
AY 24 36 48 60 72
1997 44,022 8,257 5,399 4,212 3,764
1998 42,159 10,244 4,675 7,459
1999 46,021 11,589 6,489
2000 69,411 14,374
2001 73,572
2002

CIA-4
Historical incremental paid losses prior to the development triangle are useless.

Incremental data prior to the triangle
AY
1926
I
AY
1966
C
AY
2002
Development Years (DY)
10 20 30 40 50 60
70

MUELLER INCREMENTAL TAIL METHOD

Calculate future incremental payments as a percent of the incremental payment in a given anchor year.

Cumulate and smooth these future payments as a % of payments in the anchor year.

Convert to a tail factor by applying the result above to an age to age development factor from the main triangle.

See paper for details.

CIA-5
For a given development period,
Worker’s Compensation tail factors should be constant for all accident years

Testing CIA-5 with an Illustrative Model

35 successive AYs that are identical except:

Applicable mortality table varies by CY.

Used projected Social Security mortality table for future mortality rates.

Each AY starts with 5,000 permanent disability cases. All assumptions fit SAIF’s historical patterns.

Indicated WC MPD Tail Factors
End of Development Year
AY 10 20 30 40 50 60 70 80
1970 2.570 2.177
1.773 1.438 1.210 1.075 1.015 1.0012
1975 2.628 2.223
1.805 1.456 1.220 1.080 1.016 1.0013
1980 2.701 2.279
1.842 1.477 1.231 1.085 1.018 1.0014
1985 2.774 2.336
1.879 1.499 1.242 1.090 1.020 1.0016
1990 2.848 2.393
1.918 1.521 1.253 1.095 1.021 1.0017
1995 2.921 2.451
1.957 1.543 1.265 1.101 1.023 1.0019
2000 2.990 2.505 1.993 1.563 1.275 1.105 1.023 1.0021

Life Expectancies at Different Ages—Male
Based on Social Security Administration Mortality Tables
Current
Age 1960 1980 2000 2020 2040 2060 2080
20 49.7 51.7 54.7 56.8 58.7 60.3 61.8
40 31.3
33.5
36.2
38.1
39.8
41.4
42.7
60 15.9 17.3 19.3 20.8 22.2 23.4 24.6
80 6.0 6.8 7.2 7.8 8.6 9.4 10.1

Number of Open Claims for Representative
Accident Years at Five Year Intervals of Development
End of Development Year
AY 10 20 30 40 50 60 70 80
1970 196 119 71 33 12 3.5 0.5 0.02
1975 197 120 73 34 13 3.7 0.6 0.03
1980 200 123 76 36 14 3.9 0.6 0.03
1985 202 126 79 38 14 4.2 0.7 0.04
1990 204 128 81 39 15 4.4 0.7 0.04
1995 206 130 83 41 16 4.7 0.8 0.05
2000 207 132 86 42 17 5.0 0.9 0.06

CIA-6
For a given development period,
Worker’s Compensation age-to-age paid loss development factors should be constant for all accident years

Trends in Five Year Paid Loss Development Factors
Development Years
AY 15/10 20/15 25/20 30/25 35/30 40/35 45/40 50/45 55/50
1970 1.082 1.091 1.103
1.113 1.114 1.107 1.097 1.084 1.069
1975 1.083 1.092 1.105 1.115 1.116 1.110 1.099 1.086 1.071
1980 1.084 1.094 1.107
1.118 1.119 1.114 1.103 1.089 1.073
1985 1.084 1.095 1.109
1.120 1.123 1.117 1.106 1.092 1.076
1990 1.085 1.096 1.111
1.123 1.126 1.120 1.109 1.094 1.078
1995 1.086 1.097 1.113
1.126 1.129 1.123 1.112 1.097 1.081
2000 1.087 1.098 1.114
1.128 1.132 1.126 1.115 1.100 1.083

CIA-7
Mortality rates of the disabled are distinctly greater than those for the general public


For ages < 60, injured worker mortality rates somewhat higher.
“Between age 60 and 74, the injured worker mortality rate does not differ appreciable from U.S. Life. The differences in mortality, even if accepted, do not imply significant redundancy or inadequacy of tabular reserves.” Gillam, William R., “Injured
Worker Mortality”, CAS Forum, Winter 1991

“Injured worker mortality after some years comes close to standard mortality, and after some age may actually be lower.”
Venter, Schill and Barnett, “Review of Report of Committee on
Mortality for Disabled Lives”, CAS Forum, Winter 1991

Standard mortality rates fit SAIF’s historical experience well.

As permanently disabled claimants age, neither utilization nor severity changes.
CIA-8

Model v. Actual SAIF PLDFs Less 1.0
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0.00
6
10 14 18 22 26 30 34 38 42 46 50 54 58
Year of Development
Model
SAIF
S

Case reserves based on
CIA-9 inflating payments until the expected year of death are at the expected level


Age 35, $5,000 current annual medical costs, 9% future medical inflation.

Total inflated payments through expected year of death (at age 75): $1.69 million.

Expected total payout over scenarios of all possible years of death: $2.88 million, or 70% more.

Deaths and Expected Payouts by Age
0.06
0.05
0.04
0.03
0.02
0.01
0.00
36 42 48 54 60 66 72 78 84 90 96
102 108
Age
Exp. Losses
Deaths

Monte Carlo simulation of
CIA-10
MPD losses will reasonably estimate the variability of
MPD reserves


Typical Monte Carlo simulation involves utilization of size of loss distribution based on incurred amounts, all of which are well below their expected value.

Better to model year-byyear payments for individual claimants using a
Markov chain approach.
1
2
3.2
Calendar Year of Payment
Claim 2004 2005 2006 2007
3.5
12.7
13.8
3.8
- -
4.0
- -
3 8.1
8.8
9.6
- -








Data prior to traditional triangle can be used effectively.
All 10 CIAs do not apply to MPD payments and reserves.
MPD PLDFs increase for many mature DYs.
MPD paid tails and incremental PLDFs trend upward as mortality rates decline.
Utilization and severity are higher than expected for elderly permanently disabled claimants.
Common methods significantly underestimate the expected value of MPD case reserves.
Common methods understate MPD reserve variability.