CAS Loss Reserve Seminar

CAS Loss Reserve Seminar

• Loss Reserving Issues for Small Insurance Companies

• Patrick J. Crowe, FCAS, MAAA, ARM• Vice President and Actuary• Kentucky Farm Bureau Insurance

Agenda

Ceded Reinsurance

Loss Reserve Ranges

Materiality

Ceded Reinsurance

Develop Direct and Net separately

Ceded Estimates Paid Development (Additive, Multiplicative) Incurred Development (Additive,

Multiplicative) Bornhuetter/Ferguson Approach Expected Loss Ratio Reinsurer estimates

CASUALTY ACTARIAL SEMINAR

LOSS RESERVE RANGES

Approach

The model projects lognormal loss development factors for each development period and accident year.

The expected mean and standard deviation for the lognormal distribution is selected for each loss development period.

Fifty thousand simulations were created for eight situations.

Situations Analyzed

1) Auto #1: Auto Liability Historical incurred loss development patterns for small companies

2) Auto #2: Historical variance to mean ratio increased 100%

3) Auto #3:Historical variance to mean ratio increased 50%

Situations Analyzed

1) Long Tail #1a: Long tail development

2) Long Tail #1b: Long tail development, variance to mean ratio increased 50%

3) Long Tail #1c: Long tail development, variance to mean ratio increased 100%

Situations Analyzed

1) Long Tail #2a: Long tail development increased and variance to mean ratio increased 50%

2) Long Tail #2b: 1) above with variance to mean ratio increased 100%

CAS LOSS RESERVE SEMINAR

Incurred Development Patterns

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

12 24 36 48 60 72 84 96 108 120 132 144

Development Period (months)

Auto Liability Long Tail #1 Long Tail #2

LOGNORMAL SIMULATION

Acc. Yr. 12-24 24-36 36-48 48-60 60-72 72-84 84-961990 0.0508 -0.0552 0.0847 0.0202 -0.0061 -0.0700 0.00661991 0.0910 0.0000 -0.0380 -0.0012 -0.0168 0.0012 0.00001992 0.1168 0.0172 0.0872 -0.0057 0.0267 0.0177 0.00021993 0.0753 0.0104 -0.0144 0.0505 0.0288 -0.0004 0.01201994 0.0792 0.0182 -0.0033 0.0309 0.0071 0.0006 0.00001995 0.1590 0.0608 0.0359 0.0313 -0.0122 -0.0055 -0.00011996 0.0896 0.0853 0.0560 0.0026 0.0108 0.0134 0.00201997 0.1753 0.1002 0.0100 0.0214 0.0721 0.0048 0.00831998 0.0316 0.0944 0.0531 0.0202 0.0172 0.0114 0.00531999 0.0910 0.0628 0.1248 0.0427 0.0415 0.0015 -0.00282000 0.0962 0.1386 0.0142 -0.0078 0.0129 -0.0105 0.00562001 0.2398 0.0984 0.0516 0.0322 0.0296 0.0139 0.00252002 0.1619 0.0535 0.0552 0.0545 0.0211 -0.0002 0.0095

Developed Factorsmean

Avg last 3 0.1423 0.0986 0.0626 0.0147 0.0236 0.0028 0.0040Avg all (ex hi/lo) 0.1103 0.0627 0.0398 0.0213 0.0184 0.0045 0.0001

Avg last 5 (ex hi/lo) 0.1208 0.0933 0.0483 0.0242 0.0156 0.0045 0.0030Avg last 5 0.1268 0.0963 0.0560 0.0213 0.0213 0.0051 0.0024

Average all 0.1154 0.0653 0.0437 0.0216 0.0222 0.0051 0.0030Selected 0.1200 0.1000 0.0400 0.0250 0.0180 0.0045 0.0030

Age to Ultimate Factors 2002 2001 2000 1999 1998 1997 1996mean

Avg last 3 0.3521 0.2098 0.1112 0.0486 0.0339 0.0103 0.0075Avg all (ex hi/lo) 0.2571 0.1468 0.0841 0.0443 0.0230 0.0046 0.0001


Very Small Company Private Passenger Auto Liability - IBNR Projectins - Using Net Incurred Data

0.00%

0.05%

0.10%

0.15%

0.20%

0.25%

0.30%

0.35%

0.40%

0.45%

0.50%

0.55%

0.60%

-135 -3

1 73 178

282

387

491

596

700

805

909

1,01

4

1,11

8

1,22

2

1,32

7

1,43

1

1,53

6

1,64

0

1,74

5

1,84

9

1,95

4

2,05

8

2,16

2

2,26

7

2,37

1

2,47

6

2,58

0

2,68

5

2,78

9

IBNR Amounts

Fre

quen

cy


Very Small Company Private Passenger Auto Liability - IBNR Estimate - Using Direct Incurred Data

0.00%

0.05%

0.10%

0.15%

0.20%

0.25%

0.30%

0.35%

0.40%

0.45%

0.50%

0.55%

-237 -4

7

142

332

521

710

900

1,08

9

1,27

9

1,46

8

1,65

7

1,84

7

2,03

6

2,22

6

2,41

5

2,60

4

2,79

4

2,98

3

3,17

3

3,36

2

3,55

1

3,74

1

3,93

0

4,12

0

4,30

9

4,49

8

4,68

8

4,87

7

5,06

7

IBNR Amounts

Fre

quen

cy


Auto #1 Historical Loss Development, 50,000 Simulations

0

0.01

0.02

0.03

0.04

0.05

0.06

Case and IBNR Reserves

Normal Lognormal


Auto #1 Variance increased 100%, 50,000 Simulations

0

0.01

0.02

0.03

0.04

0.05

0.06

1174

1

1325

3

1476

5

1627

7

1778

9

1930

1

2081

3

2232

5

2383

7

2534

9

2686

1

2837

3

2988

5

3139

7

3290

9

3442

1

3593

3

3744

5

3895

7


Normal Lognormal


Auto #1 Variance increased 50%, 50,000 Simulations

0

0.01

0.02

0.03

0.04

0.05

0.06


Normal Lognormal


Long Tail #1, 50,000 Simulations

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07


Normal Lognormal


Incurred Development Patterns

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

12 24 36 48 60 72 84 96 108 120 132 144

Development Period (months)

Auto Liability Long Tail #1 Long Tail #2


Long Tail #1, Variance increased 50%

0

0.01

0.02

0.03

0.04

0.05

0.06


Normal Lognormal


Long Tail #1, Variance increased 100%, 50,000 Simulations

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07


Normal Lognormal



0

0.01

0.02

0.03

0.04

0.05

0.06


Normal Lognormal



0

0.01

0.02

0.03

0.04

0.05

0.06

0.07


Normal Lognormal

CASUALTY ACTARIAL SEMINAR

MATERIALITY

Materiality

The viewpoint of some regulators is that he Statement of Opinion is intended to assure the regulator that the Company’s reserve position will be adequate for the next 12 months until a new Opinion is issued. So, those regulators feel the actuary should disclose any reason for concern that the reserves will be materially understated. They want to know if there is a need for close monitoring.

Joseph Herbers, 2002 Forum


Model EP Surplus Ratio ELR CY ULT

Auto#1 28,245 21,184 75% 70% 19,771

Auto#2 28,390 21,293 75% 70% 19,873

Auto#3 28,339 21,254 75% 70% 19,837

LT #1a 71,735 53,801 75% 70% 50,214

LT #1b 72,478 54,359 75% 70% 50,735

LT #1c 73,439 55,079 75% 70% 51,407

LT #2a 122,118 91,589 75% 70% 85,483

LT #2b 123,720 92,790 75% 70% 86,604


Model CY ULT Reserves SD SD/Sur

Auto#1 19,771 26,209 2,662 12.6%

Auto#3 19,837 26,453 3,289 15.5%

Auto#2 19,873 26,357 3,777 17.7%

LT #1a 50,214 102,407 13,114 24.4%

LT #1b 50,735 102,926 15,565 28.6%

LT #1c 51,407 104,380 18,884 34.3%

LT #2a 85,483 184,567 29,853 32.6%

LT #2b 86,604 184,841 37,538 40.5%


Model SD/

Surplus

Ceded

Recoverable

Prem/ Def Res

Total/ Surplus

Auto#1 12.6% 1.33% 5% 18.9%

Auto#3 15.5% 1.33% 5% 21.8%

Auto#2 17.7% 1.33% 5% 24.1%

LT #1a 24.4% 1.33% 5% 30.7%

LT #1b 28.6% 1.33% 5% 35.0%

LT #1c 34.3% 1.33% 5% 40.6%

LT #2a 32.6% 1.33% 5% 38.9%

LT #2b 40.5% 1.33% 5% 46.8%


Model Subtotal/ Surplus

Operating Results

Operating % Surplus

Total/ Surplus

Auto#1 18.9% 5% 6.67% 25.6%

Auto#3 21.8% 5% 6.67% 28.5%

Auto#2 24.1% 5% 6.67% 30.7%

LT #1a 30.7% 5% 6.67% 37.4%

LT #1b 35.0% 5% 6.67% 41.6%

LT #1c 40.6% 5% 6.67% 47.3%

LT #2a 38.9% 5% 6.67% 45.6%

LT #2b 46.8% 5% 6.67% 53.5%


Loss Reserve Development to Surplus Surplus/Earned Premium Ratio is 75%

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

90.0%

Auto #1 Auto #2 Auto #3 Long Tail 1a Long Tail 1b Long Tail 1c Long Tail 2a Long Tail 2b

Incurred Loss Pattern

Best Estimate Estimate .5 STD below Estimate 1 STD below


Reserves development to Surplus

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

90.0%

100.0%

33.3% 50.0% 66.7% 75.0% 90.0% 100.0% 125.0%

Surplus to Premium Ratio

Auto #1 Auto #2 Auto #3 Inc Option A #1 Inc Option A #2 Inc Option A #3 Inc Option B #1 Inc Option B #2


Documents

CAS Loss Reserve Seminar