CAS Loss Reserve Seminar Loss Reserving Issues for

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 n. Ceded Reinsurance n. Loss Reserve Ranges n. Materiality

Ceded Reinsurance n Develop Direct and Net separately n Ceded Estimates n n n Paid Development (Additive, Multiplicative) Incurred Development (Additive, Multiplicative) Bornhuetter/Ferguson Approach Expected Loss Ratio Reinsurer estimates

CASUALTY ACTARIAL SEMINAR n LOSS RESERVE RANGES

Approach n The model projects lognormal loss development factors for each development period and accident year. n The expected mean and standard deviation for the lognormal distribution is selected for each loss development period. n 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 #1 a: Long tail development 2) Long Tail #1 b: Long tail development, variance to mean ratio increased 50% 3) Long Tail #1 c: Long tail development, variance to mean ratio increased 100%

Situations Analyzed 1) Long Tail #2 a: Long tail development increased and variance to mean ratio increased 50% 2) Long Tail #2 b: 1) above with variance to mean ratio increased 100%

CAS LOSS RESERVE SEMINAR

LOGNORMAL SIMULATION

CAS LOSS RESERVE SEMINAR

CAS LOSS RESERVE SEMINAR

CAS LOSS RESERVE SEMINAR

CAS LOSS RESERVE SEMINAR

CAS LOSS RESERVE SEMINAR

CAS LOSS RESERVE SEMINAR

CAS LOSS RESERVE SEMINAR

CAS LOSS RESERVE SEMINAR

CAS LOSS RESERVE SEMINAR

CAS LOSS RESERVE SEMINAR

CAS LOSS RESERVE SEMINAR

CASUALTY ACTARIAL SEMINAR n MATERIALITY

Materiality n 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. n Joseph Herbers, 2002 Forum

CAS Loss Reserve Seminar 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 #1 a 71, 735 53, 801 75% 70% 50, 214 LT #1 b 72, 478 54, 359 75% 70% 50, 735 LT #1 c 73, 439 55, 079 75% 70% 51, 407 LT #2 a 122, 118 91, 589 75% 70% 85, 483 LT #2 b 123, 720 92, 790 75% 70% 86, 604

CAS Loss Reserve Seminar 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 #1 a 50, 214 102, 407 13, 114 24. 4% LT #1 b 50, 735 102, 926 15, 565 28. 6% LT #1 c 51, 407 104, 380 18, 884 34. 3% LT #2 a 85, 483 184, 567 29, 853 32. 6% LT #2 b 86, 604 184, 841 37, 538 40. 5%

CAS Loss Reserve Seminar 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 #1 a 24. 4% 1. 33% 5% 30. 7% LT #1 b 28. 6% 1. 33% 5% 35. 0% LT #1 c 34. 3% 1. 33% 5% 40. 6% LT #2 a 32. 6% 1. 33% 5% 38. 9% LT #2 b 40. 5% 1. 33% 5% 46. 8%

CAS Loss Reserve Seminar 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 #1 a 30. 7% 5% 6. 67% 37. 4% LT #1 b 35. 0% 5% 6. 67% 41. 6% LT #1 c 40. 6% 5% 6. 67% 47. 3% LT #2 a 38. 9% 5% 6. 67% 45. 6% LT #2 b 46. 8% 5% 6. 67% 53. 5%

CAS LOSS RESERVE SEMINAR

CAS LOSS RESERVE SEMINAR

CAS LOSS RESERVE SEMINAR