Finance 431: Property-Liability Insurance Lecture 7: Loss Reserving

1. Finance 431:Property-Liability InsuranceLecture 7:Loss Reserving

2. Anatomy of a claim 12/15/02 Auto accident 12/20/02 Insured reports accident to agent 1/7/03 Claim recorded 2/3/03 $10,000 reserve set 1/8/04 Pay $3000 medical expenses; offer $15,000 settlement; $15,000 reserve set 7/2/04 Offer refused 9/8/04 Lawsuit files 4/1/05 $20,000 reserve 1/6/06 $40,000 reserve 10/6/07 Court awards $32,000 in total Incurred loss development Accident Year 2002 2002 IBNR 2003 $10,000 2004 $18,000 2005 $23,000 2006 $43,000 2007 $32,000 Loss Reserving

3. Definitions Individual claim file estimates Paid loss development Considers only loss payments Paid loss development factors Incurred loss development Paid plus case reserves Incurred loss development factors Loss adjustment expenses Allocated Unallocated

4. What is your answer to question 1 on Class Project #7? A) -$3,400 B) $6,000 C) $10,000 D) $12,600 E) None of the above

5. What is your answer to question 2 on Class Project #7? A) -$3,400 B) $6,000 C) $10,000 D) $12,600 E) None of the above

6. What is your answer to question 3 on Class Project #7? A) -$3,400 B) $6,000 C) $12,600 D) $16,000 E) None of the above

7. What is your answer to question 4 on Class Project #7? A) -$3,400 B) $6,000 C) $12,600 D) $16,000 E) None of the above

8. Loss reserve methods Unsophisticated methods: Case reserve plus Expected loss ratio method More accurate methods: Chain ladder or loss development triangle method Bornhuetter-Ferguson method Frequency and severity estimates

9. Cumulative Loss Payments(000 omitted) Accident Development Age (Months) Year 12 24 36 48 60 72 84 96 2000 5445 8602 11052 12464 13064 13416 13847 14032 2001 5847 9333 10699 11547 12592 13646 14015 2002 5981 10835 12783 15337 17017 17506 2003 7835 12288 16176 19511 21599 2004 9763 16280 19843 23827 2005 10745 16929 21478 2006 14137 22253 2007 15162 Assume that no further losses are paid after 96 months.

10. Paid Loss Development Factors Accident Link Factors Year 12-24 24-36 36-48 48-60 60-72 72-84 84-96 2000 1.580 1.285 1.128 1.048 1.027 1.032 1.013 2001 1.596 1.146 1.079 1.090 1.084 1.027 2002 1.812 1.180 1.200 1.110 1.029 2003 1.568 1.316 1.206 1.107 2004 1.668 1.219 1.201 2005 1.576 1.269 2006 1.574 Ave. 1.625 1.236 1.163 1.089 1.047 1.030 1.013 Age- 2.779 1.710 1.384 1.190 1.092 1.043 1.013 Ultimate

11. How is 24 month-ultimate paid loss development factor calculated on the prior exhibit? A) 1.384x1.190x1.043x1.013 B) 1.625x1.236x1.163x1.089x1.047x1.030x1.013 C) 1.236x1.163x1.089x1.047x1.030x1.013 D) 1.384x1.236 E) None of the above

12. Estimated Loss Reserves Based on Average Paid Loss Development Factors(000 omitted) Age to Accident Paid to Ultimate Ultimate Loss Year Date Factor Losses Reserve 2000 14032 1.000 14032 0 2001 14015 1.013 14197 182 2002 17506 1.043 18259 753 2003 21599 1.092 23586 1987 2004 23827 1.190 28354 4527 2005 21478 1.384 29726 8248 2006 22253 1.710 38053 15800 2007 15162 2.779 42135 26973 Total 149872 208342 58470

13. Based on the prior exhibit, what are the accident year 2005 losses evaluated as of 12/31/07? A) $8,248,000 B) $21,478,000 C) $26,973,000 D) $29,726,000 E) None of the above

14. Expected Loss Ratio Method Estimated Ultimate Losses = Expected Loss Ratio x Earned Premium Estimated Loss Reserve = Estimated Ultimate Losses - Losses Paid to Date Example 2007 Earned Premium = 65,000,000 Expected Loss Ratio = 60% Estimated Ultimate Losses = 39,000,000 Losses Paid to Date = 15,162,000 Estimated Loss Reserve 23,838,000

15. Bornhuetter-Ferguson Method2007 Accident Year Estimated Loss Reserve = Total Expected Losses x % of Losses to Be Paid in Future % of Losses to Be Paid in Future = 1-(1/Age-Ultimate Factor) Example: 12 Month-Ultimate = 2.779 % of Losses Paid After 12 Months = 1-1/2.779=.640 Total Expected Losses = 65,000,000 x .60=39,000,000 Estimated Loss Reserve = 39,000,000 x .640 = 24,960,000

16. If you were applying the Bornhuetter-Ferguson Method to accident year 2006, what would be the percent of losses expected to be paid after 12/31/07? A) 1-1/1.236 = .191 B) 1-1/1.574 = .365 C) 1-1/1.71 = .415 D) 1-1/2.779 = .640 E) None of the above

17. Results of Different Loss Reserve Methods – Accident Year 2007 Paid Loss Development 26,973,000 Expected Loss Ratio 23,838,000 Bornhuetter-Ferguson 24,960,000

18. Frequency and Severity Estimates Calculate Incurred Claim Counts Determine Loss Frequency = # Claims/Exposure Determine Average Payment per Claim or Average Incurred Loss per Claim (Severity) Trend Frequency and Severity Separately Combine to Determine Ultimate Incurred Losses

19. Incurred Loss Development Similar to paid loss development, but includes case loss reserves

20. Additional Reserving Requirements Loss Adjustment Expense Allocated Sometimes included with losses Unallocated

21. Conclusion • Loss reserving combines calculations with actuarial judgement • To set accurate loss reserves requires thorough knowledge of claim settlement practices, especially regarding any changes • Current loss reserving approaches involves estimating loss reserve ranges, rather than setting a point estimate