Basic Reserving: Estimating the Liability for Unpaid Claims
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1 Basic Reserving: Estimating the Liability for Unpaid Claims September 15, 2014 Derek Freihaut, FCAS, MAAA John Wade, ACAS, MAAA Pinnacle Actuarial Resources, Inc.
2 Loss Reserve What is a loss reserve? Amount necessary to settle unpaid claims Why are loss reserves important? Accurate evaluation of financial condition and underwriting income
3 Components of a Reserve Case reserves Incurred but not reported ( IBNR ) reserves Claims incurred but not yet reported Claims reported but not yet recorded Future increases in case reserves Closed claims that reopen in the future
4 Case Reserve Basics Estimated by a claim adjuster Based on the details of the claim Various reserving philosophies Most likely settlement value (mode) Expected value of settlement (mean) Maximum settlement value Etc.
5 Case Reserve Issues Loss adjustment expenses Impact of inflation Recoveries from salvage and subrogation Recoveries from reinsurance
6 Hypothetical Claim Background Auto liability insurance Policy period: April 1, 2012 to March 30, 2013 Accident date: December 4, 2012 Date of claim report: January 15, 2013
7 Hypothetical Claim Transactions Part 1 Date Transaction Reported Claim Value Cumulativ e Paid to Date Jan. 15, 2013 Case reserve of $10,000 established $10,000 $0 Mar. 22, 2013 Apr. 18, 2013 Oct. 14, 2014 Dec. 18, 2014 $2,500 payment for medical costs; Case reserve reduced to $7,500 $500 payment to independent adjuster; No change to case reserve Case reserve increased from $7,500 to $50,000 Claim settled with $25,000 payment for lost wages and additional medical costs; Case reserve decreased to $0 $10,000 $2,500 $10,500 $3,000 $53,000 $3,000 $28,000 $28,000
8 Hypothetical Claim Transactions Part 2 Date Sep. 3, 2015 Dec. 8, 2015 Aug. 30, 2016 Sep. 15, 2016 Transaction Claim reopened with case reserve of $15,000 for legal defense costs and $5,000 for future payments to claimant Payment of $8,000 for legal costs; Case reserve for defense costs reduced to $7,000 Final payment to claimant of an additional $9,000; Case reserve for payment to claimant reduced to $0 Final payment for defense costs of an additional $8,000; Case reserve reduced to $0 Reported Claim Value Cumulative Paid to Date $48,000 $28,000 $48,000 $36,000 $52,000 $45,000 $53,000 $53,000
9 The Problem Policy was sold in early 2012 Claim isn t fully paid until late 2016 How does the company know if its business is profitable?
10 Thousands Hypothetical Claim Year-End Losses $60 $50 $40 $25.0 $5.0 $12.0 $30 $53.0 $42.5 $53.0 $20 $10 $0 $36.0 $28.0 $7.5 $3.0 12/31/ /31/ /31/ /31/ /31/2016 Paid Case Reserve IBNR Reserve
11 Interested Parties Company management Which business segments are the most/least profitable? Investors How profitable is the company? Regulators Does the company have sufficient funds available to meet its obligations to policyholders?
12 Basic Methods
13 Expected Loss Ratio - Single Accident Year Premium Earned During 2012 = $5 million Expected loss ratio = 80% Expected losses = $5 million x 80% = $4 million Total payments as of 12/31/2012 = $1.5 million Total reserves as of 12/31/2012 = $4 million - $1.5 million = $2.5 million
14 Expected Loss Ratio - Multiple Years (1) Accident Year (2) Earned Premium (3) Expected Loss Ratio (4) = (2) x (3) Expected Ultimate Loss (5) Paid Loss as of 12/31/12 (6) = (4) (5) Estimated Loss Reserve ,784 75% 11,088 10, ,468 75% 13,101 15,045 (1,944) ,550 75% 14,663 15,878 (1,215) ,243 75% 15,932 14, ,003 75% 18,002 15,425 2, ,866 75% 18,649 11,836 6, ,843 75% 19,382 5,609 13, ,487 75% 20,615 1,406 19,209 Total 175, ,433 91,018 40,415
15 Expected Loss Ratio Pros and Cons Strengths Simple calculation, easy to explain Minimal data requirements Not sensitive to data fluctuations Weaknesses Not responsive to data fluctuations Not responsive to changes in risk environment No accounting for inherent uncertainty in the expected loss ratio the key parameter
16 Paid Loss Development Data Accounting Configuration Accident Year Accident Year Paid Losses (in $000s) Cumulative Totals as of 12/31/XX ,785 5,262 8,178 9,522 10,604 10,803 10, ,907 8,383 12,748 14,161 14,805 15, ,058 4,344 8,501 11,912 15,148 15, ,106 4,589 7,929 12,618 14, ,230 4,829 10,355 15, ,281 5,696 11, ,217 5, ,406
17 Paid Loss Development Data Actuarial Configuration Accident Year Accident Year Paid Losses (in $000s) Cumulative Totals by Development Age in Months ,785 5,262 8,178 9,522 10,604 10,803 10, ,907 8,383 12,748 14,161 14,805 15, ,058 4,344 8,501 11,912 15,148 15, ,106 4,589 7,929 12,618 14, ,230 4,829 10,355 15, ,281 5,696 11, ,217 5, ,406
18 Loss Development Factor From 12 Months to 24 Months Accident Year Cumulative Paid at 12 Months Cumulative Paid at 24 Months Loss Development Factor , = 2,785 / , = 3,907 / ,058 4, = 4,344 / 1, ,106 4, = 4,589 / 1, ,230 4, = 4,829 / 1, ,281 5, = 5,696 / 1, ,217 5, = 5,609 / 1,217 Total 7,364 31, = 31,759 / 7, ,406??????
19 Loss Development Factor From 12 Months to 24 Months Accident Year Cumulative Paid at 12 Months Cumulative Paid at 24 Months Loss Development Factor , = 2,785 / , = 3,907 / ,058 4, = 4,344 / 1, ,106 4, = 4,589 / 1, ,230 4, = 4,829 / 1, ,281 5, = 5,696 / 1, ,217 5, = 5,609 / 1,217 Total 7,364 31, = 31,759 / 7, ,406 1,406 x = 6,
20 Paid Loss Development Data Actuarial Configuration Accident Year Accident Year Paid Losses (in $000s) Cumulative Totals by Development Age in Months ,785 5,262 8,178 9,522 10,604 10,803 10, ,907 8,383 12,748 14,161 14,805 15, ,058 4,344 8,501 11,912 15,148 15, ,106 4,589 7,929 12,618 14, ,230 4,829 10,355 15, ,281 5,696 11, ,217 5, ,406 6,046
21 Paid Loss Development Data Loss Development Factor Selection Accident Year Ult Wtd Avg Selected ???
22 Paid Loss Development Data Loss Development Factor Projection Accident Year Ult ??? ??? ??? ??? ??? ??? ??? ??? Selected ???
23 Paid Loss Development Data Squaring the Triangle Accident Year Accident Year Paid Losses (in $000s) Cumulative Totals by Development Age in Months ,785 5,262 8,178 9,522 10,604 10,803 10, ,907 8,383 12,748 14,161 14,805 15,045 15, ,058 4,344 8,501 11,912 15,148 15,878 16,148 16, ,106 4,589 7,929 12,618 14,967 15,940 16,211 16, ,230 4,829 10,355 15,425 18,278 19,466 19,797 19, ,281 5,696 11,836 17,754 21,038 22,405 22,786 22, ,217 5,609 11,218 16,827 19,940 21,236 21,597 21, ,406 6,046 12,090 18,135 21,490 22,887 23,276 23,392
24 Loss Development Factors The Tail Factor Loss development beyond the oldest age observed in the historical data Several approaches Insurance industry benchmarks Curve fitting / extrapolation Other mathematical / statistical models?
25 Loss Development Factors Age-Ultimate Accident Year Age (Months) Selected Age-Age LDF Selected Age-Ultimate LDF = x = x = x = x = x = x = x 3.908
26 Paid Development Method (1) Accident Year (2) Age (Months) (3) Cumulative Paid Loss as of 12/31/12 (4) Selected Age-Ultimate LDF (5) = (3) x (4) Projected Ultimate Loss , , , , , , , , , , , , , , , ,627 Total 91, ,841
27 Paid Loss Development Method Implicit Assumptions Volume of historical loss data is large enough to be credible Future payment patterns will be similar to historically observed patterns Changes to insurers operations Changes to judicial / legal environment New types of claims not seen before
28 Loss Development Factors Ultimate Loss = Paid Loss x LDF LDF = Ultimate Loss Paid Loss 1.0 = Paid Loss = % Paid LDF Ultimate Loss
29 Paid Development Method Sensitivity to Data Fluctuations (1) Accident Year (2) Paid at 12 Months (3) Estimated Ultimate Loss as of 12/31/12 (4) = (2) / (3) Percentage Paid at 12 Months (5) =(3) / (2) Implied Age-Ult LDF , % , % ,058 16, % ,106 16, % ,230 20, % ,281 23, % ,217 21, % ,406 23, %
30 Paid Loss Development Method Sensitivity to Data Fluctuations (1) Accident Year (2) Age (Months) (3) Cumulative Paid Loss as of 12/31/12 (4) Age-Ultimate LDF (5) = (3) x (4) Projected Ultimate Loss , , , , , ,669
31 Incurred Development Method Same basic idea as the Paid Development Method Use case incurred losses (paid losses + case reserves) instead of paid losses Takes advantage of the information provided by the claims adjusters Incurred losses generally develop more quickly than paid losses
32 Accident Year Incurred Loss Data Loss Development Triangle Accident Year Case Incurred Losses (in $000s) Cumulative Totals by Development Age in Months ,064 5,480 8,502 9,877 10,646 11,042 10,964 11, ,978 9,472 12,569 14,146 14,854 15,426 15, ,777 10,737 13,107 14,818 16,142 16, ,371 10,515 13,287 15,555 16, ,871 12,020 16,354 19, ,152 12,141 16, ,615 12, ,233
33 Incurred Loss Data Loss Development Factor Selection Accident Year Ult Wtd Avg Selected Age-Ultimate
34 Incurred Development Method (1) Accident Year (2) Age (Months) (3) Cumulative Incurred Loss as of 12/31/12 (4) Selected Age-Ultimate LDF (5) = (3) x (4) Projected Ultimate Loss , , , , , , , , , , , , , , , ,680 Total 115, ,346
35 Incurred Development Method Implicit Assumptions Volume of historical loss data is large enough to be credible Future reporting patterns will be similar to historically observed patterns No change in case reserving practice / philosophy No changes in data processing procedures No changes in risk exposure No new types of claims not seen before Etc.
36 Incurred Development Method Sensitivity to Data Fluctuations (1) Accident Year (2) Incurred at 12 Months (3) Estimated Ultimate Loss as of 12/31/12 (4) = (2) / (3) Percentage Reported at 12 Months (5) = (3) / (2) Implied Age-Ult LDF ,064 11, % ,978 15, % ,777 16, % ,371 17, % ,871 21, % ,152 20, % ,615 21, % ,233 20, % 2.512
37 Incurred Development Method Sensitivity to Data Fluctuations (1) Accident Year (2) Age (Months) (3) Cumulative Incurred Loss as of 12/31/12 (4) Age-Ultimate LDF (5) = (3) x (4) Projected Ultimate Loss , , , , , ,410
38 Comparison of Methods Expected Loss Ratio vs. Loss Development Expected Loss Ratio - Exposure based - Ignores actual loss experience - Stable estimates Loss Development - Ignores exposure - Based on actual loss experience - Estimates change in response to new information
39 Emergence Over Time
40 Change in Estimates Over Time Loss Rate Method Accident Year 2007 Values at 12/31/XX (1) Earned Premium 19,550 19,550 19,550 19,550 19,550 19,550 (2) Expected Loss Ratio 75% 75% 75% 75% 75% 75% (3) Expected Ultimate Loss = (1) x (2) 14,663 14,663 14,663 14,663 14,663 14,663 (4) Paid Loss 1,058 4,344 8,501 11,912 15,148 15,878 (5) Estimated Loss Reserve = (3) (2) 13,605 10,319 6,162 2,751 (485) (1,215)
41 Change in Estimates Over Time Incurred Development Method Accident Year 2007 Values at 12/31/XX (1) Age (2) Incurred Loss 6,777 10,737 13,107 14,818 16,142 16,452 (3) Age-Ult LDF (4) Projected Ultimate Loss 17,024 18,286 16,842 16,552 16,933 16,748 = (2) x (3) (5) Paid Loss 1,058 4,344 8,501 11,912 15,148 15,878 (6) Estimated Loss Reserve = (4) (5) 15,966 13,942 8,341 4,640 1,
42 Bornhuetter-Ferguson Method Accident Year 2007 Values at 12/31/XX (1) Earned Premium 19,550 19,550 19,550 19,550 19,550 19,550 (2) Expected Loss Ratio 75% 75% 75% 75% 75% 75% (3) Expected Ultimate Loss = (1) x (2) 14,663 14,663 14,663 14,663 14,663 14,663 (4) Age-Ult LDF (5) Expected Percentage 60.2% 41.3% 22.2% 10.5% 4.7% 1.8% Unreported = 1 1/(4) (6) Expected Unreported Loss = (3) x (5) 8,827 6,056 3,255 1, (7) Projected Ultimate Loss 15,604 16,793 16,362 16,358 16,831 16,716 (8) Paid Loss 1,058 4,344 8,501 11,912 15,148 15,878 (9) Estimated Loss Reserve = (7) (8) 14,546 12,449 7,861 4,446 1,
43 Bornhuetter-Ferguson Method (1) Accident Year (2) Earned Premium (3) Expected Loss Ratio (4)=(2)x(3) Expected Ultimate Loss (5) Incurred LDF (6)= /(5) Expected Percent Unreported (7)=(4)x(5) Estimated IBNR Reserve (8) Actual Incurred Loss (9)=(7)+(8) Estimated Ultimate Loss ,784 75% 11, % 33 11,014 11, ,468 75% 13, % ,496 15, ,550 75% 14, % ,452 16, ,243 75% 15, % ,239 16, ,003 75% 18, % 1,890 19,177 21, ,866 75% 18, % 4,140 16,048 20, ,843 75% 19, % 8,005 12,433 20, ,487 75% 20, % 12,410 8,233 20,643 Total 175, ,432 27, , ,688
44 Bornhuetter-Ferguson Method Implicit Assumptions Premium is an accurate measure of exposure Expected loss ratio is predictable Constant reporting, case reserving and settling
45 Final Selection (1) Accident Year (2) Paid Loss Development (3) Incurred Loss Development (4) Incurred Bornhuetter- Ferguson (5) Expected Loss Rate (6) Selected Ultimate Loss as of 12/31/12 (7) Paid Loss as of 12/31/12 (8) = (6) (7) Estimated Loss Reserve as of 12/31/ ,961 11,047 11,048 11,088 11,047 10, ,271 15,620 15,601 13,101 15,620 15, ,386 16,748 16,716 14,663 16,748 15, ,449 17,035 16,988 15,932 17,035 14,967 2, ,098 21,421 21,067 18,002 21,421 15,425 5, ,128 20,622 20,189 18,649 20,622 11,836 8, ,921 21,173 20,437 19,382 20,437 5,609 14, ,627 20,680 20,643 20,615 20,643 1,406 19,237 Total 147, , , , ,573 91,019 52,554
46 Data Considerations & Communication
47 Data Considerations Homogeneity Different types of claims develop differently Subdividing the data can improve accuracy Automobile Liability Bodily Injury Property Damage PIP Med Pay UM-BI UM-PD Physical Damage Collision Other Than Collision
48 Data Considerations Credibility Is there enough data for it to have predictive value? Homogeneity vs. Credibility Small program (e.g. self-insurer or captive) Type of coverage Low frequency / high severity Long reporting lags Long tail Use supplementary data sources (industry data, countrywide data, etc.)
49 Communicating the Results Basis of Presentation What do we think our answer means? Mean, median, mode? Percentile? Actuarial Central Estimate Are the estimates discounted for the time value of money? Have they been adjusted for future recoveries? Salvage and subrogation? Reinsurance Etc.
50 Communicating the Results Intended Purpose Know the audience Company management Potential investors Insurance regulators Others?
51 Advanced Topic
52 Advanced Topic Stochastic Reserving Actual outcome is inherently uncertain Can we understand the potential variability? Business value Risk Management Fair value of liabilities External Pressures Solvency II in Europe Own Risk and Solvency Assessment in U.S. International Financial Reporting Standards
53 Casualty Actuarial Society 4350 North Fairfax Drive, Suite 250 Arlington, Virginia
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