Casualty Actuarial Society Experienced Practitioner Pathway Seminar Lecture 4 – Calibration of Risk Parameters in Econ

1. Casualty Actuarial SocietyExperienced Practitioner Pathway SeminarLecture 4 – Calibration of Risk Parameters in Economic Capital Modeling Shaun Wang, Ph.D., FCAS Professor,Georgia State University Chairman, Risk Lighthouse LLC

2. Calibration of Risk Parameters Two issues in economic capital modeling: Part 1. Are Insurance Companies’ Reserve Risks the Same? Part 2. Correlation Modeling: Structural Approach EPP Lecture 6: Calibration of Risk Parameters In Economic Capital Modeling

3. Calibration Risk Parameters Using Data • Based on a Research Database at Risk Lighthouse • Premium and Loss triangles for the past 32 Accident Years (AY1980-2011) for all insurance companies, for all Schedule P lines of business • At both operating companies level and combined groups level • Extensive efforts in cleaning data for inconsistencies (due to past mergers and acquisitions, filing changes, failed companies, etc.) • Additional data (SNL; A.M. Best; III.org; exposure data and economic data sources) EPP Lecture 8: Risk and Light/Plural Rationality

4. References: Two Prize-winning Papers 1. Shaun Wang, John Major, Charles Pan, Jessica Leong: “U.S. Property-Casualty: Underwriting Cycle Modeling and Risk Benchmarks” • Awarded the 2012 Best Paper of the CAS Variance Journal. • Awarded the Best Paper for “Practical Risk Management Applications” at the 2011 ERM Symposium in Chicago 2. Jessica Leong, Shaun Wang, Han Chen: “Back-Testing the ODP Bootstrap of the Paid Chain-Ladder Model with Actual Historical Claims Data” received the Best Paper Prize at the 2012 Casualty Loss Reserve Seminar in Denver. EPP Lecture 8: Risk and Light/Plural Rationality

5. Part 1. Are Insurance Companies’ Reserve Risks The Same?

6. P/C Industry All Lines Calendar-Year Reserve Dev., 1992–2013F Prior year reserve releases totaled $8.8 billion in the first half of 2010, up from $7.1 billion in the first half of 2009 Reserve Releases Remained Strong in 2010 But Tapered Off in 2011. Releases Are Expected to Further Diminish in 2012 and 2103 Note: 2005 reserve development excludes a $6 billion loss portfolio transfer between American Re and Munich Re. Including this transaction, total prior year adverse development in 2005 was $7 billion. The data from 2000 and subsequent years excludes development from financial guaranty and mortgage insurance. Sources: Insurance Information Institute; Barclays Capital; A.M. Best.

7. Total loss ratio is (Total loss/Net Earned Premium). Total loss is from Schedule P part 2. Initial total loss is reported incurred loss at 12-months. Latest total loss is reported incurred loss at 120-months for accident year(AY) 2002 and prior. For AY 2003 and later, the latest total losses are as of December 31, 2011. shaun.wang@risklighthouse.com

8. Workers Compensation Reserve Risk • Accident Years 1980 to 2006, Net of reinsurance The mean and standard deviation of reserve “error” is shown. Each dot in the graph represents an insurance company group. shaun.wang@risklighthouse.com

9. Is Company Reserve Risk Consistent through the Cycle? LLR-ILR percentiles are calculated for all companies for each accident year. A higher percentile represents a more conservative reserve position compared to other insurance companies. Most Adverse shaun.wang@risklighthouse.com

10. Is Company Reserve Risk Consistent through the Cycle? The two graphs use the same company list. Each dot in the graph represents an insurance company group. A higher percentile represents a more conservative reserve position compared to other insurance companies. shaun.wang@risklighthouse.com

11. Is Company Reserve Risk Consistent through the Cycle? Over a longer time period, the positive correlation no longer exists. In fact, for the companies with worst reserving experience (0%-20%) in AY2000, most of them held a more conservative reserve estimate than average in AY2004. shaun.wang@risklighthouse.com

12. A Measure of Cycle Reserving Management Background • To measure companies’ loss reserve development and how that development compares with the industry and with the companies’ peer groups Formula • [LLR-ILR(Company)] = Alpha + Beta*[LLR-ILR(Industry)] + error Interpretation • Alpha represents a general directional trend above or below the industry • Beta represents how closely company loss reserve development follows year to year changes in industry loss reserve development in direction and magnitude. shaun.wang@risklighthouse.com

13. How is Beta distributed across companies? Only the significant betas are presented in the graph (90% confidence level). Half of the companies have significant betas. shaun.wang@risklighthouse.com

14. A Company with High Beta Company B is a company that had more adverse reserve development than the industry when industry reserves were weak, but had an over-conservative reserve when industry reserves were strong. Company B shaun.wang@risklighthouse.com

15. A Company with Beta=1 From AY 1991 to 1998, company A’s reserve development experience followed the industry closely, but its relative reserve position (LLR-ILR percentile) still deteriorated during this time period. shaun.wang@risklighthouse.com

16. Pricing Cycle vs. Reserving Cycle shaun.wang@risklighthouse.com

17. How to measure the Pricing Cycle? P&C Total Written Premium to Private Sector GDP Ratio (1967-2009) shaun.wang@risklighthouse.com

18. Division of LOBs for Reserve Cycle • Personal Lines • Private Passenger Auto Liability • Auto Physical Damage • Homeowners • Commercial Liability Lines • Commercial Auto Liability • Medical Professional Liability • Other Liability • Product Liability • Workers’ Compensation 3. Commercial Property Lines • The remaining P&C lines excluding Accident and Health. shaun.wang@risklighthouse.com

19. Division of LOBs for Reserve Cycle Reason 1: Different Players Other Companies Other Companies shaun.wang@risklighthouse.com

20. Division of LOBs for Reserve Cycle Reason 2: Different Operating Profit/Loss Cycles shaun.wang@risklighthouse.com

21. Division of LOBs for Reserve Cycle • The evidence supports the subdivision of the P&C industry. • The subdivision of the P&C industry will have new timing, magnitude, and position of the reserve cycle for each line of business. • A more accurate estimation of where we are in the cycle will help to determine companies’ reserve position. shaun.wang@risklighthouse.com

22. Insurance Markets Segments • To better analyze company reserving risk, we divided all insurance companies into seven segments. shaun.wang@risklighthouse.com

23. Subdivisions of Insurance Companies *For Medical Professional Liability, we didn’t calculate for Super Regional group since the premium and loss volume is too small. shaun.wang@risklighthouse.com

24. WC Tail Factors for Different Segments The tail factors are calculated as (120-month Net Total Loss/120-month Net Case Incurred Loss). For accident year after 2002, we develop the latest reported Net Total Loss and Net Case Incurred Loss to 120-month. shaun.wang@risklighthouse.com

25. WC Tail Factors for Different Segments The tail factors in the above charts are AY 2000-2002 loss weighted average of tail factors. shaun.wang@risklighthouse.com

26. Conclusion • Reserve risk varies significantly from company to company. • An individual company’s reserve risk varies over time. • The projection of the reserve cycle is important for estimation of individual company’s reserve risk. • We need better predictive variables/drivers. • Reserve risk varies by line of business and by market segment. • Reserve cycle timing varies by line of business. • Tail factors are important for reserve projection and they vary across the segments. shaun.wang@risklighthouse.com

27. Part2. Correlation Modeling: Structural Approach

28. Change in Commercial Rate Renewals, by Account Size: 1999:Q4 to 2012:Q2 Percentage Change (%) Pricing turned positive in Q3:2011, the first increase in nearly 8 years; Q2:2012 renewals were up 4.3% Peak = 2001:Q4 +28.5% Pricing Turned Negative in Early 2004 and Remained that way for 7 ½ years KRW : No Lasting Impact Trough = 2007:Q3 -13.6% Trough = 2007:Q3 -13.6% Source: Council of Insurance Agents and Brokers; Barclay’s Capital; Insurance Information Institute.

29. Medical Cost Inflation Has Outpaced Overall Inflation For Over 50 Years A claim that cost $1,000 in 1961 would cost nearly $17,500 based on medical cost inflation trends over the past 51 years. Source: III.org; Department of Labor (Bureau of Labor Statistics)

30. WC Medical Severity Moderate Increase in 2011 Average Medical Cost per Lost-Time Claim vs. Medical CPI Percent Change Year p Preliminary Based on the states where NCCI provides ratemaking services, including state funds; excludes high deductible policies Source: III.org; Medical CPI—All states, Economy.com; Accident year medical severity—NCCI states, NCCI

31. Reduction in Combined Ratio Necessary to Offset 1% Decline in Investment Yield to Maintain Constant ROE, by Line* Lower Investment Earnings Place a Greater Burden on Underwriting and Pricing Discipline *Based on 2008 Invested Assets and Earned Premiums **US domestic reinsurance only Source: A.M. Best; Insurance Information Institute. 31 12/01/09 - 9pm eSlide – P6466 – The Financial Crisis and the Future of the P/C

32. Wildly Different Capital Allocations Gary Venter, Feb 2002 Actuarial Review In 2001, the CAS Call For Papers to analyze a hypothetical insurer, recommend a reinsurance program, allocate capital, etc. EPP Lecture 6: Calibration of Risk Parameters In Economic Capital Modeling

33. Open up for Discussions • Are you using industry-wide average, or customized risk parameters? • Are you happy with correlation matrix? • How do you reflect the time-dependency? • Do you encounter non-intuitive capital allocation results? EPP Lecture 6: Calibration of Risk Parameters In Economic Capital Modeling