Introduction to Property & Casualty Actuarial

1. Introduction to Property & Casualty Actuarial Presenter: Matt Duke

2. What does a PC Actuary do? Examine past and present experience to predict the future. • Pricing • Rate adequacy / rate filings. • Reserving • Reserve reviews. • Predictive Modeling • Generalized linear or additive model.

3. What is an Actuary? Actuaries are experts in: • evaluating the likelihood of future events, • designing creative ways to reduce the likelihood of undesirable events, • decreasing the impact of undesirable events that do occur. www.beanactuary.org

4. Actuarial Vocabulary • Premium = Rate * Exposures • Exposure (exposure bases) • Expenses • Loss Adjustment Expense (ALAE & ULAE) • Other Underwriting Expenses • Commissions & Brokerage • General Expenses (OIE) • Taxes, Licenses, and Fees • Investment Expenses • Variable vs. Fixed

5. Actuarial Vocabulary • Losses • Claim Counts • claims/claimants, open/closed • Ratios: Loss, Expense, Combined • Frequency = Claim Count / Exposures • Severity = Losses / Claim Count • Pure Premium = Frequency * Severity = Losses / Exposures

6. A Dollar of Premium • 60% Loss (&ALAE) Ratio = $0.60 • ULAE = 10% Loss+ALAE = $0.06 • Commissions = 18% prem = $0.18 • Fixed Expenses = 10% prem = $0.10 • Taxes = 5% prem = $0.05 • The rest is left for: Profit! $0.01 • What about investment income?

7. Investment Income • In my example, for every $1.00 we collect, we pay out $0.99. • However, we get to invest the $1.00 for a length of time before we have to pay any losses. • The extent that we rely on investments for profit varies by line of business.

8. Written vs. Earned Premium • Written Premium: All Premium for a policy is assigned to a single year - the year in which the policy was “written” (when coverage became effective.) • Earned Premium: Premium is distributed to each year the policy is in effect, based on the proportion of the policy period in each year.

9. Written vs. Earned Premium

10. Written vs. Earned Premium Since the Policy was written in 2001, all written premium goes to 2001 Policy Effective Period 2001 2002

11. Written vs. Earned Premium Since 1/2 of the policy period is in 2001 and 1/2 is in 2002, the earned premium is split 50/50%

12. Written vs. Earned Premium Since 1/2 of the policy period is in 2001 and 1/2 is in 2002, the earned premium is split 50/50% 1/2 1/2 2001 2002

13. Written vs. Earned Premium

14. Written vs. Earned Premium Since the Policy was written in 2001, all written premium goes to 2001

15. Written vs. Earned Premium Since 1/4 of the policy period is in 2001 and 3/4 is in 2002, the earned premium is split 25/75% 1/4 3/4 2001 2002

16. Written vs. Earned Premium • Additional Note: • It doesn’t matter when the premium is actually collected from the policyholder for either written or earned premium.

17. Different Types of “Years” • Accident Year (Loss Only) • Policy Year (Loss or Written Premium) • Calendar Year (Loss or Written/Earned Premium) • Report Year (Loss Only) • Exposure Year (Earned Premium Only)

18. Different Types of “Years” • Accident Year (Loss Only) • Groups losses by the year in which the loss event (accident) occurred. • Policy Year (Loss or Written Premium) • Calendar Year (Loss or Written/Earned Premium) • Report Year (Loss Only) • Exposure Year (Earned Premium Only)

19. Different Types of “Years” • Accident Year (Loss Only) • Policy Year (Loss or Written Premium) • Groups losses or premiums by the year in which the associated policy was effective. • Calendar Year (Loss or Written/Earned Premium) • Report Year (Loss Only) • Exposure Year (Earned Premium Only)

20. Different Types of “Years” • Accident Year (Loss Only) • Policy Year (Loss or Written Premium) • Calendar Year (Loss or Written/Earned Premium) • All transactions (losses paid, reserves posted, etc.) counted in the year they actually took place. • Report Year (Loss Only) • Exposure Year (Earned Premium Only)

21. Different Types of “Years” • Accident Year (Loss Only) • Policy Year (Loss or Written Premium) • Calendar Year (Loss or Written/Earned Premium) • Report Year (Loss Only) • Groups losses by the year in which we (the insurance company) were notified of the claim. • Exposure Year (Earned Premium Only)

22. Different Types of “Years” • Accident Year (Loss Only) • Policy Year (Loss or Written Premium) • Calendar Year (Loss or Written/Earned Premium) • Report Year (Loss Only) • Exposure Year (Earned Premium Only) • Similar to calendar year, but premium adjustments after expiration are reassigned to the year(s) the coverage was effective.

23. Different Types of “Years” 12 Month Auto Policy Written 7/1/1994 Car Accident Happened Accident Reported to Insurer Premium Audit of $100 Claim paid in full for $1,000 1994 1995 1996 1997 1998 1999

24. Different Types of “Years” 12 Month Auto Policy Written 7/1/1994 Car Accident Happened Accident Reported to Insurer Premium Audit of $100 Claim paid in full for $1,000 1994 1995 1996 1997 1998 1999

25. Different Types of “Years” 12 Month Auto Policy Written 7/1/1994 Car Accident Happened Accident Reported to Insurer Premium Audit of $100 Claim paid in full for $1,000 1994 1995 1996 1997 1998 1999

26. Different Types of “Years” 12 Month Auto Policy Written 7/1/1994 Car Accident Happened Accident Reported to Insurer Premium Audit of $100 Claim paid in full for $1,000 1994 1995 1996 1997 1998 1999

27. Different Types of “Years” 12 Month Auto Policy Written 7/1/1994 Car Accident Happened Accident Reported to Insurer Premium Audit of $100 Claim paid in full for $1,000 1994 1995 1996 1997 1998 1999

28. Paid vs. Incurred vs. Outstanding Loss • Paid Loss = Total $$ actually paid out to policyholders for claims. • Calendar Year 2001 Paid Loss = Total $$ for claim payments made during 2001, even on accidents from prior years. • Accident Year 2001 Paid Loss = Total $$ paid for accidents that occurred in 2001, even if the claim was paid after 2001.

29. Paid vs. Incurred vs. Outstanding Loss • Outstanding Loss = $$ that the claim department has set aside for future payments on existing claims. • Outstanding Loss = Case Reserves • Case Reserves are estimates of the $$ amount remaining to be paid on individual claims.

30. Paid vs. Incurred vs. Outstanding Loss • Case Incurred Loss = Paid + Outstanding • Accident Year 2001 Incurred Loss = All paid $$ + case reserves on claims from accidents that occurred in 2001. • Calendar Year 2001 Incurred Loss = All claim payments made in 2001 + all new case reserves posted in 2001 (including reserve increases/decreases on existing claims).

31. Loss Development Loss Development = The process by which the losses on a defined group of claims changes over time. (the defined group of claims could, for instance, be all claims from accident year 2000)

32. Loss Development 2 Types of Loss Development • Paid Loss Development = Changes over time in total $$ paid to date for a defined group of claims. • Incurred Loss Development = Changes over time in total $$ incurred to date for a defined group of claims.

33. Loss Development Why do losses develop?

34. Loss Development Why do losses develop? Examples: • Unreported claims • Development on case reserves (under/overestimating the total loss when it is first recorded) • …other influences

35. Loss Development A Hypothetical Workers’ Compensation Claim LOSS DEVELOPMENT

36. Loss Development • Age = The amount of time that has elapsed since the beginning of an accident or policy period. E.g. - What is the “age” (in months) of accident year 2000 at 7/1/2001?

37. Loss Development • Age = The amount of time that has elapsed since the beginning of an accident or policy period. E.g. - What is the “age” (in months) of accident year 2000 at 7/1/2001? Answer: 18 months (From 1/1/2000 to 7/1/2001)

38. Loss Development • Ultimate Loss = The total $$ that will “ultimately” be paid to settle a claim or group of claims after all development is finished. It can take as little as a few months to over 50 years for losses to reach “ultimate”.

39. Loss Development • IBNR = (“Incurred but not reported”) • Pure IBNR = Losses on claims for accidents that have occurred that have not yet been reported to the insurer. • “IBNR” usually includes “everything else” that causes case incurred losses to develop in addition to “Pure IBNR.” Paid + Outstanding + IBNR = Ultimate Case Incurred

40. Loss Development • IBNR = (“Incurred but not reported”) • Pure IBNR = Losses on claims for accidents that have occurred that have not yet been reported to the insurer. • “IBNR” usually includes “everything else” that causes case incurred losses to develop in addition to “Pure IBNR.” • As opposed to case reserves, IBNR is not assigned to individual claims!

41. Loss Development • Loss Development that occurs at late ages is called the “tail” (e.g. - development after > 20 years). • Short Tailed Lines / Long Tailed Lines Short tailed lines - Claims settle quickly Long tailed lines - Claims can take many years to settle Which lines are short tailed? Long tailed?

42. Loss Development “Tail” $40MM IBNR Case Reserves $30MM Ultimate Loss Loss $$ Paid Loss $20MM $10MM 5 10 15 20 Age (in years)

43. Credibility • Predictive power of a statistic depends on the volume and homogeneity of the data behind it. • The more reliable the statistic is, the more weight (credibility) we give it in determining the final estimate. • Each credibility weighted item needs at least one complement. • Actuarial Exam C/4 material.

44. Credibility Example • Which has more credibility?

45. Loss Limiting/Layering Losses limited at X: • All losses < or = X are counted at their full value • All losses > X are “capped” at X Loss Limit Loss $$ Claims

46. Loss Limiting/Layering

47. Loss Limiting/Layering Loss Layering = Similar to loss limiting but also may eliminate losses below a fixed limit, as well as above a higher limit. Loss Layer Loss $$ Claims

48. Loss Limiting/Layering

49. Loss Limiting/Layering Why would we look at limited/layered losses?

50. Loss Limiting/Layering Why would we look at limited/layered losses? 1) Policy provisions limit coverage (deductibles, policy limits, etc.) 2) Smooth volatile experience in high loss layers