Session 25 L, Introduction to General Insurance Ratemaking & Reserving: An Integrated Look. Moderator: W. Scott Lennox, FSA, FCAS, FCIA

Transcription

1 Session 25 L, Introduction to General Insurance Ratemaking & Reserving: An Integrated Look Moderator: W. Scott Lennox, FSA, FCAS, FCIA Presenter: Houston Cheng, FCAS, FCIA

2 Society of Actuaries 2013 Annual Meeting & Exhibit Introduction to General Insurance Ratemaking and Reserving An Integrated Look Houston Cheng, FCAS, FCIA (416) Presentation Date: October 21, 2013 Agenda Introduction Technical key concepts Estimating ultimate claims Reserving Ratemaking 1 1

3 Introduction Introduction Industry Snapshot 2012 U.S. Property & Casualty Industry Direct Written Premiums Total written: $512.3 billion 7% 7% 8% 9% 5% 3% 21% Private Auto Liability Homeowners Private Auto Physical Damage Liability Workers' Comp Other Property 15% Other Commercial Multi Peril Commercial Auto Financial Products 13% 12% Source: A.M. Best's Global Insurance Database 3 2

4 Introduction Major Lines of Business Fire Multi Peril Crop Federal Flood Farmowners Multi Peril Homeowners Multi Peril Commercial Multi Peril Mortgage Guaranty Ocean Marine Inland Marine Financial Guaranty Medical Professional Liability Earthquake Accident and Health Workers Compensation Other Liability Products Liability Private Auto Liability Commercial Auto Liability Private Auto Physical Damage Commercial Auto Physical Damage Aircraft Fidelity Surety Burglary & Theft Boiler & Machinery Credit Warranty 4 Introduction Characteristics of General Insurance Most lines of business are short duration Investment income not as significant as non-gi products Important to understand frequency and severity of claims Nature of any particular claim usually unknown uncertainties include: Actual claim payment (including re-opening of a claim) Amount of claim payment Number of payments for a claim Timing of claim payment 5 3

5 Introduction Characteristics of General Insurance (Continued) Methodology: Underlying processes often not well understood by non-actuaries Methods historically have been ad-hoc Average as well as distribution of outcomes important Need to communicate uncertainty Modern approaches beginning to incorporate stochastic approaches 6 Technical Key Concepts 4

6 Technical Key Concepts Ultimate claims Data Credibility Trend 8 Technical Key Concepts Ultimate Claims Definition: the value of claims beyond which no other claims payments are expected To derive an estimate of ultimate claims, actuaries look years into the future to determine an estimated amount the insurer will pay when all claims have been closed and settled and no further payments are anticipated Ultimate claims consist of 4 components: Claim payments Case estimates for claims that have been reported Development on case outstanding (incurred but not enough reported IBNER) Claims that have been incurred but not yet reported (incurred buy not yet reported IBNYR) IBNR = IBNER + IBNYR Ultimate claims = cumulative claim payments + case estimates + IBNR 9 5

7 Technical Key Concepts Ultimate Claims (Continued) Why estimates of ultimate claims are needed: Final cost of goods sold is not known until long into the future Estimates of ultimate values become critical in the management of GI enterprises: Financial reporting Pricing Financial condition analysis Planning Valuations, including merger and acquisition analyses 10 Technical Key Concepts Data Typical data: Claim Amounts: paid, case estimates, reported, etc. Counts: Closed, open, reported Aggregation by calendar, accident, policy, or report year Line of business Gross, net and/or ceded of reinsurance Exposure Premiums, number of policies, number of vehicles, payroll, sales, etc. Expense Loss adjustment, general, underwriting, etc. 11 6

8 Technical Key Concepts Credibility GI actuaries use credibility procedures to improve estimates. Through credibility procedures, data from two (or more) sets of experience are blended together with the goal of improving the overall results of the actuarial work. Examples of actual experience blended with a complement of credibility: An insurer s experience with industry experience A subsidiary company s experience with experience from a larger, related company Experience in one territory within a state with statewide experience Experience in one state with regional or countrywide experience Experience in one line of business with similar lines of business Experience in one classification with all classifications Experience in one deductible or limit layer with experience in similar deductible or limit layers 12 Technical Key Concepts Trend Consider how changes over time affect items such as claim costs, claim severities, claim frequencies, expenses, exposures, and premiums Reflect the dynamic forces that exist in our society economic, societal and demographic that produce measurable changes in insurance experience over time Time periods for trend: Experience: historical Forecast: future 13 7

9 Estimating Ultimate Claims Estimating Ultimate Claims Life of a claim: When a claim is reported, insurance adjuster assigns initial estimate of the amount that will ultimately be paid by the insurer (known as a case reserve) Case reserve at any point in time is the estimated amount still outstanding to be paid as of that date to settle the claim (i.e., close the claim) Total amount of claim at any date (i.e., reported value) = amount paid to date + amount outstanding (i.e., case reserve) 15 8

10 Estimating Ultimate Claims Life of a Claim (Auto Collision Example) $2,500 $2,000 $1,500 Case Reserve $1,000 Payment $500 $0 12/15/ /22/ /31/2010 1/5/2011 1/15/ Estimating Ultimate Claims Life of a Claim (General Liability Example) $400,000 $350,000 $300,000 $250,000 $200,000 $150,000 $100,000 $50,000 $230,000 $165, $150, $150, ,000 $2 $325,000 Case Reserve Payment $0 $20,

11 Estimating Ultimate Claims Data Organization 12/31/ /31/ /31/ /31/2013 Paid 20, , , ,000 Case Reserve 230, , , Reported 250, , , ,000 Reported Age (Months) Accident Year , , , , Estimating Ultimate Claims Triangle Example Reported Age (Months) Accident Year , , , , , , , , , , , , , , ,000 Accident Year <= Age-to-age Average Selected

12 Estimating Ultimate Claims Triangle Example (Continued) Reported Age (Months) Accident Year , , , , , , , , , , , , , , , , , , , , , , , , , Selected Estimating Ultimate Claims Triangle Example (Continued) Reported Age (Months) Accident Year , , , , , , , , , , , , , , , , , , , , , , , , ,431 At 12/31/2013 Accident Year Reported Ultimate , , , , , , , , , ,

13 Estimating Ultimate Claims Methods Example highlighted: Development method Other methods: Expected Bornhuetter Ferguson Cape Cod Berquist-Sherman 22 Estimating Ultimate Claims Expected Method At 12/31/2013 Accident Year Earned Premium Reported Claims Population Claim Ratio Frequency Severity , ,196 5,000 60% 1.25% 5, , ,000 5,050 60% 1.25% 5, , ,035 4,949 60% 1.25% 5, , ,200 5,048 60% 1.25% 5, , ,000 4,998 60% 1.25% 5,412 Accident Year Ultimate at 12/31/2013 Claim Ratio Freq-Sev Selected , , , , , , , , , , , , , , ,

14 Estimating Ultimate Claims Bornhuetter Ferguson Accident Year Reported at 12/31/2013 Cumulative Dev. Factor Percent Unreported Ultimate at 12/31/2013 Expected BF , % 312, , , % 320, , , % 323, , , % 332, , , % 337, , Estimating Ultimate Claims Select Ultimate Accident Year Reported at 12/31/2013 Ultimate at 12/31/2013 Development Expected BF Selected , , , , , , , , , , , , , , , , , , , , , , , , ,

15 Reserving Reserving Financial Statement Recall that: Ultimate claims = cumulative claim payments + case estimates + IBNR Note: Claim liabilities = case estimates + IBNR or Claim liabilities = ultimate claims cumulative claim payments At 12/31/2013 Accident Year Paid Claims Case Estimates Reported Claims Selected Ultimate IBNR Unpaid Claims , , , , , , ,035 75, , , , , , , ,320 31, , , , , ,905 97, ,905 Total 447, , ,

16 Reserving Life Insurance verses General Insurance Life insurance reserves: Policy reserve = PV[expected future benefits] PV[expected future net premiums] Specific reserve for all policies Financial statement reserves = sum of all policy reserves Policy reserve increases toward face amount (i.e., gets closer to paying the death benefit) General insurance reserves: Individual reserve = case reserve Case reserve only incurred if claim is reported (i.e., not all individual policies have reserve) Financial statement reserves = sum of all case reserves + IBNR provision (i.e., bulk reserve) Case reserve typically decreases with each duration (i.e. gets closer to settling the claim and completing the payment) 28 Ratemaking 15

17 Ratemaking Objectives Essential objectives: Cover expected losses and expenses Produce rates that make adequate provision for contingencies Encourage loss control Satisfy rate regulators In general terms, the basic requirements of the regulatory agencies are that rates must be adequate, not excessive, and not unfairly discriminating Non-essential but desirable objectives: Produce rates that are reasonably stable Produce rates that are reasonably responsive to changes Be simple and easy to understand 30 Ratemaking Basics Claim frequency Frequency (i.e., probability) of an insured having a claim Claim severity Average claim size Claim cost Expected value of the incurred losses per unit of exposure i.e., pure premium [claim frequency] x [claim severity] 31 16

18 Ratemaking Pure Premium Accident Year Reported Claims Excess Claims Cumulative Dev. Factor Trend Factor ULAE Large Loss Loading , , , , , , Accident Year Adjusted Ult. Claims Population Pure Premium ,062 5, ,927 5, ,611 4, ,213 5, ,462 4, Total 1,959,276 25, Ratemaking Premium Calculation In general: Premium = expected claim + underwriting expenses + profit Assume: P = premium C = expected claim V = underwriting expenses as percent of premium = 15% Q = profit as percent of premium = 10% P C V P Q P C P 1 V Q 78.2 P

19 Ratemaking Other Considerations Adjust historic premiums to current rate levels Trend historic premiums to reflect change in mix of business Overall rate adequacy Rate adequacy by risk classification Credibility of data Competition Actuarially fair premium vs. competitive premium Regulatory constraints Operational constraints Underwriting cycle 34 Ratemaking Classification Simple one-way analysis Classical linear analysis Minimum bias procedures Generalized linear models (GLMs) 35 18

20 Ratemaking Considerations (Auto) Safety and theft statistics for the area you live in Whether you commute to work Personal or commercial use The year, make and model of your vehicle How many tickets you have had, including past at-fault insurance claims How many years you have been driving Various discounts How much coverage you wish to purchase and deductibles you choose 36 Ratemaking Considerations (Home) Building material and construction Replacement cost Whether the area is prone to flooding or wind damage Neighbourhood s crime rate Special collections or valuable items in the home Proximity to a fire station Applicable discounts and the level of deductible 37 19

21 Questions? Thank you Contact Details: Houston Cheng, FCAS, FCIA (416)

22 The information contained herein is of a general nature and is not intended to address the circumstances of any particular individual or entity. Although we endeavor to provide accurate and timely information, there can be no guarantee that such information is accurate as of the date it is received or that it will continue to be accurate in the future. No one should act on such information without appropriate professional advice after a thorough examination of the particular situation KPMG LLP, a Canadian limited liability partnership and a member firm of the KPMG network of independent member firms affiliated with KPMG International Cooperative ( KPMG International ), a Swiss entity. All rights reserved. The KPMG name, logo and cutting through complexity are registered trademarks or trademarks of KPMG International. 21