Credibility and Pooling Applications to Group Life and Group Disability Insurance

Transcription

1 Credibility and Pooling Applications to Group Life and Group Disability Insurance Presented by Paul L. Correia Consulting Actuary (207) May 20, 2014

2 What I plan to cover this morning Traditional credibility models Issues with applying traditional credibility models to group insurance 2013 Society of Actuaries survey on credibility applications in group insurance Analysis of credibility using random sampling Risk pooling Final thoughts on experience rating and data tracking 2 May 16, 2014

3 Traditional Credibility Models 3 May 16, 2014

4 Traditional Credibility Models Classical Credibility O R I G I N S Pricing of workers compensation insurance How Extensive a Payroll is Necessary to Give a Dependable Pure Premium? by A.H. Mowbray, 1914 M E T H O D O L O G Y Goal is to limit the impact of random fluctuations in the experience on the estimated premium Full credibility thresholds are developed from confidence intervals, e.g. claims experience may be considered fully credible if observed claims are within 5% of expected claims 95% of the time. Partial credibility = Exposure / Full Credibility Threshold U N D E R L Y I N G A S S U M P T I O N S Claims are assumed to be independent random variables with identical probability distributions Risk is assumed to not vary over time (homogeneous) A D V A N T A G E S Simple to develop and apply. Commonly used and generally well accepted. D I S A D V A N T A G E S Assumptions may not be true in practice. Same weight is given to the expected loss (i.e. manual rate) regardless of the accuracy of the expected loss (manual rate). Confidence interval parameters (e.g. 5% and 95% from the example to the left) are subjective. 4 May 16, 2014

5 Traditional Credibility Models Least Squares Credibility O R I G I N S Experience rating of insurance products Experience Rating and Credibility by H. Buhlmann, 1967 A D V A N T A G E S Commonly used and generally well accepted. M E T H O D O L O G Y Goal is to minimize the squared difference between the premium estimate and the true expected value Credibility factor = n / (n + k) where n = exposure k = volatility term U N D E R L Y I N G A S S U M P T I O N S Claims are assumed to be independent random variables with identical probability distributions. D I S A D V A N T A G E S Assumptions may not be true in practice. Difficult to determine the parameters expected value of process variance and variance of hypothetical means. Risk is assumed to not vary over time (homogeneous). 5 May 16, 2014

6 Issues with Applying Traditional Credibility Models to Group Insurance 6 May 16, 2014

7 Issues with Applying Traditional Credibility Models to Group Insurance N O N I N D E P E N D E N C E O F C L A I M S Traditional credibility models assume claims are independent variables Group life and group disability claims are not believed to be independent variables External factors that may affect a group s claims experience: Work conditions / employment characteristics Concentration of risk Economy Claims management practices 7 May 16, 2014

8 Issues with Applying Traditional Credibility Models to Group Insurance H E T E R O G E N E O U S C L A I M S E X P E R I E N C E Traditional credibility models assume experience will emerge as it had in the past Reasons why this may not be true in group insurance: Changes in the demographic mix of employees over time External factors like economic recessions Changes in underwriting or claim management practices Changes in plan design Constant rating may help with these issues historically, but not prospectively 8 May 16, 2014

9 Issues with Applying Traditional Credibility Models to Group Insurance G R O U P D E M O G R A P H I C S Homogeneous groups have more uniform risk characteristics (e.g. similar age, salary, etc.) Groups with a greater demographic mix of employees have greater spread of risk Credibility models that are based on expected claims may capture these dynamics C O M P E T I T I V E P R I C I N G P R E S S U R E S Rating actions that align with historical experience trends are easier to explain Market assigns higher credibility than purely statistical methods would imply 9 May 16, 2014

10 Issues with Applying Traditional Credibility Models to Group Insurance L T D C L A I M D U R A T I O N Benefit periods ranging from months to decades long Experience is generally more volatile in early durations of claim D I S A B I L I T Y B E N E F I T S F R O M O T H E R S O U R C E S Irregular benefit payment streams Claim termination rates may vary by SSDI award status 10 May 16, 2014

11 11 May 16, 2014 Results from 2013 Survey on Credibility Applications to Group Insurance

12 2013 Survey on Credibility Applications to Group Disability and Group Life Insurance Survey Participants Assurant Cigna Guardian Life O B J E C T I V E S Collect information on current methods and best practices for applying credibility in group disability and group life insurance Identify challenges in applying credibility concepts in group disability and group life insurance. The Hartford Liberty Mutual Lincoln Financial Mutual of Omaha Principal Reliance Standard Standard Unum 12 May 16, 2014

13 Survey Results Factors Affecting Credibility F A C T O R S I N C L U D E D I N C R E D I B I L I T Y F O R M U L A S Total number of participating companies = 11 Factors Short Term Disability Long Term Disability Group Life Life years of exposure are used by most carriers for all three products. Life Years of Exposure Elimination Period 7 4 Expected Claims Actual Claims Lives Demographic Mix 1 (average age) 1 Type of Product 1 1 (basic vs. additional) Occupation Class 1 Premium Benefit Period Industry Diagnosis 1 (months of experience) When claims are used, the formulas are fairly evenly split between actual and expected claims. Formulas that use expected claims capture demographics Many of the credibility formulas used for experience rating STD products vary by elimination period. Other (specify) 1 (months of experience) 1 (Avg certificate, max certificate, pooling level, and months of experience) Some carriers commented on the problems in applying the same formula to every situation. 13 May 16, 2014

14 Survey Results Exposure Limits - LTD M I N I M U M R E Q U I R E M E N T S F O R E X P E R I E N C E R A T I N G L T D P R O D U C T S Limit Number of LTD Carriers No specified limit lives lives lives life years of exposure life years of exposure life years of exposure 1 The minimum limits for experience rating LTD products vary significantly among carriers that participated in the survey. 14 May 16, 2014

15 Survey Results Exposure Limits - LTD M I N I M U M R E Q U I R E M E N T S F O R A S S I G N I N G F U L L C R E D I B I L I T Y I N L T D Limit Number of LTD Carriers 1 24,999 life years of exposure 6 25,000 34,999 life years of exposure 1 35,000+ life years of exposure claims 100+ claims 1 Varies by experience 2 Most LTD carriers assign full credibility to experience that is based on fewer than 25,000 life years of exposure. 15 May 16, 2014

16 Survey Results Exposure Limits Group Life and STD Group Life and Short Term Disability M I N I M U M R E Q U I R E M E N T S G R O U P L I F E & S T D G R O U P L I F E S T D Full credibility at 25,000 LYE (basic) and 35,000 LYE (supplemental). Credibility generally starts at 500 life years of exposure; 18,000-20,000 is considered fully credible. Cases with fewer than 500 lives get zero credibility. Experience rating starts at 300 lives; at 30 months of experience, full credibility is reached at 25,000 life years of exposure. At 12 months of experience, 25,000 life years of exposure are given 54% credibility. The minimum requirement is 500 lives. Technically, you cannot reach full credibility. The minimum level is 300 life years and full credibility is reached at 21,000 life years. We use a modified square root formula for interpolation. Full credibility at 750 LYE. Credibility starts at 100 life years; roughly 400 life years is fully credible (although it varies by EP). Experience rating starts 100 lives; experience is considered fully credible at 530 life years. Credibility is based on elimination period. Minimum = 100 life years. The minimum level is 100 life years and full credibility is reached at (1) 600 life years for <=8 day EP and (2) 750 for >8 day EP. We use a modified square root formula for interpolation. 16 May 16, 2014

17 Survey Results Credibility Curves D I F F E R E N C E S I N T H E S H A P E S O F T H E C R E D I B I L I T Y C U R V E S U S E D F O R E X P E R I E N C E R A T I N G L T D Credibility formulas based on life years of exposure Credibility formulas based on expected claims Graphs show very different pricing strategies among the LTD insurers that participated in the survey. e.g. Insurer A: Greater confidence in manual rates? e.g. Insurer B: No minimum requirement for experience rating e.g. Insurer C: Higher limit for full credibility. e.g. Insurer D: Near-linear credibility curve. 17 May 16, 2014

18 Survey Results Underwriter Adjustments to Credibility C A N U N D E R W R I T E R S M O D I F Y C R E D I B I L I T Y E S T I M A T E S? Option Short Term Disability Long Term Disability Group Life Most carriers responded that underwriters can modify the credibility of case experience. Yes No Some companies have formal guidelines for how underwriters can affect the credibility estimates, but the majority of companies make informal adjustments. S I T U A T I O N S T H A T M A Y T R I G G E R M O D I F I C A T I O N S T O C R E D I B I L I T Y Quality of data e.g. missing benefit components, missing diagnoses, missing demographic information Stability of experience e.g. exposure of lives or loss ratio changes significantly during the experience period Catastrophic events 18 May 16, 2014

19 Survey Results Data Quality Issues D O E S T H E Q U A L I T Y O F C L A I M D A T A A F F E C T C R E D I B I L I T Y? Option Short Term Disability Long Term Disability Group Life Yes No C O M M E N T S Minimum data requirements ensure quality of data (e.g. point system) Best estimate reserve assumptions are used to fill the gaps, but these don t make it into the credibility formula. One challenge is how to quantify every situation that arises in which data quality is relevant. 19 May 16, 2014

20 Survey Results Updates to Credibility Formulas H O W O F T E N A R E C R E D I B I L I T Y F O R M U L A S U P D A T E D? Option Annually or More Often Short Term Disability Long Term Disability Group Life Every 2 5 Years Every 5 Years or Less Often Majority of survey participants update their credibility formulas every 5 years or less often. 6 of 11 survey participants have tested their credibility formulas in the past 5 years. M E T H O D S F O R T E S T I N G C R E D I B I L I T Y F O R M U L A S Start with five consecutive years of historical experience. Study how three years of experience correlates with two years of subsequent experience. Calculate the level of credibility that would minimize the error between the two periods. Run a Monte Carlo simulation using assumed claim incidence rates to test number of lives required to get credible experience. Predictive modeling serves as a way to understand which items are most predictive in determining credibility. 20 May 16, 2014

21 21 May 16, 2014 Analysis of Credibility Using Random Sampling

22 LTD Credibility Analysis O B J E C T I V E Test the predictive quality of experience from groups of different sizes using historical experience from two consecutive periods S E T U P Begin with historical LTD experience from a very large group, including insured lives and claims details Partition the experience into two periods: - Period 1: 1.5 consecutive years - Period 2: 1 year of experience immediately following Period 1 Calculate probability distribution of claims directly from the experience R A N D O M S A M P L I N G Create artificial groups of various sizes by taking random samples from the Period 1 experience Generate 1,000 random samples of size n, for n = 2,500 5,000 7,500 etc. Calculate average experience trends for groups of different sizes Compare Period 2 experience from the artificial groups to the expected experience determined from Period 1 22 May 16, 2014

23 Credibility LTD Credibility Analysis 120% 100% 80% 60% Classical credibility estimates based on 95% confidence level and 10% allowable error. 40% 20% 0% Classical Credibility Full credibility at 63,046 life years of exposure Life Years Exposure 23 May 16, 2014

24 Credibility LTD Credibility Analysis 120% 100% 80% 60% 40% 20% Classical Credibility Typical Industry Formula Typical industry formula assigns full credibility at 25,000 life years of exposure 0% Life Years Exposure 24 May 16, 2014

25 Credibility LTD Credibility Analysis 120% 100% 80% 60% The Period 2 experience for groups with 25,000 LYE was within 10% of the expected experience 62% of the time. 40% 20% 0% Classical Credibility Typical Industry Formula Actual - Period 2 The Period 2 experience for groups with 15,000 LYE or fewer was within 10% of the expected experience less than 50% of the time. Life Years Exposure 25 May 16, 2014

26 Pooling Applications in Group Insurance 26 May 16, 2014

27 Risk Pooling O B J E C T I V E S Reduce volatility in the experience Develop more accurate premiums E x a m p l e 1 E x a m p l e 2 Claims in excess of pooling limit are excluded What if there are no claims in the experience? Claim Number Benefit Amount 1 $25,000 2 $25,000 3 $500,000 4 $25,000 5 $25,000 Claim Number Benefit Amount W H E N S H O U L D P O O L I N G B E A P P L I E D? Groups with executive class of employees who have significantly higher benefits than everyone else Groups with volatile experience Groups with very different manual and experience rates 27 May 16, 2014

28 2013 SOA Survey Results Claim Outliers H O W A R E O U T L I E R S I N T H E E X P E R I E N C E D E A L T W I T H? Option Short Term Disability Long Term Disability Group Life Outliers are removed from the experience and the credibility is unaffected Outliers are left in the experience and the credibility is unaffected Pooling points (e.g. floors and ceilings on the experience rate) are used and the credibility is not a function of pooled claims of the 11 participating companies responded that outlier adjustments are up to underwriter discretion (i.e. no formal process exists for dealing with outliers). Outliers are removed from the experience and the credibility is reduced Outliers are left in the experience and the credibility is reduced Pooling points (e.g. floors and ceilings on the experience rate) are used and the credibility is a function of pooled claims Some participants selected more than one option. 11 companies participated. 1 1 Many participants commented that outliers go both ways e.g. law firm with no LTD claims in the experience. 28 May 16, 2014

29 Current Practices in Pooling C O M M E N T S O N P O O L I N G F R O M S O A S U R V E Y P A R T I C I P A N T S Pooling charge are based on a typical group, although they do vary by case size range and maximum range Pooling is based on the manual claim cost algorithm. If quality claim-level details exist, the excess reserve above the pooling point is removed and replaced with a pooling charge. Pooling is up to underwriter discretion. No formal process exists. Underwriters use their judgment. Our goal is to have the pricing system do formal pooling. We are still trying to determine the thresholds. Underwriter discretion is allowed to adjust proposed rates based on the presence of outlier claims. There is no formal protocol for dealing with outliers. Outliers are handled on a case-by-case basis by underwriters and pricing actuaries. A consistent approach for LTD does not exist for removing outliers form the experience. Sometimes large LTD claims are removed, sometimes they re not. 29 May 16, 2014

30 Final Thoughts 30 May 16, 2014

31 Conclusion Formula-based rates really should be formula driven (i.e. no subjective adjustments) Credibility and pooling should be applied consistently All pricing parameters should be stored in a database (including manual rates, experience rates, formula rates, target rates, quote rates, estimated credibility, and pooled claims) Final quote rates may be significantly different than formula-based rates Quote rate should approximately equal the best estimate of the rate required to meet profit objectives over rate guarantee period, if not the difference should be identifiable Analysis of historical pricing experience can support future enhancements to pricing models 31 May 16, 2014