Rick Leavitt – ASA, MAAA - Smith Group Andy Baillargeon – FSA, MAAA – JHA Ben Yahr – FSA, MAAA – Cigna Group Insurance Session SOA Annual Meeting October 29th, 2002 Boston New Approaches to Experience Rating Disability Products

AgendaAgenda Market Overview Market Overview Theoretical Discussion Theoretical Discussion Monte Carlo Simulation Monte Carlo Simulation Case Study Case Study Question & Answer Question & Answer

AgendaAgenda Market Overview Market Overview

Group Disability Inforce Premium Growth Source: JHA 2001 Group Disability Market Survey Group Disability Inforce Premium Growth $0 $2,000 $4,000 $6,000 $8,000 $10, Year Premium in Millions LTD STD Combined 2001 Growth STD: 11% LTD: 7% Combined: 8% 10-Year C.A.G.R. - 10%

Group Disability Sales Growth Source: JHA 2001 Group Disability Market Survey Group Disability Sales Growth $0 $400 $800 $1,200 $1,600 $2, Year Sales in Millions LTD STD Combined 2001 Growth STD: 11% LTD: 2% Combined: 5% 10-Year C.A.G.R. - 12%

Employee/Employer Growth Source: JHA 2001 Group Disability Market Survey

Group Disability Profitability LTD results lagging behind targeted profitability levels, with mid-single digit after-tax ROEs in recent years LTD results lagging behind targeted profitability levels, with mid-single digit after-tax ROEs in recent years STD profit has declined in each of the last five years, and negative for the last two years STD profit has declined in each of the last five years, and negative for the last two years Large case market has been a source of growth for sure, but has it been a profitable one??? Large case market has been a source of growth for sure, but has it been a profitable one???

Other Disability Trends From the 80s to the 90s to the 00s: From the 80s to the 90s to the 00s: Declining salary inflation Declining salary inflation Declining interest rates Declining interest rates Aging workforce Aging workforce Emerging disabilities Emerging disabilities Secular economic trends Secular economic trends Large case growth Large case growth Intensified rate competition Intensified rate competition All of the above has made keeping up with rates, renewals, and experience all the more important at the case, segment, and block level. All of the above has made keeping up with rates, renewals, and experience all the more important at the case, segment, and block level.

Overview of Experience Rating Experience Rating Defects Experience Rating Theory – what is the meaning of credibility? Some possible enhancements Experience-Based Credibility Diagnosis-Based Credibility

Experience Rating Defects Four broad categories of short-comings 1.Market Price versus Actuarial Price 2.Invalid, Inaccurate, or Incomplete Data 3.Improper Application 4. Short-comings of the standard method -Risk varies over Time

Experience Rating Theory Credible Rate = Experience Rate * X + Manual Rate * (1 – X) X = Credibility Questions: How to determine credibility? Why does credibility normally not depend on observed experience? Should credibility depend on case characteristics?

Understanding Credibility Process Variance versus Variance of the Hypothetical Means Proceedings of Casualty Society of America, 1981 Vol: LXVIII pp Process Variance: You have 1,000 identical cases with the same expected mean loss ratio. What will be the distribution of the observed loss ratios?

Distribution of Observed Loss Loss Normally Distributed about Mean: Variance varies by 1 / N

Variance of the Hypothetical Means Assume you have 1000 distinct cases with the identical demographics. What is the distribution of the expected mean loss? Key Assumption : Hypothetical Means are also Normally Distributed

Select Most Likely Expected Loss Ratio

Theoretical Credibility Where N is the number of expected Claims where

Key Points Credible Rate Produces Most Likely Mean Slope Does not Depend on the Observed Rate: This fact hinges on the assumption of normal distributions

What is the Right Level of Credibility ?

Effects of Non-Normal Distributions

Non-Normal Distribution

Two Applications 1.Very Good Experience 2.Diagnosis-Based Credibility

Very Good Experience

Experience-Based Credibility Decrease Credibility for Very Good Experience

Credibility by Diagnosis Split Expectation into Predictable and Random Claims

Credibility By Diagnosis Use Ratio of Expected Variance to set Credibility Total Credibility55% Type I Credibility3.1% Type II Credibility44%

Credibility By Diagnosis Combined Actual to Expected Loss:125% Indicated Rate / Manual Rate113.8% Scenario 1: Type I A/E:250%Type II A/E: 75% Indicated Rate/Manual Rate:93.4% Scenario 2: Type I A/E:50%Type II A/E: 155% Indicated Rate / Manual Rate:117.0%

Credibility of Manual Rates CR = Z * ER + ( 1 - Z ) * MR CR = Z * ER + ( 1 - Z ) * MR Credibility is relative, not absolute Credibility is relative, not absolute If manual rates perfectly captured all risk elements, then credibility would be 0. If manual rates perfectly captured all risk elements, then credibility would be 0. Alternately, if you have no or little prior info on which to base manual rates, then credibility should be very high Alternately, if you have no or little prior info on which to base manual rates, then credibility should be very high Smaller companies tend to use higher credibility factors than larger companies* - may be a lack of belief or predictability in manual rates Smaller companies tend to use higher credibility factors than larger companies* - may be a lack of belief or predictability in manual rates * 2001 JHA Rate & Risk Management Survey

Marketplace Credibility Tough to lower credibility factors vs. the marketplace if you think they are too high Tough to lower credibility factors vs. the marketplace if you think they are too high Lower credibility means: Lower credibility means: rates will tend to be more competitive on cases with bad experience rates will tend to be more competitive on cases with bad experience rates will tend to be less competitive on cases with good experience rates will tend to be less competitive on cases with good experience Contrarian view, and if you are right you will succeed overall, but it can be an uncomfortable place to be on a case by case basis Contrarian view, and if you are right you will succeed overall, but it can be an uncomfortable place to be on a case by case basis

Theoretical Credibility Theoretical calculations of 100% credibility suggest Theoretical calculations of 100% credibility suggest LTD requires 350,000+ lives LTD requires 350,000+ lives STD 20,000+ lives STD 20,000+ lives Typical marketplace credibility Typical marketplace credibility LTD requires 20,000 lives* LTD requires 20,000 lives* STD requires 600 lives* STD requires 600 lives* * 2001 JHA Rate & Risk Management Survey

The Other Credibility Quality of experience data has been an issue Quality of experience data has been an issue Larger employers moving to fully insured, particularly on STD, and providing self-managed or self-insured claim data Larger employers moving to fully insured, particularly on STD, and providing self-managed or self-insured claim data Underwrite the source of the info Underwrite the source of the info Beware of the Myth of Detailed Data Beware of the Myth of Detailed Data Reality checks against manual rates (especially STD) Reality checks against manual rates (especially STD)

Large Case Loss Distributions Loss Distributions are not normal; there is a significant tail of losses Loss Distributions are not normal; there is a significant tail of losses Lowest loss ratio is 0%, but there is virtually no limit to the highest loss ratio Lowest loss ratio is 0%, but there is virtually no limit to the highest loss ratio In addition to claim frequency, there can also be significant variation in claim severity - claim durations, benefit amounts, offsets, etc. In addition to claim frequency, there can also be significant variation in claim severity - claim durations, benefit amounts, offsets, etc.

Large Case Loss Distributions Monte Carlo Results on a Hypothetical 5,000 Life Case: MeanMedian

Mean Loss vs. Median Loss Because of the tail of losses, the mean loss on this case is 10% higher than the median loss Because of the tail of losses, the mean loss on this case is 10% higher than the median loss When looking at claim experience, this means the typical year is, in fact, better than average! When looking at claim experience, this means the typical year is, in fact, better than average! Throwing away the bad year, as an aberration, can lead to significant underpricing of an LTD block Throwing away the bad year, as an aberration, can lead to significant underpricing of an LTD block MeanMedian On a modeled 3,000 life case, the difference was 15%

ImplicationsImplications If very large claims are to be removed from a particular case, they should be captured on all other cases via a pooling charge If very large claims are to be removed from a particular case, they should be captured on all other cases via a pooling charge Multiple years of experience should be used when available, even on very large cases Multiple years of experience should be used when available, even on very large cases Comparisons to manual provide a base level of expectation to compare experience against - get a census and run a manual rate on every case! Comparisons to manual provide a base level of expectation to compare experience against - get a census and run a manual rate on every case!

Presentation Outline Presentation of the Model Incidence Present value of claims Use book average (manual) or experience How the model works (binomial) Key Assumptions

Presentation Outline Discussion of Incidence Rate (5 min) Hypothesis test – Is the incidence rate different than the book average? When should adjustments be made? How can the underwriter apply adjustments?

Presentation Outline Discussion of the Expected Claim Costs Hypothesis test – Are the expected claim costs different than the book average? When should adjustments be made? How can the underwriter apply adjustments?

Presentation Outline Applications to Other Problems commonly encountered Group size changes dramatically Rate Guarantee Period Trend Modification of Key Assumptions