Session 13, Long Term Care Assumptions, Credibility and Modeling Moderator: Robert T. Eaton, FSA, MAAA Presenter: Missy A. Gordon, FSA, MAAA Roger Loomis, FSA, MAAA
Missy Gordon, FSA, MAAA Principal & Consulting Actuary Milliman Minneapolis, MN Roger Loomis, FSA, MAAA Consulting Actuary Actuarial Resources Corporation Overland Park, KS Robert Eaton, FSA, MAAA Consulting Actuary Milliman Tampa, Florida LTC Assumption, Credibility, and Modeling Session 13 2016 Valuation Actuary Symposium Monday August 29, 2016
Agenda Introductions Session overview Managing LTC assumptions using predictive modeling Case study in LTC credibility and predictive modeling 2
Introductions Missy Gordon, FSA, MAAA Principal & Consulting Actuary Milliman Minneapolis, MN Roger Loomis, FSA, MAAA Consulting Actuary Actuarial Resources Corporation Overland Park, KS Robert Eaton, FSA, MAAA Consulting Actuary Milliman Tampa, FL 3
Session Overview 4
Assumptions, Credibility, and Modeling Overview Historical methods Industry trend to predictive modeling Applications 5
Managing LTC assumptions using predictive modeling 6
Agenda Introduction Illustration to peek inside the black box Reviewing for reasonableness Communication Sensitivity tests and margin Session 066 7
Introduction Developing assumptions using predictive analytics Updating existing assumptions Similarities to existing processes Added benefits 8
Illustrative example GLM with log-link and Poisson error structure ln μμ = ln tt + ββ 0 + ββ ii xx ii μμ jj tt=1, xx 1,, xx kk is predicted monthly hazard rate for observation j μμ jj = eeββ 0 eeββ 1 xx 1 eeββ kk xx kk ee ββ 0 = baseline monthly hazard rate ee ββ ii xx ii = multiplicative factor to adjust baseline for variable xx ii q j = 1 ee μμ jj is probability of termination in a given month SS jj = SS jj 1 (1 qq jj ) is survival to end of month j 9
Illustrative example Variable Coefficient Variable Value Factor Base hazard rate -2.70 1 6.7% Male 0.26 0 1.00 Home health 0.07 1 1.07 Assisted living facility -0.70 0 1.00 Incurred age 80 (Incurred age - 75) -0.01 5 0.96 (Incurred age - 75)^2 0.00 25 1.01 (Incurred age - 75)^3 0.00 125 1.00 Claim duration 24 (Claim duration - 12) -0.06 12 0.48 (Claim duration - 12)^2 0.00 144 1.30 (Claim duration - 12)^3 0.00 1728 0.98 Final hazard rate = product of factors 4.3% Probability of termination = 1 - exp ( - final hazard rate ) 4.2% Base = female, nursing home, claim duration 12, incurral age 75 Factor = exp ( coefficient x variable value ) 10
Illustrative example 11
Illustrative example 12
Illustrative example Present assumptions in familiar format Monthly Claim Continuance Claim Claim Incurral Age Duration <60 60-69 70-79 80-89 90+ 0 1.00 1.00 1.00 1.00 1.00 1 0.82 0.82 0.84 0.84 0.81 2 0.69 0.68 0.71 0.72 0.67 3 0.59 0.58 0.61 0.62 0.57 360 0.00 0.00 0.00 0.00 0.00 13
Updating existing assumptions Use offset to update for New experience Additional variables What is an offset? Existing assumption as base rate Model adjusts only if experience deviates Offset = failed set ln μμ = ln tt bbbbbbbb rrrrrrrr + ββ ii xx ii 14
Reviewing for reasonableness Relationships A:E on calibration data Compare to old assumption Test for violation of valuation constraints 15
Reviewing for reasonableness 16
Reviewing for reasonableness 17
Reviewing for reasonableness A:E Summary on Calibration Set Summary Level New Model Overall Overall 1.00 Gender F 1.00 M 1.00 Situs ALF 1.00 HHC 1.00 SNF 1.00 Tax Status TQ 1.00 NTQ 1.00 Benefit Period NBP 1.00 LBP 1.00 Age Band LE_59 0.98 60_69 1.00 70_79 1.00 80_89 1.00 GE_90 1.02 Gender_Situs F_ALF 1.00 F_HHC 1.00 F_SNF 1.00 M_ALF 1.00 M_HHC 1.00 M_SNF 1.00 18
Reviewing for reasonableness A:E Deviation and Claim Termination Rates 19
Communication Present assumptions in familiar format Compare new vs. old assumptions Isolate impact of methodology vs. data changes 20
Communication Isolate impact due to methodology change Model: Data: 21
Communication Isolate impact due to data change Model: Data: 22
Sensitivity tests and margin Discounted LOS +/- 7% 23
Sensitivity tests and margin Comparison of Error Statistics on Validation Set A:E Poisson Deviance Mean Absolute Error Summary Level Weighted Straight Weighted Straight Weighted Overall Overall -1% 5% 10% 6% 6% Gender F 1% 6% 10% 6% 6% M 1% 4% 11% 5% 8% Situs ALF 4% 3% 3% 8% 5% HHC 2% 7% 17% 10% 14% SNF 11% 6% 10% 1% 3% Tax Status TQ 6% 6% 13% 8% 11% NTQ 2% 4% 8% 3% 4% Benefit Period NBP 0% 8% 14% 6% 7% LBP -1% 2% 2% 4% 3% Age Band LE_59 16% 3% 4% 1% 2% 60_69 10% 4% 7% 5% 7% 70_79 2% 6% 13% 7% 11% 80_89-2% 6% 9% 5% 6% GE_90 1% 4% 9% 5% 5% Gender_Situs F_ALF 7% 3% 2% 8% 4% F_HHC 1% 8% 18% 9% 14% F_SNF 8% 7% 10% 1% 3% M_ALF -1% 2% 7% 7% 8% M_HHC 2% 6% 14% 11% 14% M_SNF 15% 5% 11% -1% 4% 24
Summary Similarities to existing process, but added benefits Essential to review for reasonableness using LTC expertise Communicate results in familiar format Revisit sensitivity tests and margin using statistical based knowledge 25
Case study in LTC credibility and predictive modeling
How Have Projection Assumptions Changed over Last 15 Years? Analysis Drawn from 2015 LTC Pricing Project Jointly sponsored by the SOA s LTC Section and ILTCI Research Question: For traditional LTCI, how stable are premiums on new blocks?
Assumption Methodology Six large insurers who have been in the market continuously for at least 15 years participated Each provided the research team with pricing data for 3 points in time: December 2000 December 2007 June 2014 Data aggregated into illustrative market assumptions
Actual Gross Premiums for 5 Companies
Lapse Assumptions Are Now Very Conservative
Lapse Assumption Considerations Long-term care is a lapse-supported (and deathsupported) product No benefits on lapse or death (return of premium riders only exception) Level premium and increasing claim costs Very high policy reserves Release of reserves of policies that die or lapse is needed to help fund reserve increases of policies that persist Past lapse assumption too high is the largest culprit for past premium increases Assumption is now close to floor little prospective downside risk
Change in Morbidity Assumptions YEAR Average Industry Morbidity (Ultimate attained age 80/90/100) 2000 Claim costs using the 1984 NNHS Tables with underwriting selection 2007 Claim costs 10% more than 2000 at age 80; 15% at 90; same at 100 2014 Claim costs 15% more than 2000 at age 80; 45% at 90; 25% at 100 Claim cost assumptions have moderately risen Changes not uniform across claim cost curve
Companies More Conservative 2015 SOA experience study shows actual claims from 2000 to 20001 Companies average pricing best estimate claim costs are now 108% of actual industry data
Prospective Morbidity Considerations In uninsured population, morbidity has improved by 1%-2% per year Increases in morbidity of insured population is largely driven by differences between insured and uninsured populations: People want to use benefits Less averse to using nicer facilities that are financed with insurance Morbidity has potential to improve substantially e.g. discovery of effective Alzheimer's prevention and treatment 34
More Data for All Policy Years 2014 assumptions based on 16 times as much data as 2000 Pricing Year Policy-Years of Data 2000 428,198 2007 1,895,965 2014 6,999,086 35
Much More Data for High-Claim Years 2014 assumptions based on 70 times the data for cells in attained Age 80+ and policy duration 10+ Pricing Year Policy-Years of Data 2000 3,348 2007 39,869 2014 230,836 36
Change in Mortality Assumptions YEAR Average Industry Mortality Assumptions 2000 1994 Group Annuity Mortality Table with selection 2007 10% less than 2000 with greater early duration selection 2014 20% less than 2007 with greater early duration selection
Mortality Assumption Considerations When stress testing assumptions in isolation, mortality is perhaps the biggest prospective risk In general population, improvements in mortality have been correlated with improvements in morbidity Morbidity and mortality improving in tandem is a net positive for insurance company Will future mortality improvements be offset by morbidity improvements?
Risk Margins Higher
So, what is the probability of a rate increase on new issues? How do we calculate this? How do we interpret the results? Predictive modeling provides a way to create future assumption scenarios based upon our confidence in the data
Predictive Modeling Methodology What was the probability of a rate increase for policies issued in 2000, 2007, and 2014? Rule 1: Assumptions based only upon information available at each respective time period (no 20/20 hindsight) Rule 2: Except for those explicit differences, run the precise same calculations for the same distribution of policies at each of the three issue dates Rule 3: Model incorporates level of confidence in assumptions when assumptions were made not with hindsight
Modeling Parameter Risk Three random uncertainty factors (i.e. fuzz factors) chosen for each simulation. One each for: Claim costs Lapses Mortality Distribution of fuzz factors should reflect nature of assumptions and boundaries (e.g. no negative lapse rates allowed!) Variance of fuzz factors chosen with predictive analytics based on: Quantity of data used to calculate assumptions Include extra variance for future being different than past
CC Confidence Intervals 43
PV Claims as Percentage of Expected PV Claims
Lower Lapses Mean More People Collect Benefits When They Need it 45
Probability of Rate Increase
Summary Issue Year Prob Rate Increase Average Projected Increase 2000 40% 34% 2007 30% 18% 2014 10% 10% Based on: Best-estimate of parameter risk at time of issue (no 20-20 hindsight) Rock-bottom lapse assumptions Higher Margins 47
48