Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association

Background 2

Introduction to Post-Level Term 10-Year Term: Premium Structure with Jump to ART $7,395 Duration 11 Premium 20 times Premium Jump $375 Level Premium 3

 The Sick… Who Pays the $7,395 Rather Than Dropping Coverage or Getting a New Policy? 4  The Lazy…  The Unaware… …And ALL 3 have extra mortality risk!

Lapse Rate 2008 VBT Mortality Ratio Sharp increase in premium after level period leads to large anti-selective shock lapse. Mortality on persisting policyholders is substantially worse in the post-level period. 5

SOA/RGA Post-Level Term Study Lapse Study Experience Results 6

Shock Lapse Experience Results Overview Policy-Year Study Source: 7

Shock Lapse Experience (Jump to ART) T10 By Duration 8 Source:

Shock Lapse Experience T15 By Duration 9 Source:

Shock Lapse Experience (Jump to ART) T10 By Premium Jump Ratio 10 Source:

Shock Lapse Experience (Jump to ART) T10 By Duration & Premium Jump 11 Source:

Shock Lapse Experience (Jump to ART) T10 By Duration & Premium Jump 12 Source:

Shock Lapse Experience T10 By Duration and Issue Age 13 Source:

Shock Lapse Experience (Jump to ART) T10 By Premium Jump and Issue age – duration Source:

Shock Lapse Experience T10 By Duration & Face Amount Band 15 Source:

Shock Lapse Experience (Jump to ART) T10 By Premium Jump and Face Amount Band – duration Source:

Shock Lapse Experience T10 By Duration & Gender 17 Source:

Shock Lapse Experience T10 By Duration & Risk Class 18 Source:

Shock Lapse Experience T10 By Duration & Premium Payment Mode 19 Source:

SOA/RGA Post-Level Term Study Mortality Study Experience Results 20

Mortality Experience Overview Calendar Year Study 21 Source:

Mortality Experience (Jump to ART) T10 By Duration 22 Source:

Mortality Experience T15 By Duration 23 Source:

Mortality Experience (Jump to ART) T10 Duration 11 Mortality by Premium Jump 24 Source:

Mortality Experience (Jump to ART) T10 Duration 11+ Mortality by Issue Age 25 Source:

Mortality Experience (Jump to ART) T10 Duration 11+ Mortality by Face Amount Band 26 Source:

Mortality Study Experience Results – Jump to ART T10 Duration 11+ Mortality by Gender 27 Source:

Mortality Study Experience Results – Jump to ART T10 Duration 11+ Mortality by Risk Class 28 Source:

Mortality Experience (Jump to ART) T10 Duration 11 Mortality by Duration 10 Shock Lapse by Company 29 Source:

Practical Applications 30

Shock Lapse Experience Skewness of Lapses 31 Source:

Grace period creates mismatch between exposure basis for claims and premiums No duration 11 premium received, but effective duration 10 exposure extends into grace period. Premium-paying persisters must subsidize “free insurance” during the grace period for policyholders who intended to lapse on their anniversary. Much bigger impact with shock lapse Small number of premium-payers…lots of lapsers Magnitude increases for higher lapse rates or longer grace periods Grace Period Subsidy 32

Assumptions: Cohort mortality = 0.1 / 1000 monthly in durations 10 & 11 Lapse on anniversary at end of duration 10 All lapsers will passively lapse and enter the grace period 2-month grace period Grace Period Subsidy - Example 33

Grace Period Subsidy – Example 5% Lapse Rate; No Anti-Selection 34

Grace Period Subsidy – Example 60% Lapse Rate; No Anti-Selection 35

Grace Period Subsidy – Example 90% Lapse Rate; No Anti-Selection 36

Grace Period Subsidy – Example 90% Lapse Rate; 200% Anti-Selection 37

Mortality Experience Duration 11 Mortality by Month 38 Source:

SOA/RGA Post-Level Term Study Assumption Survey Results 39

 Sent to top 100 term providers based on 2012 term insurance sales  Responses from 41 companies  Responses represented 62% of 2012 term sales Assumption Survey Results Overview 40 Source:

Assumption Survey Results Post-Level Premium Structure  Dominant Structure is Jump to an ART Scale 41 Source:

Assumption Survey Results Expected Changes to Post-Level Premium Structure  No change expected for most term new business  Minimal changes reported to inforce term business 42 Source:

Lapse Assumptions Post-Level Lapse Rate Structure  Most companies assume only one shock lapse, generally grading down thereafter 43 Source:

 Used a common pricing cell for consistent comparisons in upcoming charts Lapse Assumptions Factors impacting shock lapse assumptions 44 Source:

Lapse Assumptions Annual and cumulative lapse assumptions by duration, 10-year term 45 Source:

Lapse Assumptions Duration 10 lapse assumptions by issue age, 10-year term 46 Source:

Lapse Assumptions Post-Level Lapse Rate Assumption by Premium Jump, 10-year term  Broad range of assumptions by premium jump  Trend is somewhat inconsistent with experience 47 Source:

Mortality Deterioration Assumptions Post-Level Mortality Deterioration Structure  Assumptions vary broadly by structure of mortality deterioration 48 Source:

 The same pricing cell that was used in the Lapse Assumptions charts is used in this section Mortality Deterioration Assumptions Factors impacting mortality deterioration assumptions 49 Source:

Mortality Deterioration Assumptions Post-Level Mortality Methodology  Dukes-MacDonald (or derivatives) and Flat Multiple are the primary assumptions used in developing mortality after the shock lapse 50 Source:

Mortality Deterioration Assumptions Annual mortality deterioration multiple, 10 year term 51 Source:

Mortality Deterioration Assumptions Post-Level Mortality Assumptions vs. Premium Jump  Mortality deterioration assumptions do not differ dramatically by premium jump, inconsistent with experience 52 Source:

Mortality Deterioration Assumptions Post-Level Mortality Assumptions vs. Premium Jump and Lapse Rate  When split by lapse rate, it does not appear assumptions vary dramatically by premium jump 53 Source:

Lapse Assumptions Skewness assumptions from the level period through the post- level period  Today’s skewness assumptions do not always follow past experience 54 Monthly Lapse Skewness During Level Premium Period Response Respondents Lapses are uniformly distributed 18 Lapses occur on premium payment modes 10 Lapses occur at the end of the year 7 Other 4 Monthly Lapse Skewness During Year of Shock Lapse Lapses are uniformly distributed 5 Lapses occur on premium payment modes 3 Lapses occur at the end of the year 17 Lapses graded toward end of the year with shock in month 1212 Monthly Lapse Skewness During Post-Level Period Lapses are uniformly distributed 6 Lapses occur on premium payment modes 7 Lapses occur at the end of the year 9 Lapses skewed to the beginning of L+1, Uniform thereafter8 Source:

SOA/RGA Post-Level Term Study Assumptions vs. Experience 55

Survey Responses vs. Experience Study 56

Survey Responses vs. Experience Study 57

Survey Responses vs. Experience Study 58

Survey Responses vs. Experience Study 59

Survey Responses vs. Experience Study 60

SOA/RGA Post-Level Term Study Predictive Model 61

 Multivariate Lapse Rate Model – T10 Duration 10 Shock Lapse  Model:  Generalized Linear Model (GLM)  Target variable follows distribution in the exponential family  Response variable = observed lapse count  Follows a Poisson distribution  Benefits:  Elimination of possible bias from a uni-variate approach  Systematic way of controlling lapse assumption complexity  Transparent insight into true drivers of lapse rates  Distribution of target variables Predictive Model 62

Predictive Model – Model 1 63

Predictive Model – Model 2 64

Predictive Model – Model 1 65

Predictive Model – Model 2 66

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 “Jump to an ART Scale” continues to be the dominant post-level structure, although some are considering changes  Wide range of lapes and mortality assumptions are currently being used in the post-level period  Many companies have not implemented appropriate skewness assumptions for lapses based on past experience 2013 SOA Post-Level Term Survey Report Key Takeaways 68

 Lapse rates beyond the level period are largely driven by the level of the premium compared to the original level premium  Mortality in the post-level period is driven by the size of the shock lapse  Lapses are skewed towards the end of the last duration of the level period and the beginning of the first duration after the level period  Grace period can lead to excess mortality, especially at the higher shock lapse levels  Advanced analytics, such as predictive modeling, can be critical in understanding the correlations of the many drivers of post-level term experience 2014 SOA Post-Level Term Experience Report Key Takeaways 69

Questions? 70