soa post-level term experience resultssoa sponsored post-level term reports 2007 – report on the...

Derek Kueker, FSA

SOA Post-Level Term

Experience Results

Actuaries’ Club of the Southwest

June 19, 2014

Introduction to Post-Level Term

Background

Assumption Survey Results

Experience Study Results

Predictive Model

Acknowledgements

Table of Contents

2


3


10-Year Term: Premium Structure with Jump to ART

-

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

18,000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Level Period Post-Level Period

An

nu

al P

rem

ium

Duration

10-Year Term45-Year Old, $500,000 Death Benefit

Super-Preferred Non-Smoker

$7,395

Duration 11

Premium

20 times

Premium Jump

$375 Level

Premium

4

Background

5

SOA Sponsored Post-Level Term Reports

2007 – Report on the Survey of Post-Level Premium Period Lapse and Mortality

Assumptions and Experience For Level Premium Term Plans


Assumptions for Level Premium Term Plans

2010 – Report on the Lapse and Mortality Experience of Post-Level Premium

Period Term Plans


Assumptions for Level Premium Term Plans

2014 – Report on the Lapse and Mortality Experience of Post-Level Premium

Period Term Plans

Background

6


7

Sent to top 100 term providers based on 2012 term insurance sales

Responses from 41 companies

Responses represented 62% of 2012 term sales


Overview

8


Product Distribution

x=5% x=15% x=30%

5 Year Term 1.20% 3 1 0

10 Year Term 22.70% 42 36 8

15 Year Term 8.60% 32 6 1

20 Year Term 52.00% 44 44 42

25-30 Year Term 15.10% 33 23 9

Other 0.40% 5 2 1

Level Premium Term Product Mix by Level Period

Product Level PeriodAggregate Distribution

for Respondents

Number of companies where product

represents at least x% of individual

company's term sales

9


Post-Level Premium Structure

Dominant Structure is Jump to an ART Scale

Product Structure Responses

Premium jump to ART 40

Premium grade to ART 4

Jump to new level period 3

Face amount decrease 1

Product terminates 2

Flexible Premiums (Term UL) 1

Post-Level Product Design

10


Expected Changes to Post-Level Premium Structure

No change expected for most term new business

Minimal changes reported to inforce term business

No change 23

Grade premiums into an ART scale over 'x' years 3

Other 3

Changes to Post-Level Premium Structure for Term New Business

DescriptionImplemented in

last 5 yearsConsidering

Lower post-level premiums 1 5

Grade into an ART scale 3 3

Other 0 2

Changes to Post-Level Premium Structure for Term In Force

11


Structure of Current & Guaranteed Ultimate Rates

Trend towards increasing level of guaranteed ultimate rates

Relationship between current and guaranteed continues to vary

Description 2013 2009

% of 1980 CSO

Between 150-300% 2 8

% of 2001 CSO

Less than 200% 5 1

Exactly 200% 7 12

Between 200-300% 11 7

Exactly 300% 11 12

More than 300% 7 1

Other 3 5

Structure of Guaranteed Ultimate Rates

Description 2013 2009

Product has Guaranteed Rates only 14 15

Current Rates = Guaranteed Rates 15 12

Current Rates < Guaranteed Rates 14 16

Current Rates grade to Guaranteed Rates 1 2

Relationship between Current Ultimate and Guaranteed Ultimate Premiums

12


Post-Level Lapse Rate Structure

Most companies assume only one shock lapse, generally grading

down thereafter

10-Year Term 20-Year Term

Duration L Shock, then level 8 7

Duration L Shock, then grade down 12 10

2 Shocks, Duration L>=L+1 6 5

2 Shocks, Duration L+1>L 3 2

Responses

Lapse Rate Trend By Duration

Description

13


Post-Level Lapse Rate Assumption by Premium Jump

Broad range of assumptions by premium jump

Trend is somewhat inconsistent with experience

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.0 10.0 20.0 30.0 40.0

Sh

oc

k L

ap

se

Premium Jump

Premium Jump vs. Shock Lapse10 Year term

14


Post-Level Lapse rate Assumptions

Today’s skewness assumptions do not always follow past experience

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

No response 5

Monthly Lapse Skewness During Level Premium Period





Lapses graded toward end of the year with shock in month 12 12

No response 7

Monthly Lapse Skewness During Year of Shock Lapse





Lapses skewed to the beginning of L+1, Uniform thereafter 8

No response 14

Monthly Lapse Skewness During Post-Level Period

15


Post-Level Mortality Methodology

Dukes-MacDonald (or derivatives) and Flat Multiple are the primary

assumptions used in developing mortality after the shock lapse

Method Responses

N/A - 100% shock lapse 9

Dukes-MacDonald or derivatives of Dukes-MacDonald 14

Canadian Institute of Actuaries Valuation Technique Paper #2 4

Flat Multiple 13

Other: Set by reinsurer/external consultant 3

Other: Internally developed method 3

Method of Developing Mortality Assumption

16


Post-Level Mortality Assumptions vs. Cumulative Lapse Rate

Mortality deterioration increases gradually with increasing lapse rates

0%

100%

200%

300%

400%

500%

600%

700%

800%

30% 40% 50% 60% 70% 80% 90% 100%

Mo

rtality

Dete

iora

tio

n D

ura

tio

n 1

2

Cumulative Lapse Rate Duration 10 through 11

Shock Lapse vs. Mortality Deterioration10 Year term

DM

CIA

Flat Multiple

Other

17


Post-Level Mortality Assumptions vs. Premium Jump

Mortality deterioration assumptions do not differ dramatically by

premium jump, inconsistent with experience

0%

100%

200%

300%

400%

500%

600%

700%

800%

900%

1000%

0.0 10.0 20.0 30.0 40.0

Mo

rtality

Dete

rio

rati

on

Du

rati

on

11

Premium Jump

Premium Jump vs. Mortality Deterioration10 Year term

18


Post-Level Mortality Assumptions vs. Prem Jump and Lapse Rate

When split by lapse rate, it does appear assumptions vary by

premium jump

0%

100%

200%

300%

400%

500%

600%

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Mo

rtality

Dete

iora

tio

n D

ura

tio

n 1

2

Cumulative Lapse Rate Duration 10 through 11

Shock Lapse vs. Mortality Deterioration by Premium Jump10 Year term

1-10X Jump

11-20X Jump

20X Jump or Greater

19


Post-Level Mortality Deterioration Structure

Assumptions vary broadly by structure of mortality deterioration

10-Year Term 20-Year Term

Level all durations 7 6

Decreasing or grade to ultimate level 13 11

Increasing then decreasing 6 1

Generally increasing 1 3

Description

Mortality Deterioration Assumption Trend By Duration

Responses

20

Experience Study Results

21

2000-2012 Policy-Year Study

Lapse Study Experience Results

Overview

Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx

2014 Study 2010 Study Change

Number of Companies w/ Post Level Experience 36 25 144%

Post-Level Lapses with Premiums 436,307 87,544 498%

Post-Level Lapses without Premiums 258,030 170,171 152%


Post-Level Lapses with Premiums 37,673 12,191 309%Post-Level Lapses without Premiums 1,364 1,359 100%

10-Year Term

15-Year Term

22

http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx













Lapse Study Experience Results – Jump to ART

Lapse Rates by Duration


1

10

100

1,000

10,000

100,000

1,000,000

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

6 7 8 9 10 11 12 13 14 15 16+


Nu

mb

er

of

La

pse

s

Lap

se

Rate

T10 Jump to ART Lapse Rates by Duration

Lapse Rate Median Lapse Rate Number of Lapses (right axis)

23















Lapse Rates by Premium Jump


1

10

100

1,000

10,000

100,000

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Nu

mb

er

of

La

pse

s

Lap

se

Rate

Duration 11/10 Premium Jump Ratio

T10 Jump to ARTDuration 10 Lapse Rate by Duration 11/10 Premium Jump Ratio

Duration 10 Lapse Rate Count Duration 10 Lapses

24















Lapse Rates by Duration & Premium Jump

Duration 11/10

Premium Jump

Ratio Band

Dur 11 /

Dur 10

Dur 12 /

Dur 11

1.01x - 2x 79.5% 59.5%

2.01x - 3x 77.0% 46.7%

3.01x - 4x 73.2% 44.9%

4.01x - 5x 73.1% 42.7%

5.01x - 6x 70.5% 45.4%

6.01x - 7x 73.5% 45.1%

7.01x - 8x 73.2% 46.3%

8.01x - 9x 74.5% 45.9%

9.01x - 10x 78.7% 54.7%

10.01x-12x 79.1% 49.7%

12.01x-14x 79.7% 49.4%

14.01x-16x 82.9% 56.8%

16.01x + 86.0% 59.8%

Subtotal Prem Data Available 59.4% 42.9%

No Prem Data Available 55.0% 43.1%

Grand Total 57.4% 42.9%


0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%


T10 Jump to ART Lapse Rate

by Duration 11/10 Premium Jump Ratio

Duration 10 Lapse Rate Duration 11 Lapse Rate Duration 12 Lapse Rate

Dur 11 / Dur 10 Dur 12 / Dur 11

25















Lapse Rates by Duration and Issue Age

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0-19 20-29 30-39 40-49 50-59 60-69 70+

Lap

se

Rate

Issue Age

T10 Lapse Rates by Issue Age

Duration 6-9 Duration 10 Duration 11 Duration 12+


26















Lapse Rates by Duration & Gender

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Male Female

Lap

se

Rate

Gender

T10 Lapse Rates by Gender



27















Lapse Rates by Duration & Risk Class

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Super-Preferred

Preferred Non-Preferred Undiff Preferred Non-Preferred Undiff

Non-Smoker Smoker Unk/Agg

La

ps

e R

ate

Risk Class

T10 Lapse Rates by Risk Class



28















Lapse Rates by Duration & Face Amount Band

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

< $50,000 $50,000 -$99,999

$100,000 -$249,999

$250,000 -$999,999

$1,000,000 -$4,999,999

$5,000,000 +

La

ps

e R

ate

Face Amount

T10 Lapse Rates by Face Amount Band



29















Lapse Rates by Duration & Premium Payment Mode

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Annual Semi-Annual Quarterly Monthly

La

ps

e R

ate

Premium Payment Mode

T10 Lapse Rates by Premium Payment Mode



30















Lapse Rates (duration 10) Premium Jump and Issue age

1

10

100

1,000

10,000

100,000

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

<40 40-49 50-59 60+ <40 40-49 50-59 60+ <40 40-49 50-59 60+ <40 40-49 50-59 60+ <40 40-49 50-59 60+

1.01x - 3x 3.01x - 5x 5.01x - 7x 7.01x - 9x 9.01x +

Nu

mb

er

of

La

ps

es

Lap

se

Rate

T10 Jump to ARTDuration 10 Lapse Rate

by Issue Age and Duration 11/10 Premium Jump Ratio

Duration 10 Lapse Rate Duration 10 Lapses


31















Lapse Rates (duration 10) Premium Jump and Face Amount Band

1

10

100

1,000

10,000

100,000

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

<100k 100k-249k

250k-999k

1M+ <100k 100k-249k

250k-999k

1M+ <100k 100k-249k

250k-999k

1M+ <100k 100k-249k

250k-999k

1M+ <100k 100k-249k

250k-999k

1M+

1.01x - 3x 3.01x - 5x 5.01x - 7x 7.01x - 9x 9.01x +

Nu

mb

er

of

La

ps

es

La

ps

e R

ate

T10 Jump to ARTDuration 10 Lapse Rate

by Face Amount and Duration 11/10 Premium Jump Ratio

Duration 10 Lapse Rate Duration 10 Lapses


32















Skewness of Lapses


0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

6-9 10 11 12+

Pro

po

rtio

n o

f L

ap

se

s

Duration

T10: Lapse Skewness by MonthCompanies without Grace Period Adjustments

12

11

10

9

8

7

6

5

4

3

2

1

33















Comparison of RGA to SOA

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

45,000

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1.0

1 -

2.0

0

2.0

1 -

3.0

0

3.0

1 -

4.0

0

4.0

1 -

5.0

0

5.0

1 -

6.0

0

6.0

1 -

7.0

0

7.0

1 -

8.0

0

8.0

1 -

9.0

0

9.0

1 -

10

.00

10

.01

- 1

1.0

0

11

.01

- 1

2.0

0

12

.01

- 1

3.0

0

13

.01

- 1

4.0

0

14

.01

- 1

5.0

0

15

.01

- 1

6.0

0

16

.01

- 1

7.0

0

17

.01

- 1

8.0

0

18

.01

- 1

9.0

0

19

.01

- 2

0.0

0

20

.01

- 2

1.0

0

21

.01

- 2

2.0

0

22

.01

- 2

3.0

0

23

.01

- 2

4.0

0

24

.01

AN

D U

P

Lap

e C

ou

nt

Lap

se R

ate

Premium Jump

10-YR Term Duration 10 - Jump to ART

SOA LapseCount

RGA LapseCount

SOA LapseRate

RGA LapseRate

34

Mortality Study Experience Results

Overview

2000-2012 Calendar Year Study


2014 Study 2010 Study Change


Post-Level Claims with Premiums 2,651 382 694%

Post-Level Claims without Premiums 729 381 191%


Post-Level Claims with Premiums 432 145 298%

Post-Level Claims without Premiums 12 13 92%

10-Year Term

15-Year Term

35














Mortality Study Experience Results – Jump to ART

Mortality by Duration


1

10

100

1,000

10,000

0%

50%

100%

150%

200%

250%

300%

350%

400%

450%

6 7 8 9 10 11 12 13 14 15 16+


Nu

mb

er

of

De

ath

s

Mo

rtali

ty R

ela

tive

to

Du

rati

on

s 6

-10

T10 Jump to ARTMortality by Duration

A/E Mortality Median A/E Mortality Number of Deaths (right axis)

36















Mortality by Duration & Premium Jump


1

10

100

1,000

10,000

0%

200%

400%

600%

800%

1000%

1200%

1400%

1600%

1800%

2000%

1.01x -2x

2.01x -3x

3.01x -4x

4.01x -5x

5.01x -6x

6.01x -7x

7.01x -8x

8.01x -9x

9.01x -12x

12.01x-15x

15.01x-18x

18.01x +

Nu

mb

er

of

De

ath

s

Mo

rtali

ty R

ela

tive

to

Du

rati

on

s 6

-10


T10 Jump to ARTDuration 11 Mortality Relative to Level Period

by Duration 11/10 Premium Jump Ratio

Relative Mortality Ratio Number of Deaths (right axis)

37















Mortality by Duration & Issue Age


0%

50%

100%

150%

200%

250%

300%

350%

400%

0-29 30-39 40-49 50-59 60+

Issue Age

T10 Jump to ART2008 VBT Mortality Ratios

by Issue Age

Duration 6-10 Duration 11+ Post-Level Relative to Dur 6-10

38















Mortality by Duration & Gender


0%

50%

100%

150%

200%

250%

300%

350%

Male FemaleGender


by Gender


39















Mortality by Duration & Risk Class


0%

50%

100%

150%

200%

250%

300%

350%

400%

450%

500%

550%

Super-Preferred

Preferred Non-Preferred Undiff Preferred Non-Preferred Undiff

Non-Smoker Smoker Unk/Agg

Risk Class


by Risk Class


40















Mortality by Duration & Face Amount Band


0%

50%

100%

150%

200%

250%

300%

350%

400%

450%

500%

< $50,000 $50,000 -$99,999

$100,000 -$249,999

$250,000 -$999,999

$1,000,000 +

Face Amount Band


by Face Amount Band


41














Mortality Study Experience Results

Mortality by Monthly Duration

0

25

50

75

100

125

150

175

0%

50%

100%

150%

200%

250%

300%

350%

1 2 3 4 5 6 7 8 9 10 11 12

Nu

mb

er

of

De

ath

s

20

08

VB

T M

ort

ali

ty R

ati

os

Months since start of Duration 11

T10 Duration 112008 VBT Mortality Ratios by Month

Companies without Grace Period Adjustments

2008 VBT Mortality Ratios Number of Deaths (right axis)


42















Mortality Deterioration by Shock Lapse

0%

150%

300%

450%

600%

750%

900%

1050%

1200%

1350%

1500%

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Du

rati

on

11 M

ort

ality

Re

lati

ve

to

Du

rait

on

s 6

-10

Duration 10 Shock Lapse

T10 Jump to ARTDur 10 Shock Lapse vs. Dur 11 Mortality Deterioration

by Company

>=35 claims

<35 claims

Expon. ()


43















Mortality Deterioration by Shock Lapse

0

20

40

60

80

100

120

140

160

0%

200%

400%

600%

800%

1000%

1200%

1.01 -3.00

3.01 -5.00

5.01 -7.00

7.01 -9.00

9.01 -11.00

11.01 -13.00

13.01+

Cla

im C

ou

nt

A/E

08

VB

T

Premium Jump

10-YR Term Duration 11 - Jump to ART

RGA ClaimCount

SOA ClaimCount

RGA A/E

SOA A/E

44

Predictive Model

45

Multivariate Lapse Rate Model – T10 Duration 10 Shock Lapse

Model:

Generalized Linear Model (GLM)

Target variable follows distribution in the exponential familly

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

46

Predictive Model – Model 1 Model Parameter

Intercept - -2.676 <2.0E-16

Issue Age Numerical 0.0552 <2.0E-16

(Issue Age)^2 Numerical -0.000316 <2.0E-16

Risk Class Categorical

Super-Pref NS 0 1.00 0 11.3% 82.6% 82.6% 100.1%

NS -0.06736 0.93 <2e-16 76.9% 69.1% 68.8% 100.4%

SM -0.01296 0.99 0.0339 11.8% 63.5% 63.5% 100.0%

Face Amount Categorical

<50K 0 1.00 0 1.2% 14.9% 17.9% 83.2%

50-100K 0.600 1.82 <2.0E-16 3.9% 61.8% 62.7% 98.5%

100K-250K 1.262 3.53 <2.0E-16 51.9% 67.5% 67.4% 100.1%

250K-1M 1.559 4.75 <2.0E-16 36.9% 74.4% 73.8% 100.8%

>1M 1.585 4.88 <2.0E-16 6.1% 80.7% 80.4% 100.4%

Premium Mode Categorical

Annual 0 1.00 0 22.9% 85.8% 85.3% 100.5%

Semi/Quarter -0.1365 0.87 <2.0E-16 24.5% 74.9% 75.1% 99.7%

Monthly/BiWeekly -0.3506 0.70 <2.0E-16 45.4% 56.9% 56.6% 100.5%

Other/Unknown -0.08481 0.92 <2.0E-16 7.2% 85.3% 84.8% 100.7%

Cross Term Mixed

Issue Age:Face Amt <50 0 0

Issue Age:Face Amt 50-100K -0.001288 0.3162

Issue Age:Face Amt 100-250K -0.01074 <2e-16

Issue Age:Face Amt 250K-1M -0.01653 <2e-16

Issue Age:Face Amt >1M -0.0172 <2e-16

Validation of Results

Data

Proportion

Actual

Lapse

Rate

Predicted

Lapse

Rate

Variable Type P-ValueCoefficientActual /

PredictedFactor

47

Predictive Model – Model 1

0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

80,000

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0-19 20-29 30-39 40-49 50-59 60-69 70+

Exp

osu

re

Lap

se R

ate

Issue Age

Model Predicted vs. Actual Lapse Rate

Exposure

Predicted

Actual

48

Predictive Model – Model 2

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

18,000

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Exp

osu

re

Lap

se R

ate

Premium Jump


Exposure

Predicted

Actual

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0-19 20-29 30-39 40-49 50-59 60-69 70+

Exp

osu

re

Lap

se R

ate

Issue Age


Exposure

Predicted

Actual

49

Acknowledgements

50

Contributing Companies

SOA and SOA Staff

Project Oversight Group Jeff Beckley

Brian Carteaux

David Wylde

RGA Contributors Derek Kueker

Tim Rozar

Michael Cusumano

Susan Willeat

Tatiana Berezin

Tony Phipps

Richard Xu

Scott Rushing

Minyu Cao

Kathleen Broom

Acknowledgements

Special Thanks

51

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