Lapse and Mortality of Post-Level
Period Term Plans
Tim Rozar FSA, MAAA, CERA
Derek Kueker FSA
International Actuarial Association
Background
2
Introduction to Post-Level Term
10-Year Term: Premium Structure with Jump to ART
10-Year Term - Sample Premium Structure
Male Age 45, $500,000 Death Benefit
Super-Preferred Non-Smoker
18,000
16,000
14,000
Annual Premium
12,000
$7,395
Duration 11
Premium
10,000
8,000
20 times
Premium Jump
6,000
4,000
$375 Level
Premium
2,000
1
2
3
4
5
6
7
8
9
10
11
Level Period
12
13
14
15
16
17
18
19
20
Post-Level Period
Duration
3
Who Pays the $7,395 Rather Than Dropping Coverage or
Getting a New Policy?
 The Sick…
 The Lazy…
…And ALL 3 have
extra mortality risk!
 The Unaware…
4
• Sharp increase in
premium after level
period leads to large
anti-selective shock
lapse.
Lapse Rate
70%
60%
50%
40%
30%
20%
10%
0%
6
7
8
9
10
11
Level Period
300%
• Mortality on persisting
policyholders is
substantially worse in
the post-level period.
12
13+
Tail Period
2008 VBT Mortality Ratio
250%
200%
150%
100%
50%
0%
6
7
8
9
Level Period
10
11
12
13+
Tail Period
5
SOA/RGA Post-Level Term Study
Lapse Study Experience Results
6
Shock Lapse Experience Results Overview
2000-2012 Policy-Year Study
2014 Study 2010 Study Change
Number of Companies w/ Post Level Experience
10-Year Term
Post-Level Lapses with Premiums
Post-Level Lapses without Premiums
36
436,307
258,030
25
87,544
170,171
144%
498%
152%
Number of Companies w/ Post Level Experience
15-Year Term
Post-Level Lapses with Premiums
Post-Level Lapses without Premiums
15
37,673
1,364
7
12,191
1,359
214%
309%
100%
7
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
Shock Lapse Experience (Jump to ART)
T10 By Duration
100%
1,000,000
90%
Lapse Rate
70%
10,000
60%
50%
1,000
40%
100
30%
20%
Number of Lapses
100,000
80%
10
10%
0%
1
6
7
8
9
10
11
Level Period
Lapse Rate
12
13
14
15
16+
Post-Level Period
Median Lapse Rate
Number of Lapses (right axis)
8
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
Shock Lapse Experience
T15 By Duration
100%
100,000
90%
10,000
Lapse Rate
70%
60%
1,000
50%
40%
100
30%
20%
Number of Lapses
80%
10
10%
0%
1
11
12
13
14
15
Level Period
Lapse Rate
Median Lapse Rate
16
17
18
19+
Post-Level Period
Number of Lapses (right axis)
9
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
Shock Lapse Experience (Jump to ART)
T10 By Premium Jump Ratio
100,000
100%
90%
Lapse Rate
70%
1,000
60%
50%
100
40%
30%
Number of Lapses
10,000
80%
10
20%
10%
1
0%
Duration 11/10 Premium Jump Ratio
Duration 10 Lapse Rate Count
Duration 10 Lapses
10
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
Shock Lapse Experience (Jump to ART)
T10 By Duration & Premium Jump
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
Duration
Duration 10 Lapse
Rate
11/10Duration
Premium
Jump
11 Lapse
Rate Ratio Duration 12 Lapse Rate
11
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
Shock Lapse Experience (Jump to ART)
T10 By Duration & Premium Jump
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
Duration 10 Lapse Rate
Duration 11 Lapse Rate
Dur 11 / Dur 10
Dur 12 / Dur 11
Duration 11/10 Premium Jump Ratio
Duration 11/10
Premium Jump
Ratio Band
Dur 11 /
Dur 10
Dur 12 /
Dur 11
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 - 10x
10.01x-12x
12.01x-14x
14.01x-16x
16.01x +
Subtotal Prem Data Available
No Prem Data Available
Grand Total
79.5%
77.0%
73.2%
73.1%
70.5%
73.5%
73.2%
74.5%
78.7%
79.1%
79.7%
82.9%
86.0%
59.4%
55.0%
57.4%
59.5%
46.7%
44.9%
42.7%
45.4%
45.1%
46.3%
45.9%
54.7%
49.7%
49.4%
56.8%
59.8%
42.9%
43.1%
42.9%
Duration 12 Lapse Rate
12
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
Shock Lapse Experience
T10 By Duration and Issue Age
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
0-19
20-29
30-39
40-49
50-59
60-69
70+
Issue Age
Duration 6-9
Duration 10
Duration 11
Duration 12+
13
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
Shock Lapse Experience (Jump to ART)
T10 By Premium Jump and Issue age – duration 10
100%
100,000
90%
80%
10,000
70%
1,000
50%
40%
100
30%
20%
Number of Lapses
Lapse Rate
60%
10
10%
0%
1
<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 +
Duration 10 Lapse Rate
Duration 10 Lapses
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
14
Shock Lapse Experience
T10 By Duration & Face Amount Band
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
< $50,000
$50,000 $99,999
$100,000 $249,999
$250,000 $999,999
$1,000,000 $4,999,999
$5,000,000 +
Face Amount
Duration 6-9
Duration 10
Duration 11
Duration 12+
15
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
Shock Lapse Experience (Jump to ART)
T10 By Premium Jump and Face Amount Band – duration 10
100%
100,000
90%
80%
10,000
70%
1,000
50%
40%
100
30%
20%
Number of Lapses
Lapse Rate
60%
10
10%
0%
1
<100k 100k- 250k- 1M+ <100k 100k- 250k- 1M+ <100k 100k- 250k- 1M+ <100k 100k- 250k- 1M+ <100k 100k- 250k- 1M+
249k 999k
249k 999k
249k 999k
249k 999k
249k 999k
1.01x - 3x
3.01x - 5x
Duration 10 Lapse Rate
5.01x - 7x
7.01x - 9x
9.01x +
Duration 10 Lapses
16
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
Shock Lapse Experience
T10 By Duration & Gender
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
Male
Female
Gender
Duration 6-9
Duration 10
Duration 11
Duration 12+
17
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
Shock Lapse Experience
T10 By Duration & Risk Class
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
Super-Preferred
Preferred
Non-Preferred
Undiff
Preferred
Non-Preferred
Non-Smoker
Undiff
Smoker
Unk/Agg
Risk Class
Duration 6-9
Duration 10
Duration 11
Duration 12+
18
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
Shock Lapse Experience
T10 By Duration & Premium Payment Mode
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
Annual
Semi-Annual
Quarterly
Monthly
Premium Payment Mode
Duration 6-9
Duration 10
Duration 11
Duration 12+
19
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
SOA/RGA Post-Level Term Study
Mortality Study Experience Results
20
Mortality Experience Overview
2000-2012 Calendar Year Study
2014 Study 2010 Study Change
Number of Companies w/ Post Level Experience
10-Year Term
Post-Level Claims with Premiums
Post-Level Claims without Premiums
36
2,651
729
24
382
381
150%
694%
191%
Number of Companies w/ Post Level Experience
15-Year Term
Post-Level Claims with Premiums
Post-Level Claims without Premiums
6
432
12
5
145
13
120%
298%
92%
21
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
Mortality Experience (Jump to ART)
T10 By Duration
450%
10,000
400%
1,000
300%
250%
100
200%
150%
10
100%
Number of Deaths
Mortality Relative to
Durations 6-10
350%
50%
0%
1
6
7
8
9
10
11
Level Period
A/E Mortality
12
13
14
15
16+
Post-Level Period
Median A/E Mortality
Number of Deaths (right axis)
22
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
Mortality Experience
T15 By Duration
450%
10,000
400%
1,000
300%
250%
100
200%
150%
Number of Deaths
Mortality Relative to
Durations 11-15
350%
10
100%
50%
0%
1
11
12
13
14
15
Level Period
A/E Mortality
Median AE Rate
16
17
18
19+
Post-Level Period
Number of Deaths (right axis)
23
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
Mortality Experience (Jump to ART)
T10 Duration 11 Mortality by Premium Jump
2000%
10,000
1800%
1600%
1,000
Mortality Relative to
Durations 6-10
1200%
1000%
100
800%
600%
Number of Deaths
1400%
10
400%
200%
0%
1
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- 15.01x- 18.01x +
15x
18x
Duration 11/10 Premium Jump Ratio
Relative Mortality Ratio
Number of Deaths (right axis)
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
24
Mortality Experience (Jump to ART)
T10 Duration 11+ Mortality by Issue Age
400%
350%
300%
250%
200%
150%
100%
50%
0%
0-29
30-39
40-49
50-59
60+
Issue Age
Duration 6-10
Duration 11+
Post-Level Relative to Dur 6-10
25
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
Mortality Experience (Jump to ART)
T10 Duration 11+ Mortality by Face Amount Band
500%
450%
400%
350%
300%
250%
200%
150%
100%
50%
0%
< $50,000
$50,000 $99,999
Duration 6-10
$100,000 $250,000 $249,999
$999,999
Face Amount Band
Duration 11+
$1,000,000 +
Post-Level Relative to Dur 6-10
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
26
Mortality Study Experience Results – Jump to ART
T10 Duration 11+ Mortality by Gender
350%
300%
250%
200%
150%
100%
50%
0%
Male
Duration 6-10
Gender
Duration 11+
Female
Post-Level Relative to Dur 6-10
27
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
Mortality Study Experience Results – Jump to ART
T10 Duration 11+ Mortality by Risk Class
550%
500%
450%
400%
350%
300%
250%
200%
150%
100%
50%
0%
SuperPreferred
Preferred
Non-Preferred
Undiff
Preferred
Non-Smoker
Non-Preferred
Undiff
Smoker
Unk/Agg
Risk Class
Duration 6-10
Duration 11+
Post-Level Relative to Dur 6-10
28
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
Mortality Experience (Jump to ART)
T10 Duration 11 Mortality by Duration 10 Shock Lapse
by Company
1500%
Duration 11 Mortality Relative to Duraitons 6-10
1350%
1200%
1050%
900%
750%
>=35 claims
600%
<35 claims
Expon. ()
450%
300%
150%
0%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Duration 10 Shock Lapse
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
29
Practical Applications
30
Shock Lapse Experience
Skewness of Lapses
100%
90%
12
80%
Proportion of Lapses
11
70%
10
60%
9
8
50%
7
6
40%
5
30%
4
20%
3
10%
2
1
0%
6-9
10
11
12+
Duration
31
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
Grace Period Subsidy
• 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
32
Grace Period Subsidy - Example
• 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
33
Grace Period Subsidy – Example
5% Lapse Rate; No Anti-Selection
No Grace Period
Duration
BOM
Monthly
Year Month Lives
Mort Rate
10
1
100,000
0.10
10
2
99,990
0.10
10
3
99,980
0.10
10
4
99,970
0.10
10
5
99,960
0.10
10
6
99,950
0.10
10
7
99,940
0.10
10
8
99,930
0.10
10
9
99,920
0.10
10
10
99,910
0.10
10
11
99,900
0.10
10
12
99,890
0.10
11
1
94,886
0.10
11
2
94,877
0.10
11
3
94,867
0.10
11
4
94,858
0.10
11
5
94,848
0.10
11
6
94,839
0.10
11
7
94,829
0.10
11
8
94,820
0.10
11
9
94,810
0.10
11
10
94,801
0.10
11
11
94,791
0.10
11
12
94,782
0.10
10
11
Total
Deaths
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
9.5
9.5
9.5
9.5
9.5
9.5
9.5
9.5
9.5
9.5
9.5
9.5
Lapses
(Anniv)
4,994
Exposure Mort Rate Deaths
Lapses
100,000
1.20
119.9
4,994
94,886
1.20
113.8
194,886
1.20
233.7
4,994
Duration 11/10:
100%
w/ Grace Period
Experience Study Basis
w/ Grace Period
BOM
Lives
100,000
99,990
99,980
99,970
99,960
99,950
99,940
99,930
99,920
99,910
99,900
99,890
99,880
99,870
94,867
94,858
94,848
94,839
94,829
94,820
94,810
94,801
94,791
94,782
Monthly
Mort Rate
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
Deaths
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
9.5
9.5
9.5
9.5
9.5
9.5
9.5
9.5
9.5
9.5
Lapses
(Anniv)
4,993
BOM
Monthly
Lives
Mort Rate
100,000
0.10
99,990
0.10
99,980
0.10
99,970
0.10
99,960
0.10
99,950
0.10
99,940
0.10
99,930
0.10
99,920
0.10
99,910
0.10
99,900
0.10
99,890
0.10
94,887
0.10
94,877
0.10
94,867
0.10
94,858
0.10
94,848
0.10
94,839
0.10
94,829
0.10
94,820
0.10
94,810
0.10
94,801
0.10
94,791
0.10
94,782
0.10
Deaths
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
9.5
9.5
9.5
9.5
9.5
9.5
9.5
9.5
9.5
9.5
Lapses
(Anniv)
4,993
Exposure Mort Rate Deaths
Lapses
100,000
1.20
119.93
4,993
94,887
1.21
114.80
194,887
1.20
234.73
4,993
Duration 11/10:
101%
34
Grace Period Subsidy – Example
60% Lapse Rate; No Anti-Selection
No Grace Period
Duration
BOM
Monthly
Year Month Lives
Mort Rate
10
1
100,000
0.10
10
2
99,990
0.10
10
3
99,980
0.10
10
4
99,970
0.10
10
5
99,960
0.10
10
6
99,950
0.10
10
7
99,940
0.10
10
8
99,930
0.10
10
9
99,920
0.10
10
10
99,910
0.10
10
11
99,900
0.10
10
12
99,890
0.10
11
1
39,952
0.10
11
2
39,948
0.10
11
3
39,944
0.10
11
4
39,940
0.10
11
5
39,936
0.10
11
6
39,932
0.10
11
7
39,928
0.10
11
8
39,924
0.10
11
9
39,920
0.10
11
10
39,916
0.10
11
11
39,912
0.10
11
12
39,908
0.10
10
11
Total
Deaths
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
Lapses
(Anniv)
59,928
Exposure Mort Rate Deaths
Lapses
100,000
1.20
119.9
59,928
39,952
1.20
47.9
139,952
1.20
167.9
59,928
Duration 11/10:
100%
w/ Grace Period
Experience Study Basis
w/ Grace Period
BOM
Lives
100,000
99,990
99,980
99,970
99,960
99,950
99,940
99,930
99,920
99,910
99,900
99,890
99,880
99,870
39,944
39,940
39,936
39,932
39,928
39,924
39,920
39,916
39,912
39,908
Monthly
Mort Rate
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
Deaths
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
Lapses
(Anniv)
59,916
BOM
Monthly
Lives
Mort Rate
100,000
0.10
99,990
0.10
99,980
0.10
99,970
0.10
99,960
0.10
99,950
0.10
99,940
0.10
99,930
0.10
99,920
0.10
99,910
0.10
99,900
0.10
99,890
0.10
39,964
0.10
39,954
0.10
39,944
0.10
39,940
0.10
39,936
0.10
39,932
0.10
39,928
0.10
39,924
0.10
39,920
0.10
39,916
0.10
39,912
0.10
39,908
0.10
Deaths
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
Lapses
(Anniv)
59,916
Exposure Mort Rate Deaths
Lapses
100,000
1.20
119.93 59,916
39,964
1.50
59.90
139,964
1.28
179.84 59,916
Duration 11/10:
125%
35
Grace Period Subsidy – Example
90% Lapse Rate; No Anti-Selection
No Grace Period
Duration
BOM
Monthly
Year Month Lives
Mort Rate
10
1
100,000
0.10
10
2
99,990
0.10
10
3
99,980
0.10
10
4
99,970
0.10
10
5
99,960
0.10
10
6
99,950
0.10
10
7
99,940
0.10
10
8
99,930
0.10
10
9
99,920
0.10
10
10
99,910
0.10
10
11
99,900
0.10
10
12
99,890
0.10
11
1
9,988
0.10
11
2
9,987
0.10
11
3
9,986
0.10
11
4
9,985
0.10
11
5
9,984
0.10
11
6
9,983
0.10
11
7
9,982
0.10
11
8
9,981
0.10
11
9
9,980
0.10
11
10
9,979
0.10
11
11
9,978
0.10
11
12
9,977
0.10
10
11
Total
Deaths
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
Lapses
(Anniv)
89,892
Exposure Mort Rate Deaths
Lapses
100,000
1.20
119.9
89,892
9,988
1.20
12.0
109,988
1.20
131.9
89,892
Duration 11/10:
100%
w/ Grace Period
Experience Study Basis
w/ Grace Period
BOM
Lives
100,000
99,990
99,980
99,970
99,960
99,950
99,940
99,930
99,920
99,910
99,900
99,890
99,880
99,870
9,986
9,985
9,984
9,983
9,982
9,981
9,980
9,979
9,978
9,977
Monthly
Mort Rate
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
Deaths
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
Lapses
(Anniv)
89,874
BOM
Monthly
Lives
Mort Rate
100,000
0.10
99,990
0.10
99,980
0.10
99,970
0.10
99,960
0.10
99,950
0.10
99,940
0.10
99,930
0.10
99,920
0.10
99,910
0.10
99,900
0.10
99,890
0.10
10,006
0.10
9,996
0.10
9,986
0.10
9,985
0.10
9,984
0.10
9,983
0.10
9,982
0.10
9,981
0.10
9,980
0.10
9,979
0.10
9,978
0.10
9,977
0.10
Deaths
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
Lapses
(Anniv)
89,874
Exposure Mort Rate Deaths
Lapses
100,000
1.20
119.93 89,874
10,006
2.99
29.96
110,006
1.36
149.89 89,874
Duration 11/10:
250%
36
Grace Period Subsidy – Example
90% Lapse Rate; 200% Anti-Selection
No Grace Period
Duration
BOM
Monthly
Year Month Lives
Mort Rate
10
1
100,000
0.10
10
2
99,990
0.10
10
3
99,980
0.10
10
4
99,970
0.10
10
5
99,960
0.10
10
6
99,950
0.10
10
7
99,940
0.10
10
8
99,930
0.10
10
9
99,920
0.10
10
10
99,910
0.10
10
11
99,900
0.10
10
12
99,890
0.10
11
1
9,988
0.20
11
2
9,986
0.20
11
3
9,984
0.20
11
4
9,982
0.20
11
5
9,980
0.20
11
6
9,978
0.20
11
7
9,976
0.20
11
8
9,974
0.20
11
9
9,972
0.20
11
10
9,970
0.20
11
11
9,968
0.20
11
12
9,966
0.20
10
11
Total
Deaths
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
Lapses
(Anniv)
89,892
Exposure Mort Rate Deaths
Lapses
100,000
1.20
119.9
89,892
9,988
2.40
23.9
109,988
1.31
143.9
89,892
Duration 11/10:
200%
w/ Grace Period
Experience Study Basis
w/ Grace Period
BOM
Lives
100,000
99,990
99,980
99,970
99,960
99,950
99,940
99,930
99,920
99,910
99,900
99,890
99,880
99,870
9,986
9,984
9,982
9,980
9,978
9,976
9,974
9,972
9,970
9,968
Monthly
Mort Rate
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
Deaths
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
Lapses
(Anniv)
89,874
BOM
Monthly
Lives
Mort Rate
100,000
0.10
99,990
0.10
99,980
0.10
99,970
0.10
99,960
0.10
99,950
0.10
99,940
0.10
99,930
0.10
99,920
0.10
99,910
0.10
99,900
0.10
99,890
0.10
10,006
0.10
9,996
0.10
9,986
0.20
9,984
0.20
9,982
0.20
9,980
0.20
9,978
0.20
9,976
0.20
9,974
0.20
9,972
0.20
9,970
0.20
9,968
0.20
Deaths
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
Lapses
(Anniv)
89,874
Exposure Mort Rate Deaths
Lapses
100,000
1.20
119.93 89,874
10,006
3.99
39.93
110,006
1.45
159.86 89,874
Duration 11/10:
333%
37
Mortality Experience
350%
175
300%
150
250%
125
200%
100
150%
75
100%
50
50%
25
0%
0
1
2
3
4
5
6
7
8
9
Months since start of Duration 11
2008 VBT Mortality Ratios
10
11
Number of Deaths
2008 VBT Mortality Ratios
Duration 11 Mortality by Month
12
Number of Deaths (right axis)
38
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
SOA/RGA Post-Level Term Study
Assumption Survey Results
39
Assumption Survey Results
Overview
 Sent to top 100 term providers based on 2012 term insurance sales
 Responses from 41 companies
 Responses represented 62% of 2012 term sales
Level Premium Term Product Mix by Level Period
Product Level Period
Aggregate Distribution
for Respondents
Number of companies where product
represents at least x% of individual
company's term sales
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
40
Source: http://www.soa.org/Files/Research/Projects/research-shock-lapse-survey-report.pdf
Assumption Survey Results
Post-Level Premium Structure
 Dominant Structure is Jump to an ART Scale
Post-Level Product Design
Product Structure
Responses
Premium jump to ART
Premium grade to ART
Jump to new level period
Face amount decrease
Product terminates
Flexible Premiums (Term UL)
40
4
3
1
2
1
41
Source: http://www.soa.org/Files/Research/Projects/research-shock-lapse-survey-report.pdf
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
Changes to Post-Level Premium Structure for Term New Business
No change
23
Grade premiums into an ART scale over 'x' years
3
Other
3
Changes to Post-Level Premium Structure for Term In Force
Description
Lower post-level premiums
Grade into an ART scale
Other
Implemented in
last 5 years
1
3
0
Considering
5
3
2
42
Source: http://www.soa.org/Files/Research/Projects/research-shock-lapse-survey-report.pdf
Lapse Assumptions
Post-Level Lapse Rate Structure
 Most companies assume only one shock lapse, generally grading
down thereafter
Lapse Rate Trend By Duration
Description
Duration L Shock, then level
Duration L Shock, then grade down
2 Shocks, Duration L>=L+1
2 Shocks, Duration L+1>L
Responses
10-Year Term
20-Year Term
8
7
12
10
6
5
3
2
43
Source: http://www.soa.org/Files/Research/Projects/research-shock-lapse-survey-report.pdf
Lapse Assumptions
Factors impacting shock lapse assumptions
 Used a common pricing cell for consistent comparisons in upcoming
charts
Vary by These Parameters
No Variance
Issue Age & Level Period
Level Period
Issue Age & Risk Class
Risk Class
Premium Jump Ratio
No Other
Variance
9
5
5
2
1
1
Additional Variations
Risk Class &
Premium
Premium
Premium
Mode
Jump Ratio
Jump Ratio
1
1
1
1
1
1
44
Source: http://www.soa.org/Files/Research/Projects/research-shock-lapse-survey-report.pdf
Lapse Assumptions
Annual and cumulative lapse assumptions by duration, 10-year
term
100%
100%
80th
percentile
Median
80%
20th
percentile
Lapse Rate
70%
60%
50%
90%
80%
Cumulative Lapse Rate
90%
70%
60%
50%
30%
80th
percentile
Median
20%
20%
20th
percentile
10%
10%
40%
30%
40%
0%
0%
10
11
12
13
Duration
14
15
10
11
12
13
Duration
14
15
45
Source: http://www.soa.org/Files/Research/Projects/research-shock-lapse-survey-report.pdf
Lapse Assumptions
Duration 10 lapse assumptions by issue age, 10-year term
100%
Lapse Rate
90%
80%
80th percentile
70%
Median
60%
20th percentile
50%
2009 Median
40%
30%
20%
10%
0%
25
35
45
55
65
Issue Age
46
Source: http://www.soa.org/Files/Research/Projects/research-shock-lapse-survey-report.pdf
Lapse Assumptions
Post-Level Lapse Rate Assumption by Premium Jump, 10-year
term
100%
90%
80%
Shock Lapse
 Broad range of
assumptions by
premium jump
 Trend is somewhat
inconsistent with
experience
70%
60%
50%
40%
30%
20%
10%
0%
0.0
5.0
10.0
15.0
20.0
25.0
30.0
Premium Jump
47
Source: http://www.soa.org/Files/Research/Projects/research-shock-lapse-survey-report.pdf
Mortality Deterioration Assumptions
Post-Level Mortality Deterioration Structure
 Assumptions vary broadly by structure of mortality deterioration
Mortality Deterioration Assumption Trend By Duration
Responses
Description
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
48
Source: http://www.soa.org/Files/Research/Projects/research-shock-lapse-survey-report.pdf
Mortality Deterioration Assumptions
Factors impacting mortality deterioration assumptions
 The same pricing cell that was used in the Lapse Assumptions charts
is used in this section
Vary by These Parameters
Duration, Level Period and Issue Age
Policy Duration
Constant
Duration and Level Period
Level Period
Issue Age
No other
Variation
6
5
4
3
2
1
Additional Variations
Size of
Risk Class
Shock
and Gender
Gender
Lapse
4
1
1
49
Source: http://www.soa.org/Files/Research/Projects/research-shock-lapse-survey-report.pdf
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
Method of Developing Mortality Assumption
Method
N/A - 100% shock lapse
Dukes-MacDonald or derivatives of Dukes-MacDonald
Canadian Institute of Actuaries Valuation Technique Paper #2
Flat Multiple
Other: Set by reinsurer/external consultant
Other: Internally developed method
Responses
9
14
4
13
3
3
50
Source: http://www.soa.org/Files/Research/Projects/research-shock-lapse-survey-report.pdf
Mortality Deterioration Assumptions
Annual mortality deterioration multiple, 10 year term
Mortality Deterioration Multiple
500%
450%
80th percentile
400%
Median
350%
20th percentile
300%
2009 Median
250%
200%
150%
100%
50%
0%
11
12
13
14
15
20
Duration
51
Source: http://www.soa.org/Files/Research/Projects/research-shock-lapse-survey-report.pdf
Mortality Deterioration Assumptions
Post-Level Mortality Assumptions vs. Premium Jump
 Mortality deterioration assumptions do not differ dramatically by
premium jump, inconsistent with experience
Mortality Deterioration Duration 11
1000%
900%
800%
700%
600%
500%
400%
300%
200%
100%
0%
0.0
5.0
10.0
15.0
20.0
25.0
30.0
Premium Jump
52
Source: http://www.soa.org/Files/Research/Projects/research-shock-lapse-survey-report.pdf
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
600%
500%
Mortality Deterioration Duration 12
1-10X Jump
11-20X Jump
400%
20X Jump or Greater
300%
200%
100%
0%
0%
20%
40%
60%
80%
100%
Cumulative Lapse Rate Duration 10 through 11
53
Source: http://www.soa.org/Files/Research/Projects/research-shock-lapse-survey-report.pdf
Lapse Assumptions
Skewness assumptions from the level period through the postlevel period
 Today’s skewness assumptions do not always follow past experience
Monthly Lapse Skewness During Level Premium Period
Respondents
Response
18
Lapses are uniformly distributed
10
Lapses occur on premium payment modes
7
Lapses occur at the end of the year
4
Other
Monthly Lapse Skewness During Year of Shock Lapse
5
Lapses are uniformly distributed
3
Lapses occur on premium payment modes
17
Lapses occur at the end of the year
Lapses graded toward end of the year with shock in month 12
12
Monthly Lapse Skewness During Post-Level Period
Lapses are uniformly distributed
Lapses occur on premium payment modes
Lapses occur at the end of the year
Lapses skewed to the beginning of L+1, Uniform thereafter
6
7
9
8
54
Source: http://www.soa.org/Files/Research/Projects/research-shock-lapse-survey-report.pdf
SOA/RGA Post-Level Term Study
Assumptions vs. Experience
55
10
11
12
Duration
13
14
60%
Aggregate
50%
20th percentile
Experience
Results (Phase 2)
Assumption
Survey (Phase 1)
Experience
Results (Phase 2)
Assumption
Survey (Phase 1)
Experience
Results (Phase 2)
Assumption
Survey (Phase 1)
Experience
Results (Phase 2)
100%
Assumption
Survey (Phase 1)
Experience
Results (Phase 2)
Assumption
Survey (Phase 1)
Experience
Results (Phase 2)
Assumption
Survey (Phase 1)
Lapse Rate
Survey Responses vs. Experience Study
T10 Jump to ART
Lapse Rates by Duration
Phase 1 vs. Phase 2
90%
80%
70%
80th percentile
Median
40%
30%
20%
10%
0%
15
56
Survey Responses vs. Experience Study
T15 Lapse Rates by Duration
Phase 1 vs. Phase 2
100%
90%
80%
80th percentile
60%
Median
50%
Aggregate
40%
20th percentile
30%
20%
10%
Experience
Results (Phase 2)
Assumption
Survey (Phase 1)
Experience
Results (Phase 2)
0%
Assumption
Survey (Phase 1)
Lapse Rate
70%
15
16
Duration
57
25
35
Issue Age
45
55
Experience
Results (Phase 2)
Assumption
Survey (Phase 1)
Experience
Results (Phase 2)
Assumption
Survey (Phase 1)
Experience
Results (Phase 2)
Assumption
Survey (Phase 1)
Experience
Results (Phase 2)
Assumption
Survey (Phase 1)
Experience
Results (Phase 2)
Assumption
Survey (Phase 1)
Lapse Rate
Survey Responses vs. Experience Study
T10 Jump to ART
Duration 10 Lapse Rates by Issue Age
Phase 1 vs. Phase 2
100%
90%
80%
70%
80th percentile
60%
Median
50%
Aggregate
40%
20th percentile
30%
20%
10%
0%
65
58
0%
11
12
13
Duration
14
Experience
Results (Phase 2)
Assumption
Survey (Phase 1)
Experience
Results (Phase 2)
Assumption
Survey (Phase 1)
Experience
Results (Phase 2)
Assumption
Survey (Phase 1)
Experience
Results (Phase 2)
Assumption
Survey (Phase 1)
Experience
Results (Phase 2)
Assumption
Survey (Phase 1)
Mortality Deterioration
(Relative to Duration 6-10)
Survey Responses vs. Experience Study
T10 Jump to ART
Mortality Deterioration by Duration
Phase 1 vs. Phase 2
900%
800%
700%
600%
80th percentile
500%
Median
Aggregate
400%
20th percentile
300%
200%
100%
15
59
Survey Responses vs. Experience Study
T10 Duration 11
Mortality Deterioration by Issue Age
Phase 1 vs. Phase 2
1800%
1600%
1200%
80th percentile
1000%
Median
Aggregate
800%
20th percentile
600%
400%
200%
55
Experience
Results (Phase 2)
Assumption
Survey (Phase 1)
Experience
Results (Phase 2)
Experience
Results (Phase 2)
45
Assumption
Survey (Phase 1)
0%
Assumption
Survey (Phase 1)
Mortality Deterioration
(Relative to Duration 6-10)
1400%
65
Issue Age
60
SOA/RGA Post-Level Term Study
Predictive Model
61
Predictive Model
 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
62
Predictive Model – Model 1
Model Parameter
Variable
Type
Validation of Results
Coefficient
Factor
P-Value
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
Actual Predicted
Data
Actual /
Lapse
Lapse
Proportion
Predicted
Rate
Rate
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%
0
1.00
Face Amount
Categorical
<50K
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%
0
22.9%
85.8%
85.3%
100.5%
Premium Mode
Categorical
Annual
0
1.00
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%
-0.08481
0.92 <2.0E-16
7.2%
85.3%
84.8%
100.7%
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
-0.0172
<2e-16
Other/Unknown
Cross Term
Issue Age:Face Amt <50
Issue Age:Face Amt >1M
Mixed
63
Predictive Model – Model 2
Model Parameter
Type
Variable
Premium Jump
Coefficient
Factor
P-Value
Categorical
-
Premium Jump 1.01-2x
0
1.00
Premium Jump 2.01-3x
1.135
3.11
<2.00E-16
Premium Jump 3.01-4x
1.492
4.45
<2.00E-16
3.246
2.03E-14
Premium Jump 4.01-5x
1.826
6.21
<2.00E-16
Numerical
0.1621
<2.00E-16
Premium Jump 5.01-6x
2.082
8.02
<2.00E-16
(Issue Age)^2
Numerical
-0.0006419
<2.00E-16
Premium Jump 6.01-7x
2.118
8.31
<2.00E-16
log(Issue Age)
Numerical
-2.7250000
<2.00E-16
Premium Jump 7.01-8x
2.176
8.81
<2.00E-16
Risk Class
Categorical
Premium Jump 8.01-10x
2.246
9.45
<2.00E-16
Intercept
-
Issue Age
Super-Pref NS
NS
SM
Face Amount
0
1.00
-
Premium Jump 10.01-12x
2.304
10.01
<2.00E-16
0.03427
1.03
0.00
Premium Jump 12.01-16x
2.342
10.40
<2.00E-16
0.1205
1.13
<2.00E-16
Premium Jump 16.01-20x
2.385
10.86
<2.00E-16
Premium Jump 20.01x+
2.356
10.55
<2.00E-16
Categorical
-
Cross Term
Mixed
0
1.00
50-100K
0.3153
1.37
0.00
Issue Age:Premium Jump 1.01-2x
0
0
100K-250K
0.3437
1.41
<2.00E-16
Issue Age:Premium Jump 2.01-3x
-0.02241
<2.00E-16
250K-1M
0.3652
1.44
<2.00E-16
Issue Age:Premium Jump 3.01-4x
-0.02589
<2.00E-16
>1M
0.3645
1.44
<2.00E-16
Issue Age:Premium Jump 4.01-5x
-0.03042
<2.00E-16
Issue Age:Premium Jump 5.01-6x
-0.03383
<2.00E-16
<50K
Premium Mode
Categorical
0
1.00
-
Issue Age:Premium Jump 6.01-7x
-0.03381
<2.00E-16
-0.03244
0.97
0.00
Issue Age:Premium Jump 7.01-8x
-0.03479
<2.00E-16
Monthly/BiWeekly
-0.2755
0.76
<2.00E-16
Issue Age:Premium Jump 8.01-10x
-0.03567
<2.00E-16
Other/Unknown
0.02057
1.02
0.06
Issue Age:Premium Jump 10.01-12x
-0.03615
<2.00E-16
Issue Age:Premium Jump 12.01-16x
-0.03665
<2.00E-16
Issue Age:Premium Jump 16.01-20x
-0.03687
<2.00E-16
Issue Age:Premium Jump 20.01x+
-0.03601
<2.00E-16
Annual
Semi/Quarter
64
Predictive Model – Model 1
Model Predicted vs. Actual Lapse Rate
100%
80,000
90%
70,000
80%
60,000
50,000
60%
Exposure
50%
Predicted
40%
40,000
30,000
Actual
Exposure
Lapse Rate
70%
30%
20,000
20%
10,000
10%
0%
0
0-19
20-29
30-39
40-49
50-59
60-69
70+
Issue Age
65
Predictive Model – Model 2
Model Predicted vs. Actual Lapse Rate
100%
40,000
90%
35,000
80%
30,000
60%
Exposure
25,000
50%
Predicted
20,000
Actual
40%
Exposure
Lapse Rate
70%
15,000
30%
10,000
20%
5,000
10%
0%
0
0-19
20-29
30-39
40-49
50-59
60-69
70+
Issue Age
Model Predicted vs. Actual Lapse Rate
100%
18,000
90%
16,000
Exposure
Lapse Rate
Predicted
70%
Actual
14,000
12,000
60%
10,000
50%
8,000
40%
Exposure
80%
6,000
30%
4,000
20%
2,000
10%
0%
0
Premium Jump
66
Multivariate Lapse Rate Model - With Premium Jump
10-Year term Duration 10 Lapse Rate
Assumptions
Issue Age
Risk Class
Face Amount
Premium Mode
Premium Jump
45
NS
250K-1M
Annual
Premium Jump 8.01-10x
Beta Coefficients
(a)
Model Variables
Sample Value of xi
(b)
Sample
Calculation
(c) = (a) * (b)
Variables
Intercept
3.2460468406
1
3.2460
Issue Age
0.1620764522
45
7.2934
(Issue Age)^2
-0.0006419533
2025
(1.3000)
log(issue Age)
-2.7246684047
4
(10.3719)
0.0342716521
1
0.0343
0.3651595476
1
0.3652
0.0000000000
1
-
2.2456634786
1
2.2457
-0.0356704787
45
(1.6052)
Risk Class
NS
Face Amount
250K-1M
Premium Mode
Annual
Premium Jump
Premium Jump 8.01-10x
Cross Term
Issue Age:Premium Jump 8.01-10x
Results
Linear Predictor = Sum(Beta i * x i) = Sum (c)
Linear Predictor
Modeled Lapse Rate = e
(0.0924)
91.2%
67
2013 SOA Post-Level Term Survey Report
Key Takeaways
 “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
68
2014 SOA Post-Level Term Experience Report
Key Takeaways
 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
69
Questions?
70