Mark Andrews - Canadian Reinsurance CRC Session 12 Term Mort… · Mark Andrews Director, Life...
Transcript of Mark Andrews - Canadian Reinsurance CRC Session 12 Term Mort… · Mark Andrews Director, Life...
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Mark AndrewsDirector, Life Pricing
Sun Life Financial
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Looking Back:Term Insurance in Canada
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Term In Canada – A ‘Typical’ productlooks like:• Level Premiums for Fixed Term Lengths (T10 and
T20 most common)• Renewable and convertible (age limits apply)• Issue ages 15-75• Issue face amounts from $50,000 to ?• Can be single or joint first-to-die• Multiple underwriting classes (e.g. – preferred or
“super-preferred”)
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Term Sales in Canada• Based on recent sales activity, a typical year of
Term sales would look like:
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Risk Profile for (Re) Insurers• Relatively low on interest rate risks.
• Shorter Term liabilities
• Relatively high on policyholder behavior risk• Lapses (Anti-Selective)• Conversions (a little Anti-Selective)• Mortality
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Key Turning Point• Around Y2k, Term in Canada migrated from Single
Scale Premiums to Select And Ultimate.
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Key Turning Point• New financial incentive to lapse coverage at the
end of the initial term and purchase a new planwith new underwriting (anti-selection).
• Competitive Pressures have increased the incentiveover the last 10 years.
• Significant impact on Lapse & Mortality.• Experience Emerging as we speak!
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Term 10 Premiums Over the Years
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Emile ElefteriadisSwiss Re
SVP Reinsurance Client MarketsExperience Studies
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What are “experience studies”?
In a study of 500 people we asked“On a scale of 1-10, how wouldyou rate your experience…”
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Experience Studies in insurance aremuch more interesting!**
ActualClaims by
Policy
A/ERatio1 by
Count
A/ERatio1 byAmount
ActualClaims by
Policy
A/ERatio1 by
Count
A/ERatio1 byAmount
ActualClaims by
Policy
A/ERatio1 by
Count
A/ERatio1 byAmount
ActualClaims by
Policy
A/ERatio1 by
Count
A/ERatio1 byAmount
Overall 83,518 109.8% 88.8% 26,013 106.1% 91.3% 57,348 108.1% 88.8% 22,109 107.5% 97.2%
Issue Age 18-24 1,905 140.5% 109.6% 508 120.4% 101.2% 996 135.6% 110.9% 246 119.6% 89.6%25-29 2,800 114.6% 92.6% 812 123.1% 92.6% 1,525 106.0% 91.3% 396 125.3% 97.4%30-34 4,642 113.6% 94.6% 1,311 107.4% 101.3% 2,456 104.8% 86.9% 674 113.2% 92.6%35-39 6,396 110.3% 92.1% 2,075 107.5% 92.7% 3,519 110.9% 89.8% 1,061 105.0% 92.6%40-49 16,805 110.7% 89.5% 6,703 111.9% 89.9% 9,060 113.0% 93.1% 3,822 105.3% 95.3%50-59 22,261 106.3% 94.2% 7,929 106.1% 91.5% 12,804 105.1% 91.7% 6,243 107.6% 89.7%60-69 22,349 111.3% 89.5% 5,493 99.5% 90.7% 18,000 107.7% 94.2% 7,666 106.8% 107.1%70-79 5,928 105.2% 74.2% 1,117 91.7% 78.1% 8,051 108.8% 90.7% 1,864 110.8% 107.5%80+ 432 81.9% 39.7% 65 73.8% 56.4% 937 89.7% 58.0% 137 89.7% 71.0%
Duration 1 1,047 153.4% 98.1% 219 115.6% 61.3% 505 149.5% 66.3% 134 139.2% 78.3%2 1,185 124.1% 71.3% 264 109.4% 68.4% 615 125.4% 63.8% 160 119.0% 76.3%3 1,450 123.1% 78.8% 331 116.2% 94.5% 809 125.6% 72.7% 244 145.1% 84.6%4-5 3,651 117.7% 84.8% 856 115.6% 98.3% 2,193 121.9% 82.2% 649 129.7% 102.0%6-10 11,186 111.9% 89.9% 2,643 110.6% 83.1% 7,250 114.9% 84.7% 1,948 117.1% 93.6%11-15 12,610 110.8% 88.2% 3,348 106.5% 89.1% 10,631 113.6% 100.9% 3,146 114.4% 100.9%16-20 21,646 109.5% 92.6% 6,776 111.8% 99.6% 16,940 109.5% 98.2% 6,477 114.1% 106.7%21-25 30,743 106.0% 93.1% 11,576 100.9% 94.4% 18,405 98.8% 92.2% 9,351 97.6% 91.6%
Face Amount 1-9,999 6,677 130.8% 128.1% 3,789 120.3% 117.8% 13,146 113.1% 112.0% 8,785 113.2% 114.5%10,000-24,999 15,501 128.2% 126.0% 6,750 113.6% 110.2% 15,222 116.0% 115.4% 6,467 109.6% 107.3%25,000-49,999 15,297 120.0% 119.1% 5,078 106.4% 105.2% 9,465 113.4% 113.1% 2,761 105.0% 104.1%50,000-99,999 19,188 113.2% 112.7% 5,177 102.9% 101.8% 9,115 105.3% 105.1% 2,280 99.6% 99.1%100,000-249,999 17,322 97.5% 96.0% 3,919 95.6% 95.0% 7,312 96.0% 95.7% 1,391 91.0% 91.4%250,000-499,999 5,170 85.9% 85.6% 801 84.8% 85.1% 1,914 87.9% 87.5% 255 86.7% 87.5%500,000-999,999 2,727 83.8% 83.2% 326 83.2% 81.3% 728 79.0% 79.6% 104 99.4% 97.5%1,000,000-2,499,999 1,387 77.2% 75.8% 159 92.8% 90.0% 374 81.0% 78.4% 54 103.8% 102.6%2,500,000-4,999,999 147 77.9% 77.5% 12 36 63.5% 63.6% 75,000,000-9,999,999 75 73.8% 71.2% 1 30 76.3% 74.7% 510,000,000+ 27 82.5% 98.2% 1 6 0
Male Nonsmoker Male Smoker Female Nonsmoker
Select period only (durations 1 - 25)
Appendix C - Experience by gender and smoking status for all face amountsSOA industry individual life experience in observation periods 2008 - 2009
Expected basis: 2008 VBT - Primary Table
Female Smoker
** in a survey of 1003.1415 actuaries
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What are experience studies ?• A report showing something about some aspect
of the performance of the business• We’re focused on those reports which try to
answer the questions• What kind of mortality rates are we seeing?• What kind of lapse rates are we seeing?
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Mortality Experience Analysis
• A common way of reviewing mortality experience iscomparing how actual experience compares to what wasexpected (or priced for)
Hypothetical By Number ofPolicies
By Face Amount Average FaceAmount
Exposures 600 $360,000,000 $600,000
Actual deaths 8 $7,200,000 $900,000
Expected deaths 3 $1,800,000 $600,000
Actual MortalityRate
8/600=1.33% 7.2/360=2.0%
Expected Mort Rate 3/600 =0.5% 1.8/360 =0.5%
Actual/Expected ~267% (8/3) ~400% (7.2/1.8)•If the A/E by face amount is higher than the A/E by number of policies,could be an indication of anti-selection.
Just a fancy wordfor population or
sample size
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Mortality Experience- Chart
267%
400%
0%
50%
100%
150%
200%
250%
300%
350%
400%
450%
Mortality Experience
A/E
Ratio
Number Amount
Same results as intable on other page.
Many experiencestudies show anactual to expectedratio.
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Two concepts: “Credibility” and“Statistical Significance”
• Significance: is seeing 8 deathsexpected/normal?
• Credibility: how much weight would we give thisnew data when reconsidering experience relativeto our prior expectations/beliefs?
Hypothetical By Number ofPolicies
By Face Amount Average FaceAmount
Exposures 600 $360,000,000 $600,000
Actual deaths 8 $7,200,000 $900,000
Expected deaths 3 $1,800,000 $600,000
Actual Mort Rate 8/600=1.33% 7.2/360=2.0%
Expected Mort Rate 3/600 =0.5% 1.8/360 =0.5%
Actual/Expected ~267% (8/3) ~400% (7.2/1.8)
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Significance
0%
5%
10%
15%
20%
25%
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
PRO
BABI
LITY
OF
SEEI
NG
# O
F DE
ATHS
# OF DEATHS
97.5% Confidence IntervalMeans that 975 times out of 1000, wewould expect to see deaths fall intothis range.If what you see is outside this rangethen either it is a fluke or more likely,that your assumptions are incorrect.
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Credibility• We reduced the exposure (sample size) by half• Let’s just focus on experience by number for this
example and assume all policies are the samesizeHypothetical By Number of
PoliciesBy Face Amount Average Face
Amount
Exposures 300 $180,000,000 $600,000
Actual deaths 4 $3,600,000 $900,000
Expected deaths 1.5 $900,000 $600,000
Actual MortalityRate
4/300=1.33% 3.6/180=2.0%
Expected MortRate
1.5/300 =0.5% 0.9/180 =0.5%
Actual/Expected ~267% (4/1.5) ~400% (3.6/0.9)
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Credibility Significance
0%
5%
10%
15%
20%
25%
30%
35%
40%
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
PRO
BABI
LITY
OF
SEEI
NG
# O
F DE
ATHS
# OF DEATHS
97.5% Confidence IntervalIn this case, observing 4 deaths is inthe “normal” range. (But just)
So is seeing 4 deaths “credible”?
It depends.
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Credibility• It depends. Judgement is required• We expected 1-2 deaths (1.5), consistent with a
mortality rate of 0.5% which was based on amuch larger sample (e.g. the experience of allinsurance companies). (Prior Beliefs)
• However in the industry study, all of thoseinsurance companies obtained medical evidence.
• A: If our company also obtained medical evidence?• B: If our company did not obtain medical evidence?
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Credibility Application• Updated mortality:
• I update my mortality rate assumption to a blend of what thedata is telling me (mortality rate of 1.33%) and the industryaverage (0.5%).
• New Mortality Rate = Z% *1.33% + (1-Z%)*0.5%• Z% = credibility of your new data
• If A is true.• Z% is small. (e.g. 5%-10%) My own data is not credible.• (However, maybe there’s another important difference that
I’m not aware of)• If B is true.
• Z% is large. (e.g. 90%-95%). Although not statisticallysignificant, what the data is showing is more important thanwhat I assumed. I will try to update my “prior beliefs”.
How to estimateZ% is complex
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0
500
1000
1500
2000
2500
3000
3500
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
MNS 45 $375,000
T10 Yesterday
T10 Today
4.5 x premiumincrease
What kind of an “experience” doyou get when you have this?
22
6.8 x premiumincrease
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• Our analysis centers around 4 different studies− Swiss Re US reinsurance study− Swiss Re US industry study (including Admin Re® data)− SOA study− CIA T10 Lapse study
Swiss ReIndustry Study
Swiss ReReinsured Study
SOA Study CIA study
Companies 8 33 27 10
Issue years 1990-2002 1990-2003 1989-2002 1981-2008
Exposure years 1995-2012 2007-9/2013 2000-2012 2005-2010Post Level Term
claims 2,246 2,241 1,297 0
Dur 10+ lapses 360,357 485,937 336,866 234,328
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Comprehensive Research,Credible Results
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Lapse rates correlate withpremium jumps
Sources: 2014 SOA study and Swiss Re 's Reinsurance study
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1.01x - 2x 2.01x - 3x 3.01x - 4x 4.01x - 5x 5.01x - 6x 6.01x - 7x 7.01x - 8x 8.01x - 10x 10.01x +
T10 shock lapse rate by premium jump ratio by amount
Swiss Re Reinsured Experience Lapse Rt $ SOA Experience Study Lapse Rt $
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Results similar for 10- and 15-year level premium plans
25
Sources: Swiss Re 's Reinsurance study
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1.01x - 2x 2.01x - 3x 3.01x - 4x 4.01x - 5x 5.01x - 6x 6.01x - 7x 7.01x - 8x 8.01x - 10x 10.01x +
Comparison of shock lapse rates for T10 & T15 by premium jump
T10 Lapse Rates T15 Lapse Rates
*Note: There is limited experience for T15
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Lapse experience –Canada vsUSA
Sources: 2014 CIA T10 lapse study, 2014 SOA study and*Year 10+2 month's lapse in 11
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
30-34 35-39 40-44 45-49 50-54 55-59 60-64
CIA 10+11* SOA 10 Prem Jump (right scale)
2 times
0.0%
10.0%
20.0%
30.0%
40.0%
1 2 3 4 5 6 7 8 9 101112
% of Yr 11 lapse
% of Yr 11 lapse
Intent here is to show a relationship betweenCanadian and US T10 lapse rates
4 times
3 times
5 times
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Mortality Experience- CIAIndustry
27
0%
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100%
150%
200%
250%
6 7 8 9 10 11 12 13 14 15
Rel
ativ
e M
orta
lity
Policy Year
Renewable T10 Relative Mortality ExperienceCIA Mortality Studies 2011/12-2012/13
A/E # (97-04) A/E $ (97-04)
Notice A/E by $ much worse.
?
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Mortality Experience- CIAIndustry
28
0%
50%
100%
150%
200%
250%
6 7 8 9 10 11 12 13 14 15
Rel
ativ
e M
orta
lity
Policy Year
Renewable T10 Relative Mortality ExperienceCIA Mortality Studies 2011/12-2012/13
A/E # (97-04) A/E $ (97-04)
Notice A/E by $ much worse.Relative mortality 193%based on ~500 claims (ages 30-59)
This cohort of policies experienced~70% total shock lapse rate (4.0-5.0x)
This cohort ofpoliciesexperienced~65% total shocklapse rate (3.0-4.0x)
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Past vs Future- Experience• So all the studies have focused on Term 10
policies issued more than ten years ago.• Those policies have lower premium jumps than
Term 10 policies issued today.• Therefore how can we predict what are the most
appropriate lapse and mortality assumptions toprice and value Term 10 policies issued today?
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Past vs Future-Lapse• Get clues from US experience-where large jump
experience exists• Tricky, since US T10 products are quite different.
They are the same for 1-10, and year 11 only.
• If T10 premiums jumps are approximately 7xwhat does the US experience say lapse rate is ?
•
US T10 : Lapse rates at durations 10
Premium jump ratio DurationLapse rate
Based on amount Based on number
5.01-6.0010 82.7% 83.3%
6.01-7.0010 88.3% 88.5%
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Past vs Future-Mortality• Get clues from US experience.
• So provides a clue for year 11 mortality only.
Duration
Actual to Expected ratio
(Premium jump of 5-7x)
Based on face amount Based on number of deaths6-10 100.0% 100.00%11 399.6% 393.6%
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Past vs Future-Mortality Models• Use Mortality Models• Fit Mortality Models to Canadian data and
extrapolate
• q''[x]+t = q'[x]+t + S * (q'[x]+t - q[x+t]) / (1-S-A-U)
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Jean-PierreCormier
VP PricingRGA Canada
Term Mortality Models
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Mortality deterioration 101• Development of the formula
• Let’s assume that 85% will lapse just before the end of the 10thpolicy anniversary
• What will be the mortality assumption of the remaining group ?• Model presented by Jeffery Dukes and Andrew MacDonald in
1980
• To determine the mortality of the 15% who persist, we need tomake a few assumptions about the 85% who lapsed 85
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Mortality deterioration 101• We need to split the 85 men who lapsed into 3
distinct groups• GROUP 1 = Assumption #1, the underlying (UL)• % of lapses already embedded in the experience of the mortality
table.
Assume 5
85
5• They are assumed to
have the samemortality as the entiregroup just before theyrenew (0.00482)
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Mortality deterioration 101• The 80 (85 – 5) men left are called additional
lapses• GROUP 2 = Assumption #2, the select men (SL-> select
proportion or effectiveness)
80 • Those who can get a brand newpolicy and pay a cheap T10 priceagain (they are now age 45)
• We will assume it’s 60% ofthe 80 men
• Their mortality is assumed to bethe same as newly underwritteninsured lives
Q[45] = 0.00283 < Q[35]+10 = 0.00482
4860% proportionof selectivelapse (60% X80)
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Mortality deterioration 101• The 32 (85 – 5 – 48) men left are the average
men• GROUP 3 = Assumption #3, the average men
32• They are assumed to
have the same mortalityas the entire group justbefore they renew(0.00482)
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Mortality deterioration 101• Key principles
• Conservation of deaths principle: The total number ofdeaths for a group of policyholders is the sameregardless of how the group is split
• Average, selective and underlying lapses occur only atpolicy anniversaries
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Mortality deterioration 101• The formula
100
=
48
5+ +
32+
SL =0.00283
AL =0.00482
(100-UL-SL-AL) = ?UL =0.00482
Prior to renewal= 0.00482
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Mortality deterioration 101• With some algebra
• Mortality deterioration = 232 % !!!
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Mortality deterioration 101• Examples under different scenarios
Total Lapse Underlying AdditionalLapse
Proportion ofselective lapse
Deterioration
70% 5% 65% 60% 154%
70% 5% 65% 90% 181%
70% 5% 65% 100% 190%
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Mortality deterioration 101• If all policyholders were acting rationally
• Renewal premium: T10 Mns, 250k, residual class, Issued in2004
• Newly-issued: T10 Mns , 250k, residual class, Lifeguide, issued in2014
200%
210%
220%
230%
240%
250%
260%
270%
280%
290%
300%
40 45 50 55 60
Rene
wal
/ In
itial
Issue Age
Renewal premium versus a newly-issued T10
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Looking Forward:Term Insurance in
CanadaMark Andrews
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Challenges for Direct Writers• Though we can make educated guesses, we can’t
be sure of what the future holds in terms of:• Lapses• Mortality• Techniques for predicting the above• Competitor Actions• Reinsurer Actions• Capital Requirements
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Challenges for Direct Writers• We know significantly more about managing this
risk than we did even a few short years ago:• Premium increases at renewal can be a valuable input
in predicting lapse rates (and anti-selection).• Increases are materially higher today than what our
experience is based on.
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What Can We Do?• Changing the Product Design?
• Changing the nature of premiums after the initial levelterm?
• Changing the nature of writing business?• Simplified Issue Term products introduced in 2015.
(Up to $500k of coverage).• Direct to consumer products (could change behaviour
landscape).
• Changing Reinsurance?• New solutions for managing lapse and mortality risk?
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Questions?