Mark AndrewsDirector, Life Pricing

Sun Life Financial

Looking Back:Term Insurance in Canada

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”)

Term Sales in Canada• Based on recent sales activity, a typical year of

Term sales would look like:

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

Key Turning Point• Around Y2k, Term in Canada migrated from Single

Scale Premiums to Select And Ultimate.

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!

Term 10 Premiums Over the Years

Emile ElefteriadisSwiss Re

SVP Reinsurance Client MarketsExperience Studies

What are “experience studies”?

In a study of 500 people we asked“On a scale of 1-10, how wouldyou rate your experience…”

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

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?

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

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.

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)

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.

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)

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.

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?

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

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

• 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

23

Comprehensive Research,Credible Results

24

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 $

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

26

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

Mortality Experience- CIAIndustry

27

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.

?

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)

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?

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%

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%

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)

Jean-PierreCormier

VP PricingRGA Canada

Term Mortality Models

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

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)

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)

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)

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

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

Mortality deterioration 101• With some algebra

• Mortality deterioration = 232 % !!!

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%

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

Looking Forward:Term Insurance in

CanadaMark Andrews

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

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.

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?

Questions?