2008 Annual Meeting ● Assemblée annuelle 2008

Québec

2008 Annual Meeting ● Assemblée annuelle 2008

Québec

Canadian Institute

of Actuaries

Canadian Institute

of Actuaries

L’Institut canadien desactuaires

L’Institut canadien desactuaires

PD-11 Group Capital requirements

• Changes to approximations for Mortality MCCSR – Daniel Mayost – OSFI

• Morbidity MCCSR – changes suggested by Group Committee to Capital Committee (not yet sent to OSFI) – David Neaven

• Pricing for a return on capital – Gary Walters

• Questions

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Changes to approximations for Mortality MCCSR – Daniel Mayost – OSFI

Mortality Requirement

• Requirement before 2005 used simple factors applied to net amount at risk

• New requirement introduced at year-end 2005, with separate volatility and catastrophe components

• Volatility component is non-linear, and appropriately gives a company credit for diversification across its whole book of business.

• Volatility formula requires seriatim death benefit amounts and mortality rates for the upcoming year

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Approximations• CIA permitted approximations for group (but not

individual) basic death and AD&D business when seriatim data is not available

• Approximation formulas were calibrated to Canadian salary and age data, but do not scale correctly with a group’s own particular mortality rates

• Led to formation of a small CIA working group in 2006 to study improvements

• New approximation formulas for the volatility component to be implemented January 1, 2009

• “39” approximation will be removed and replaced by three new alternatives

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Method 1

• Best approximation:

where C is projected death claims, b’s are certificate amounts, F is total face amount

• Can be used for any set of products (including individual) for which seriatim data is not available, but requires all death benefit amounts

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F

bCA

2

Method 2

• Comparison method:

• Comparison set must be at least as large as the set being approximated

• Intended for small blocks of business, and as a replacement for the current AD&D comparison approximation

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N

C

n

FC

C

NAA

c

cc ,max

Method 3

• Worst-case approximations:

• Intended as a last resort when minimal data is available20

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avg

maxminmaxmin b

bbbbCA

maxbCA

Certificate Volatility Approximation

• Industry-wide factor under discussion with the CIA

• Constant factor would replace in comparison set method

– Current estimates lie between 1.5 and 2

• May be used only for traditional group business

• Possible phase-out on January 1, 2012– Companies should ideally collect data on

certificate amounts as this is a fundamental driver of volatility

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ccc CNA

Policyholder Deposits

• Current formula for maximum credit allocates total marginal requirement for group block to particular policies

• Revised formula will calculate maximum credit based on marginal requirement for the policy

• Maximum credit will be reduced if company cannot recover 100% of excess losses from the deposit (e.g. risk sharing)

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Morbidity Requirement

• Treatment of policyholder deposits and CFRs to be updated to be consistent with treatment in mortality requirement

– Implies that credit will be based on marginal requirement calculated post-SFF, not pre-SFF as currently

• New formula for SFF?

M = basic morbidity requirement before

unregistered reinsurance, policyholder deposits, and CFRs

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$9,000,000when ,900

7.0 MM

SFF

Morbidity MCCSR – (changes suggested by

Group Committee to Capital Committee)

– David Neaven

Letter to CIA Risk and Capital

Committee on Morbidity Requirements • Morbidity risk relates to risk arising from volatility in

claims experience and from events that would lead to increased claims

• Dental least risky – MCCSR should be lowest• EHC more volatile/risky than Dental – MCCSR

should be higher than Dental• LTD risk greater than Dental or EHC – both

incidence and continuing claims risks exist

Dental morbidity risks

Risk of misestimating inflation• Fee guide minimizes this risk

Risk of misestimating utilization• Limited supply• Limited demand

Dental morbidity risks

Risk of misestimating mean• High frequency of claims• Low variation in claim size• As a result, high credibility of past experience

Risk of catastrophe? Very low - Impossible!!

Estimation of risk using claims Estimation of risk using claims experienceexperience

• Obtain distribution of Dental claims using nearly 500,000 claims records

• Develop a distribution of potential claims using claims data and Monte Carlo modeling

Probability density (low end)Probability density (low end)

Claim frequency- claims under $2000

0%

2%

4%

6%

8%

10%

12%

14%

$50 $150 $250 $350 $450 $550 $650 $750 $850 $950 $1,050 $1,150 $1,250 $1,350 $1,450 $1,550 $1,650 $1,750 $1,850 $1,950

Probability density (right tail)Probability density (right tail)

Claim frequency- amounts in excess of $2000

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

$2,125 $2,375 $2,625 $2,875 $3,125 $3,375 $3,625 $3,875 $4,125 $4,375 $4,625 $4,875 $6,175

Estimation of risk using claims Estimation of risk using claims experienceexperience

• Used 95% CTE as benchmark• Estimated required capital much lower than

current formula – about half of existing 12% of gross premium requirement

LTD current requirements

• New Claims risk – 12% of gross premium• Continuing Claims risk varies by duration of

disability and benefit period remaining 8% to 4% of reserve for benefits of greater than 2 years

• Multiply by statistical fluctuation factor

LTD current requirements

• New claims– Gross premium = expense + profit load +

expected cost of claims– Charging 12% on expense and profit load

• Continuing claims – X% of reserve but reserve includes pfads– Larger pfad => larger MCCSR

LTD current requirements

• Continuing claims requirement on a mature block of open claims is about 6% of reserve

• Pfad on a mature block of open claims assuming a mid range margin is about 6% of reserve

• 12% total roughly equivalent to 20% to 25% decrease in expected recoveries forever

– Is this a plausible level? – This is just the 100% MCCSR + Pfad

LTD concept

• LTD reserves calculated at x% of expected terminations

• Propose that a Total Balance Sheet approach be used with total requirement calculated at y% of expected terminations

• y<x<100%

Pricing for a return on capital – Gary Walters

Pricing Challenges

• MCCSR – Macro solvency– Benefits from pooling risks

• Pricing– Allocation of profit by group– Charging for risk represented by group– Level of CFR needed

Pricing each group

• Incremental MCCSR v group’s risk– Capital goes up with more groups– Capital per unit exposure goes down– Group Capital influenced by Individual

and vice-versa– Future capital requirement isn’t known

• Pooled v Refund accounting– To what extent can capital be shared?

MCCSR Diversification

• More diversification means capital can be shared by more than one policy

• MCCSR uses square root of sum of squares

• For example if Group requirement is only 15% of Individual then overall capital is 101% of Individual– Incremental group capital just 1%– Who gets this benefit?

Group Example

• Company has 3 policies needing capital of– 100, 200 and 300 respectively

• Total capital needed is 374 or 38% reduction as a diversification benefit

• However if – Just 100 and 200 then 224 or 25%– Just 100 and 300 then 316 or 21%– Just 200 and 300 then 361 or 28%

• So what diversification benefit can we take in setting a price?

What to price for (1)?

• Policy 2 has a “stand alone risk” of 200

• If allow for existing policy 1 then– Incremental capital is 124– Averaged capital is 150

• If allow for Individual (component of 2500)– Incremental capital is 8– Averaged capital is 179

What to price for (2)?

• Next renewal of policy 2 takes place after policy 3 has been added

• If allow for only group then– Incremental capital is 58 (124*)– Averaged capital is 125 (150*)

• If allow for Individual (component of 2500)– Incremental capital is 7.9 (8*)– Averaged capital is 163 (179*)

*From previous slide

What level of CFR?

• CFR– Available for poor experience on that group

only– Money in CFR can offset capital required that

is not shared with other policies or lines (incremental amount)

• Prior example – Incremental amount only 8 (allowing for

individual) – amount by which MCCSR can be reduced

– Risk is however 200 (allowing no diversification benefit)

• What level of CFR should be targeted?

Conclusion

• MCCSR formula not helpful for pricing– Where should diversification benefit be

allocated– Cannot know future

• MCCSR formula very unhelpful for setting CFR– Offset is only incremental capital– Risk is full capital as no diversification

available

Questions for any of us?