2008 Annual Meeting ● Assemblée annuelle 2008 Québec
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Transcript of 2008 Annual Meeting ● Assemblée annuelle 2008 Québec
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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
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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
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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
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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
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Method 3
• Worst-case approximations:
• Intended as a last resort when minimal data is available20
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avg
maxminmaxmin b
bbbbCA
maxbCA
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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
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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
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Morbidity MCCSR – (changes suggested by
Group Committee to Capital Committee)
– David Neaven
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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
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Dental morbidity risks
Risk of misestimating inflation• Fee guide minimizes this risk
Risk of misestimating utilization• Limited supply• Limited demand
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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!!
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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
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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
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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
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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
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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
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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
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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
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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%
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Pricing for a return on capital – Gary Walters
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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
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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?
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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?
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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?
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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
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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
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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?
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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
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Questions for any of us?