Transcript Canadian Institute of Actuaries L’Institut canadien des

Canadian
Institute
of
Actuaries
L’Institut
canadien
des
actuaires
2008 Annual Meeting ● Assemblée annuelle 2008
Québec
PD-11 Group Capital
requirements
2008 Annual Meeting
Assemblée annuelle 2008
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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
Changes to approximations
for Mortality MCCSR –
Daniel Mayost – OSFI
Mortality Requirement
2008 Annual Meeting
Assemblée annuelle 2008
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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
Approximations
2008 Annual Meeting
Assemblée annuelle 2008
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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
Method 1
2008 Annual Meeting
Assemblée annuelle 2008
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Best approximation:
A 
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C 

b2
F
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
Method 2
2008 Annual Meeting
Assemblée annuelle 2008
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Comparison method:
Ac  N c
F C
A
 C  max  , 
Cc
n N
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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
Method 3
2008 Annual Meeting
Assemblée annuelle 2008
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Worst-case approximations:
A
C  bmin  bmax
A 
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bmin  bmax

bavg
C  b max
Intended as a last resort when minimal
data is available
Certificate Volatility Approximation
2008 Annual Meeting
Assemblée annuelle 2008
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Industry-wide factor under discussion with
the CIA
Constant factor would replace A  N C in
comparison set method
c
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c
Current estimates lie between 1.5 and 2
May be used only for traditional group
business
Possible phase-out on January 1, 2012
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Companies should ideally collect data on
certificate amounts as this is a fundamental
driver of volatility
c
Policyholder Deposits
2008 Annual Meeting
Assemblée annuelle 2008
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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)
Morbidity Requirement
2008 Annual Meeting
Assemblée annuelle 2008
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Treatment of policyholder deposits and
CFRs to be updated to be consistent with
treatment in mortality requirement
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Implies that credit will be based on marginal
requirement calculated post-SFF, not pre-SFF as
currently
New formula for SFF?
SFF  0.7 
900
, when M  $9,000,000
M
M = basic morbidity requirement before
unregistered reinsurance, policyholder
deposits, and CFRs
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
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High frequency of claims
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Low variation in claim size
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As a result, high credibility of past experience
Risk of catastrophe? Very low - Impossible!!
Estimation of risk using claims
experience
• 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)
Claim frequency- claims under $2000
14%
12%
10%
8%
6%
4%
2%
0%
$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)
Claim frequency- amounts in excess of $2000
2.5%
2.0%
1.5%
1.0%
0.5%
0.0%
$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
experience
• 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?