1. 2007 Annual Meeting ● Assemblée annuelle 2007 Vancouver
Canadian
Institute of
Actuaries
L’Institut canadien
des
actuaires
John Have
Group Life and AD&D MCCSR
IP-18 & IP-27
2007 Annual Meeting ● Assemblée annuelle 2007
Vancouver

2. GL MCCSR - Contents Working Group Previous formulae Current formulae
Some issues
Proposed solutions
ER surplus credits
Your input
Assemblée annuelle 2007
2007 Annual Meeting

3. GL MCCSR – Task Force
Committee on Risk Management and Capital Requirements initiated Work Group to review Group Approximations
Wally Bridel – Munich Re
Daniel Mayost - OSFI
Les Rehbeli – Oliver Wyman (Mercer)
John Have – Have Associates
Assemblée annuelle 2007
2007 Annual Meeting

4. The GL MCCSR Change From .0005 x Insured amount x Stats Fact To
Volatility + Catastrophic Components
where
V(olatility) = 2.5 x Std Dev next yr’s claims
Phase In Period
Dec quarters ending Sep 2008
Assemblée annuelle 2007
2007 Annual Meeting

5. GL MCCSR – Prior Formulae
Active GL
.0005 x Net Insured Amt (guar <=1yr)
(.001 and .002 for longer guar)
AD&D – 30% of GL
WP mortality – above using .002
WP morbidity – new claim and ongoing > morbidity MCCSR
Adjustments
X .15 if hold harmless agreement
reduce ER policy component by surplus
Assemblée annuelle 2007
2007 Annual Meeting

6. GL MCCSR – Prior Formulae
Mortality Component X Stats Factor
1.25 at $1 million
1.00 at $10 million
.60 at $1 billion
Based on total individual / group mortality component
Assemblée annuelle 2007
2007 Annual Meeting

7. GL MCCSR Current Volatility
Volatility for Specfic SET
S = 2.5 x A x B x E / F
A – Std Dev next yr’s exp claims
B – Max(ln(D1),1) of exp claims
- for prem guar period
E – Net amt at risk (Face – Reserve)
F – Face Amt
2.5 is CTE(95%) ≈ Normal Dist 97.5%
+ margin (ie: ongoing risk)
Assemblée annuelle 2007
2007 Annual Meeting

8. GL MCCSR Current Volatility
Assemblée annuelle 2007
2007 Annual Meeting
b - certificate amount
q - certificate mortality rate
If b and q unknown use:
C - next year’s net claims
n – number of lives

9. AD&D MCCSR Current Volatility
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2007 Annual Meeting
E - AD&D net amount
G – GL net amount
If no comparable GL use:
C - next year’s net claims
n – number of lives

10. Combined Volatility
Combined Volatility component for all basic death and AD&D products.
- Both Group and Individual SETs
Assemblée annuelle 2007
2007 Annual Meeting

11. MCCSR Current Catastrophic
Catastrophic Component for each SET
Assemblée annuelle 2007
2007 Annual Meeting
E – net amount at risk
F – face amount
Use .10 if rate guaranteed > 1year

12. MCCSR Current Adjustments X .15 if hold harmless agreement
.05 if Fed or Prov Government
Reduce ER policy component by surplus
to maximum of
Assemblée annuelle 2007
2007 Annual Meeting
E – AP for GL and AD&D for ER policy
G – AP for all GL and AD&D policies

13. MCCSR Approx Issues
Assemblée annuelle 2007
2007 Annual Meeting
Does not scale properly with mortality level since the factor 39 assumes a certain level of mortality. If mortality rate doubles, A should increase by factor of
not 2.

14. Solutions - no Detail q
Assemblée annuelle 2007
2007 Annual Meeting
Set 1 - q ≈ 1 since q is small. Then using avg q we have
then with avg q = C / F

15. Solutions - no Detail q or b
Assemblée annuelle 2007
2007 Annual Meeting
Set 1-q ≈ 1 since q is small.
Since no detail, use average q or average b instead. Then
Where K is factor necessary to increase volatility lost by using averages.

16. Solutions - no Detail q or b
Assemblée annuelle 2007
2007 Annual Meeting
Summing this becomes
With N = nq, C = bnq and F = nb

17. Solutions - no Detail q or b
Assemblée annuelle 2007
2007 Annual Meeting OR
bFace is average insured amount
bClaim is average claim amount
And K is evaluate from camparison SET

18. Solutions - no Detail q or b
Limitation on the use of K:
If number lives exceed comparison set must use intercompany value of K.
Intercompany value of K can be developed by using detailed GL bill data from 5-6 large insurers.
Allowed for both GL and AD&D
Assemblée annuelle 2007
2007 Annual Meeting

19. Approximation Solutions
Assemblée annuelle 2007
2007 Annual Meeting
Proposed Effective Date
Jan 1, 2008

20. Cuurent ER Surplus Credits
Does it properly reflect reduction is capital needs??
John Have:
There are many types of ER formulae using various types of risk sharing methods.
An extra $1 of claim, over expected, is not always offset by $1 from ER surplus.
May need to develop metric to test the sensitivity of an extra, say, 5-10% of claims on an INSURER’s capital.
Assemblée annuelle 2007
2007 Annual Meeting

21. Your Input?
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2007 Annual Meeting

22. Detail Proposed Formula Derivations
Appendix
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2007 Annual Meeting
Detail Proposed Formula Derivations

23. Solutions - no Detail q Set 1 - q ≈ 1 since q is small. Use avg q.
Assemblée annuelle 2007
2007 Annual Meeting
Set 1 - q ≈ 1 since q is small.
Use avg q.

24. Solutions - no Detail q Which gives you Assemblée annuelle 2007
2007 Annual Meeting
Which gives you

25. Solutions - no Detail q or b
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2007 Annual Meeting
Since N = nq and C = bnq
With AC, NC and CC derived from comparison SET

26. Solutions - no Detail q or b
Other term
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2007 Annual Meeting
Can be restated as follows:
Using C = bnq and b = F / n

27. Solutions - no Detail q or b
Other term
Assemblée annuelle 2007
2007 Annual Meeting
Can also be restated as follows:
Using C = bnq and b = C / N

28. Solutions - no Detail q or b
Assemblée annuelle 2007
2007 Annual Meeting OR
BFace is average insured amount
bClaim is average claim amount
And K is evaluate from camparison SET