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

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

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

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 2005 +12 quarters ending Sep 2008 Assemblée annuelle 2007 2007 Annual Meeting

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

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

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

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

AD&D MCCSR Current Volatility Assemblée annuelle 2007 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

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

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

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

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.

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

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.

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

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 evaluated from comparison SET

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

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

Current ER Surplus Credits Does it properly reflect reduction in 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

Your Input? Assemblée annuelle 2007 2007 Annual Meeting

Detail of Proposed Formula Derivations Appendix Assemblée annuelle 2007 2007 Annual Meeting Detail of Proposed Formula Derivations

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

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

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

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 evaluated from comparison SET