APRA’s GI Capital Requirements: Prescribed Method v Internal Model Christian Sutherland-Wong Actuarial Studies Faculty of Commerce and Economics University of NSW Actuarial Studies Symposium, UNSW 14 th November, 2003

Purpose of Study APRA recently introduced two methods to calculate MCR  Prescribed Method  Internal Model Based (IMB) Method Aim is to analyse the implications for two key stakeholders  Insurers  APRA

Contents Background Data & Methodology  Internal Model Results  Implications Further Work

Background APRA recently updated their GI Prudential Standards External Developments  Basel II  IAA Insurer Solvency Working Party  NAIC, FSA, Canada Calculating the MCR  Prescribed Method  IMB Method

Data & Methodology Data Sources  APRA’s June 2002 GI statistics  Tillinghast and Trowbridge Risk Margins  Allianz, Promina, IAG Methodology  Model Insurer 5 Business Lines – Domestic Motor, Household, Fire & ISR, Public Liability and CTP Large, mature portfolio – 10% market share Industry Investment Mix  6000 simulations  Compare capital requirements

Data & Methodology (cont’d) Methodology  Scenario Analysis Different Volatility Assumptions Riskier Investment Portfolio Short Tail only and Long Tail only Smaller business size

Internal Model Prophet DFA model used Economic Model – The Smith Model (TSM) Insurance Model  3 Claims Processes Attritional Claims, Large Claims, Catastrophe Claims  Superimposed Inflation – Two state Model  Reinsurance – Individual XoL and Catastrophe XoL Economic Model Insurance Model DFA Simulation DFA Output Inflation

Internal Model (cont’d) Assumptions  Expected Claims (incl. expenses and reins. costs) Set to provide a 15% after-tax return on capital (capital = 1.5x Prescribed MCR)  Claims Volatility – Tillinghast report  Reinsurance – Maximum Event Retention (MER) set to $15M

Results MCR calculated under IMB Method > MCR calculated under Prescribed Method H 0 : IMB Method MCR = Prescribed Method MCR H A : IMB Method MCR ≠ Prescribed Method MCR

Results (cont’d)

IMB v Prescribed: Short & Long Tail split Small difference between IMB and Prescribed Method IMB v Prescribed Capital Allocations 0% 10% 20% 30% 40% 50% 60% 70% 80% Short TailLong Tail % Allocated IMB Prescribed

Results (cont’d) IMB v Prescribed: Business line split Significant differences by business line  Household > Motor under IMB Method  CTP > Public Liability under IMB Method Short Tail Allocations Motor Home 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% IMB MethodPrescribed Method % Of Short Tail Allocated Long Tail Allocations CTP Public Liability Public Liability 0% 20% 40% 60% 80% 100% IMB MethodPrescribed Method % Long Tail Allocated

Results (cont’d) Scenario Results H 0 : IMB Method MCR = Prescribed Method MCR H A : IMB Method MCR ≠ Prescribed Method MCR

Results (cont’d) Scenario Results  Trowbridge scenario: IMB << Prescribed  Riskier Asset Mix: Greater increase under IMB ($61.0M v $49.0M)  Other scenarios: MCR as % of Original 43% 71% 65% 60% 32% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Original Scenario Short Tail Only Long Tail Only Small Insurer Scenario % of Original IMB Prescribed

Implications Dependence on outcome on volatility assumptions  Insurers will choose different methods depending on volatility assumed  Need for greater agreement in the industry Prescribed Method not necessarily conservative  Even if we believe Trowbridge report, the Tillinghast CVs will be representative of some insurers  APRA may need to address business line capital charges Increase CVs for household or CTP Include diversification discounts, concentration charges or charges by business size

Implications (cont’d) Inadequacy of investment risk charge  Increase charges for risky asset classes (equities)  Include diversification discounts or concentration charges Lack of an incentive to use the internal model  Lower MCR under Prescribed Method  “Black-box” stigma  Trust in method from financial analysts

Further Work Results in this study are preliminary and highly dependent on assumption that the MCR calculated by the internal model reflects the actual MCR Further research:  Consensus on CVs  Different dependence models eg Copulas  Different internal model calibrations