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APRA’s GI Capital Requirements: Prescribed Method v Internal Model Christian Sutherland-Wong Actuarial Studies Faculty of Commerce and Economics University of NSW Email: [email protected] Actuarial Studies Symposium, UNSW 14th 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 Results Internal Model 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 Inflation DFA Simulation Insurance Model 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 DFA Output 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 Minimum Capital Requirement (MCR) IMB Met hod Prophet MCR + Adjust ment for Credit Risk TOTAL Prescribed Met hod TOTAL 233,323 Std Error IMB Probability H0: IMB Method MCR = Prescribed Method MCR HA: IMB Method MCR ≠ Prescribed Method MCR Original Scenario $'000 309,396 28,705 338,101 10,912 0.000 Results (cont’d) 99.5th Percentile ± 2 Standard Errors Results (cont’d) IMB v Prescribed: Short & Long Tail split IMB v Prescribed Capital Allocations 80% 70% % Allocated 60% IMB Prescribed 50% 40% 30% 20% 10% 0% Short Tail Long Tail Small difference between IMB and Prescribed Method Results (cont’d) IMB v Prescribed: Business line split Short Tail Allocations Long Tail Allocations 100% % Of Short Tail Allocated Home 80% 70% 60% 50% Home 40% Motor 30% 20% 10% Motor 80% 60% CTP IMB Method Prescribed Method 20% Public Liability Public Liability IMB Method Prescribed Method Significant differences by business line CTP 40% 0% 0% % Long Tail Allocated 100% 90% Household > Motor under IMB Method CTP > Public Liability under IMB Method Results (cont’d) Scenario Results Comparisons for All Scenarios IMB Met hod Prophet Credit Risk TOTAL Invest ment Risk Prescribed Credit Risk Met hod OSC Liabilit y Premium Liabilit y Concent rat ion Risk TOTAL Std Error IMB Probability Original Scenario $'000 309,396 28,705 338,101 Trowbridge CVs $'000 94,586 28,705 123,291 80% Equities $'000 370,414 28,705 399,119 Short T ail Only $'000 209,196 10,745 219,941 Long T ail Only $'000 228,828 12,513 241,341 Small Insurer $'000 139,951 5,577 145,528 36,391 28,705 91,290 61,641 15,000 233,027 36,391 28,705 88,237 59,415 15,000 227,749 85,366 28,705 91,290 61,641 15,000 282,001 9,157 10,745 7,890 30,885 15,000 73,677 22,656 12,513 80,999 23,789 0 139,956 9,098 5,577 28,808 15,876 15,000 74,359 10,912 0.000 3,469 0.000 13,517 0.000 5,221 0.000 9,056 0.000 5,413 0.000 H0: IMB Method MCR = Prescribed Method MCR HA: 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 % of Original 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% IMB Prescribed 71% 65% 60% 43% 32% Scenario 32% 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