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CASUALTY LOSS RESERVE SEMINAR CAPITAL MODELS AND THEIR RELATIONSHIP WITH LOSS RESERVING Matthew C. Mosher Managing Actuary September 28, 1998 1998 Meeting.

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Presentation on theme: "CASUALTY LOSS RESERVE SEMINAR CAPITAL MODELS AND THEIR RELATIONSHIP WITH LOSS RESERVING Matthew C. Mosher Managing Actuary September 28, 1998 1998 Meeting."— Presentation transcript:

1 CASUALTY LOSS RESERVE SEMINAR CAPITAL MODELS AND THEIR RELATIONSHIP WITH LOSS RESERVING Matthew C. Mosher Managing Actuary September 28, Meeting

2 DISCUSSION OUTLINE l Background l Areas of Capital Charges l Areas Impacted by Reserves l Examples of Various Impacts

3 B1 - Fixed Income B2 - Equity Securities B3 - Interest Rate Capital B4 - Credit Capital B5 - Reserve Capital B6 - NPW Capital B7 - Business Risk Capital OVERVIEW OF COMPONENTS

4 CALCULATION OF NET REQUIRED CAPITAL (NRC) l NRC= B1 2 +B2 2 +B3 2 +(.5xB4) 2 +(.5xB4+B5) 2 +B6 2 + B7 l Similar to RBC Covariance Calculation

5 CAPITAL ADEQUACY WITHIN BEST'S RATING ANALYSIS l Company BCAR Score = Company Baseline Score Composite Baseline Score l Company Baseline Score = APHS / NRC ã APHS = Adjusted Policyholder Surplus ã NRC = Net Required Capital

6 AREAS IMPACTED BY RESERVES l Reserve Charge (B5) l Surplus Adjustment l Credit Charge (B4) l Premium harge (B6)

7 RESERVE RISK CHARGE l Carried Reserves ä Adjusted for Adequacy ä Adjusted to Present Value l Industry Capital Factors based on Risk ä Adjusted for Company Size ä Adjusted for Company Reserve Stability l Growth Charge

8 RESERVE RISK CHARGE CALCULATION Adjusted ReservesCapital Factor 1) Reserves 1,955,8041) Industry Baseline Factor ) Size Adjustment0.76 2) Deficiency 0.943) Company Stability ) Discount ) Adjustment 0.844) Company Capital Factor0.25 5) Adj Res 1,647,024 Reserve Risk Charge 404,307 Growth Charge x 1.00 Reserve Risk Charge 404,307

9 NET WRITTEN PREMIUM CHARGE l Industry Capital Factors based on Risk ä Adjusted for Company Size ä Adjusted for Company’s Premium Adequacy l Growth Charge

10 Net Written Premium639,747 1) Industry Baseline Factor0.36 2) Size Adjustment0.82 3) Company Premium Adequacy Factor0.98 4) Company Capital Factor0.29 Premium Risk Charge186,151 Growth Charge 1.00 Premium Risk Charge 186,151 NET WRITTEN PREMIUM CHARGE CALCULATION

11 SAMPLE CALCULATION B1 = 21,703 B2 = 65,218 B3 = 16,969 B4 = 56,184 B5 = 404,307 B6 = 186,151 B7 = 647 Gross = 751,180 Net = 477,536 APHS = 800,000 Company Baseline = 800, ,536 Company BCAR =

12 ADJUSTED RESERVE RISK CHARGE Adjusted ReservesCapital Factor 1) Reserves 1,955,8041) Industry Baseline Factor ) Size Adjustment0.76 2) Deficiency 1.003) Company Stability ) Discount ) Adjustment 0.904) Company Capital Factor0.25 5) Adj Res 1,760,224 Reserve Risk Charge 440,056 Growth Charge x 1.00 Reserve Risk Charge 440,056

13 ADJUSTED FOR RESERVE ADEQUACY Baseline B1 = 21,703 B2 = 65,218 B3 = 16,969 B4 = 56,184 B5 = 404,307 B6 = 186,151 B7 = 647 Gross = 751,180 Net = 477,536 APHS = 800,000 Adjusted B1 = 21,703 B2 = 65,218 B3 = 16,969 B4 = 56,184 B5 = 440,056 B6 = 186,151 B7 = 647 Gross = 786,928 Net = 510,173 APHS = 686,800

14 ADJUSTED FOR RESERVE ADEQUACY Company Baseline = 800, ,536 Company BCAR = Company Adjusted = 686, ,173 Company BCAR 84.4 =

15 Net Written Premium639,747 1) Industry Baseline Factor0.36 2) Size Adjustment0.82 3) Company Premium Adequacy Factor0.89 4) Company Capital Factor0.26 Premium Risk Charge166,334 Growth Charge 1.00 Premium Risk Charge166,334 ADJUSTED NET WRITTEN PREMIUM CHARGE

16 ADJUSTED FOR PREMIUM CHARGE Baseline B1 = 21,703 B2 = 65,218 B3 = 16,969 B4 = 56,184 B5 = 404,307 B6 = 186,151 B7 = 647 Gross = 751,180 Net = 477,536 APHS = 800,000 Adjusted B1 = 21,703 B2 = 65,218 B3 = 16,969 B4 = 56,184 B5 = 404,307 B6 = 166,334 B7 = 647 Gross = 731,362 Net = 470,155 APHS = 800,000

17 ADJUSTED FOR PREMIUM CHARGE Company Baseline = 800, ,536 Company BCAR = Company Adjusted = 800, ,155 Company BCAR =

18 ADJUSTED FOR EQUITY CHARGE Baseline B1 = 21,703 B2 = 65,218 B3 = 16,969 B4 = 56,184 B5 = 404,307 B6 = 186,151 B7 = 647 Gross = 751,180 Net = 477,536 APHS = 800,000 Adjusted B1 = 21,703 B2 = 215,218 B3 = 16,969 B4 = 56,184 B5 = 404,307 B6 = 186,151 B7 = 647 Gross = 901,362 Net = 519,769 APHS = 800,000

19 ADJUSTED FOR EQUITY CHARGE Company Baseline = 800, ,536 Company BCAR = Company Adjusted = 800, ,769 Company BCAR 96.6 =


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