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Capital Allocation with a DFA Model

This guide explores the purpose of capital allocation in insurance operations, different methods for allocating capital, and provides an example of using a DFA model. It also covers assumptions that the DFA model reflects, such as historical experience, market conditions, pricing adequacy, and growth rate by line of business.

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Capital Allocation with a DFA Model

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  1. Capital Allocation with a DFA Model Kevin J. Olsen, FCAS, ASA, MAAA GuideOne Insurance March 9/10, 2000

  2. Outline • Purpose of Capital • Methods to Allocate • Example of one method • Summary

  3. Assumptions DFA model already reflects • Company’s historical experience • Current Market Conditions • Current pricing adequacy • Growth rate by line of business • Reinsurance that will be in place

  4. What is the Purpose of Capital? To support insurance operations • To ensure the company is able to cover current and future liabilities. To support other activities

  5. Capital is necessary to account for variation • Cover adverse development on reserves • Unexpected events or variations from the norm. • Cover expenses or losses in bad years

  6. How should the Capital be allocated to line of business to cover the capital needs?

  7. Methods Before DFA Models • Proportional to Carried Reserves • Proportional to Premium • Based on Premium to Surplus Ratios and rules of thumb • Relative to Duration

  8. Allocate Capital based on the standard deviation of [ Net Operating Gain / Net Written Premium ] by line of business over many iterations of a DFA Model

  9. Why use [Net Oper. Gain / NWP]? • Captures the variability • Includes Calendar Year development on Reserves • Includes Incurred Losses and premium for that Calendar Year • Incorporates Reinsurance

  10. Why divide by Net WP? Puts all lines of business on a comparable base • Net Operating Gain per $ of Net WP • Otherwise, within the company larger lines of business would look more variable

  11. Std. Deviation of [Net Oper Gain / NWP] Expected 2000 2001 2002 2003 2004 Value Home 0.4532 2.2769 0.6970 0.6594 0.4550 0.9083 P Auto Liab 0.1574 0.1235 0.1461 0.1395 0.1536 0.1440 P A Phys Dam 0.1199 0.9526 0.2524 0.2326 0.1184 0.3352 C Auto Liab 1.3752 1.4673 1.6137 1.6697 1.7350 1.5722 C A Phys Dam 0.4705 2.3967 0.7265 0.6892 0.5526 0.9671 CPP Liab 0.0575 0.0646 0.1012 0.0772 0.0841 0.0769 CPP Prop 0.5931 4.5416 1.1913 1.0898 0.5455 1.5923 Other Liab 0.1688 0.2055 0.2183 0.2339 0.2391 0.2131 Umbrella 0.8574 0.9288 1.1948 1.2197 1.3292 1.1060 Workers Comp 0.1308 0.1456 0.1748 0.1856 0.2019 0.1677 Enterprise 0.1544 1.1122 0.2955 0.2666 0.1367 0.3931 * Expected Value is the average across the years

  12. Credibility Can credibility weight • Across the 5 years as points • Through multiple runs using the first year • A combination between the two

  13. Expected Cred. Wtd. Value CredibilityStd Deviations Relativity Home 0.9083 0.7691 0.8621 2.1932 P Auto Liab 0.1440 0.9999 0.1441 0.3665 P A Phys Dam 0.3352 0.9418 0.3569 0.9079 P Auto Liab 1.5722 0.9891 1.5628 3.9757 C A Phys Dam 0.9671 0.7541 0.9035 2.2985 CPP Liab 0.0769 0.9999 0.0770 0.1959 CPP Prop 1.5923 0.4155 1.0756 2.7363 Other Liab 0.2131 0.9996 0.2133 0.5427 Umbrella 1.1060 0.9798 1.0980 2.7933 Workers Comp 0.1677 0.9996 0.1680 0.4273 Enterprise 0.3931 0.3931 1.000

  14. Company • Premium / Surplus ratio = 1.67 • Inverted • Surplus / Premium ratio = 0.60

  15. Surplus- Premium Est. Surplus Relativityto-Prem(000)Surplus Dist (000) (1) * 0.60 (2)*(3) (1) (2) (3) (4) (5) (6) Home 2.1932 1.3133 54,553 71,645 13.0% 65,000 P Auto Liab 0.3665 0.2195 179,204 39,331 7.1% 35,500 P Auto Phys Dam 0.9079 0.5436 164,175 89,252 16.2% 81,000 P Auto Liab 3.9757 2.3807 24,370 58,017 10.5% 52,500 C Auto Phys Dam 2.2985 1.3763 8,872 12,221 2.2% 11,000 CPP Liab 0.1959 0.1173 102,640 12,041 2.2% 11,000 CPP Prop 2.7363 1.6385 137,154 224,728 40.8% 204,000 Other Liab 0.5427 0.3250 15,130 4,917 0.9% 4,500 Umbrella 2.7933 1.6727 631 1,055 0.2% 1,000 Workers Comp 0.4273 0.2559 148,116 37,899 6.9% 34,500 Enterprise 1.000 834,844 551,095 100% 500,000

  16. Resulting P/S Ratios Premium Surplus Premium- (000)(000)-to-Surplus Home 54,553 65,000 0.84 P Auto Liab 179,204 35,500 5.05 P Auto Phys Dam 164,175 81,000 2.03 P Auto Liab 24,370 52,500 0.46 C Auto Phys Dam 8,872 11,000 0.81 CPP Liab 102,640 11,000 9.33 CPP Prop 137,154 204,000 0.67 Other Liab 15,130 4,500 3.36 Umbrella 631 1,000 0.63 Workers Comp 148,116 34,500 4.29 Enterprise 834,844 500,000 1.67

  17. Method Incorporates desired Characteristics • Reserving Risk • Asset Risk • Pricing Risk • Catastrophe Risk

  18. DFA methods surpass others Incorporates • Going - Concern • Company Growth plans • Variability of experience • Catastrophes

  19. Caveats • Each LOB allocation is NOT stand alone • Capital is Allocated as a piece of the whole

  20. Uses • ROE by line of business • Pricing • Acquisition analysis

  21. Summary

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