1. Marginalizing the Cost of Capital Daniel Isaac, FCAS Nathan Babcock, ACAS Washington, D.C. July 28-30, 2003

2. 1 Background Based on the paper “Marginalizing the Cost of Capital” presented at the Bowles Symposium Available at the CAS website at: www.casact.org/coneduc/specsem/sp2003/papers/Isaac- Babcock.doc

3. 2 Cost of Capital Discussion Most work has focused on “How to Allocate” First, need to answer “Should We Allocate?” Economic theory says the answer should be “No”

4. 3 Why Do We Allocate? Three basic actuarial assumptions Decreasing marginal capital per policy Constant cost of capital per dollar of capital Loss ratio and expense ratio unaffected by volume

5. 4 Why Do We Allocate?

6. 5 One Big Problem Decreasing Marginal Cost  Monopoly Insurance industry is very fragmented Very easy entry -Bermuda CAT companies after Hurricane Andrew -Specialized reinsurers post 9/11

7. 6 One “Little” Problem Fixed Cost of Capital => Maximize Return No Reinsurance All Equities Nothing like Actual Companies

8. 7 How Do We Address This Strategy-Specific Cost of Capital Regulatory Costs

9. 8 Strategy-Specific Cost of Capital “Cost of Capital” is the return forgone by Investors Needs to be related to: -Returns available for other investments -Company’s riskiness -Time horizon Described in “Beyond the Frontier: Using a DFA Model to Derive the Cost of Capital” from the AFIR Colloquim (2001)

10. 9 Strategy-Specific Cost of Capital Proposed Methodology -Determine asset-only efficient frontier -Calculate company’s results for selected strategy -Determine “Best Fit” portfolio -This portfolio gives us the strategy’s hurdle rate

11. 1010 Strategy-Specific Cost of Capital Main problem: Creates a maximum hurdle rate -Hurdle rate can’t exceed highest returning asset -Particularly problematic when strategy involves investing in this asset class

12. 1 Strategy-Specific Cost of Capital Proposed Solution: Allow leverage -Combine investment in benchmark with a long or short position in risk-free asset -Shorting eliminates maximum hurdle rate

13. 1212 Practical Example #1 Based on DFAIC -Company “created” for 2001 CAS Spring Forum -See “DFAIC Insurance Company Case Study, Parts I and II” for more details

14. 1313 Practical Example #1 Consider varying levels of new business -Scaled underwriting results for new business -Scaling ranged from 0% to 300% of baseline -Kept surplus and existing reserves the same

15. 1414 Practical Example #1: Asset-Only Efficient Frontier

16. 1515 Practical Example #1: Baseline Strategy’s Fit 0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000 Asset Only Efficient Frontier Points Standard Deviation

17. 1616 Practical Example #1: Results

18. 1717 Practical Example #1: Key Insights Hurdle rate is positive even with no new business -Investors get paid as long as there is risk -Means timing, not just amount, of Cost of Capital must be considered

19. 1818 Practical Example #1: Key Insights Hurdle rate increases with level of business -New business is like “borrowing” from policyholders *Premium  “loan” proceeds *Losses and expenses  repayments -Economic theory suggests increased borrowing leads to increased hurdle rates

20. 1919 Practical Example #1: Key Insights Marginal cost is positive -Better than traditional approach -Still not increasing

21. 2020 Practical Example #1: Key Insights

22. 2121 Practical Example #2 Economic theory includes the Cost of “Financial Distress” -Direct: Additional costs associated within liquidating company -Indirect: Lost profits due to reduced business -Indirect much bigger problem for insurers

23. 2 Practical Example #2 Revise model to restrict business when capital constrained -Maximum premium to surplus ratio set at 3:1 -If surplus is insufficient, future years’ writings are reduced -Reductions are permanent and cumulative

24. 2323 Practical Example #2

25. 2424 Practical Example #2: Key Insights No impact on lowest levels of business Slight “benefit” at interim levels -Low probability of insufficient capital  extremely bad results -Serial correlation of results  lost business was also unprofitable

26. 2525 Practical Example #2: Key Insights Rapid increase in costs at highest levels -Higher probability -Loss of expected profitability Combining with cost of capital creates more traditional cost curve -Initially decreasing -Increasing at higher levels

27. 2626 Practical Example #2: Key Insights

28. 2727 Practical Example #3 Capital Allocation is NOT typically the end goal Almost always used to ask: “Which is the Cost of Capital for Line X?” Used to measure profitability Help determine which lines to grow/shrink Proposed method skips straight to this answer

29. 2828 Practical Example #3 Ran different levels of new business For each run, scaled one line’s new business so that total premium was at the 125% level Compared marginal costs to marginal premium Only need to focus on marginal impact due to increasing cost curve

30. 2929 Practical Example #3: Results

31. 3030 Practical Example #3: Key Insights Cost of Capital varies between lines High of 0.82% of Premium for Auto down to 0.06% for All Other Based on dynamics of each line: payment pattern, economic sensitivities Unlikely with typical approach given premium to surplus capital constraints

32. 3131 Practical Example #3: Key Insights Regulatory costs also differ by line High of 0.01% for GL down to -0.11% for Auto Not directly related to line’s cost of capital Comp and GL have roughly the same total cost Very different composition: GL has a regulatory cost, Comp has regulatory benefit Likely to lead to relative changes at different business levels General cost shifts more towards regulatory costs at higher levels of business

33. 3232 Discussion Why bother? Very complicated Difficult to explain Sensitive to poorly understood parameters e.g. nature and impact of regulatory costs

34. 3 Discussion: Regulatory Cost Impact

35. 3434 Discussion Three main benefits Reflects future prospects Directly links cost of capital to projected economics Nature of capital is becoming more complicated

36. 3535 Discussion: Main Benefits Reflects future prospects Traditional approach uses historical stock price movements Assumed to reflect future movements May not be appropriate given flexibility to change rapidly e.g. recent exodus from Med Mal Proposed method calibrated to projected results

37. 3636 Discussion: Main Benefits Directly links cost of capital to projected economics Increase in budgeted equity returns increases budgeted cost of capital Not the case with targets like “15% ROE”

38. 3737 Discussion: Main Benefits Nature of capital is becoming more complicated Traditional method assumes well-defined, fixed amount Reality is being much more complex e.g. Contingent Capital

39. 3838 Discussion: Contingent Capital Consider the following cover for DFAIC $5 Million commitment fee per year At end of 5 years, DFAIC can get $1 Billion cash infusion Can only be exercised if: DFAIC is solvent with extra capital DFAIC is still writing business Premium to Surplus Ratio is above 3:1 without extra capital Exercising leads to a 33% dilution

40. 3939 Discussion: Contingent Capital Traditional approach needs to answer two questions: How much capital has been added? $1 Billion - Maximum possible recovery 0 - “Capital” is not available in liquidation scenarios $37 Million - Average infusion ? - Take your pick

41. 4040 Discussion: Contingent Capital How much does this “capital” cost? Initial commitment fee Impact of dilution Benefit of ability to write more business

42. 4141 Discussion: Contingent Capital Proposed method’s approach Directly model impact of buying cover Calculate cost of capital on net results

43. 4242 Discussion: Contingent Capital

44. 4343

45. 4 These results can be compared to other methods of raising capital Consider: $1 Billion of traditional capital raised Same 33% dilution

46. 4545 Discussion: Contingent Capital

47. 4646 Two main differences being played out Impact on rewards With contingent, current owners have more of the upside potential Impact on risk With extra capital, current owners have 2/3 of risk on the same investment Leads to a lower cost of capital Tradeoff leads to differences