Marginalizing the Cost of Capital Daniel Isaac, FCAS Nathan Babcock, ACAS Washington, D.C.

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

2. 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. 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. 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. Why Do We Allocate?

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

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

9. 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. 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. 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. 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. 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. 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. Practical Example #1: Asset-Only Efficient Frontier

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

17. Practical Example #1: Results

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

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

21. Practical Example #1: Key Insights

22. 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. 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. Practical Example #2

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

26. 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. Practical Example #2: Key Insights

28. 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. 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. Practical Example #3: Results

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

34. Discussion: Regulatory Cost Impact

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

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

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

43. Discussion: Contingent Capital

44. Discussion: Contingent Capital

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

46. Discussion: Contingent Capital

47. Discussion: Contingent Capital • 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