Marginalizing the Cost of Capital Daniel Isaac, FCAS Nathan Babcock, ACAS Bowles Symposium

1. Marginalizing the Cost of Capital Daniel Isaac, FCAS Nathan Babcock, ACAS Bowles Symposium April 10-11, 2003

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”

3. Why Do We Allocate?

4. 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

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

6. 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)

7. Strategy Specific Cost of Capital • Initial 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 • 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

8. 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

9. Practical Example • Based on DFAIC • Company “created” for 2001 CAS Spring Forum • See “DFAIC Insurance Company Case Study, Parts I and II” for more details • Consider varying levels of new business • Scaled underwriting results for new business • Scaling ranged from 0% to 300% of baseline • Kept initial surplus and existing reserves the same

10. Practical Example: Results

11. Practical Example: 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 • 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

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

13. Practical Example: Key Insights

14. 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 • Revise model to restrict business when capital is inadequate • Maximum premium to surplus ratio set at 3:1 • If surplus is insufficient, future year’s writings are reduced • Reductions are permanent and cumulative

15. Practical Example #2

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

17. 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

18. Practical Example #2: Key Insights

19. Practical Example #3 • Calculate costs by line • Typical use of Capital Allocation • Only need to look at marginal impact • Result of Economic Theory • Easier than Traditional Approach • For each line: • Scale line’s Premium so that Total Premium is at 125% level • Compare results to Baseline run

20. Practical Example #3: Results

21. Practical Example #3: Key Insights • Very different Costs of Capital • Consistent with Economic Theory • Unlikely with Traditional Approach • Different composition of Total Cost • GL only line with positive Regulatory Cost • Means relative costs are likely to change • Cost of Capital decreases • Regulatory Costs increase

22. Methodology Concerns • VERY complex • Sensitivity to Assumptions • Projection Horizon • Economic Sensitivity of Liabilities • Regulatory Costs

23. Methodology Concerns

24. Key Advantages • Relies on future strategies • Traditional calculation relies on historical stock prices (e.g. CAPM) • Insurance companies can change rapidly • Particularly important since DFA is used to analyze strategy change • Consistency • Increasing asset returns increases lines’ profitability • Offset by increased Cost of Capital

25. Key Advantages • Ability to handle complexity • Traditional model based on: • Fixed capital base • Single source of capital • Reality becoming more complex • “Integrated” reinsurance • Contingent capital