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

2. 1 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. 2 Why Do We Allocate?

4. 3 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. 4 How Do We Address This Strategy Specific Cost of Capital Regulatory Costs

6. 5 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. 6 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. 7 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. 8 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. 9 Practical Example: Results

11. 1010 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  “loan” proceeds *Losses and expenses  repayments -Economic theory suggests increased borrowing leads to increased hurdle rates

12. 1 Practical Example: Key Insights Marginal cost is positive -Better than traditional approach -Still not increasing

13. 1212 Practical Example: Key Insights

14. 1313 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. 1414 Practical Example #2

16. 1515 Practical Example #2: Key Insights No impact on lowest levels of business Slight “benefit” at interim levels -Low probability  extremely bad results -Serial correlation of results  lost business was unprofitable

17. 1616 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. 1717 Practical Example #2: Key Insights

19. 1818 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. 1919 Practical Example #3: Results

21. 2020 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. 2121 Methodology Concerns VERY complex Sensitivity to Assumptions -Projection Horizon -Economic Sensitivity of Liabilities -Regulatory Costs

23. 2 Methodology Concerns

24. 2323 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. 2424 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