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Marginalizing theCost of Capital

Daniel Isaac, FCASNathan Babcock, ACAS

Bowles SymposiumApril 10-11, 2003

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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”

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Why Do We Allocate?

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Average Marginal

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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

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How Do We Address This

• Strategy Specific Cost of Capital

• Regulatory Costs

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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)

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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

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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

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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

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Practical Example: Results

7.0%

7.2%

7.4%

7.6%

7.8%

8.0%

8.2%

8.4%

8.6%

8.8%

9.0%

0% 25% 50% 75% Baseline 125% 150% 175% 200% 250% 300%Business Growth Strategy

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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

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Practical Example: Key Insights

• Marginal cost is positive

- Better than traditional approach

- Still not increasing

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Practical Example: Key Insights

0.0%

0.1%

0.2%

0.3%

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0.6%

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0.8%

0% 25% 50% 75% Baseline 125% 150% 175% 200% 250% 300%

Business Growth Strategy

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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

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Practical Example #2

-50,000

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0% 25% 50% 75% Baseline 125% 150% 175% 200% 250% 300%

Business Growth Strategy

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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

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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

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Practical Example #2: Key Insights

0.0%

0.5%

1.0%

1.5%

2.0%

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0% 25% 50% 75% Baseline 125% 150% 175% 200% 250% 300%

Business Growth Strategy

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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

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Practical Example #3: Results

0.34% 0.35%

0.82%

0.43%

0.29%

-0.07%-0.11%

-0.07%

0.01%

0.06%

-0.01%-0.04%

-0.20%

0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

125% Comp Auto Property GL All Other

Business Growth Strategy

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Cost of Capital Regulatory Costs

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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

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Methodology Concerns

• VERY complex

• Sensitivity to Assumptions

- Projection Horizon

- Economic Sensitivity of Liabilities

- Regulatory Costs

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Methodology Concerns

0.0%

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1.0%

1.5%

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0% 25% 50% 75% Baseline 125% 150% 175% 200% 250% 300%

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Original Restrictions Tighter Restrictions

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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

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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