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Marginalizing theCost of Capital

Daniel Isaac, FCASNathan Babcock, ACAS

Washington, D.C.July 28-30, 2003

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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

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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?

• 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

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Why Do We Allocate?

Number of Policies

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Number of Policies

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% =

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/ C

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Number of Policies

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Number of Policies

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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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One “Little” Problem

• Fixed Cost of Capital => Maximize Return

• No Reinsurance

• All Equities

• Nothing like Actual Companies

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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

• 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

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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

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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 #1

• Based on DFAIC

- Company “created” for 2001 CAS Spring Forum

- See “DFAIC Insurance Company Case Study, Parts I and II” for more details

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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

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Practical Example #1: Asset-Only Efficient Frontier

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

cash us US Stock Corp 1-5 Corp 5-10 Corp 10-30

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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

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Practical Example #1: 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 #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

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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

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Practical Example #1: Key Insights

• Marginal cost is positive

- Better than traditional approach

- Still not increasing

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Practical Example #1: Key Insights

0.0%

0.1%

0.2%

0.3%

0.4%

0.5%

0.6%

0.7%

0.8%

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

Business Growth Strategy

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of

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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

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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

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Practical Example #2

-50,000

0

50,000

100,000

150,000

200,000

250,000

300,000

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

Business Growth Strategy

Reg

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tory

Co

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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

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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%

2.5%

3.0%

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

Business Growth Strategy

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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

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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

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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

• 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

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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

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Discussion

• Why bother?

• Very complicated

• Difficult to explain

• Sensitive to poorly understood parameters

•e.g. nature and impact of regulatory costs

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Discussion: Regulatory Cost Impact

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

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

Business Growth Strategy

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Original Restrictions Tighter Restrictions

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Discussion

• Three main benefits

• Reflects future prospects

• Directly links cost of capital to projected economics

• Nature of capital is becoming more complicated

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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

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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”

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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

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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

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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

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Discussion: Contingent Capital

• How much does this “capital” cost?

• Initial commitment fee

• Impact of dilution

• Benefit of ability to write more business

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Discussion: Contingent Capital

• Proposed method’s approach

• Directly model impact of buying cover

• Calculate cost of capital on net results

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Discussion: Contingent Capital

-200,000

-150,000

-100,000

-50,000

0

50,000

100,000

150,000

200,000

250,000

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

act

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A

Commitment Fee Extra Business Dilution Cost of Capital

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Discussion: Contingent Capital

-40,000

-20,000

0

20,000

40,000

60,000

80,000

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

Ch

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Discussion: Contingent Capital

• These results can be compared to other methods of raising capital

• Consider:

• $1 Billion of traditional capital raised

• Same 33% dilution

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Discussion: Contingent Capital

-200,000

-150,000

-100,000

-50,000

0

50,000

100,000

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

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Contingent Capital Impact Regular Capital Impact

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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