Marginalizing the
Cost of Capital
Daniel Isaac, FCAS
Nathan Babcock, ACAS
Washington, D.C.
July 28-30, 2003
CON N I N G
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/IsaacBabcock.doc
CON N I N G
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”
CON N I N G
2
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
CON N I N G
3
Cost p e r Polic y (Cost of Cap ital + L oss an d E xp e n se )
A v era g e H u rd l e R a te (% = R etu rn / C a p i ta l )
Ave r age L oss an d E xp e n se p e r Polic y
Ave r age Cap ital p e r Polic y
Why Do We Allocate?
N um ber of Policies
N u m b e r o f P o lic ie s
CON N I N G
N um ber of Policies
N um ber of Policies
A verage
M arginal
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
CON N I N G
5
One “Little” Problem
• Fixed Cost of Capital => Maximize Return
• No Reinsurance
• All Equities
• Nothing like Actual Companies
CON N I N G
6
How Do We Address This
• Strategy-Specific Cost of Capital
• Regulatory Costs
CON N I N G
7
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)
CON N I N G
8
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
CON N I N G
9
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
CON N I N G
1
0
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
CON N I N G
1
1
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
CON N I N G
1
2
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
CON N I N G
1
3
Practical Example #1: Asset-Only Efficient Frontier
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
cash us
CON N I N G
US Stock
Corp 1-5
Corp 5-10
Corp 10-30
1
4
Practical Example #1: Baseline Strategy’s Fit
1,000,000
900,000
Standard Deviation
800,000
700,000
600,000
500,000
400,000
300,000
200,000
100,000
0
Asset Only Efficient Frontier Points
CON N I N G
1
5
Practical Example #1: Results
CON N I N G
1
6
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
CON N I N G
1
7
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
CON N I N G
1
8
Practical Example #1: Key Insights
• Marginal cost is positive
- Better than traditional approach
- Still not increasing
CON N I N G
1
9
Practical Example #1: Key Insights
M ar gin al Cost as % of W r itte n Pr e miu m
0.8%
0.7%
0.6%
0.5%
0.4%
0.3%
0.2%
0.1%
0.0%
0%
25%
50%
75%
B aseline
125%
150%
175%
200%
250%
300%
B usiness G row th Strategy
CON N I N G
2
0
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
CON N I N G
2
1
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
CON N I N G
2
2
Practical Example #2
300,000
250,000
Re gu lator y Cost
200,000
150,000
100,000
50,000
0
0%
25%
50%
75%
B aseline
125%
150%
175%
200%
250%
300%
-50,000
B usiness G row th Strategy
CON N I N G
2
3
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
CON N I N G
2
4
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
CON N I N G
2
5
Practical Example #2: Key Insights
M ar gin al Cost as % of W r itte n Pr e miu m
3.0%
2.5%
2.0%
1.5%
1.0%
0.5%
0.0%
0%
25%
50%
75%
B aseline
125%
150%
175%
200%
250%
300%
B usiness G row th Strategy
CON N I N G
2
6
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
CON N I N G
2
7
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
CON N I N G
2
8
Practical Example #3: Results
M argin al C ost as % of W ritten Prem iu m
1.00%
0.80%
0.60%
0.82%
0.40%
0.01%
0.20%
0.43%
0.34%
0.35%
0.29%
0.06%
0.00%
-0.07%
-0.04%
-0.11%
-0.07%
-0.01%
-0.20%
125%
C om p
A uto
Property
GL
A ll O ther
B usiness G row th Strategy
C ost of C apital
CON N I N G
R egulatory C osts
2
9
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
CON N I N G
3
0
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
CON N I N G
3
1
Discussion
• Why bother?
• Very complicated
• Difficult to explain
• Sensitive to poorly understood parameters
•e.g. nature and impact of regulatory costs
CON N I N G
3
2
Discussion: Regulatory Cost Impact
M ar gin al Cost as % of W r itte n Pr e miu m
3.0%
2.5%
2.0%
1.5%
1.0%
0.5%
0.0%
0%
25%
50%
75%
B aseline
125%
150%
175%
200%
250%
300%
B usiness G row th Strategy
O riginal R estrictions
CON N I N G
T ighter R estrictions
3
3
Discussion
• Three main benefits
• Reflects future prospects
• Directly links cost of capital to projected economics
• Nature of capital is becoming more complicated
CON N I N G
3
4
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
CON N I N G
3
5
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”
CON N I N G
3
6
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
CON N I N G
3
7
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
CON N I N G
3
8
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
CON N I N G
3
9
Discussion: Contingent Capital
• How much does this “capital” cost?
• Initial commitment fee
• Impact of dilution
• Benefit of ability to write more business
CON N I N G
4
0
Discussion: Contingent Capital
• Proposed method’s approach
• Directly model impact of buying cover
• Calculate cost of capital on net results
CON N I N G
4
1
Discussion: Contingent Capital
250,000
200,000
150,000
Impact on EVA
100,000
50,000
0
0%
25%
50%
75%
Baseline 125%
150%
175%
200%
250%
300%
-50,000
-100,000
-150,000
-200,000
Commitment Fee
CON N I N G
Extra Business
Dilution
Cost of Capital
4
2
Discussion: Contingent Capital
80,000
60,000
Change in EVA
40,000
20,000
0
0%
25%
50%
75%
Baseline
125%
150%
175%
200%
250%
300%
-20,000
-40,000
CON N I N G
4
3
Discussion: Contingent Capital
• These results can be compared to other methods of
raising capital
• Consider:
• $1 Billion of traditional capital raised
• Same 33% dilution
CON N I N G
4
4
Discussion: Contingent Capital
100,000
50,000
Change in EVA
0
0%
25%
50%
75%
Baseline 125%
150%
175%
200%
250%
300%
-50,000
-100,000
-150,000
-200,000
Contingent Capital Impact
CON N I N G
Regular Capital Impact
4
5
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
CON N I N G
4
6