marginalizing the cost of capital daniel isaac, fcas nathan babcock, acas bowles symposium april...
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CONN ING
Marginalizing theCost of Capital
Daniel Isaac, FCASNathan Babcock, ACAS
Bowles SymposiumApril 10-11, 2003
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2CONN ING
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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3CONN ING
Why Do We Allocate?
Number of Policies
Av
era
ge
Ca
pit
al
per
Po
licy
Number of Policies
Av
era
ge
Hu
rdle
Ra
te (
% =
Ret
urn
/ C
ap
ita
l)
Number of Policies
Av
era
ge
Lo
ss a
nd
Ex
pen
se p
er P
oli
cy
Number of Policies
Co
st p
er P
oli
cy (
Co
st o
f C
ap
ita
l +
Lo
ss a
nd
Ex
pen
se)
Average Marginal
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4CONN ING
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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5CONN ING
How Do We Address This
• Strategy Specific Cost of Capital
• Regulatory Costs
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6CONN ING
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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7CONN ING
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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8CONN ING
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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9CONN ING
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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10
CONN ING
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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11
CONN ING
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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CONN ING
Practical Example: Key Insights
• Marginal cost is positive
- Better than traditional approach
- Still not increasing
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CONN ING
Practical Example: 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
Ma
rgin
al
Co
st a
s %
of
Wri
tten
Pre
miu
m
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14
CONN ING
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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CONN ING
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
ula
tory
Co
st
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CONN ING
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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CONN ING
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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CONN ING
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
Ma
rgin
al
Co
st a
s %
of
Wri
tten
Pre
miu
m
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19
CONN ING
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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20
CONN ING
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
Ma
rgin
al
Co
st a
s %
of
Wri
tten
Pre
miu
m
Cost of Capital Regulatory Costs
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CONN ING
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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22
CONN ING
Methodology Concerns
• VERY complex
• Sensitivity to Assumptions
- Projection Horizon
- Economic Sensitivity of Liabilities
- Regulatory Costs
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23
CONN ING
Methodology Concerns
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
Ma
rgin
al
Co
st a
s %
of
Wri
tten
Pre
miu
m
Original Restrictions Tighter Restrictions
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CONN ING
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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25
CONN ING
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