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CONN ING
Marginalizing theCost of Capital
Daniel Isaac, FCASNathan Babcock, ACAS
Washington, D.C.July 28-30, 2003
2CONN ING
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
3CONN 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”
4CONN ING
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
5CONN 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
6CONN 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
7CONN ING
One “Little” Problem
• Fixed Cost of Capital => Maximize Return
• No Reinsurance
• All Equities
• Nothing like Actual Companies
8CONN ING
How Do We Address This
• Strategy-Specific Cost of Capital
• Regulatory Costs
9CONN 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)
10
CONN ING
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
11
CONN ING
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
12
CONN 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
13
CONN ING
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
14
CONN ING
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
15
CONN ING
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
16
CONN ING
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
Sta
nd
ard
De
via
tio
n
17
CONN ING
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
18
CONN ING
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
19
CONN ING
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
20
CONN ING
Practical Example #1: Key Insights
• Marginal cost is positive
- Better than traditional approach
- Still not increasing
21
CONN ING
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
Ma
rgin
al
Co
st a
s %
of
Wri
tten
Pre
miu
m
22
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
23
CONN ING
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
24
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
25
CONN ING
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
26
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
27
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
28
CONN ING
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
29
CONN ING
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
30
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
31
CONN ING
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
32
CONN ING
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
33
CONN ING
Discussion
• Why bother?
• Very complicated
• Difficult to explain
• Sensitive to poorly understood parameters
•e.g. nature and impact of regulatory costs
34
CONN ING
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
Ma
rgin
al
Co
st a
s %
of
Wri
tten
Pre
miu
m
Original Restrictions Tighter Restrictions
35
CONN ING
Discussion
• Three main benefits
• Reflects future prospects
• Directly links cost of capital to projected economics
• Nature of capital is becoming more complicated
36
CONN ING
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
37
CONN ING
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”
38
CONN ING
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
39
CONN ING
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
40
CONN ING
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
41
CONN ING
Discussion: Contingent Capital
• How much does this “capital” cost?
• Initial commitment fee
• Impact of dilution
• Benefit of ability to write more business
42
CONN ING
Discussion: Contingent Capital
• Proposed method’s approach
• Directly model impact of buying cover
• Calculate cost of capital on net results
43
CONN ING
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
on
EV
A
Commitment Fee Extra Business Dilution Cost of Capital
44
CONN ING
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
an
ge
in E
VA
45
CONN ING
Discussion: Contingent Capital
• These results can be compared to other methods of raising capital
• Consider:
• $1 Billion of traditional capital raised
• Same 33% dilution
46
CONN ING
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%
Ch
an
ge
in E
VA
Contingent Capital Impact Regular Capital Impact
47
CONN ING
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