marginalizing the cost of capital daniel isaac, fcas nathan babcock, acas washington, d.c
DESCRIPTION
Marginalizing the Cost of Capital Daniel Isaac, FCAS Nathan Babcock, ACAS Washington, D.C. July 28-30, 2003. Background. Based on the paper “Marginalizing the Cost of Capital” presented at the Bowles Symposium Available at the CAS website at: - PowerPoint PPT PresentationTRANSCRIPT
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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
Ave
rage
Cap
ital p
er P
olic
y
Number of Policies
Ave
rage
Hur
dle
Rat
e (%
= R
etur
n / C
apita
l)
Number of Policies
Ave
rage
Los
s and
Exp
ense
per
Pol
icy
Number of Policies
Cos
t per
Pol
icy
(Cos
t of C
apita
l + L
oss a
nd E
xpen
se)
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)
10
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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
11
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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
12
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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
13
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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
14
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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
15
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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
16
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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
Stan
dard
Dev
iatio
n
17
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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
18
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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
20
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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
Mar
gina
l Cos
t as %
of W
ritt
en P
rem
ium
22
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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
23
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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
24
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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
ulat
ory
Cos
t
25
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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
Mar
gina
l Cos
t as %
of W
ritt
en P
rem
ium
28
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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
Mar
gina
l Cos
t as %
of W
ritt
en P
rem
ium
Cost of Capital Regulatory Costs
31
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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
33
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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
Mar
gina
l Cos
t as %
of W
ritt
en P
rem
ium
Original Restrictions Tighter Restrictions
35
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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
37
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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
41
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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
42
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Discussion: Contingent Capital
• Proposed method’s approach
• Directly model impact of buying cover
• Calculate cost of capital on net results
43
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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%Impa
ct o
n E
VA
Commitment Fee Extra Business Dilution Cost of Capital
44
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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%
Cha
nge
in E
VA
45
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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
46
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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%
Cha
nge
in E
VA
Contingent Capital Impact Regular Capital Impact
47
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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