Marginalizing the
Cost of Capital
Daniel Isaac, FCAS
Nathan Babcock, ACAS
Bowles Symposium
April 10-11, 2003
CON N I N G
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
1
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
2
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
3
How Do We Address This
• Strategy Specific Cost of Capital
• Regulatory Costs
CON N I N G
4
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
5
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
CON N I N G
6
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
7
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
CON N I N G
8
Practical Example: Results
CON N I N G
9
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
CON N I N G
1
0
Practical Example: Key Insights
• Marginal cost is positive
- Better than traditional approach
- Still not increasing
CON N I N G
1
1
Practical Example: 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
1
2
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
CON N I N G
1
3
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
1
4
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
CON N I N G
1
5
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
1
6
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
1
7
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
CON N I N G
1
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
P roperty
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
1
9
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
CON N I N G
2
0
Methodology Concerns
• VERY complex
• Sensitivity to Assumptions
- Projection Horizon
- Economic Sensitivity of Liabilities
- Regulatory Costs
CON N I N G
2
1
Methodology Concerns
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
2
2
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
CON N I N G
2
3
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
CON N I N G
2
4