CONNING ASSET MANAGEMENT
Analyzing Reinsurance
with DFA
Practical Examples
Daniel Isaac
Washington, D.C.
July 28-30, 2003
CON N I N G
Key Considerations
 Why are we changing?
- Cost of current program
- Rating agencies
- Regulatory capital
- Change in business mix/philosophy
1
Key Considerations
 How long do we need protection?
- Impacts potential reinsurers
- Impacts types of covers considered
 How long will benefits last?
- Will that change if there is a claim?
2
Key Considerations
 What other changes can we make?
- Asset strategy
- Capital structure
- Business mix
 How do these fit together?
- Mitigate cost
- Enhance benefits
3
General Rules
 Use several different measures
- We prefer Economic Value as primary
 Just considers cash flows
 Eliminates accounting “noise”
- Also evaluate financial metrics
 Statutory Surplus
 GAAP Equity
 RBC Ratio
4
Company Profile
 Name:
Make Believe Inc. (MBI)
 Size:
$150 MM Net Premium
 Growth:
10 - 15% per year
 Mix
60/40 Commercial/Personal
60/40 Liability/Property
 Time Horizon: 5 years
5
MBI Concerns
 Recently went public
- Very concerned about GAAP Income
- Also very concerned about volatility
 Wants to increase equity exposure
- Very conservative asset portfolio
- 98% bonds
- Mostly high quality (A or better) and short-term
- Expect higher returns long-term
6
Option #1
 Buy traditional coverage
- 10 x 70 accident year loss ratio coverage
- 2% of earned premium
- 1 year cover which is annually renewed
 Increase equity allocation
- Consider 10 and 20% allocations
7
Results Option #1
GAAP Income
Year 1
Percentiles
99th
95th
20,000
75th
50th
25th
5th
10,000
1st
0
Current
Option #1
Option #1 + 10% Equity
Option #1 + 20% Equity
-10,000
Mean
Std Dev
7,662
3,988
6,443
3,024
5,668
3,038
4,603
3,081
8
Results Option #1
GAAP Income
Year 5
Percentiles
99th
95th
60,000
75th
50th
40,000
25th
5th
20,000
1st
0
Current
Option #1
Option #1 + 10% Equity
Option #1 + 20% Equity
-20,000
-40,000
-60,000
Mean
Std Dev
16,376
18,489
16,388
13,249
16,012
13,511
15,590
13,918
9
Summary - Option #1
 Reinsurance
- Successfully reduces risk

25% lower standard deviation

less downside
- Negatively impacts income
 Equities
- Further drop in GAAP Income
- Little additional risk
 Overall
- Hit to income is too great
1
0
Option #2
 Add experience account balance to Option #1
- Same coverage 10 x 70 accident year loss ratio
- Increase price from 2% to 5%
- 5 year cover with separate limits by accident year
 Experience account balance
- 80% of reinsurance premium added for each
accident year
- Positive balances earn equity returns
- Any time after the end of the fifth calendar year,
MBI can commute the treaty and claim the positive
balance
 No change in asset allocation
1
1
Results - Option #2
GAAP Income
Year 1
Percentiles
99th
95th
20,000
75th
50th
25th
5th
10,000
1st
0
Current
Option #1
Option #2
-10,000
Mean
Std Dev
7,662
3,988
6,443
3,024
7,286
3,646
1
2
Results - Option #2
GAAP Income
Year 5
Percentiles
99th
95th
100,000
75th
50th
25th
5th
1st
0
Current
Option #1
Option #2
16,388
13,249
17,538
18,376
-100,000
Mean
Std Dev
16,376
18,489
1
3
Summary - Option #2 (cont.)
Shareholder's Equity
End of Year 5
Percentiles
99th
95th
300,000
75th
50th
25th
200,000
5th
1st
100,000
0
Current
Option #1
Option #1 + 10% Equity
Option #1 + 20% Equity
Option #2
-100,000
Mean
Std Dev
146,572
60,403
143,333
45,881
146,706
47,192
150,659
50,359
147,692
56,083
1
4
Summary - Option #2
 Achieves company’s goals
- Improves average GAAP income
- Increases equity exposure
 Other benefits
- Lock in the price and coverage for five years
- Commutation provision allows company flexibility
- Lower RBC charge for reinsurance recoverable
than equity
1
5
Summary - Option #2
 Disadvantages
- Makes stock returns currently taxable

Normally, stock returns are only taxed when
realized

Changes in experience account balance flow
through income

Hurts ending shareholder equity

No reduction in volatility
1
6
Summary - Option #2
 Disadvantages
- In good scenarios, experience account balance
would become a large (-20%) portion of assets

May concern regulators

Muted, to some extent, by commutation provision
1
7
How Many Scenarios?
 Most DFA models create large number of scenarios
- Monte Carlo simulation
- Allows “complete” scenarios
- Other methods are available
 Simulation creates the possibility of sampling error
- Large samples reduce this possibility
- Can be very time and resource consuming
1
8
How Many Scenarios?
 The “right” number of scenarios is based on:
- Volatility of results
- Metrics being used
- Simulation methodology
- Independent vs Dependent
1
9
How Many Scenarios?
Current
Value
Est. St Dev
Reward
382,190
3,246
Risk
287,569
29,275
Alternative
Value
Est. St Dev
376,950
2,751
239,654
19,889
Difference
Value
5,240
47,915
Definitions:
Reward: Average ending Economic Value
Risk:
Mean - 1st percentile
2
0
How Many Scenarios?
Difference
Value
Independent St Dev
Sample Size
Dependent
St Dev
Sample Size
Correlation
Reward
5,240
Risk
47,915
4,255
125,378
35,392
79,978
793
4,355
18,226
21,210
98%
79%
Sample Size based on:
Reward: Net cost under $6 million
Risk:
Reduced at least $40 million
2
1
How Many Scenarios?
 Different strategies are highly correlated
- Same gross underwriting
- Same economy
 Maintaining correlation in modeling process reduces
sampling error
- Still have to consider parameter risk
2
2