Mix of Business Review Example
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Mix of Business Review Example
Executive Level Decision Making Using DFA
Patrick J. Crowe, FCAS, MAAA
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Goals of Study
Review Mix of Business Options
Evaluate Optimal Growth Patterns using simulation model results
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Mix of Business Options
1. Base Model WC+5%, HO+5%2. Increase Base Model, HO+10%3. Increase Base Model, WC+10%4. Decrease Base Model, HO-10%5. Decrease Base Model, WC-10%
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Financial Measures
Earned PremiumNet Loss RatioPremium to Surplus RatioExpected Return\Standard DeviationCash FlowNet Operating Results
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Model / Assumptions
Assumptions Behind
Simulation
Underwriting operations and investment strategy are not affected by change in policy growth assumptions.
The DFA model assumes there is a tradeoff between growth and profitability.
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DRM Flow
Workers Compensation
Homeowners FinancialCalculator
Starting Policy Holder Surplus $40 million
Corporate Elements
Reinsurance Investment
UnderwritingUnderwriting Taxes
Financial Results
Simulated over Five Years
•Balance Sheet•Income Statement
Analyze Results
Financial Measures Net Earned Premium Net Loss RatioPremium to Surplus RatioReturn on SurplusCash FlowNet Operating Results
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Caveats
Effect on expense ratios has not been modeled Reducing exposures could result in higher expense ratios
and thus may not result in the best alternative
Effect of change in investment strategies has not been modeled Reducing exposures will most likely result in a change in
investment strategies Not considered as significant as the effect on company
expenses
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Initial Balance Sheet
Liabilities and Surplus
34,402
25,500
2,598
40,000
Loss Reserves
UEPR
Other
Surplus
Assets
93,000
2,500
1,150
5,850
Bonds
StocksCast
Other
Loss & loss expense reserves = 64% of Surplus
Bonds = 91% of Assets
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Net Earned PremiumFifth Year Projection
0
67,0
00
74,0
00
81,0
00
88,0
00
95,0
00
102,
000
109,
000
116,
000
123,
000
130,
000 Base
HO-10%WC-10%HO+10%WC+10%
0
0.1
0.2
0.3
0.4
0.5
Prob
abili
ty
Millions
Years
Net Earned Premium
Base HO-10% WC-10% HO+10% WC+10%
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Net Loss RatioFifth Year Projection
Loss Ratios by Option
0%5%
10%15%20%25%30%35%40%45%50%
68% 69% 70% 71% 72% 73% 74% 75% 76%
Net Loss Ratio
Prob
abili
ty
Base WC+10% WC-10% HO+10% HO - 10%
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Net Loss RatioFifth Year Projection
66%68%70%72%74%76%78%80%82%84%86%WC+10%
WC-10%BaseHO+10%HO - 10%
0%
10%
20%
30%
40%
50%
Prob
abili
ty
Loss Ratio
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Premium to Surplus Ratio by Option
0%10%20%30%40%50%60%70%80%90%
100%
0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5Premium to Surplus Ratio
Prob
abili
ty
Base HO-10% WC-10% HO+10% WC+10%
Premium to Surplus RatiosFifth Year Projection
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(1.0)0.01.02.03.04.05.06.07.08.09.0HO+10%
WC+10%
Base
HO-10%WC-10%
0%
20%
40%
60%
80%
100%
Prob
abili
ty
Premium to Surplus Ratio
Premium to Surplus RatioFifth Year Projection
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Return on SurplusFifth Year Projection
99% Range of Outcomes
HO -10%
HO +10%
WC +10%
Base
WC -10%
-40 -30 -20 -10 0 10 20 30 40Annualized Return on Surplus (%)
Low Mean High
Less risky
Less rewarding
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Performance for Options with Positive Return on Surplus
0.00%
13.00%
0.00%
13.00%
3.89%
5.36%
6.06%
3.0%
3.5%
4.0%
4.5%
5.0%
5.5%
6.0%
6.5%
7.0%
10% 11% 12% 13% 14% 15%Standard Deviation
Ret
urn
on S
urpl
usReturn on SurplusFifth Year Projection
Better
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CashFlow (% Net Earned Premium)
0%
5%
10%
15%
20%
25%
-0.010
%
-0.006
%
-0.002
%0.0
02%
0.006
%0.0
10%
0.014
%0.0
18%
0.022
%0.0
26%
0.030
%
Cashflow
Prob
abili
ty
Base HO-10% WC-10% HO+10% WC+10%
Cash FlowFifth Year Projection
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Net Operating Results (% Net Earned Premium) Cumulative Function
0%10%20%30%40%50%60%70%80%90%
100%
60% 72% 84% 96% 108% 120% 132% 144% 156% 168% 180%
Net Operating Return
Prob
abili
ty
Base HO-10% WC-10% HO+10% WC+10%
Net Operating ResultsFifth Year Projection
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Net Operating Results (% Net Earned Premium) Density Function
0%10%20%30%
40%50%60%70%
60% 72% 84% 96% 108% 120% 132% 144% 156% 168% 180%
Net Operating Results
Prob
abili
ty
Base HO-10% WC-10% HO+10% WC+10%
Net Operating ResultsFifth Year Projection
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Conclusion – Risk vs. Return
Decreasing Homeowners exposures (10)% results in: Higher expected return and Lower standard deviation… vs. the current and other strategies.
Expected StandardOption Return Deviation
HO (-10%) +6.1% ± 12.0%WC (-10%) +5.4% ± 12.3%Base +3.9% ± 12.8%WC (+10%) -1.1% ± 18.5%HO (+10%) -3.9% ± 19.7%
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Conclusion – Cash Flow
Decreasing Homeowners exposures (10)% also results in: Higher cash flow
… vs. the current and other strategies.
CashOption Flow
HO (-10%) 0.0167%Base 0.0163%HO (+10%) 0.0157%WC (-10%) 0.0137%WC (+10%) 0.0136%
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Conclusion – P:S Ratio at the 50% Percentile
Decreasing HO & WC exposures (10)% results in: Lowest premium to surplus ratios
… vs. the current and other strategies.
Premium toOption Surplus Ratio
HO (-10%) 1.26WC (-10%) 1.33Base 1.81WC (+10%) 2.91HO (+10%) 3.14
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Conclusion – Net Operating Ratio
Decreasing HO exposures (10)% results in: Highest probability of operating ratio < 100%
… vs. the current and other strategies.
Probability ofOption Operating Ratio < 100%
HO (-10%) 79.4%WC (-10%) 61.7%Base 45.2%WC (+10%) 27.6%HO (+10%) 14.8%
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Conclusion – Net Loss Ratio
Decreasing HO & WC exposures (10)% results in: Lowest net loss ratio
… vs. the growth strategies.
NetOption Loss Ratio
WC (-10%) 71.4%HO (-10%) 71.5%Base 71.5%HO (+10%) 71.7%WC (+10%) 72.9%
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Conclusion – Rankings
Decreasing HO exposures (10)% results in: Most return and least risk Greatest cash flow Lowest P:S Ratio Lowest Operating Ratio Lowest Net Loss Ratio
Risk vs. Cash P:S Net NetOption Return Flow Ratio Op Ratio Loss Ratio
HO (-10%) # 1 # 1 Tied # 1 # 1 Tied # 1WC (-10%) # 2 # 4 Tied # 1 # 2 Tied # 1Base # 3 # 2 # 3 # 3 Tied # 1WC (+10%) # 4 # 5 # 4 # 4 # 5HO (+10%) # 5 # 3 # 5 # 5 # 4
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Conclusion
Although decreasing Homeowners exposures is the best option, neither the current U/W strategy nor the alternatives are expected to result in an adequate return or a sufficient financial position to support the company’s business!