Mix of Business Review Example

Executive Level Decision Making Using DFA

Patrick J. Crowe, FCAS, MAAA

Goals of Study

Review Mix of Business Options

Evaluate Optimal Growth Patterns using simulation model results

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%

Financial Measures

Earned PremiumNet Loss RatioPremium to Surplus RatioExpected Return\Standard DeviationCash FlowNet Operating Results

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.

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

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

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

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%

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%

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

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

(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

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

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

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

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

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

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%

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%

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

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%

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%

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

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!