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.
2.
3.
4.
5.
Base Model WC+5%, HO+5%
Increase Base Model, HO+10%
Increase Base Model, WC+10%
Decrease Base Model, HO-10%
Decrease Base Model, WC-10%
Financial Measures
Earned Premium
Net Loss Ratio
Premium to Surplus Ratio
Expected Return\Standard Deviation
Cash Flow
Net 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
Starting Policy Holder
Surplus $40 million
Corporate Elements
Reinsurance
Investment
Underwriting
Taxes
Financial
Calculator
Financial Measures
Financial Results
Simulated over
Five Years
•Balance Sheet
•Income Statement
Analyze
Results
Net Earned Premium
Net Loss Ratio
Premium to Surplus Ratio
Return on Surplus
Cash Flow
Net 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
Assets
5,850
Bonds =
91% of
Assets
1,150
Bonds
2,500
Stocks
Cast
Other
93,000
Liabilities and Surplus
25,500
2,598
Loss & loss
expense
reserves =
64% of
Surplus
Loss Reserves
UEPR
Other
34,402
Surplus
40,000
Net Earned Premium
Fifth Year Projection
Net Earned Premium
0.5
Probability
0.4
0.3
0.2
WC+10%
HO+10%
WC-10%
Years
HO-10%
0
67,000
74,000
81,000
Base
88,000
95,000
102,000
109,000
116,000
123,000
0
130,000
0.1
Millions
Base
HO-10%
WC-10%
HO+10%
WC+10%
Net Loss Ratio
Fifth Year Projection
Probability
Loss Ratios by Option
50%
45%
40%
35%
30%
25%
20%
15%
10%
5%
0%
68%
69%
70%
71%
72%
73%
74%
75%
76%
Net Loss Ratio
Base
WC+10%
WC-10%
HO+10%
HO - 10%
Net Loss Ratio
Fifth Year Projection
50%
Probability
40%
30%
20%
HO - 10%
HO+10%
Base
10%
0%
WC-10%
86% 84%
82% 80%
78% 76%
74% 72%
70%
Loss Ratio
WC+10%
68%
66%
Premium to Surplus Ratios
Fifth Year Projection
Premium to Surplus Ratio by Option
100%
90%
Probability
80%
70%
60%
50%
40%
30%
20%
10%
0%
0.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
Prem ium to Surplus Ratio
Base
HO-10%
WC-10%
HO+10%
WC+10%
Premium to Surplus Ratio
Fifth Year Projection
100%
Probability
80%
60%
40%
WC-10%
20%
HO-10%
Base
0%
WC+10%
9.0
8.0
7.0
6.0
5.0
4.0
Premium to Surplus Ratio
HO+10%
3.0
2.0
1.0
0.0
(1.0)
Return on Surplus
Fifth Year Projection
99% Range of Outcomes
Base
WC +10%
WC -10%
HO +10%
HO -10%
-40
-30
-20
-10
0
10
Annualized Return on Surplus (%)
Low
Mean
High
20
30
40
Return on Surplus
Fifth Year Projection
13.00%
7.0%
Performance for Options with Positive Return on
Surplus
6.5%
6.06%
Return on Surplus
6.0%
5.36%
5.5%
5.0%
4.5%
3.89%
4.0%
3.5%
3.0%
10%
0.00%
11%
12%
13%
Standard Deviation
14%
15%
Cash Flow
Fifth Year Projection
CashFlow (% Net Earned Premium)
25%
15%
10%
5%
0.
03
0%
0.
02
6%
0.
02
2%
0.
01
8%
0.
01
4%
0.
01
0%
0.
00
6%
0.
00
2%
.0
02
%
-0
.0
06
%
-0
.0
10
%
0%
-0
Probability
20%
Cashflow
Base
HO-10%
WC-10%
HO+10%
WC+10%
Net Operating Results
Fifth Year Projection
Probability
Net Operating Results (% Net Earned Premium)
Cumulative Function
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
60%
72%
84%
96%
108% 120% 132%
144% 156%
168% 180%
Net Operating Return
Base
HO-10%
WC-10%
HO+10%
WC+10%
Net Operating Results
Fifth Year Projection
Net Operating Results (% Net Earned Premium)
Density Function
70%
Probability
60%
50%
40%
30%
20%
10%
0%
60%
72%
84%
96%
108%
120%
132%
144%
156%
168%
Net Operating Results
Base
HO-10%
WC-10%
HO+10%
WC+10%
180%
Conclusion – Risk vs. Return
Option
Expected
Return
Standard
Deviation
HO (-10%)
WC (-10%)
Base
WC (+10%)
HO (+10%)
+6.1%
+5.4%
+3.9%
-1.1%
-3.9%
± 12.0%
± 12.3%
± 12.8%
± 18.5%
± 19.7%
Decreasing Homeowners exposures (10)% results in:
 Higher expected return and
 Lower standard deviation
… vs. the current and other strategies.
P
Conclusion – Cash Flow
Option
Cash
Flow
HO (-10%)
Base
HO (+10%)
WC (-10%)
WC (+10%)
0.0167%
0.0163%
0.0157%
0.0137%
0.0136%
P
Decreasing Homeowners exposures (10)% also results in:
 Higher cash flow
… vs. the current and other strategies.
Conclusion – P:S Ratio
at the 50% Percentile
Option
Premium to
Surplus Ratio
HO (-10%)
1.26
P
WC (-10%)
1.33
Base
1.81
O
WC (+10%)
2.91
O
HO (+10%)
3.14
Decreasing HO & WC exposures (10)% results in:
 Lowest premium to surplus ratios
… vs. the current and other strategies.
Conclusion – Net Operating Ratio
Option
HO (-10%)
WC (-10%)
Base
WC (+10%)
HO (+10%)
Probability of
Operating Ratio < 100%
79.4%
61.7%
45.2%
27.6%
14.8%
Decreasing HO exposures (10)% results in:
 Highest probability of operating ratio < 100%
… vs. the current and other strategies.
P
Conclusion – Net Loss Ratio
Option
WC (-10%)
HO (-10%)
Base
HO (+10%)
WC (+10%)
Net
Loss Ratio
71.4%
71.5%
71.5%
71.7%
72.9%
P
Decreasing HO & WC exposures (10)% results in:
 Lowest net loss ratio
… vs. the growth strategies.
Conclusion – Rankings
Option
HO (-10%)
WC (-10%)
Base
WC (+10%)
HO (+10%)
Risk vs. Cash P:S
Net
Net
Return Flow Ratio Op Ratio Loss Ratio
#1
#2
#3
#4
#5
# 1 Tied # 1
# 4 Tied # 1
#2
#3
#5
#4
#3
#5
#1
#2
#3
#4
#5
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
Tied # 1
Tied # 1
Tied # 1
#5
#4
P
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!