Presenting DFA Results
to Decision Makers
Spring 2008
Midwest Actuarial Forum
Agenda
 Overview of committee work
 Sample presentation (illustration purposes
only)
 Examples of slides using Power Point
Presenting DFA Results
to Decision Makers
2003 CAS Research Working Party:
Executive Level Decision Making using DFA
Scott Sobel, FCAS, MAAA
Agenda
 What are the challenges in presenting DFA
results?
 What are some common elements in a
DFA presentation?
 What elements vary in DFA presentations?
 What are the end products of the working
party’s efforts?
Challenges in Presenting DFA
Results
 DFA studies driven by probability distributions
 Volume of data can be overwhelming
 Complexity of the modeling process

Easy to get lost in the details
Common Elements in DFA
Presentations
 State the options to be evaluated
 State the financial metrics for the evaluation
 Summarize the model assumptions
 Display ranges of results for the financial
statistics of interest
 Compare key financial statistics
 Conclude with evaluation of the options
Varying Elements in DFA
Presentations
 Options to be evaluated are specific to the
DFA study
 Financial metrics are the choice of the
management team – varies by company
 Display of results need to reflect these
choices


The particular graphs selected
Comments placed on the graphs
 Conclusion – dependent on option types
End Products of the Working
Party Efforts
 Summary report
 PowerPoint template for graphs
 Paper describing concepts behind template
 Three sample presentations applying
template graphs
 Guidelines for Presenting DFA.doc
 Web site
http://www.casact.org/research/drmwp/
Investment Option
Review Example
2003 CAS Research Working Party:
Executive Level Decision Making using DFA
Michael R. Larsen, FCAS, MAAA
Goals of Study
 Review Reinvestment Options
 Measure results using simulation model
results


Risk as Average Loss in Surplus in Worst 1%
of Cases over Five Years
Return as Average Increase in Policy Holder
Surplus at End of Five Years
Change in Reinvestment Allocation
Reinvestment Strategy
100%
2%
0%
2%
2%
15%
15%
90%
2%
20%
10%
80%
54%
25%
70%
30%
60%
44%
50%
29%
40%
24%
30%
44%
20%
29%
29%
24%
10%
0%
Option A
Option B
Option C
Cash
2%
2%
2%
Option D
2%
Common Stock Unaffiliated
0%
15%
15%
20%
0%
10%
25%
30%
Municipal
54%
44%
29%
24%
U.S. Govt Bond
44%
29%
29%
24%
Unaffiliated Bonds
DFA flow
Work Comp
Grow 5% a year
Starting Policy Holder
Surplus 40,000
Multi_Peril
Grow 5% a year
Corporate Elements
Reinsurance
Investment
Capital Mix
Taxes
Financial
Calculator
Analyze
Results
Financial Results
Simulated over
Five Years
Measures of
•Risk
•Return
Change in Policy
Holder Surplus
Model / Assumptions
Assume Underwriting Operations Not Affected
Assumption
s Behind
Simulation
• Ability to take rate changes not driven by investment results
• Growth rates in exposure does not change
Investment Scenario
• Long run average interest rate of 4%
•Starting interest rate of 4%
Investment Models
• Short term interest rate model is a mean reversion model
•Long term rates are a function of short term rates
•Stock returns modeled as a function of short term rates and interest rate changes
•Stable relationship between bond and equity market
Policyholder Surplus Change by Reinvestment Option
Option A
Option B
0.4
1
0.4
0.36
0.32
0.8
0.32
0.8
0.28
0.24
0.6
0.2
0.16
0.4
Probability
0.28
Probability
1
0.36
0.12
0.24
0.6
0.2
0.16
0.4
0.12
0.08
0.2
0.08
0.04
0.2
0.04
0
0
-40
-30
-20
-10
0
10
20
30
0
40
0
-40
-30
-20
-10
0
10
20
30
40
Mil
pdf
Mil
cdf
pdf
Option C
Option D
0.4
1
0.4
0.36
1
0.36
0.32
0.8
0.32
0.28
0.8
0.28
0.24
0.6
0.2
0.16
0.4
0.12
Probability
Probability
cdf
0.24
0.6
0.2
0.16
0.4
0.12
0.08
0.2
0.04
0.08
0.2
0.04
0
0
-40
-30
-20
-10
0
10
20
30
40
0
0
-40
-30
-20
-10
0
10
Mil
pdf
cdf
20
30
40
Mil
pdf
cdf
Surplus Change Over Time by Investment Option
Option B
(10 - 90 percentiles)
20.0
Thousands
Thousands
Option A
(10 - 90 percentiles)
15.0
20.0
15.0
10.0
10.0
5.0
5.0
0.0
0.0
2004
2005
2006
2007
2008
2004
-5.0
-5.0
-10.0
-10.0
2005
2007
2008
2007
2008
Option D
(10 - 90 percentiles)
20.0
Thousands
Thousands
Option C
(10 - 90 percentiles)
2006
15.0
20.0
15.0
10.0
10.0
5.0
5.0
0.0
0.0
2004
2005
2006
2007
2008
2004
-5.0
-5.0
-10.0
-10.0
2005
2006
Investment Option Comparison
Average Surplus Gain
Thousands
Risk-Reward
20
19
Option D highest
return less risk
18
17
16
Option A
15
Option B
Option C
14
Option D
13
12
11
10
10
11
12
13
14
15
16
Average Surplus Loss in Worst Case
17
18
19
20
Thousands
Investment Option Summary
Option
Return
Risk
A
12.6
17.2
B
13.6
17.0
C
13.8
17.0
D
14.2
16.9
Conclusion
 Reviewed four reinvestment options
 Option D gives best gain in Surplus with less
additional risk
DFA presentation
Template
Uncertainty
Aggregate Distribution
Profit distribution
1
0.28
0.24
0.8
Probability
0.2
0.16
0.6
Stop Loss
0.12
0.4
0.08
0.2
0.04
0
0
-60
-50
-40
-30
-20
-10
10
0
20
30
40
Mil
pdf
cdf
Liability cash flow
Billions
Range of Liability Cash Flow Over Time
3.0
Max
90-95%ile
2.5
75-90%ile
50-75%ile
2.0
25-50%ile
10-25%ile
1.5
5-10%ile
0-5%ile
1.0
Min
Avg
0.5
0.0
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
Ranking
Value of Reinsurance
Projected Combined Ratios with and without reinsurance
3.4
2.9
current
reinsurance
Projected Likelihood
2.4
1.9
no
reinsurance
1.4
0.9
what you get back
0.4
what you give up
-0.1
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Development & Trends
Cash Flow over time
Billions
Run-Off Payout
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
1997
1998
1999
2000
2001
2002
2003
2004
Cash Flow over time
Billions
Range of Liability Cash Flow Over Time
(10 - 90 percentiles)
3.0
2.5
Theoretically possible ranges
2.0
More realistic outcomes
1.5
1.0
0.5
0.0
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
Allocations
Change in Allocation
11.0%
7.0%
51.0%
Bonds
31.0%
Equity
Cash
7.0%
Other
11.0%
11.0%
71.0%
Less Equity
More bonds
Change in Allocation
Investment Strategies
More bonds
Less Equity
71.0%
80.0%
70.0%
60.0%
50.0%
51.0%
40.0%
Curr
30.0%
31.0%
20.0%
11.0%
11.0%
10.0%
11.0%
0.0%
7.0%
7.0%
Bonds
Equity
Alt
Cash
Other
Curr
Alt
Not to Do
Too Much Info