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?
DFA studies driven by probability distributions
Volume of data can be overwhelming
Complexity of the modeling process Easy to get lost in the details
Challenges in Presenting DFA Results
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
Common Elements in DFA Presentations
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
44%
54%
0%0%2%
29%
44%
10%
15%
2%
29%
29%
25%
15%
2%
24%
24%
30%
20%
2%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Reinvestment Strategy
Cash 2% 2% 2% 2%
Common Stock Unaffiliated 0% 15% 15% 20%
Unaffiliated Bonds 0% 10% 25% 30%
Municipal 54% 44% 29% 24%
U.S. Govt Bond 44% 29% 29% 24%
Option A Option B Option C Option D
Change in Reinvestment Allocation
DFA flow
Work CompGrow 5% a year
Multi_PerilGrow 5% a year
FinancialCalculator
Starting Policy Holder Surplus 40,000
Corporate Elements
Reinsurance Investment
Capital Mix Taxes
Financial Results
Simulated over Five Years
Analyze Results
Measures of
•Risk•Return Change in Policy
Holder Surplus
Model / Assumptions
Assumptions Behind
Simulation
Assume Underwriting Operations Not Affected• 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
0
0.04
0.08
0.12
0.16
0.2
0.24
0.28
0.32
0.36
0.4
-40 -30 -20 -10 0 10 20 30 40
Mil
Pro
babi
lity
0
0.2
0.4
0.6
0.8
1
pdf cdf
Option B
0
0.04
0.08
0.12
0.16
0.2
0.24
0.28
0.32
0.36
0.4
-40 -30 -20 -10 0 10 20 30 40
Mil
Pro
babi
lity
0
0.2
0.4
0.6
0.8
1
pdf cdf
Option C
0
0.04
0.08
0.12
0.16
0.2
0.24
0.28
0.32
0.36
0.4
-40 -30 -20 -10 0 10 20 30 40
Mil
Pro
babi
lity
0
0.2
0.4
0.6
0.8
1
pdf cdf
Option D
0
0.04
0.08
0.12
0.16
0.2
0.24
0.28
0.32
0.36
0.4
-40 -30 -20 -10 0 10 20 30 40
Mil
Pro
babi
lity
0
0.2
0.4
0.6
0.8
1
pdf cdf
Option A(10 - 90 percentiles)
-10.0
-5.0
0.0
5.0
10.0
15.0
20.0
2004 2005 2006 2007 2008
Thou
sand
s
Surplus Change Over Time by Investment Option
Option B(10 - 90 percentiles)
-10.0
-5.0
0.0
5.0
10.0
15.0
20.0
2004 2005 2006 2007 2008
Thou
sand
s
Option C(10 - 90 percentiles)
-10.0
-5.0
0.0
5.0
10.0
15.0
20.0
2004 2005 2006 2007 2008
Thou
sand
s
Option D(10 - 90 percentiles)
-10.0
-5.0
0.0
5.0
10.0
15.0
20.0
2004 2005 2006 2007 2008
Thou
sand
s
Risk-Reward
10
11
12
13
14
15
16
17
18
19
20
10 11 12 13 14 15 16 17 18 19 20
Th
ou
san
ds
Thousands
Average Surplus Loss in Worst Case
Ave
rag
e S
urp
lus
Gai
n
Option A
Option B
Option C
Option D
Investment Option Comparison
Better
Option D highest return less risk
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
Profit distribution
0
0.04
0.08
0.12
0.16
0.2
0.24
0.28
-60 -50 -40 -30 -20 -10 0 10 20 30 40
Mil
Pro
bab
ilit
y
0
0.2
0.4
0.6
0.8
1
pdf cdf
Aggregate Distribution
Stop Loss
Liability cash flow
Range of Liability Cash Flow Over Time
0.0
0.5
1.0
1.5
2.0
2.5
3.0
2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014
Bill
ion
s Max
90-95%ile
75-90%ile
50-75%ile
25-50%ile
10-25%ile
5-10%ile
0-5%ile
Min
Avg
Practically,
no chance of
paying this
much
Ranking
Value of Reinsurance
Projected Combined Ratios with and without re insurance
-0.1
0.4
0.9
1.4
1.9
2.4
2.9
3.4
0.6 0.8 1 1.2 1.4 1.6 1.8 2
Pro
ject
ed L
ikel
iho
od
what you give upwhat you get back
noreinsurance
currentreinsurance
Development & Trends
Run-Off Payout
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
1997 1998 1999 2000 2001 2002 2003 2004
Bil
lio
ns
Cash Flow over time
Still going and going and going…
Range of Liability Cash Flow Over Time(10 - 90 percentiles)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014
Bill
ion
sCash Flow over time
Theoretically possible ranges
More realistic outcomes
Allocations
51.0%
31.0%
11.0%7.0%
Bonds
Equity
Cash
Other
71.0%
11.0%
11.0%7.0%
Change in Allocation
More bonds
Less Equity
BondsEquity
CashOther Curr
Alt
71.0%
11.0%11.0%
7.0%
51.0%
31.0%
11.0%
7.0%0.0%
10.0%
20.0%
30.0%
40.0%
50.0%
60.0%
70.0%
80.0%
Investment Strategies
Curr Alt
Change in Allocation
More bonds
Less Equity
Not to Do
Too Much Info