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