report on cas research working parties moderator: donald mango, fcas, maaa cas vice president of...

Report on CAS Report on CAS Research Working Research Working

PartiesPartiesModerator: Donald Mango, FCAS, MAAAModerator: Donald Mango, FCAS, MAAA

CAS Vice President of Research and CAS Vice President of Research and DevelopmentDevelopment

Director of Research and Development, GE Director of Research and Development, GE ERCERC

2004 ERM Symposium2004 ERM SymposiumApril 27, 2004April 27, 2004

AgendaAgenda

Working Parties OverviewWorking Parties Overview Correlations and Dependencies WPCorrelations and Dependencies WP Executive Decision Making Using Executive Decision Making Using

DFA WPDFA WP Elicitation and Elucidation of Risk Elicitation and Elucidation of Risk

Preferences WPPreferences WP Q&A throughoutQ&A throughout

What is a “working What is a “working party”?party”?

Essentially a task force focused on Essentially a task force focused on research of a specific topic or research of a specific topic or solution of a specific problemsolution of a specific problem

Group effort with a single work Group effort with a single work productproduct

Modeled on GIRO platform where it Modeled on GIRO platform where it has been used successfullyhas been used successfully

What can WP’s What can WP’s deliver?deliver?

Original ResearchOriginal Research Survey papersSurvey papers

Overview of research published to date on a Overview of research published to date on a particular topicparticular topic

Could be used as syllabus materialCould be used as syllabus material Compendiums of papers by different authorsCompendiums of papers by different authors

Correlation of Risk working party will use this formatCorrelation of Risk working party will use this format Similar approach taken by Reserve Variability WPSimilar approach taken by Reserve Variability WP

Studies of industry experience based on special Studies of industry experience based on special data callsdata calls

What are the What are the current working current working

parties?parties? Correlations and Dependencies Correlations and Dependencies

Among All Risk SourcesAmong All Risk Sources Executive Level Decision Making Executive Level Decision Making

Using Dynamic Financial AnalysisUsing Dynamic Financial Analysis Elicitation and Elucidation of Risk Elicitation and Elucidation of Risk

PreferencesPreferences Quantifying Variability in Reserves Quantifying Variability in Reserves

EstimatesEstimates Implication of Fair Value on Asset Implication of Fair Value on Asset

Allocation (on hold)Allocation (on hold)

Report of the Report of the Correlation Correlation

Working PartyWorking PartyGlenn MeyersGlenn Meyers

Insurance Services Office, Insurance Services Office, Inc.Inc.

Charge of the Charge of the Working PartyWorking Party

ERM requires the quantification of ERM requires the quantification of the total risk of an enterprise. One the total risk of an enterprise. One must consider correlation to properly must consider correlation to properly combine the individual risk combine the individual risk components.components.

ConsiderationsConsiderations TheoreticalTheoretical EmpiricalEmpirical ComputationalComputational

Theoretical Theoretical ConsiderationsConsiderations

Conclusion – No overriding “theory of Conclusion – No overriding “theory of correlation.”correlation.”

We will provide examples of multivariate We will provide examples of multivariate models that exhibit correlation.models that exhibit correlation.

Experts prefer the term “dependencies” Experts prefer the term “dependencies” rather than correlation.rather than correlation. I find myself reverting the common usage so I find myself reverting the common usage so

nonexperts will know what I am talking nonexperts will know what I am talking about.about.

Empirical Empirical ConsiderationsConsiderations

Historical problem – lack of dataHistorical problem – lack of data One observation per yearOne observation per year

If correlation matters, we should be able If correlation matters, we should be able to find data that exhibits that to find data that exhibits that correlation.correlation.

One approach One approach Create a model that depends on a “driver” Create a model that depends on a “driver”

for correlation.for correlation. Use data from several insurers to Use data from several insurers to

parameterize the driver.parameterize the driver. Example to followExample to follow

Computational Computational ConsiderationsConsiderations

ERM demands the aggregation of ERM demands the aggregation of segments.segments.

SimulationSimulation Iman Conover and CopulasIman Conover and Copulas

Fourier transformsFourier transforms Faster than simulations, but less Faster than simulations, but less

flexible and require more setup time.flexible and require more setup time.

Chapters Written by Chapters Written by Individual AuthorsIndividual Authors

Common Shock Models – Glenn MeyersCommon Shock Models – Glenn Meyers The Iman-Conover Method – Stephen The Iman-Conover Method – Stephen

MildenhallMildenhall Correlation over time – Hans WaszinkCorrelation over time – Hans Waszink Aggregating Bivariate Distributions – David Aggregating Bivariate Distributions – David

HomerHomer Dependency in Market Risk – Younju LeeDependency in Market Risk – Younju Lee Modeling Time Series with Non-Constant Modeling Time Series with Non-Constant

Correlations – Dan HeyerCorrelations – Dan Heyer Correlations in a General Stochastic Setting – Correlations in a General Stochastic Setting –

Lijia GuoLijia Guo 4 CAS Members and 3 non members4 CAS Members and 3 non members

From Meyers ChapterFrom Meyers ChapterThe Negative Binomial The Negative Binomial

DistributionDistribution Select Select at random from a gamma at random from a gamma

distribution with mean 1 and variance distribution with mean 1 and variance cc.. Select the claim count Select the claim count KK at random from at random from

a Poisson distribution with mean a Poisson distribution with mean KK has a negative binomial distribution has a negative binomial distribution

with:with:

2 and VarE K K c

Multiple Line Parameter Multiple Line Parameter UncertaintyUncertainty

Select Select from a distribution with from a distribution with EE[[] = ] = 1 and 1 and VarVar[[] = ] = bb..

For each line For each line hh, multiply each loss by , multiply each loss by .. Can calculate Can calculate if desired. if desired.

| |

, | , | | , |

,

Var X E Var X Var E X

Cov X Y E Cov X Y Cov E X E Y

Cov X Y

Std X Std Y

Multiple Line Parameter Multiple Line Parameter UncertaintyUncertainty

A simple, but nontrivial exampleA simple, but nontrivial example

1 2 31 3 , 1, 1 3b b

1 3 2Pr Pr 1/ 6 Pr 2 / 3and

E = 1 and Var[] = b

Low VolatilityLow Volatility bb = 0.01 = 0.01 rr= 0.50= 0.50

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

0 1,000 2,000 3,000 4,000

Y 1= X 1

Y2=

X2

Low VolatilityLow Volatility bb = 0.03 = 0.03 rr= 0.75= 0.75

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

0 1,000 2,000 3,000 4,000

Y 1= X 1

Y2=

X2

High VolatilityHigh Volatility bb = 0.01 = 0.01 rr= 0.25= 0.25

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

0 1,000 2,000 3,000 4,000

Y 1= X 1

Y2=

X2

High VolatilityHigh Volatility bb = 0.03 = 0.03 rr= 0.45= 0.45

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

0 1,000 2,000 3,000 4,000

Y 1= X 1

Y2=

X2

About CorrelationAbout Correlation

There is no direct connection There is no direct connection between between and and bb..

For the same value of For the same value of bb:: Small insurers have large process risk Small insurers have large process risk

and hence smaller correlation and hence smaller correlation Large insurers have smaller process risk Large insurers have smaller process risk

and hence larger correlations.and hence larger correlations. Pay attention to the Pay attention to the processprocess that that

generates correlations.generates correlations.

Estimating Estimating bb From From DataData

,

| , | | , |

Cov X Y

E Cov X Y Cov E X E Y =0

,

Thus:

E X E Y Cov

b E X E Y

x E X y E Yb

E X E Y

Reliable estimates of Reliable estimates of bb are possible with lots are possible with lots of data.of data.

Real estimates provided by Meyers, Real estimates provided by Meyers, Klinker and LalondeKlinker and Lalonde

http://www.casact.org/pubs/forum/03sforum/03sf015.pdfhttp://www.casact.org/pubs/forum/03sforum/03sf015.pdf

For example, 50 insurers with 10 years of

50data gives 10 12,250 observations.

2

Sample CalculationsSample CalculationsCommon Shocks to Frequency and Common Shocks to Frequency and

SeveritySeverity Multiply expected claim count by a Multiply expected claim count by a

random shock.random shock. Negative binomial count distributionsNegative binomial count distributions Var[Shock] called covariance generatorVar[Shock] called covariance generator

Multiply scale of claim severity by a Multiply scale of claim severity by a random shock.random shock. Lognormal severity distributions Lognormal severity distributions Var[Shock] called the mixing parameterVar[Shock] called the mixing parameter

Look at spreadsheetLook at spreadsheet

Scroll Down

Parting MessageParting Message

Build models of underlying processes.Build models of underlying processes. Common shock model illustrated hereCommon shock model illustrated here Other chapters build other modelsOther chapters build other models

Quantify parameters of modelsQuantify parameters of models Use data! (If data will never exist, why Use data! (If data will never exist, why

worry?)worry?) Express parameters in a form that has Express parameters in a form that has

intuitive meaning.intuitive meaning. Correlation is a consequence of the Correlation is a consequence of the

models.models.

Working Party:Working Party:Presenting DFA Presenting DFA

Results to Results to Decision MakersDecision Makers

Nathan BabcockNathan Babcock

Conning Asset ManagementConning Asset Management

Statement of Statement of PurposePurpose

““Executive-Level Decision Making Executive-Level Decision Making Using Dynamic Financial Analysis”Using Dynamic Financial Analysis”

Facilitate Facilitate effectiveeffective DFA DFA presentations to senior managementpresentations to senior management

Survey existing presentationsSurvey existing presentations Create tools and documentationCreate tools and documentation

Summary of EventsSummary of Events

Enroll volunteersEnroll volunteers Survey past presentationsSurvey past presentations Develop graphical template and manualDevelop graphical template and manual Create sample dynamic financial Create sample dynamic financial

analyses and presentationsanalyses and presentations Write summary reportWrite summary report Review presentations, report, templateReview presentations, report, template

End ProductsEnd Products

Summary reportSummary report PowerPoint template for graphsPowerPoint template for graphs Paper describing concepts behind Paper describing concepts behind

templatetemplate Three sample presentations Three sample presentations

(applying template graphs)(applying template graphs) Document of presentation guidelinesDocument of presentation guidelines

Lessons of the Lessons of the WorkingWorking

Party ProcessParty Process Chairpersons - management Chairpersons - management

responsibilitiesresponsibilities

Communication with oversight Communication with oversight

committeecommittee

Ability to direct a group of volunteersAbility to direct a group of volunteers

Multiple rewrites of the project Multiple rewrites of the project

timelinetimeline

Working Party Working Party DiscoveriesDiscoveries

WebEx WebEx - online presentations- online presentations- paired with simultaneous - paired with simultaneous teleconferenceteleconference

HyperlinksHyperlinks- useful in documents, not just Internet- useful in documents, not just Internet- one reading electronically can page - one reading electronically can page within set of {manual, template, report}within set of {manual, template, report}

GraphicsGraphics

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

ba

bil

ity

0

0.2

0.4

0.6

0.8

1

pdf cdf

Sample Graph: Profit Sample Graph: Profit DistributionDistribution

Stop Loss

Sample Graph: Liability Sample Graph: Liability cash flowcash flowRange 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

Bil

lio

ns

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

Increase in Capital & Surplus

-10.00%

-8.00%

-6.00%

-4.00%

-2.00%

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

-10.00% -8.00% -6.00% -4.00% -2.00% 0.00% 2.00% 4.00% 6.00% 8.00% 10.00%

Increase Without Hedge

Inc

rea

se

Wit

h H

ed

ge

Sample Graph: Sample Graph: HedgingHedging

Hedge is inexpensive,

but useful

Working Party:Working Party:Elicitation and Elicitation and Elucidation of Elucidation of

Risk PreferencesRisk Preferences

David RuhmDavid Ruhm

The HartfordThe Hartford

Risk PreferencesRisk PreferencesWorking Party Working Party

Motivation:Motivation: Most DFA and Risk Management exercises Most DFA and Risk Management exercises

assume management has a clear, assume management has a clear, consistent, well-understood, transparent consistent, well-understood, transparent set of risk preferencesset of risk preferences

Such a set is a prerequisite for many risk Such a set is a prerequisite for many risk analysis efforts, including asset portfolio analysis efforts, including asset portfolio composition and reinsurance purchasing.composition and reinsurance purchasing.

The WP members and others do not believe The WP members and others do not believe this to be the case in generalthis to be the case in general


Goals:Goals: Describe or develop techniques and Describe or develop techniques and

exercises that can be used to assist exercises that can be used to assist company senior management in company senior management in developing (elicitation) and refining developing (elicitation) and refining (elucidation) a consistent set of risk (elucidation) a consistent set of risk preferences. preferences.

The Working Party may draw from The Working Party may draw from research in decision theory, prospect research in decision theory, prospect theory, and behavioral finance.theory, and behavioral finance.


Framework:Framework: Company level assessment (i.e., not Company level assessment (i.e., not

riskiness/leverage of individual products sold) riskiness/leverage of individual products sold) supporting planning decisions (product lines).supporting planning decisions (product lines).

Provide decision support for the selection of the Provide decision support for the selection of the most desirable prospective portfolio mix.most desirable prospective portfolio mix.

But moving beyond Markowitz by considering many But moving beyond Markowitz by considering many measures and timeframes.measures and timeframes.

Consider one-year, two-year, and three-year time Consider one-year, two-year, and three-year time horizonshorizons

Net Income, both absolute and scaled on PHSNet Income, both absolute and scaled on PHS Several likelihood thresholds (1 in 5, 10, 25, 50, Several likelihood thresholds (1 in 5, 10, 25, 50,

100, 250 years)100, 250 years)


Two Sub-Teams:Two Sub-Teams: Senior Management Silent AuctionSenior Management Silent Auction Survey Research of Psychology Studies Survey Research of Psychology Studies

of Preferencesof Preferences Silent AuctionSilent Auction

Attempts to elicit consistent Attempts to elicit consistent preferences while correcting for preferences while correcting for framing effectsframing effects

Give to Sr. Mgmt members, then plot Give to Sr. Mgmt members, then plot their answers on a single charttheir answers on a single chart

Net Income Silent AuctionAssumptions:

Plan Net Income 200,000$ PHS 1,000,000$

User Inputs in BLUE

Part 1: Amounts Part 2: LikelihoodsDELTA-FRAMING LEVEL-FRAMING DELTA-FRAMING LEVEL-FRAMING

Time Net Income Time Net Income Relative Net IncomeHorizon Shortfall Horizon Net Income Shortfall Likelihood Shortfall Likelihood

1 in 5 (100,000)$ 1 in 5 100,000$ (100,000)$ 1.00 base (100,000)$ 25.0%1 in 10 (150,000)$ 1 in 10 50,000$ (150,000)$ 0.50 times as likely as amount above (150,000)$ 10.0%1 in 25 (200,000)$ 1 in 25 -$ (200,000)$ 0.50 times as likely as amount above (200,000)$ 5.0%1 in 50 (300,000)$ 1 in 50 (100,000)$ (300,000)$ 0.50 times as likely as amount above (300,000)$ 4.0%

1 in 100 (400,000)$ 1 in 100 (200,000)$ (400,000)$ 0.50 times as likely as amount above (400,000)$ 2.0%1 in 250 (500,000)$ 1 in 250 (300,000)$ (500,000)$ 0.50 times as likely as amount above (500,000)$ 1.0%

Net IncomeTime Shortfall Time Net Income Relative

Horizon As % of Plan Horizon As % of Plan Net Income Likelihood Net Income Likelihood

1 in 5 50.0% 1 in 5 150.0% 100,000$ 1.00 base 100,000$ 25.0%1 in 10 75.0% 1 in 10 175.0% 50,000$ 0.50 times as likely as amount above 50,000$ 10.0%1 in 25 100.0% 1 in 25 200.0% -$ 0.50 times as likely as amount above -$ 5.0%1 in 50 150.0% 1 in 50 250.0% (100,000)$ 0.50 times as likely as amount above (100,000)$ 4.0%

1 in 100 200.0% 1 in 100 300.0% (200,000)$ 0.50 times as likely as amount above (200,000)$ 2.0%1 in 250 250.0% 1 in 250 350.0% (300,000)$ 0.50 times as likely as amount above (300,000)$ 1.0%

Time Drop in TimeHorizon PHS Horizon PHS

1 in 5 5.0% 1 in 5 5.0%1 in 10 2.0% 1 in 10 2.0%1 in 25 -1.0% 1 in 25 -1.0%1 in 50 -5.0% 1 in 50 -5.0%

1 in 100 -10.0% 1 in 100 -10.0%1 in 250 -20.0% 1 in 250 -20.0%


Behavioral FinanceBehavioral Finance Non-Bayesian ForecastingNon-Bayesian Forecasting: must have a prior : must have a prior

before you can apply Bayes' Theorem. Also tend to before you can apply Bayes' Theorem. Also tend to overweight recent experience.overweight recent experience.

HerdingHerding: need content providers, expressing actual : need content providers, expressing actual opinions, rather than relativistic participants (what opinions, rather than relativistic participants (what do my peers do?). If all the peers are asking about do my peers do?). If all the peers are asking about the other peers, who is putting content in? the other peers, who is putting content in?

Over-reactionOver-reaction: beware of this tendency, which is : beware of this tendency, which is particularly troubling in this buy-and-hold, non-particularly troubling in this buy-and-hold, non-exchange market. What should the threshold for exchange market. What should the threshold for reaction be? How many bad quarters or years in a reaction be? How many bad quarters or years in a row?row?


Behavioral FinanceBehavioral Finance Myopic Loss AversionMyopic Loss Aversion: risk premium is a function : risk premium is a function

of time horizon. If you look at returns and results of time horizon. If you look at returns and results more frequently (shorter time horizon), you will more frequently (shorter time horizon), you will demand a higher risk premium. demand a higher risk premium.

Earnings ManagementEarnings Management: owner's often want : owner's often want unrealistic earnings stability, often at odds with unrealistic earnings stability, often at odds with the desired return. the desired return.

Growth/Decline/ReorganizationGrowth/Decline/Reorganization: Expansion occurs : Expansion occurs more readily than redeployment and destruction. more readily than redeployment and destruction. Function in part of myopic focus on sunk costs and Function in part of myopic focus on sunk costs and difficulty of exit. difficulty of exit.


The Road AheadThe Road Ahead We need a chairperson!We need a chairperson! Finalize research summaryFinalize research summary Finish Senior Mgmt Silent AuctionFinish Senior Mgmt Silent Auction Report out later this yearReport out later this year

Thank you for Thank you for your attentionyour attention

Questions?Questions?

report on cas research working parties moderator: donald mango, fcas, maaa cas vice president of...

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