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Modeling of Economic Series Modeling of Economic Series Coordinated withCoordinated with
Interest Rate ScenariosInterest Rate Scenarios
Research Sponsored by theResearch Sponsored by theCasualty Actuarial Society and theCasualty Actuarial Society and the
Society of ActuariesSociety of Actuaries
Investigators:Investigators:Kevin Ahlgrim, ASA, PhD, Illinois State UniversityKevin Ahlgrim, ASA, PhD, Illinois State University
Steve D’Arcy, FCAS, PhD, University of IllinoisSteve D’Arcy, FCAS, PhD, University of IllinoisRick Gorvett, FCAS, ARM, FRM, PhD, University of IllinoisRick Gorvett, FCAS, ARM, FRM, PhD, University of Illinois
Enterprise Risk Management SymposiumEnterprise Risk Management SymposiumApril 2004April 2004
AcknowledgementsAcknowledgements
We wish to thank the Casualty Actuarial We wish to thank the Casualty Actuarial Society and the Society of Actuaries for Society and the Society of Actuaries for providing financial support for this providing financial support for this research, as well as guidance and feedback research, as well as guidance and feedback on the subject matter.on the subject matter.
Note: All of the following slides reflect Note: All of the following slides reflect tentative findings and results; these tentative findings and results; these results are currently being reviewed by results are currently being reviewed by committees of the CAS and SoA.committees of the CAS and SoA.
Outline of PresentationOutline of Presentation
Motivation for Financial Scenario Motivation for Financial Scenario Generator ProjectGenerator Project
Short description of included Short description of included economic variableseconomic variables
An overview of the modelAn overview of the model Applications of the modelApplications of the model ConclusionsConclusions
Overview of ProjectOverview of Project CAS/SOA Request for Proposals on CAS/SOA Request for Proposals on
““Modeling of Economic Series Modeling of Economic Series Coordinated with Interest Rate Coordinated with Interest Rate Scenarios”Scenarios”• A key aspect of A key aspect of dynamic financial analysisdynamic financial analysis• Also important for regulatory, rating agency, Also important for regulatory, rating agency,
and internal management tests – e.g., and internal management tests – e.g., cash cash flow testingflow testing
Goal: to provide actuaries with a model Goal: to provide actuaries with a model for for projectingprojecting economic and financial economic and financial indicesindices, , with realistic with realistic interdependenciesinterdependencies among the variables among the variables..• Provides a Provides a foundationfoundation for future efforts for future efforts
Scope of ProjectScope of Project Literature reviewLiterature review
• From finance, economics, and actuarial From finance, economics, and actuarial sciencescience
Financial scenario modelFinancial scenario model• Generate scenarios over a 50-year time Generate scenarios over a 50-year time
horizonhorizon Document and facilitate use of Document and facilitate use of
modelmodel• Report includes sections on data & Report includes sections on data &
approach, results of simulations, user’s approach, results of simulations, user’s guideguide
• To be posted on CAS & SOA websitesTo be posted on CAS & SOA websites• Writing of papers for journal publicationWriting of papers for journal publication
Economic Series ModeledEconomic Series Modeled
InflationInflation Real interest Real interest
ratesrates Nominal interest Nominal interest
ratesrates Equity returnsEquity returns
• Large stocksLarge stocks• Small stocksSmall stocks
Equity dividend Equity dividend yieldsyields
Real estate Real estate returnsreturns
UnemploymentUnemployment
Current Report StructureCurrent Report Structure
Text SectionsText Sections1) Intro & Overview1) Intro & Overview
2) Excerpts from RFP2) Excerpts from RFP
3) Selected Proposal3) Selected Proposal
4) Literature Review4) Literature Review
5) Data & Approach5) Data & Approach
6) Issue Discussion6) Issue Discussion
7)7) Results ofResults of
SimulationsSimulations
8) Conclusion8) Conclusion
AppendicesAppendicesA) User’s Guide toA) User’s Guide to
the Modelthe Model
B) Presentations of thisB) Presentations of this
ResearchResearch
C) Simulated FinancialC) Simulated Financial
Scenario DataScenario Data
D) Financial ScenarioD) Financial Scenario
ModelModel
Prior WorkPrior Work Wilkie, 1986 and 1995Wilkie, 1986 and 1995
• Widely used internationallyWidely used internationally Hibbert, Mowbray, and Turnbull, 2001Hibbert, Mowbray, and Turnbull, 2001
• Modern financial toolModern financial tool CAS/SOA project (a.k.a. the Financial CAS/SOA project (a.k.a. the Financial
Scenario Generator) applies Scenario Generator) applies Wilkie/HMT to U.S.Wilkie/HMT to U.S.
Relationship between Relationship between Modeled Economic SeriesModeled Economic Series
Inflation Real Interest Rates
Real EstateUnemployment Nominal Interest
Lg. Stock Returns Sm. Stock ReturnsStock Dividends
Inflation (Inflation (qq)) Modeled as an Ornstein-Uhlenbeck Modeled as an Ornstein-Uhlenbeck
processprocess• One-factor, mean-revertingOne-factor, mean-reverting
dqdqtt = = qq ((qq – – qqtt) ) dtdt + + dB dBqq
Speed of reversion:Speed of reversion: qq = 0.40 = 0.40 Mean reversion level:Mean reversion level: qq = 4.8%= 4.8% Volatility:Volatility: qq = 0.04= 0.04
Explanation of the Explanation of the Ornstein-Uhlenbeck processOrnstein-Uhlenbeck process
Deterministic componentDeterministic componentIf inflation is below 4.8%, it reverts back toward If inflation is below 4.8%, it reverts back toward 4.8% over the next year 4.8% over the next year
Speed of reversion dependent on Speed of reversion dependent on Random componentRandom component
A shock is applied to the inflation rate that is a A shock is applied to the inflation rate that is a random distribution with a std. dev. of 4%random distribution with a std. dev. of 4%
The new inflation rate is last period’s The new inflation rate is last period’s inflation rate changed by the combined inflation rate changed by the combined effects of the deterministic and the effects of the deterministic and the random components.random components.
Real Interest Rates (Real Interest Rates (rr)) Problems with one-factor interest rate modelsProblems with one-factor interest rate models Two-factor Vasicek term structure modelTwo-factor Vasicek term structure model Short-term rate (Short-term rate (rr) and long-term mean () and long-term mean (ll) are both ) are both
stochastic variablesstochastic variables
drdrtt = = rr (l (ltt – r – rtt) dt + ) dt + rr dB dBrr
dldltt = = ll ( (ll – r – rtt) dt + ) dt + ll dB dBll
Nominal Interest RatesNominal Interest Rates Combines inflation and real interest Combines inflation and real interest
ratesrates
ii = {( = {(11++qq) x () x (11++rr)} - )} - 11
where where ii = nominal interest rate = nominal interest rate
qq = inflation = inflation
rr = real interest rate = real interest rate
Figure 12 Actual 1 Year Interest Rates (4/53-4/03)
versus Model 1 Year Interest Rates
0.00
0.05
0.10
0.15
0.20
0.25
-0.1
0
-0.0
5
0.00
0.05
0.10
0.15
0.20
Interest Rate
Model
Actual
Equity ReturnsEquity Returns
Empirical “fat tails” issue regarding Empirical “fat tails” issue regarding equity returns distributionequity returns distribution
Thus, modeled using a “regime Thus, modeled using a “regime switching model”switching model”
1.1. High return, low volatility regimeHigh return, low volatility regime
2.2. Low return, high volatility regimeLow return, high volatility regime Model equity returns as an excess Model equity returns as an excess
return (return (xxtt) over the nominal interest ) over the nominal interest raterate
sstt = q = qtt + r + rtt + x + xtt
Figure 16 Actual S&P 500 (1871-2002)
versus Model Large Stock Returns
00.020.040.060.080.1
0.120.140.16
-0.8 -0.5 -0.3 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2
1 Year Return
Model
Actual
Figure 17Actual Small Stock Returns (1926-1999) versus
Model Small Stock Returns
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
-0.8 -0.5 -0.2 0.1 0.4 0.7 1 1.3 1.6 1.9 2.2 2.5
Model
Actual
Other SeriesOther Series Equity dividend yields Equity dividend yields ((y) and y) and
real estatereal estate• Mean-reverting processesMean-reverting processes
UnemploymentUnemployment ( (uu))• Phillip’s curve: inverse relationship Phillip’s curve: inverse relationship
between between uu and and qq
dudutt = = uu ((uu – u – utt)) dt + dt + uu dq dqtt + + uu utut
Selecting ParametersSelecting Parameters
Historical or calibration with current Historical or calibration with current market pricesmarket prices
Model is meant to represent range of Model is meant to represent range of outcomes possible for the insureroutcomes possible for the insurer
Default parameters are chosen from Default parameters are chosen from history (as long as possible)history (as long as possible)
Of course, different parameters may Of course, different parameters may affect analysisaffect analysis
Model DescriptionModel Description
Excel spreadsheet Excel spreadsheet Simulation package - @RISK add-inSimulation package - @RISK add-in 50 years of projections50 years of projections Users can select different parameters Users can select different parameters
and track any variableand track any variable
Applications of the Applications of the Financial Scenario GeneratorFinancial Scenario Generator
Financial engine behind many types of Financial engine behind many types of analysisanalysis
Insurers can project operations under a Insurers can project operations under a variety of economic conditions variety of economic conditions (Dynamic financial analysis)(Dynamic financial analysis)
Useful for demonstrating solvency to Useful for demonstrating solvency to regulators regulators
May propose financial risk management May propose financial risk management solutionssolutions
Pension Obligation Bonds Pension Obligation Bonds of the State of Illinoisof the State of Illinois
Severe underfunding problem for Severe underfunding problem for Illinois’ public pension programsIllinois’ public pension programs
Severe state budget crisis 2002-?Severe state budget crisis 2002-? Low interest rate environmentLow interest rate environment Issue $10 billion of bonds to meet short-Issue $10 billion of bonds to meet short-
term (interest rate ~ 5.0%)term (interest rate ~ 5.0%) Provide $7.3 billion to state pension Provide $7.3 billion to state pension
funds to invest funds to invest How risky is the strategy?How risky is the strategy?
Customizing the ModelCustomizing the Model
Use the financial scenario generator Use the financial scenario generator to develop financial market scenariosto develop financial market scenarios
Add international equitiesAdd international equities Track assets and debt obligationsTrack assets and debt obligations Are there funds remaining after the Are there funds remaining after the
debt is repaid?debt is repaid?
Asset AllocationAsset Allocation
Type of Investment AllocationSimulated
Avg Ret
Fixed Income Securities 28.3% 6.8%
U. S. Equities:
Large Stocks 40.6% 13.2%
Small Stocks 10.7% 13.7%
International Equities 18.3% 7.2%
Real Estate 2.1% 9.4%
Projected Distribution of OutcomesProjected Distribution of Outcomes
X <=010.2%
0
1
2
3
4
5
6
7
-25 50 125
How to Obtain ModelHow to Obtain Model
Coming soon to the following sites:Coming soon to the following sites: http://casact.org/research/research.htmhttp://casact.org/research/research.htm http://www.soa.org/research/index.asphttp://www.soa.org/research/index.asp
Or contact us at: Or contact us at: [email protected]@ilstu.edu
[email protected]@uiuc.edu
[email protected]@uiuc.edu