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: kahlgrim@ilstu.edukahlgrim@ilstu.edu

s-darcy@uiuc.edus-darcy@uiuc.edu

gorvett@uiuc.edugorvett@uiuc.edu