Modeling of Economic Series Research Sponsored by the Casualty Actuarial Society and the Society of ActuariesOutline of PresentationERM Frameworks: “Traditional” Risk Management ProcessCOSO ERM FrameworkSlide 5Overview of ProjectScope of ProjectEconomic Series ModeledPrior WorkRelationship between Modeled Economic SeriesInflation (q)Explanation of the Ornstein-Uhlenbeck processSlide 13Nominal Interest RatesSlide 15Equity ReturnsSlide 17Slide 18Other SeriesModel DescriptionParameter SelectionApplications of the Financial Scenario GeneratorCAS/SOA vs. AAAFunnel of Doubt Graphs 3 Month Nominal Interest Rates (U. S. Treasury Bills)Histogram of 3 Month Nominal Interest Rates Model Values and Actual Data (01/34-01/06)Funnel of Doubt Graphs 10 Year Nominal Interest Rates (U. S. Treasury Bonds)Histogram of 10 Year Nominal Interest Rates Model Values and Actual Data (04/53-01/06)Histogram of Large Stock Return Model Values and Actual Data (1872-2006)Histogram of Small Stock Return Model Values and Actual Data (1926-2004)Quantification of Model FitSlide 31Slide 32Slide 33Summary of DifferencesHow to Obtain ModelsModeling of Economic Series Research Sponsored by theCasualty Actuarial Society and theSociety of ActuariesInvestigators:Kevin Ahlgrim, ASA, PhD, Illinois State UniversitySteve D’Arcy, FCAS, PhD, University of IllinoisRick Gorvett, FCAS, ARM, FRM, PhD, University of IllinoisOutline of Presentation•Motivation for Financial Scenario Generator Project•Short description of included economic variables•An overview of the model•Applications of the model•Comparison of this model with another actuarial return generating model•ConclusionsERM Frameworks:“Traditional” Risk Management Process1. Identify loss exposure2. Measure impact potential3. Evaluate alternative methods of control4. Implement best alternative5. Monitor outcomesCOSO ERM FrameworkERM Frameworks:“Traditional” Risk Management Process1. Identify loss exposure2. Measure impact potential3. Evaluate alternative methods of control–Based on “risk appetite” of organization4. Implement best alternative5. Monitor outcomesOverview of Project•CAS/SOA Request for Proposals on “Modeling of Economic Series Coordinated with Interest Rate Scenarios”–A key aspect of dynamic financial analysis–Also important for regulatory, rating agency, and internal management tests – e.g., cash flow testing•Goal: to provide actuaries with a model for projecting economic and financial indices, with realistic interdependencies among the variables.–Provides a foundation for future effortsScope of Project•Literature review–From finance, economics, and actuarial science•Financial scenario model–Generate scenarios over a 50-year time horizon•Document and facilitate use of model–Report includes sections on data & approach, results of simulations, user’s guide–Posted on CAS & SOA websites–Writing of papers for journal publicationEconomic Series Modeled•Inflation•Real interest rates•Nominal interest rates•Equity returns–Large stocks–Small stocks•Equity dividend yields•Real estate returns•UnemploymentPrior Work•Wilkie, 1986 and 1995–Used internationally•Hibbert, Mowbray, and Turnbull, 2001–Modern financial tool•CAS/SOA project (a.k.a. the Financial Scenario Generator) applies Wilkie/HMT to U.S.Relationship between Modeled Economic SeriesInflation Real Interest RatesReal EstateUnemployment Nominal InterestLg. Stock Returns Sm. Stock ReturnsStock DividendsInflation (q)•Modeled as an Ornstein-Uhlenbeck process–One-factor, mean-revertingdqt = q (q – qt) dt +  dBq•Speed of reversion: q = 0.40•Mean reversion level: q = 4.8%•Volatility: q = 0.04Explanation of the Ornstein-Uhlenbeck process•Deterministic componentIf inflation is below 4.8%, it reverts back toward 4.8% over the next year Speed of reversion dependent on •Random componentA shock is applied to the inflation rate that is a random distribution with a std. dev. of 4%•The new inflation rate is last period’s inflation rate changed by the combined effects of the deterministic and the random components.Real Interest Rates (r)•Problems with one-factor interest rate models•Two-factor Vasicek term structure model•Short-term rate (r) and long-term mean (l) are both stochastic variablesdrt = r (lt – rt) dt + r dBrdlt = l (l – lt) dt + l dBlNominal Interest Rates•Combines inflation and real interest ratesi = {(1+q) x (1+r)} - 1where i = nominal interest rateq = inflationr = real interest rateHistogram of 10 Year Nominal Interest Rates Model Values and Actual Data (04/53-01/06) 00.10.20.30.40.0000.0050.0150.0250.0350.0450.0550.0650.0750.0850.0950.1050.1150.1250.1350.1450.1550.1650.1750.185CAS-SOA ModelActual DataEquity Returns•Empirical “fat tails” issue regarding equity returns distribution•Thus, modeled using a “regime switching model”1. High return, low volatility regime2. Low return, high volatility regime•Model equity returns as an excess return (xt) over the nominal interest ratest = qt + rt + xtHistogram of Large Stock ReturnModel Values and Actual Data (1872-2006)00.050.10.150.20.25-0.75-0.65-0.55-0.45-0.35-0.25-0.15-0.050.050.150.250.350.450.550.650.750.850.951.051.151.251.351.451.551.651.751.85CAS-SOA ModelActual DataHistogram of Small Stock ReturnModel Values and Actual Data (1926-2004)00.050.10.150.20.25-0.75-0.65-0.55-0.45-0.35-0.25-0.15-0.050.050.150.250.350.450.550.650.750.850.951.051.151.251.351.451.551.651.751.85CAS-SOA ModelActual DataOther Series•Equity dividend yields (y) and real estate–Mean-reverting processes•Unemployment (u)–Phillip’s curve: inverse relationship between u and qdut = u (u – ut) dt + u dqt + u utModel Description•Excel spreadsheet •Simulation package - @RISK add-in•50 years of projections•Users can select different parameters and track any variableParameter Selection•Selecting parameters can be based on:1. Matching historical distributions or 2. Replicating current market prices (calibration)•Of course, different parameters may yield different results•Model is meant to represent range of outcomes deemed “possible” for the insurer–Default parameters are chosen from history (as long as possible)Applications of the Financial Scenario Generator•Financial engine behind many types of analysis•Insurers can project operations under a variety of economic