1 Math 479 / 568 Casualty Actuarial Mathematics Fall 2014 University of Illinois at Urbana-Champaign Professor Rick Gorvett Session 17: Dynamic Financial Analysis November 18, 2014

What is Dynamic Financial Analysis Dynamic –Stochastic / variable –Not deterministic / fixed / static –Reflects uncertainty Financial –Integration of underwriting and finance –Assets and liabilities Analysis –“ An examination of a complex, its elements and their relations ” –Complex: “ a whole made up of complicated or interrelated parts ”

What is DFA? (cont.) “ Dynamic Financial Analysis is the process by which an actuary analyzes the financial condition of an insurance enterprise. Financial condition refers to the ability of the company ’ s capital and surplus to adequately support the company ’ s future operations through an unknown future environment. : The process of DFA involves testing a number of adverse and favorable scenarios regarding an insurance company ’ s operations. DFA assesses the reaction of the company ’ s surplus to the various selected scenarios. ” -- CAS DFA Handbook

Key Ideas in this Definition “ Financial condition ” –Specifically, capital and surplus “ Future operations ” –Going concern “ Unknown future environment ” –Uncertainty / stochastic “ Testing a number of.... scenarios ” –Analysis across different environments “ Assesses the reaction of.... surplus ” –Analyze acceptability of results

What is a “ Model ” ? “ A model is a set of verifiable mathematical relationships or logical procedures which is used to represent observed, measurable real-world phenomena, to communicate alternative hypotheses about the causes of the phenomena, and to predict future behavior of the phenomena for the purposes of decision-making. ” - William S. Jewell, 1983, “ A Survey of Mathematical Models in Insurance ” (Emphases added)

Distinguishing Characteristics of DFA Incorporates both liability and asset processes Accounts for the stochastic nature of insurance operations Treats company as an ongoing operation -- Warthen and Sommer “ Dynamic Financial Modeling - Issues and Approaches ”

Types of DFA Scenario testing –Projects results under specific conditions –Catastrophe, interest rate shift –Used for cash flow or stress testing –New York Life Insurance Regulation 126 Stochastic simulation –Models uncertainty by distributions –Uses randomly selected values to calculate a large number of outcomes –Evaluate risk by proportion of unacceptable outcomes

8 Where and Why Did DFA First Emerge? Banks first began to develop DFA-type models –Result of the S&L crisis caused by interest rate increases –Determine impact of an economic event –Quantify risk (e.g., VaR, earnings volatility) –Depends on asset correlations Later spread to non-financial corporations and insurers

What Caused DFA to Become an Important Issue for Insurers? Data per FRED, St. Louis FRB, for 3-Month T-Bills, Secondary Market

What Caused DFA to Become an Important Issue for Insurers? (cont.) Data per FRED, St. Louis FRB, for 3-Month T-Bills, Secondary Market

Duration Measures the sensitivity of a financial instrument to interest rate changes Macaulay duration measures the weighted average time to receipt of the cash flow If the cash flow is insensitive to changes in the interest rate, then Macaulay duration (more precisely, modified duration) is a reasonable approximation of interest rate sensitivity Otherwise, duration must be measured by changes in the present value of the cash flow

Surplus Duration: Sensitivity of Surplus to Interest Rate Changes D S S = D A A - D L L D S = (D A - D L )(A/S) + D L D =Duration S =Surplus A = Assets L= Liabilities

Life Insurers D S = ( D A - D L )(A/S) + D L Let D A = 12 D L = 10 S = 1 A = 20 Then D S = (12-10)(20/1) + 10 = 50  With a two year duration mismatch, for every 1% increase in interest rates, the insurer ’ s surplus declines by 50%. For example

Important Distinctions between Life and Property-Liability Insurers P-L insurers less sensitive to interest rate risk New business loss experience –Life insurers - select mortality –P-L insurers - higher new business loss ratio Catastrophe exposure greater for P-L insurers Rate regulation significantly affects P-L insurers Inflation affects P-L insurance loss costs

Property-Liability Insurers D S = ( D A - D L )(A/S) + D L Let D A = 6 D L = 4 S = 1 A = 3 Then D S = (6-4)(3/1) + 4 = 10  With a two year duration mismatch, for every 1% increase in interest rates, the insurer ’ s surplus declines by 10%. For example

What Can DFA Accomplish? DFA is to financial planning what confidence intervals are to loss reserving DFA allows users to look at the distribution of potential financial developments under specific conditions DFA allows users to change the conditions and examine the effects of the change DFA is a critical step in financial risk management

Financial Risk Management Steps Determine the corporation ’ s objectives Identify risk exposure (e.g., interest rate risk) Quantify the exposure (e.g., measure volatility) Assess the impact (DFA) Examine financial risk management tools –Reinsurance, business plans –Forwards, futures, options, swaps –Contingent risk financing Select appropriate risk management approach Implement and monitor program

DFA in Canada “ Dynamic Capital Adequacy Testing ” (DCAT) “ (DCAT) is the process of analyzing and projecting the trends of a company ’ s capital position given its current circumstances, its recent past, and its intended business plan under a variety of future scenarios…. The DCAT process is to include the running of a base scenario and several adverse scenarios… ” -- Canadian Institute of Actuaries, Dynamic Capital Adequacy Testing – Life and Property and Casualty

DFA in Canada (cont.) “ (One possible approach would consist of…) … ‘ stress- testing ’ of the risk category in question… Stress- testing means a determination of just how far the risk factor in question has to be changed in order to drive the company ’ s surplus negative during the forecast period, and then evaluating if that degree of change is plausible or not. When stochastic models with reasonable predictability are available, an adverse scenario would be considered plausible if all remaining probability in the tail beyond this scenario is in the range of 1% to 5%. ” -- Ibid

20 DFA Models Most DFA models are proprietary For educational purposes, significant transparency is desirable DynaMo is public-access DFA software – available at t-actuarial-consulting- firm/solutions/actuarial-products/dynamic- financial-analysis/dynamo

21 Objectives of “ DynaMo ” Develop a financial model for a U.S. property-liability insurer that is: –Realistic enough to be useable –Simple enough to be understood –Freely available

22 Caveats Any model is a simplified version of reality This model deals with quantifiable risk only –Examples of excluded items: A line of business being socialized Management fraud Devastating meteor strike

23 What Does DynaMo Do? Simulates results for the next 5 years Generates financial statements –Balance sheet –Operating statement –IRIS results Indicates expected values and distribution of results for any value selected

24 What Corporate Info is Required? Underwriting data –Premiums and exposures, by line, state, and age –Renewal patterns –Projected growth rates –Loss frequency and severity –Loss development patterns –Reinsurance program Investment data –Statutory and market asset values by asset class –Maturities and coupon rates for bonds –Beta for equity portfolio

U/W Inputs Investment & Economic Inputs U/W Generator Payment Patterns U/W Cycle Catastrophe Generator Investment Generator U/W Cashflows Investment Cashflows Tax Outputs & Simulation Results DynaMo Interest Rate Generator

26 Specific Provisions of DynaMo Six separate, but interrelated modules InvestmentsCatastrophes UnderwritingTaxation Interest rate generatorLoss reserve dev. Multi-state Multi-line For each line of business –New business –1st renewals –2nd and subsequent renewals

Key DFA Variables in DynaMo Financial Short-term interest rate Term structure Default potential Equity performance Inflation Mortgage pre-payment patterns Underwriting Loss freq. / sev. Rates and exposures Expenses Underwriting cycle Loss reserve dev. Jurisdictional risk Aging phenomenon Payment patterns Catastrophes Reinsurance Taxes

Short-Term Interest Rate U.S. Treasury bills The “ workhorse ” variable - Correlated with other variables -Impacts market values Add “ premiums ” to derive asset rates of return: –Term premiums ==> Longer-term gov ’ ts. –Default premium ==> Corporate bonds –Equity premium ==> Stocks

29 Short-Term Interest Rate Generator Cox-Ingersoll-Ross one factor model

Other Interest Rate Models Are Possible Many different interest rate models are used in academia and on Wall Street –Vasicek –Cox-Ingersoll-Ross –Hull and White –Black-Derman-Toy –Heath-Jarrow-Morton One- versus multi-factor models Equilibrium versus arbitrage-free models

31 Investment Risk: Summary Bonds –Market values calculated based on term structure of interest rates –Includes provision for default premiums Equities: –Function of Historical patterns Contemporaneous changes in interest rates –Change in value of insurer ’ s equity portfolio is a function of its systematic risk

Inflation Affects future values of liabilities In theory, a function of –Contemporaneous interest rates –Current yield spreads –Some autoregressive properties Three-step simulation process 1) Simulate interest rate 2) Simulate general inflation rate 3) Determine claim inflation by line

Losses (non-cat.) Frequency and Severity Modeled separately By line of business Based on historic variability Stochastically generated Aging phenomenon

Pricing: Rates and Exposures Future Rates -- Function of –Underwriting cycle –Current rates –Interest rates –Inflation –Jurisdictional risk Exposures -- Function of –Management ’ s growth objectives –Retention ratios

35 Underwriting Cycle Four phases: Immature hardMature hard Immature softMature soft Each phase has different supply-demand relationship Probability distribution for moving to different phase next period New business penalty

36 Loss Reserve Development Risk Initial reserve levels based on actuarial analysis, not statement values Still subject to random variation Inflation also affects reserve development –Initial reserves reflect specific inflation rate –Changes in inflation rate affect development

Jurisdictional Risks Insurance Risk Unique to Geographical Location Loss ratio volatility Rate change constraints Residual market burdens Legislative climate Competition

38 Jurisdictional Risk (cont.) State specific Range of rate changes established –Narrower range in more restrictive states Time lag for implementing rate change –Longer in more restrictive states –Increases take longer to implement than decreases

Payment Patterns Historical loss triangles Selected age-to-age development factors Variability around “ mean ” selected factors from historical data Beta distribution fit for each age-to-age period

40 Catastrophe Risk Poisson distribution for number of catastrophes Each catastrophe assigned to a geographic focal point Based on focal point, size of catastrophe is determined based on a lognormal distribution Geographical “ contagion ” factor is used to distribute catastrophe to nearby states Losses allocated to company based on market share by state

Using the DFA Output Proportion of outcomes that are unacceptable –Revise operations and re-run Analysis of the unacceptable outcomes –Reduce risk that led to result Useful for: –Solvency testing – Business planning

42 Year 2004 Surplus Distribution Original Assumptions

43 Year 2004 Surplus Distribution Constrained Growth Assumptions

Outputs Available 5-year projections Balance sheets Income statements Loss ratio reports IRIS tests Others as needed –Select any cell of spreadsheet –Graphs and histograms

Model Uses Internal Strategic Planning Ratemaking Reinsurance Valuation / M&A Market Simulation and Competitive Analysis Asset / Liability Management External External Ratings Communication with Financial Markets Regulatory / Risk- Based Capital Capital Planning / Securitization

DFA in Canada “ … the concept of capital adequacy envisioned by DCAT extends beyond the balance sheet at a specific date to the continued vitality of the organization… The principal goal of this process is to help prevent insolvency by arming the company with the best information on the course of events that may lead to capital depletion, and the relative effectiveness of alternative corrective actions. ” -- Canadian Institute of Actuaries, ibid.