Financial Risk Management of Insurance Enterprises Dynamic Financial Analysis 1. D’Arcy, Gorvett, Herbers, and Hettinger - Contingencies 2. D’Arcy and Gorvett - JRI

Overview What is DFA? How is it different from other modeling procedures? How did DFA evolve? What are the basic approaches in DFA modeling?

Dynamic, Financial, Analysis Dynamic –“Energy, continuous activity, intensity, interactive” –Insurer variables are not fixed, but stochastic Financial –“Related to management of money or investments” –Evaluate insurer activities, both liabilities and assets Analysis –“Examination of an interrelated system and its elements”

Definition of Dynamic Financial Analysis (DFA) Casualty Actuarial Society definition: –Analyze the financial condition of an insurance enterprise –Financial condition refers to ability of capital and surplus to meet future obligations of insurer in “unknown future environment” –For life insurers, similar modeling procedures are known as dynamic solvency testing or dynamic financial condition analysis

A Broader Concept DFA does not need to focus only on solvency issues Other uses: –Model ongoing operations over time instead of concentrating on the current position –Determining the sensitivity of financial results to various environmental factors –Identify specific scenarios where the insurer is exposed to significant risk of loss –Valuation of a line of business or entire insurer

Definitions Appointed actuary –A “qualified” actuary that is appointed by the Board of Directors of an insurer –Files actuarial opinion with the states stating that all reserves are appropriate and assets are adequate to meet liabilities

Analytic vs. Simulation Analytic model provides exact solution based on precise relationships Simulation models can be used if exact mathematical representations do not exist –Can accommodate complex relationships The “answer” in a simulation model is not just one number –It is a range or distribution of plausible results

Prior Techniques Previous models evaluated insurer strategies under certain assumptions with respect to: –Asset returns –Underwriting results –Economic environment (recession, expansion) Typically, these models ignored interaction of assets and liabilities The future was assumed to be essentially the same as the present –Regardless of lifetime of policy/project

The Impetus Behind DFA Interest rate fluctuations in the 1970s –Life insurers are sensitive to interest rate changes –Disintermediation resulted from high interest rates Rating agencies began to consider effect of interest rate swings on surplus/solvency

The “Seeds” of DFA RBC is first attempt at linking capital to risk of insurers –The various RBC factors are the same for all insurers RBC has short term focus DFA customizes the analysis by accounting for specific insurer business plan both now and in the future

The DFA Approach Model variability of all important variables –Claims, catastrophes –Asset returns –Premium income Account for correlation among all factors within each scenario –When modeling the entire insurer, include correlation among lines of business Project cash flows under the assumptions Determine the insurer’s financial position

Two Approaches to DFA: (1) Scenario Testing Select several assumptions for all variables –e.g., optimistic, pessimistic, and average A scenario is a set of assumptions about the future environment Determine financial position Better than point estimate but does not provide any likelihood information Range of outcomes is frequently too wide to make decisions

Two Approaches to DFA: (2) Stochastic Simulation Select distributions for and correlations among all variables Draw randomly from each distribution Determine the aggregate financial outcome for each iteration –Incorporate any variable interactions Analyze distribution of outcomes

Uses of Stochastic Simulation Stochastic simulation provides more information than scenario testing Use of information depends on objectives –How often does insurer go insolvent? –Which assumptions are the most critical? –What accounts for good/bad scenarios? If possible, select hedges to protect against bad scenarios

Categories of Insurer Risk Balance sheet risk –Changes in value of assets and liabilities Operating risk –Investment and underwriting activities Actuaries have traditionally looked at liabilities and underwriting Balance sheet and operating risks are interrelated

Building a DFA Model Determine the objective –Evaluating solvency, valuation of a block of business or insurer Include only the most relevant factors –Only model general asset classes such as bonds, equities, and mortgages –Reserves should reflect economic value and incorporate discounting Model only the factors that are measurable

Variables in a DFA Model Claim distributions are a result of frequency and severity Frequency of claims is affected by: –Catastrophe –Society trends (e.g., smoking, speed limit) Severity of claims is affected by inflation

DFA for Life Insurers Life insurer products are long term and are interest rate sensitive –Option of policyholder to withdraw is very important Cash flow testing is a primitive form of DFA –Test adequacy of assets vs. liabilities under a few scenarios –NY Regulation 126 specifies seven scenarios

NY 126 Interest Rate Scenarios Remain level for 10 years Increase ½ % per year for 10 years Increase 1% for 5 years, then decrease 1% for 5 years Pop-up 3% immediately, then level Pop-down 3% immediately, then level Decrease ½ % per year for 10 years Decrease 1% for 5 years, then increase 1% for 5 years

Dynamic Financial Analysis Model How to Access and Run DFA Model Components of Model Underwriting ModuleCatastrophe Module Financial ModuleTax Module Reinsurance Module Generating and Using the Output Future of DFA

Basics of DFA Model Model is available for general use at: Runs with Microsoft Excel Entire model subject to peer review Key variables of concern to U.S. property- liability insurers included Model is as simplified as practical Flexibility for future enhancements Potential use as a DFA teaching tool

Underwriting Module Loss Frequency and Severity Rates and Exposures Underwriting Cycle Jurisdictional Risk Aging Phenomenon

New business has a very high loss ratio, often in excess of the initial premium The loss ratio then declines with each renewal cycle to the profitable point Longer-term business has an even lower loss ratio, making it very profitable A P-L insurer’s growth rate has a significant effect on profitability

Catastrophe Module Number based on Poisson distribution Focal point determined Size based on lognormal distribution Geographical distribution determined by correlation matrix Loss allocated to company based on market share

Financial Module Financial Variables Short-Term Interest Rate Term Structure Default Premium Default Risk Equity Premium (Market Risk Premium) Inflation

Short-Term Interest Rate Based on U.S. Treasury Bill rate Considered the “Workhorse” Variable Correlated with other variables Impacts market values of assets Add risk-premiums to derive other asset rates of return Term premium Default premium Equity premium

Short-Term Interest Rate Cox-Ingersoll-Ross Model dr = a(b-r)dt + sr 0.5 dz r = short term interest rate a = speed of mean reversion = b = mean interest rate = s = volatility parameter = Volatility proportional to square root of r Values taken from Chan, et al, 1992 Journal of Finance

Inflation Affects future values of liabilities Function of: Contemporaneous interest rates Current yield spreads Some autoregressive properties Three-step simulation process Simulate short-term interest rate Simulate general inflation rate Determine claim inflation by line of business

Tax Module Calculates income taxes based on both standard corporate tax rate and alternative minimum tax

Reinsurance Module Current approach Quota share reinsurance Under development Excess of loss Catastrophe Aggregate excess

Using the DFA Output Proportion of outcomes that are unacceptable Revise operations and rerun Analysis of the unacceptable outcomes Reduce risk that led to result Useful for: Solvency Testing Business Planning

Utilize a DFA model to determine the optimal growth rate based on - mean-variance efficiency - stochastic dominance - constraints of leverage Objective of Optional Growth Paper

Market Value of P-L Insurance Company Determining the market value of a hypothetical property-liability insurer is not a simple task. Only a few P-L insurers are stand-alone companies that are publicly traded, allowing the market value of the firm to be observed

The market value of an insurer is measured by - Policyholders’ Surplus - Net Written Premium (the size of the book of business) - Combined Ratio and Operating Ratio (profitability) Multiple Regression Approach

Mean-Variance illustration

Operating Constraints The optimal growth rate cannot be determined based on –mean-variance analysis –first- or second-degree stochastic dominance Impact of adding constraints

Constraining Premium-to-Surplus Ratios The proportion of outcomes that lead to unacceptable premium-to-surplus levels can be added as a constraint in the maximization process.

The Future of DFA Is becoming a widely used actuarial tool Will cause actuaries to work on both asset and liability sides of insurance business Will require actuaries to become proficient with financial tools and techniques Will increase the importance of finance on actuarial exams