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 Module Catastrophe Module

Financial Module Tax Module

Reinsurance Module

Generating and Using the Output

Future of DFA

Basics of DFA ModelModel is available for general use at:

http://www.pinnacleactuaries.com/servicesproducts.asp

Runs with Microsoft Excel and @Risk

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

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

Automobile Insurance Loss Ratios by Age of Cohort

0

20

40

60

80

100

120

1 2 3 4 5 6 7 8 9 10 11 12

Age of Cohort (in Years)

Los

s R

atio

(%

)

Firm A

Firm B

Firm C

Firm D

Firm E

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 RateBased 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 RateCox-Ingersoll-Ross Model

dr = a(b-r)dt + sr0.5dz

r = short term interest rate

a = speed of mean reversion = 0.2339

b = mean interest rate = 0.0808

s = volatility parameter = 0.0854

Volatility proportional to square root of r

Values taken from Chan, et al, 1992 Journal of Finance

InflationAffects 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 illustrationTable 4Base Case

1 2 3 4 5 6 7 8 9 10

NI+22701635+2.13*PHS+ Standard Deviation

(Column 6) NI+1906580+1.85*PHS+ Standard Deviation

(Column 8)

Growth Rate 1.57*NWP-23787168*CR

(000) 0.28*NWP-2076192*CR

0% 55,234 13,239 68,956 1.057 236,706 17,621 134,442 17,968 0.6%

2.5% 52,252 10,547 78,531 1.060 242,633 19,941 128,908 20,171 1.2%

5% 48,632 7,243 89,079 1.063 248,091 24,181 121,853 23,745 3.0%

7.5% 44,059 3,012 100,661 1.069 252,180 30,556 112,394 28,896 15.2%

10% 38,277 -2,400 113,292 1.076 254,112 39,253 99,807 35,801 42.0%

12.5% 31,028 -9,247 127,027 1.085 253,178 50,543 83,376 44,672 76.8%

15% 22,117 -17,732 141,934 1.096 248,855 64,099 62,558 55,345 91.6%

Unacceptable Premium to

Surplus Ratio

Without AIG

Mean Values of 500 Simulations

PHS in 2007 (000)

NI from 2003-07

(000) NWP in

2007 (000) CR in 2007

All Companies

Figure 3Histogram of Company Values

under Different Projected Growth RatesBase Case

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

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160

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180

190

-9 -7 -5 -3 -1 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45

Each Unit is $10 Million

Fre

qu

ency

(O

ut o

f 500

Sim

ula

tion

s)

0% 2.50% 5% 7.50% 10%

Figure 4Commulative Distribution of Company Values

under Different Projected Growth RatesBase Case

0. 00

0. 10

0. 20

0. 30

0. 40

0. 50

0. 60

0. 70

0. 80

0. 90

1. 00

-9 -7 -5 -3 -1 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45

Each Unit is $10 Million

Pro

bab

ility

0% 2.50% 5% 7.50% 10%

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