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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
150
160
170
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.
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