Finance 590
Enterprise Risk Management
Steve D’Arcy
Department of Finance
Lecture 2
Risk Analytics
March 28, 2006
Reference Material
• Chapters 8 and 9 – Enterprise Risk Management
by Lam
• Overview of Enterprise Risk Management by
the Casualty Actuarial Society
http://www.casact.org/research/erm/overview.pdf
• Risk and Insurance by Anderson and Brown
http://www.soa.org/ccm/cms-service/stream/asset/?asset_id=8027034
Overview
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Risk Control Analytics
Risk Optimization Analytics
Classification of Risk Types
Risk Analytics by Risk Type
Performance Measures
Risk Measures
Risk Modeling
Risk Integration
Characteristics of Hazard Risk
Insurance Terminology
Risk Control Analytics
• Scenario Analysis
– Stress testing
– Simulation
• Economic Capital
– Solvency standards
• Risk Indicators
– External
– Internal
Risk Optimization Analytics
• Return on Capital (Financial Services Industry)
– Risk-adjusted return on capital (RAROC)
– Return on risk-adjusted capital (RORAC)
– Risk-adjusted return on risk-adjusted capital
(RARORAC)
• Economic Income Created
– Risk-adjusted return – (Hurdle rate x economic capital)
• Shareholder Value
– Shareholder value (SHV)
– Shareholder value added (SVA)
Risk Types
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Hazard or Insurance Risk
Financial or Market Risk
Credit Risk
Operational Risk
Strategic Risk
Hazard Risk Management Analytics
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Probable Maximum Loss (PML)
Maximum Possible Loss (MPL)
Loss Frequency
Loss Severity
Actuarial Models
– Loss Distributions
Financial Risk Management
Analytics
• Interest Rate Models
– Equilibrium models
– Arbitrage free models
• Value-at-Risk (VaR)
– Parametric
– Monte Carlo simulation
– Historical simulation
• Asset/Liability Management (ALM)
Credit Risk Analytics
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Credit Scoring Models
Credit Migration Models
Credit Exposure Models
Credit Portfolio Models
– Financial models
– Econometric models
– Actuarial models
Operational and Strategic Risk
Analytics
• Top-Down Approaches
– Analogs
– Historical loss data
• Bottom-Up Approaches
– Self assessment
– Cash flow model
Performance Measures
General
• Return on Equity (ROE)
• Operating Earnings
• Earnings before interest, dividends, taxes,
depreciation and amortization (EBITDA)
• Cash Flow Return on Investments (CFROI)
• Weighted Average Cost of Capital (WACC)
• Economic Value Added (EVA)
Performance Measures
Insurance Industry
• Economic Capital
• RAROC
– Expected net income divided by economic capital
• Embedded value
• Risk Based Capital (RBC)
Risk Measures
Solvency Related
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Probability of Ruin
Shortfall Risk
Value-at-Risk (VaR)
Expected Policyholder Deficit (EPD) or
Economic Cost of Ruin (ECOR)
• Tail Value at Risk (Tail VaR) or Tail
Conditional Expectation (TCE)
• Tail Events
Risk Measures
Performance Related
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Variance
Standard Deviation
Semi-variance and Downside Standard Deviation
Below-target-risk (BTW)
Risk Modeling
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Analytic Methods
Simulation Methods
Statistical Methods
Structural Methods
Dynamic Financial Analysis (DFA)
Risk Integration
• Covariance
• Covariance Matrix
• Structural Simulation Model
Characteristics of Hazard Risk
• Loss/no loss situations (pure risk)
• Independence of individual exposures
– Important for risk to be insurable
• Types of hazard risk
– Persons
– Property
– Liability
Insurance Terminology
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Exposures
Deductibles or retentions
Policy limits
Coinsurance
Claims or losses
– Incurred
– Paid
– Loss adjustment expenses
• Loss frequency and severity
• Triggers
Alternative Risk Transfer (ART)
Terminology
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Captives
Finite insurance or reinsurance
Insurance-linked bonds
Insurance securitization
Cat-E-Puts (Catastrophe equity put options)
Contingent surplus notes
Loss Frequency
• Number of losses during policy period
• Often modeled as a Poisson distribution
Pr(k) = e-λλk/k!
where Pr = probability
k = number of claims per year (0,1,2,...)
λ = expected number of claims per year
Loss Severity
• Size of loss given a loss has occurred
• Variety of potential severity distributions
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Empirical
Exponential (Gamma)
Lognormal
Pareto
• Distribution characteristics
– Non-negative
– Positively skewed
– Variance positively correlated with mean
Hazard Risk Example
• Assume independent losses
• Loss frequency
–0
–1
–2
80%
15%
5%
• Loss severity
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$1,000
$10,000
$25,000
$100,000
40%
30%
20%
10%
Hazard Risk Example (2)
Probability of losses
1 loss
1000
0.060
10000
0.045
25000
0.030
100000
0.015
2 losses
1000
10000
25000
100000
1000
0.0080
0.0060
0.0040
0.0020
10000
0.0060
0.0045
0.0030
0.0015
25000
0.0040
0.0030
0.0020
0.0010
100000
0.0020
0.0015
0.0010
0.0005
Total value of two losses
2000
11000
26000
11000
20000
35000
26000
35000
50000
101000 110000 125000
101000
110000
125000
200000
Total Losses Prob.
Expected Losses
0 0.8000
0
1000 0.0600
60
2000 0.0080
16
10000 0.0450
450
11000 0.0120
132
20000 0.0045
90
25000 0.0300
750
26000 0.0080
208
35000 0.0060
210
50000 0.0020
100
100000 0.0150
1500
101000 0.0040
404
110000 0.0030
330
125000 0.0020
250
200000 0.0005
100
1.0000
4600
Analysis of Potential Losses
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Expected losses = 4,600
Maximum possible loss = 200,000
Maximum probable loss (0.25%) = 125,000
Expected losses excess of a $100,000 retention
= 1,084
Current State of Hazard Risk Management
• Insurance industry has developed a high level of
mathematical sophistication for valuing hazard
risks
• Alternative market has also developed for
dealing with hazard risks
• Key questions for organizations involve amount
of risk to retain (deductible) and how much
coverage to purchase (policy limits)
• These questions begin to tie hazard risk into
enterprise risk management
Conclusion
• There is a standard approach for dealing with
each type of risk
• Each area has its own terminology and
techniques
• The ERM challenge is to combine these
different approaches into a common method
that can deal with risk in an integrated manner
• The first step is to understand the different
approaches