1. Finance 590 Enterprise Risk Management
Steve D’Arcy Department of Finance
Lecture 2
Risk Analytics
March 28, 2006

2. Reference Material
Chapters 8 and 9 – Enterprise Risk Management by Lam
Overview of Enterprise Risk Management by the Casualty Actuarial Society
Risk and Insurance by Anderson and Brown

3. Overview 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

4. Risk Control Analytics
Scenario Analysis
Stress testing
Simulation
Economic Capital
Solvency standards
Risk Indicators
External
Internal

5. 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)

6. Risk Types Hazard or Insurance Risk Financial or Market Risk
Credit Risk
Operational Risk
Strategic Risk

7. Hazard Risk Management Analytics
Probable Maximum Loss (PML)
Maximum Possible Loss (MPL)
Loss Frequency
Loss Severity
Actuarial Models
Loss Distributions

8. 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)

9. Credit Risk Analytics Credit Scoring Models Credit Migration Models
Credit Exposure Models
Credit Portfolio Models
Financial models
Econometric models
Actuarial models

10. Operational and Strategic Risk Analytics
Top-Down Approaches
Analogs
Historical loss data
Bottom-Up Approaches
Self assessment
Cash flow model

11. 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)

12. Performance Measures Insurance Industry
Economic Capital
RAROC
Expected net income divided by economic capital
Embedded value
Risk Based Capital (RBC)

13. Risk Measures Solvency Related
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

14. Risk Measures Performance Related
Variance
Standard Deviation
Semi-variance and Downside Standard Deviation
Below-target-risk (BTW)

15. Risk Modeling Analytic Methods Simulation Methods Statistical Methods
Structural Methods
Dynamic Financial Analysis (DFA)

16. Risk Integration Covariance Covariance Matrix
Structural Simulation Model

17. 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

18. Insurance Terminology
Exposures
Deductibles or retentions
Policy limits
Coinsurance
Claims or losses
Incurred
Paid
Loss adjustment expenses
Loss frequency and severity
Triggers

19. Alternative Risk Transfer (ART) Terminology
Captives
Finite insurance or reinsurance
Insurance-linked bonds
Insurance securitization
Cat-E-Puts (Catastrophe equity put options)
Contingent surplus notes

20. 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

21. Loss Severity Size of loss given a loss has occurred
Variety of potential severity distributions
Empirical
Exponential (Gamma)
Lognormal
Pareto
Distribution characteristics
Non-negative
Positively skewed
Variance positively correlated with mean

22. Hazard Risk Example Assume independent losses Loss frequency
0 80%
1 15%
2 5%
Loss severity
$1, %
$10,000 30%
$25,000 20%
$100,000 10%

23. Hazard Risk Example (2)

24. Analysis of Potential Losses
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

25. 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

26. 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