Finance 590Enterprise Risk Management

Steve D’ArcyDepartment 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• 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

• Hazard or Insurance Risk

• Financial or Market Risk

• Credit Risk

• Operational Risk

• Strategic Risk

Hazard Risk Management Analytics

• 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

• 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 MeasuresGeneral

• 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 MeasuresInsurance Industry

• Economic Capital

• RAROC – Expected net income divided by economic capital

• Embedded value

• Risk Based Capital (RBC)

Risk MeasuresSolvency 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

Risk MeasuresPerformance Related

• Variance

• Standard Deviation

• Semi-variance and Downside Standard Deviation

• Below-target-risk (BTW)

Risk Modeling

• 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• 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

• 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

– 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 80%– 1 15%– 2 5%

• Loss severity– $1,000 40%– $10,000 30%– $25,000 20%– $100,000 10%

Hazard Risk Example (2)Probability of losses Total Losses Prob. Expected Losses1 loss 0 0.8000 0

1000 0.060 1000 0.0600 6010000 0.045 2000 0.0080 1625000 0.030 10000 0.0450 450

100000 0.015 11000 0.0120 13220000 0.0045 90

2 losses 1000 10000 25000 100000 25000 0.0300 7501000 0.0080 0.0060 0.0040 0.0020 26000 0.0080 208

10000 0.0060 0.0045 0.0030 0.0015 35000 0.0060 21025000 0.0040 0.0030 0.0020 0.0010 50000 0.0020 100

100000 0.0020 0.0015 0.0010 0.0005 100000 0.0150 1500101000 0.0040 404

Total value of two losses 110000 0.0030 3302000 11000 26000 101000 125000 0.0020 250

11000 20000 35000 110000 200000 0.0005 10026000 35000 50000 125000 1.0000 4600

101000 110000 125000 200000

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

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