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 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 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 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 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)

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