Lotter Actuarial Partners 1 Pricing and Managing Derivative Risk Risk Measurement and Modeling Howard Zail, Partner AVW

2 Risk Measurement and Modeling Laying the Foundations –Establish business-driven risk management goals –Identifying risks Risk Management Metrics –Value-at-Risk –Risk-Adjusted Performance Measurement –Others –Adjusting metrics designed for banking industry for use in the insurance industry Modeling Approach –Parametric Modeling, Distributional Approaches –Historic Simulation –Stress testing techniques Avoiding the Pitfalls –Stochastic vs. Parameter Risk –Correlation risk –Comparing the “Statistical” and “Market” price of risk –Communicating Results to Target Audiences

3 Laying the Foundations

4 Establish Business-Driven Risk Management Goals Modeling process must provide practical answers to questions like: –How much capital is required to support business? –Where should we be investing our equity? –What risks should we keep and what risks should we pass to others? –How do we compare different types of risks on a consistent basis? –What instruments best hedge our risks?

5 Identify The Key Risks Financial Market Risk –Interest rate risk –Equity –Liability option Credit Risk –Non financial market (fixed income, credit derivatives) –Counterparty risk (credit risk exposure to reinsurers, OTC counterparty) Operational Risk –Underwriting Liquidity

6 Risk Management Metrics

7 Definition of Value-at-Risk JP Morgan Definition: Value at Risk is a measure of the maximum potential change in value of a portfolio of financial instruments over a pre-set horizon. or VaR answers the question: How much can I lose with x% probability over a given time horizon?

8 What is Value-at-Risk

9 Uses of VaR Risk reporting Portfolio optimization Component of performance measurement & product pricing Capital allocation Limit setting Deriving economic capital

10 Example of VaR Risk Reporting Goldman Sachs daily VaR (95% level) CategoryDaily VaR ($ in millions) Interest Rate Risk $ 39 Currency Rates 13 Equity Prices 21 Commodity Prices 12 Diversification effect (33) Total $ 52

11 Pros and Cons of VaR Simple to understand Rating agencies are beginning to use the methodology Widely used in banking industry Accepted by banking regulators Requires a lot of work to implement firm-wide Relatively new to insurance industry Not yet accepted by insurance regulators Various technical problems

12 VaR and Economic Capital EC is the amount of capital that an institution would devote to support its financial activities in the absence of regulatory constraints VaR can be used as a proxy for economic capital with some adjustments: –Time horizon –Confidence level –Targeted credit Rating –Present Value

13 Other Risk Measures Variance / Standard Deviation Downside variance Maximum Possible Loss Shortfall measures / tail outcomes

14 Why Analyze Economic Capital Regulatory capital (e.g. RBC) may be too high or too low relative to an institutions risk profile Actual capital held is rarely the most efficient amount of capital

15 Risk Adjusted Performance Measurement (RAPM) (Single period model)

16 An Example of RAPM StrategyNotionalE[Profit]IRRStandard Deviation VaR Unhedged$400 m$ 5 m15%816 Hedged$400 m$ 2 m10%24 Should we hedge a portfolio of 1-year GIC’s?

17 An Example of RAPM (cont’d) Traditional financial analysis suggests that we should remain unhedged: –IRR unhedged > IRR hedged –NPV unhedged > NPV hedged

18 An Example of RAPM (cont’d) RAPM analysis suggests otherwise: –RAPM unhedged = Profit / VaR = 5 / 16 = 31.25% –RAPM hedged = Profit / VaR = 2 / 4 = 50% RAPM unhedged < RAPM hedged

19 Adjusting Metrics for the Insurance Industry The one day or week horizons used in banking industry are not appropriate for insurance industry Very difficult to measure correlations between risk categories Changes in volatility are important over longer term horizons

20 Modeling Approaches

21 Types of models Parametric Modeling –Closed-form and monte-carlo simulation Historic modeling

22 Stress Testing Techniques Back-testing of model on historic data –In sample and out-of-sample Scenario Analysis (or Dynamic Financial Analysis)

23 VaR Difficulties Determining: –Confidence level –Time interval Stochastic vs. Parameter Risk Correlation risk Comparing the “Statistical” and “Market” price of risk Communicating Results to Target Audiences Does not incorporate all types of risk Risk management is part art and not just science

24 Summary of Benefits Provides managers with better understanding of: –sources of risk –interactions between different types of risks Enables comparison of different types of risk Forms a basis for risk-return performance analysis