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Lotter Actuarial Partners

Pricing and Managing Derivative Risk

Risk Measurement and Modeling

Howard Zail, Partner

AVW10290293

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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

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Laying the Foundations

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Establish Business-DrivenRisk 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?

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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

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Risk Management Metrics

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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?

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What is Value-at-Risk

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Uses of VaR• Risk reporting• Portfolio optimization• Component of performance measurement &

product pricing• Capital allocation• Limit setting• Deriving economic capital

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Example of VaR Risk Reporting• Goldman Sachs daily VaR (95% level)

Category Daily VaR ($ in millions)

Interest Rate Risk $ 39

Currency Rates 13

Equity Prices 21

Commodity Prices 12

Diversification effect (33)

Total $ 52

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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

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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

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

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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

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Risk Adjusted Performance Measurement (RAPM)

(Single period model)

VaRAdjusted

Profit

CapitalEconomic

ProfitRAPM

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An Example of RAPM

Strategy Notional E[Profit] IRR Standard

Deviation

VaR

Unhedged $400 m $ 5 m 15% 8 16

Hedged $400 m $ 2 m 10% 2 4

Should we hedge a portfolio of 1-year GIC’s?

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An Example of RAPM (cont’d)• Traditional financial analysis suggests that we

should remain unhedged:

– IRRunhedged > IRRhedged

– NPVunhedged > NPVhedged

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An Example of RAPM (cont’d)• RAPM analysis suggests otherwise:

– RAPMunhedged = Profit / VaR = 5 / 16 = 31.25%

– RAPMhedged = Profit / VaR = 2 / 4 = 50%

• RAPMunhedged < RAPMhedged

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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

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Modeling Approaches

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Types of models• Parametric Modeling

– Closed-form and monte-carlo simulation

• Historic modeling

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Stress Testing Techniques• Back-testing of model on historic data

– In sample and out-of-sample

• Scenario Analysis (or Dynamic Financial Analysis)

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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

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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