Economic Capital and Risk Modeling

February 22, 2008 • Iowa Actuaries Club Session #2

Jeff Fitch, Senior Actuary - Corporate

Outline

• Principal’s Risk Metric and Economic Capital Framework

• Lesson’s Learned from Principal’s Implementation

• Applications of Economic Capital models

• Emerging Industry Economic Capital Trends

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Principal’s Risk Metrics and Economic Capital Framework

• Background

– Where we were

– Where we are at now

– Looking forward

• My role in the process

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Driving Forces & Objectives

• Better understanding of risk exposures and incorporate into decision making process

• Improve our ability to measure and manage risk and return

• Appropriate capital level and capital allocation

• Competitive Pressures

• Economic Uncertainty

• Rating Agencies

• Board

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Principal’s Economic Risk Metrics

3 Primary Risk Metrics

1. Earnings at Risk (EaR)

2. Embedded Value at Risk (EVaR)

3. Economic Total Asset Requirement

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Earnings at Risk (EaR)

• Measures short-term volatility of GAAP Operating Earnings

• Difference between:

– Best Estimate (baseline) GAAP Operating Earnings; and

– 90th percentile confidence level GAAP Operating Earnings

• Difference expressed as percent of Best Estimate (baseline) GAAP Operating Earnings

• Time horizon of one year GAAP Operating Earnings

• New business included in projection

• Also look at GAAP Net Income

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Earnings at Risk (EaR) Example1 year EaR at 90th Percentile

• Run 1,000 scenarios of 1 year operating earnings

• Rank them from best to worst

• EaR is difference between Best Estimate and 900th scenario

HYPOTHETICAL GAAP OE by Scenario

Best Estimate 90%

EaR

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Embedded Value (EV) and Embedded Value at Risk (EVaR)

• Measures value of inforce business – doesn’t reflect new business or intangibles (brand, reputation)

• Present Value of Distributable Earnings

• Embedded Value at Risk measures potential volatility in value

– Difference between:

• Best Estimate (baseline) Embedded Value; and

• 90th percentile confidence level Embedded Value

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Economic Total Asset Requirement

• Economic Total Asset Requirement is the amount of assets needed to cover our obligations at a given risk tolerance level over a specified time horizon.

– 99.5% risk tolerance level for a AA rated company

– 30 year time horizon

• Economic Total Asset Requirement =

Economic Reserves (cover obligations based on ourbest estimate of claims plus a margin)

+

Economic Capital (cushion on top of Economic Reservesto cover potential obligations from unanticipated adverse experience)

• Our external Total Asset Requirement is equal to statutory regulatory reserves plus rating agency required capital.

• Trapped Capital is the difference between external Total Asset Requirement and our Economic Total Asset Requirement.

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Economic Total Asset Requirement (cont.)Reconstruction of Economic Balance Sheet

Required Capital Trapped Capital

Economic Capital

Statutory Reserves Economic Reserves

External Capital Model Internal Economic Capital Model

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Principal’s Economic Risk Metrics - RecapEarnings at Risk

(EaR)Embedded Value

At Risk(EVaR)

Economic TotalAsset Requirement

ConfidenceLimit

90% (1-in 10 year event) 90% 99.5%

Time Horizon 1 year Life of Business Life of Business

Metric GAAP Operating Earnings (also GAAP Net Income)

Embedded Value (EV) = Present Value of Distributable Earnings

Total Economic Asset Requirement = Economic Reserves plus Economic Capital

Measures Potential shortfall in operating earnings relative to baseline under relatively adverse business & economic conditions

Potential shortfall in embedded value relative to baseline under relatively adverse business & economic conditions

Total assets required to ensure we can meet all obligations with 99.5% confidence

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Steps in quantifying Economic Capital

1. Identify and categorize risks

• Credit

• Market

• Product / Pricing

• Operational / Business

2. Quantify each risk individually

• Deterministic Stress Test and / or stochastic modeling

3. Aggregate risks and capture any diversification impact

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Risk Hierarchy – Deeper Dive

Mortality Risk, for example, can be broken down into 4 components

1. Volatility – statistical mortality fluctuation

2. Level – misestimation of mortality mean

3. Trend – misestimation of mortality improvement

4. Calamity – 1 time spike mortality (flu pandemic)

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Hypothetical Example of Risk Aggregation

Risk Correlation MatrixRisk Type measure Cr Mkt UW Op

R1 Credit 1,250 Credit 1 0.75 0 0.5R2 Market 1,500 Market 0.75 1 0 0.5R3 Underwriting 750 Underwriting 0 0 1 0.25R4 Operational 500 Operational 0.5 0.5 0.25 1

Undiversified Risk Measure 4,000

Diversified Risk Measure 3,000 =

Diversification $ Benefit 1,000

Diversification % Benefit 25.0%

RR jj iiji

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Top 10 Lessons Learned from Principal’s Implementation

1. Importance of Quick Wins

2. Simplify

3. It isn’t all about modeling

4. Involve all parties in the process

5. Set up guiding principles up front

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Top 10 Lessons Learned from Principal’s Implementation (cont.)

6. Set up risk appetite and tolerances up front.

7. Not a project. Never really done.

8. Look at entire distribution of results (don’t focus only on the downside)

9. Use lots of pictures

10.Communication, communication, communication.

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Applications of Economic Capital Models (if you build it they will come)

Initial Uses:

• Product / Business Unit decision making

• Hedging / Reinsurance

• Internal Risk Reporting

Medium Term Uses:

• Strategic Decision Making

• Capital Allocation

• Performance Measurement

• External Reporting

Long Term Uses:

• Pricing

• Incentive Compensation

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Emerging Industry Trends – Economic Capital

Two methods have emerged as the most common:

1. Liability Run Off Approach

• Level of starting assets needed to pay all future policyholder obligations at a chosen confidence level

• Approach used for RBC C3 Phase 2

2. One Year Mark to Market Approach

• Level of assets needed to cover a fall in the market value of net assets over a one-year time horizon at a chosen confidence level

• Approach used for Solvency 2

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Lots of different variations in approaches

• Many decisions to make:

– Time Horizon

– Confidence Level

– What risks to include and how to measure

– Stochastic vs. Stress Testing

Many possible combinations!

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One Year Mark to Market Approach

• Emerging as most common method to calculate Economic Capital

• Driven by emerging solvency standards, particularly in Europe (Basel II, Swiss Solvency Test, Solvency II)

• Consistent with emerging international accounting and solvency standards

• US principles based approach for reserves and capital is more of a liability runoff approach

– Although use of one year market-to-market for EC is increasing in the US

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One Year Mark To Market Approach Diagram

MCEV MCEVMV MV

Assets AssetsMV MVLiab Liab

Economic Capital

Normal Stressed

Stressed ConditionsNormal Conditions

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Is One Year Enough?

• Since our products have a long duration, how can you capture the risk using a 1 year approach?

– You are still projecting your cash flows out to maturity and factoring in the residual impact of that 1 year event.

– Confidence interval on a 1 year approach is likely higher than a multi-year approach

• Ex: 99.95% instead of 99.5% for a AA Rated Company

• After one year company can likely recapitalize and take other management action

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Market Consistent Valuation

• Market price to transfer a liability between willing participants

• Applies capital market principles to liabilities

– No arbitrage (identical cash flows must have the same value)

• Uses risk neutral scenarios, discount at risk free rates

– Calibrated to current market conditions & prices

– Captures embedded options & guarantees

• Add an additional margin for non-hedgeable risks (Market Value Margin)

– Percentile Method

– Cost of Capital Method

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In a Market Consistent Embedded Value Framework, selecting assets does not create value

Example:

Company has Capital of 25, Borrows 75 at 4%, and invests 100 in equities expected to earn 8%

• Using traditional EV techniques, the 30 might be discounted at say 9%, giving a value of 27.5 on day 1.

• Under MCEV the asset CFs are discounted at 8% and the liability CFs at 4%, giving a value of 25 on day 1.

• The effective discount rate on capital is 20%.

• The risk discount rate is an output of the MCEV valuation, and not an input.

• Under a Market Consistent Framework you can’t take credit up front for taking market risk.

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Day 1One Year

LaterAssets 100 108Liabilities 75 78Capital 25 30

Questions?

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