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**Economic Capital and Risk Modeling**

February 22, • Iowa Actuaries Club Session #2 Economic Capital and Risk Modeling Jeff Fitch, Senior Actuary - Corporate

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**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 Ask me questions as I go, and I’ll try to leave time at the end also 2

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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 Past: lot of risk measurements, but primarily separate by risk and product. Not a consolidated look. Capital, no real feel for what amount we think we should hold. Present: 2007 Work of EC model development, quantifying risk metrics, internal reporting, Board discussion, starting to utilize Future: production mode, ingrain into our culture. Consistent view of risk & return on an Economic framework. My role: Corp Model / Common Platform / EC Modeling 3

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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 We are doing this for us, not the rating agencies. Links risk / capital / value. 4

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**Principal’s Economic Risk Metrics**

3 Primary Risk Metrics Earnings at Risk (EaR) Embedded Value at Risk (EVaR) Economic Total Asset Requirement Risk Metrics are complementary to each other. These aren’t our only risk metrics. Still look at liquidity, duration mismatch, etc. 5

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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 6

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**Earnings at Risk (EaR) Example 1 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 7

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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 8

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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 our best estimate of claims plus a margin) + Economic Capital (cushion on top of Economic Reserves to 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. Mention policyholder claim vs. shareholder claim Trapped capital. More flexibility? Try to reduce 9

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**Economic Total Asset Requirement (cont**

Economic Total Asset Requirement (cont.) Reconstruction of Economic Balance Sheet Important to look at Total Asset Requirement and not just compare Economic Capital to rating agency required capital. This hypothetical diagram shows ETAR = Stat Reserves. Statutory reserves may be at such a conservative level that they have an element of capital. 10

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**Principal’s Economic Risk Metrics - Recap**

Earnings at Risk (EaR) Embedded Value At Risk (EVaR) Economic Total Asset Requirement Confidence Limit 90% (1-in 10 year event) 90% 99.5% Time Horizon 1 year 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 Risk Metrics are complementary to each other. Earnings / Value / Capital 11

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**Steps in quantifying Economic Capital**

Identify and categorize risks Credit Market Product / Pricing Operational / Business Quantify each risk individually Deterministic Stress Test and / or stochastic modeling Aggregate risks and capture any diversification impact 12

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**Risk Hierarchy – Deeper Dive**

Mortality Risk, for example, can be broken down into 4 components Volatility – statistical mortality fluctuation Level – misestimation of mortality mean Trend – misestimation of mortality improvement Calamity – 1 time spike mortality (flu pandemic) 13

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**Hypothetical Example of Risk Aggregation**

Talk about “correlation in the tail” If 100% correlations then results are additive (no diversification benefit) If 0% correlation then maximum benefit (square root of the sum of the squares). Risk = DB = 46% If all concentrated in 1 risk then little DB. 14

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**Top 10 Lessons Learned from Principal’s Implementation**

Importance of Quick Wins Simplify It isn’t all about modeling Involve all parties in the process Set up guiding principles up front #2 Also avoid unnecessary precision (can be misleading) #5 Guiding principles (what risks, how measure, level of complexity, materiality, how diversification reflected) 15

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

Set up risk appetite and tolerances up front. Not a project. Never really done. Look at entire distribution of results (don’t focus only on the downside) Use lots of pictures Communication, communication, communication. #7: Evolutionary process. #9: Bubble charts, pie charts, distributions -- much better than a table of numbers 16

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

Medium Term Uses: Strategic Decision Making Capital Allocation Performance Measurement External Reporting Initial Uses: Product / Business Unit decision making Hedging / Reinsurance Internal Risk Reporting Evolutionary process. We just getting into the Medium Term Uses category. Another lens to look at your business. Still will need to manage to GAAP / Stat / Rating Agencies / etc. Long Term Uses: Pricing Incentive Compensation 17

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**Emerging Industry Trends – Economic Capital**

Two methods have emerged as the most common: 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 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 18

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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! 19

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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 20

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**One Year Mark To Market Approach Diagram**

Do this for each risk item. 21

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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 22

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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 Go into Percentile vs. Cost of Capital Method if time 23

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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. You can’t “create value” by investing in riskier assets (until realized). Would also hold true in terms of shifting from A to BBB assets. This is a problem with Traditional EV calculations. You only get the right answer by adjusting your discount rate, but you don’t really know. The real "value" at time zero is 25, no matter how your assets are invested. This problem goes away under a MC framework because you are projecting and discounting at risk free rates. Under a Traditional EV approach, you would need to adjust your discount rate to get to the "right" answer. In this example your discount rate in the invest 100 in equity scenario would need to be 20% to get back to that 25 at time zero. Now, as you progress through time and earn something higher than risk free then value is created, but you can't take credit for it up front. 24

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Questions? 25

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