Economic Capital (EC) ERM Symposium, CS 1-B Chicago, IL April 26-27, 2004 Hubert Mueller, Tillinghast Phone (860) Profit Growth Value/$ Capital

Overview EC Measurement and Allocation Uses of EC EC vs. Rating Agency or Regulatory Capital

Determining EC involves an analysis of the risk profile for a selected risk tolerance level Selected risk tolerance level Economic Capital Ranked distribution of present values of future profits from each simulation Cumulative probability + – 0 $m = “sufficient surplus capital to cover potential losses, at a given risk tolerance level, over a specified time horizon”

EC typically covers both financial and non- financial risks * * Results of a 2002 SOA Survey

When determining EC, various risk tolerance measures are used* * Results of a 2002 SOA Survey ** Conditional Tail Expectation (or TVAR)

There are a variety of approaches in use for measuring EC  Full economic scenarios  Stress testing  Factor tables  Stochastic models (risk free / real world)  Mean-Variance-Covariance model  Credit risk methods  Option pricing (Black – Scholes)  Includes operational risk (increasingly)

Many companies calculate EC on both a total company and a LOB basis Source: SOA/Tillinghast Risk & Capital Management Seminar (March 2003)

Various methods are in use for allocating EC  Diversification benefit Results from combining products with different risk profiles  Allocating EC at the enterprise level Diversification benefit goes to corporate segment  Allocating EC to business segments Diversification benefit stays at LOB  Allocating EC for pricing purposes Generally, simplified formulas are used

Typical Approaches used in allocation of EC  By risk measure (e.g. VAR, TVAR, ECOR)  Based on exposure  Based on exposure times default probability  Based on loss simulations  Based on incremental capital

Example 1,000 1,200 1,500 Economic Capital Regulatory Capital Free Surplus Total Capital and Surplus

Best Practices  Including both financial and non-financial risks  Determining EC as the difference between required assets and MV of liabilities (or Embedded Value)  Allowing for diversification benefit  For pricing, LOB is held at EC level Excess of regulatory capital over EC (if any) is leveraged through the use of reinsurance or LOC, typically at a lower cost

Typically, the diversification benefit resides at the corporate level Diversification Benefit

Overview EC Measurement and Allocation Uses of EC EC vs. Rating Agency or Regulatory Capital

Many companies use EC to determine and manage the “right” level of capital Source: SOA/Tillinghast Risk & Capital Management Seminar, March 2003

There are many other uses of Economic Capital – all requiring stochastic analyses  Solvency II (IAA Working Party)  OSFI regulation for segregated funds  C-3 Phase II capital model  Proposed STAT reserves for variable annuities  GAAP SOP 03-1: requires explicit reserves for guarantees  Variable annuity risk profiles and hedging analysis  Pricing and risk management  Measuring Economic Value  Measuring exposure to catastrophic events

Solvency II – Overview  Three-pillar approach to supervision  All types of risks are to be included  Total balance sheet approach  Requires use of appropriate risk measures, and an appropriate time horizon  Need to allow for risk management  Company-specific approaches recommended  Capital requirements should be market-efficient Encouragement of best practices  Expected to be effective by 2005?

Various activities in the U.S. marketplace require life insurers to improve their stochastic modeling capabilities  New capital requirements according to C-3 Phase II RBC proposal  New reserving requirements (STAT/GAAP)  Pricing of guarantees (GMDB, GMWB, GMAB, GMIB) within VA contracts  Analysis of current risk exposure for guarantees on EIAs, VAs and UL products  Analysis of credit risk on assets backing interest- sensitive business

C3 Phase II – proposed modeling standard for required capital on variable annuities  Model Assets begin with Starting Assets equal to Statutory Reserves (or a best estimate based on a roll forward from prior quarter reserves)  Model Surplus is defined as Model Assets less Cash Surrender Value (proxy for reserve liability) – Starting Surplus generally positive  For each scenario, compute its Additional Asset Requirement (AAR)

C3 Phase II – required capital (continued)  AAR for scenario (i) is added to Starting Assets: Total Asset Requirement (TAR) TAR(i) = Starting Assets + AAR(i)  Stochastic process is repeated N times  C3-Phase II capital = CTE(90) - Statutory Reserves  Alternative Factor Method is possible  Implementation is expected for year-end 2004

Illustrative Capital Requirements for Variable Annuities under C3 Phase II (bps of AV) Source: Tillinghast

Proposed STAT Reserves for Variable Annuities  Stochastic modeling of risk exposure  Using CTE (65), i.e. average of worst 35% of outcomes  Alternative factor method is possible  Expected to cause reserve volatility  Implementation expected for 2005

New GAAP Reserves for Guarantees (“SOP 03-1”)  Stochastic modeling of cost of guarantees Scenarios should be consistent with DAC EGP calculations  Additional reserve required if guarantees in-the- money: PV (excess benefits) / PV (reserves)  Will cause reserve volatility  Effective since 1Q04

Example: Creating risk profiles for VA guarantees

Example: Hedging the Tail Exposure – Case Study (Gain) Loss as % of Fund Value

Overview EC Measurement and Allocation Uses of EC EC vs. Rating Agency or Regulatory Capital

Regulators use capital to determine a company’s financial solvency AREA 2 Under State Review AREA 3 Inadequate Returns on Capital Area 1 AREA 4 Value Added INSOLVENTINSOLVENT

EC vs. Regulatory / Rating Agency Capital  Companies internal EC models are designed to reflect proprietary risks  Company-specific, tailored to risks  Prospective method  Regulatory capital (RBC) is generally based on industry factors  Not company-specific  Formulaic method, retrospective  Reconciliation through rating agencies?  Historically, a retrospective view  Current trend towards evaluating capital requirements based on proprietary models

All major rating agencies have recently come out with enhanced capital adequacy models  Standard & Poor’s capital model (FPC) applies an EC approach  AM Best has enhanced their BCAR model to allow for correlation of risks  Moody’s is coming out with a new capital adequacy model as well  Allows for correlation of different risk factors as well