Economic Capital (EC)

ERM Symposium, CS 1-BChicago, ILApril 26-27, 2004

Hubert Mueller, Tillinghast Phone (860) 843-7079  

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 *

79%

86%

91%

92%

93%

96%

Operational Risk

Liquidity Risk

Equity Market Risk

Credit Risk

Pricing Risk

Interest Rate Risk

* Results of a 2002 SOA Survey

When determining EC, various risk tolerance measures are used*

60%

15%

9%

17%

SpecifiedPercentile

Multiple ofStandardDeviation

CTE * *

Other * 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

40%

7%

9%

15%

17%

12%

Total Company & LOB Basis

LOB Basis

Total Company Basis

Do Not Calculate EC, but Plan towithin 12 months

Do Not Calculate EC, but Plan to12+ months from now

Do Not Calculate EC & Don't Plan to

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

Line 1 Line 2 Line 3 Company

Actual Capital Economic Capital by Line Total Economic Capital

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

Uses of EC - Top 5 Answers

25%

20%

13%

10%

23%

To better manage overall business

For capital management purposes

To determine the "right" level of capital

To more appropriately allocate capital tospecific LOBs

To determine the benefits of correlating risksfrom various LOBs

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 = TAR @ 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) Current Proposed Current Proposed Current Proposed Current Proposed

ITM 120% 32 150 8 30 - 20 GMDB Return of ATM 100% 57 100 7 30 2 - - -

Premium OTM 80% 7 - 2 - - -

ITM 120% 32 390 8 150 - 110 GMDB 5% Roll-up ATM 100% 57 330 7 130 2 40 - 30

OTM 80% 7 30 2 10 - -

ITM 120% 32 80 8 10 - 10 GMDB Ratchet ATM 100% 57 110 7 20 2 - - -

OTM 80% 7 10 2 - - -

ITM 120% 32 360 8 90 - 50 GMDB Maximum of ATM 100% 57 330 7 110 2 20 - 10

(MAV, Roll-up) OTM 80% 7 30 2 - - -

ITM 120% 132 1,610 102 1,410 100 1,650 GMIB Roll-up ATM 100% 157 770 107 790 102 590 100 740

OTM 80% 107 210 102 130 100 180

Current: C1 + C3Proposed: C3-Phase II Source: Tillinghast - Towers Perrin

Duration 0 Duration 3.5

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

Risk Profile Curve - GMDB & EEDB & GMIB

(200,000)

(150,000)

(100,000)

(50,000)

0

50,000

100,000

150,000

200,000

250,000

300,000

1 10 19 28 37 46 55 64 73 82 91 100

Percentiles

Dis

trib

uta

ble

Ear

nin

gs

at 1

2%

Base Run

Base + GMDB

Base + GMDB + EEDB

Base + GMDB + EEDB + GMIB

SELECTED STATISTICSMean: 82,854.05Standard Deviation: 58,676.59% Negative: 5.0Minimum: -144,642.97Maximum: 260,495.401st Percentile: -42,076.155th Percentile: 232.88

Example:Hedging the Tail Exposure – Case Study

(Gai

n)

Lo

ss a

s %

of

Fu

nd

Val

ue

Comparison Hedged vs Unhedged - Annualized as a % of Fund Value

-1.60%

-1.40%

-1.20%

-1.00%

-0.80%

-0.60%

-0.40%

-0.20%

0.00%

0.20%

0.40%

0.60%

1 101 201 301 401

Scenario

Hedged (Gain) Loss

Unhedged (Gain) Loss

Hedged (Gain) Loss with 2X trades

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

0.0

0.1

0.2

0.3

0.4

0.5

Lifetime Return on 250% RBC

Pro

ba

bili

ty

AREA 2

Under State Review

AREA 3

Inadequate Returns on Capital

Area 1

AREA 4

Value Added

INSOLVENT

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 wellAllows for correlation of different risk

factors as well