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Economic Capital (EC)
ERM Symposium, CS 1-BChicago, ILApril 26-27, 2004
Hubert Mueller, Tillinghast Phone (860) 843-7079
Profit
Growth
Value/$
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
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
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