economic & regulatory capital · rcm – rai · christian duesterberg · page 23 risk &...

Economic & Regulatory Capital

Christian DuesterbergRCM Risk Analytics & Instruments

Basel II and Financial Stability SeminarBali, 21 September 2006

RCM – RAI · Christian Duesterberg · page 2

Risk & Capital Management

Agenda

3. Regulatory Requirements

1. Economic Capital Overview

2. EC Methodology - Credit Risk Example

4. Comparison EC and RC



Economic Capital – What is it?

Motivationprotects the bank’s assets against extreme events - stakeholder view

protects the bank’s assets against systematic shock - regulatory view

“a measure of the amount of capital that a firm believes is needed to support its business activities or set of risks” –management & shareholder view– reflecting the bank’s risk appetite– enabling business decisions on a risk/return

basis

Economic Capital (EC) is the amount of capital needed to cover accumulated excess (“unexpected”) losses over a fixed time period with a set confidence level

value at riskexpected loss

EC



Market Risk

Market movements

Credit Risk

Counterparty defaults

Operational Risk

Adverse operational events

Business Risk

P&L volatility

Economic Capital – How is it used in Banks ?

Performance evaluation of– Business units– Client relationships– Portfolio strategies

Steering of bank’s risk &capital profile on

– Transaction level– Portfolio level

Unifying risk measure concept for aggregating different risk types



Economic Capital – Benefits for Banking System Stability

Sound economic capital methodology provides a good measure of any bank’s risk in relation to its stated targets

=> individually healthy banks: stable banking system

Bank specific risk measure including– Concentration risk– Systematic drivers– Stress testing capabilities– Scenario analysis– Ex-post performance evaluation– Ex-ante relevance for pricing, portfolio management and capitalisation



Economic Capital - Allocation

99.98% quantile

Portfolio:

ESFQ = E[Lportfolio | Lportfolio > quantileQ (Lportfolio)],

Business Unit:

ESF(BU) = E[LBU | Lportfolio > quantileQ (Lportfolio)]

Q quantile

probability

portfolio loss

Expected Shortfall Allocation:Contribution of a Business Unit to the Economic Capital of the Bank

Average loss of the Business Unit in the tail of the portfolio loss distribution

EC

cec cec cec cec cec

EC Allocation

Expected Shortfall Allocation:Contribution of a Business Unit to the Economic Capital of the Bank

=Average loss of the Business Unit in the tail of the portfolio loss distribution



Agenda







Utilisation of commitmentFacility structureMarket risk drivers

Risk rating SeniorityCollateral type/value

Probabilityof

Default(PD)(%)

Loss Given

Default(LGD)

(%)

Exposureat

Default(EAD)

Borrower RiskQuantification

Facility Risk Quantification

Expected Loss X X

EconomicCapital

PD

LGD

EAD

Industry,

Country,

Public orPrivate Entity

,Industry +Countryindices,

Portfoliocomposition

,Client specific Portfolio specific

EC for Credit Risk

f( )



EC for Credit Risk

Expected Loss: amount of Portfolio Losses expected in the following year

Unexpected Loss: volatility of Portfolio Losses (measured in Standard Deviations)

Value at Risk: defined as a quantile

Confidence Level: derived from Target Rating

Economic Capital: (Value at Risk) minus (Expected Loss)

Expected Shortfall: average of ‘large’ Portfolio Losses (‘large’ defined by threshold)

Economic Capital

Expected Shortfall

Unexpected Loss

Expected Loss

Portfolio Loss

Loss

Thr

esho

ld

Valu

e at

Ris

k

Prob

abili

ty

Average



The Loss of Credit Portfolio is a random variable

Time Horizon: Equal to the planning horizon 1 year

EC for Credit RiskDefinition of Portfolio Loss

=)D1 i( 1 if i-th loan defaults0 otherwise

li: Exposure-at-DefaultLimit

OutstandingNetting

RatingCountryIndustry

∑=

⋅⋅=M

iiiiP DLGDlL

1)(1

LGDi: Loss-Given-Default RecoveryCollateral

Source of Randomness



EC for Credit RiskHistogram of a Portfolio’s Total Losses

Expected Loss

10

15

20

Years / Scenarios

5

2

4

6

23

4

8

12

2

4

7

34

32

15

6

1

7

0

5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Economic CapitalEconomic Capital

95 % of all cases (19 out of 20)



Generation of asset returnfor all counterpartiescorrelated via the

factor model

No default Default

Add exposure ofcounterparty to loss

Next counterparty

Portfolio lossin simulation

Next simulation

Loss distribution(after last simulation)

after last counterparty

after last simulation

Empirical loss distribution

EC for Credit RiskLoss Distribution from Monte-Carlo Simulation



EC for Credit Risk Correlations

Default correlations are driven bycorrelations of Ability-to-Pay processesdecomposed into

– systematic part (correlated to industryand country factors)

– specific partCorrelations between systematic risk factorsare calibrated using equity data

Today Planninghorizon

CP A CP B

Factor

corr > 0

corr > 0corr > 0

Asset value Obligor 1

Asset value Obligor 2

Default Threshold 2

Default Threshold 1

Defaults happen if an “ability-to-pay” of afirm falls below a threshold

systematic part(country & industry) specific part

∑=

−+=K

jjj RfactorweightRA

1

22 1 ε

systematic part(country & industry) specific part

∑=

−+=K

jjj RfactorweightRA

1

22 1 ε

R2 quantifies the fraction of systematic risk inthe counterparty: most important driver of correlation of an obligor



Average systematic riskLow systematic risk, e.g. Retail

[ 10 % ]

[ 1 % ] EC(2BP) = 0.51 % of Exp.

EC (2BP)= 4.00 % of Exp.

0 0.2 0.4 0.6 0.8 1.

EL

High systematic risk, e.g. Corporates

[ 30 % ] EC (2BP)= 16.38 % of Exp.

EC for Credit Risk Correlations: Impact on Loss Distribution



EC for Credit RiskRating Migration

Multi-State

Rating migration depends on initial rating& a migration matrix

Value in rating class at horizon depends oncash flow valuation:– dependence on EAD and LGD– dependence on maturity, default curve, interest

rates

Two-State

Default probability depends on initial rating

Value in default/no default state – depends only on EAD and LGD

2

Default

No Defaul

t

Simulate default state at

horizon

Loss value in default state

Loss = 0

Loss = LGD*EAD

2

Default

B

CCC

BB

BBB

AAA

AA

A

Simulate rating state at horizon

Loss value in rating state

VREF -VAAA

VREF -VA

VREF -VBBB

VREF -VBB

VREF -VB

VREF -VCCC

VREF -VDef

VREF -VAA

Today: rating R0 Planning horizonValue with rating R0: VREF



EC for Credit RiskVendor Models – Similarities and Differences

CreditMetrics (Risk Metrics)

Portfolio Manager (KMV)

CreditRisk+ (Credit Suisse Financial Products)

Definition of Risk ∆ Market value Default losses Default losses

Credit EventsDowngrade/ Default

Downgrade/ Default Default

Includes interest rate risk No No No

Risk driversCountry and industry factors

Factors through assets values Default rates

Transition Probabilities Constant Constant N/A

Correlation of credit eventsStandard multivariate

Standard multivariate N/A

Recovery ratesRandom (beta distribution)

Random (beta distribution)

Loss given default (constant)

Numerical approach Simulation Simulation Analytic

WP1

WP1 Please insert / convert to table -needs to be updated corrected.Wilfried Paus, 8/25/2006



Agenda







Regulatory Requirements

Risk Sensitivity

Transparency

Simplicity

Benchmarking



Regulatory Requirements: Credit Risk ParametersProbability of Default (PD), Loss Given Default (LGD), and Exposure at Default (EAD) are essential for Expected Loss (EL), Economic Capital (EC) and Basel II capital calculation

( ) ( ) ( ) ( )( ) ⎥

⎥⎦

⎤

⎢⎢⎣

⎡

⋅−⋅−+

⋅⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎥⎦

⎤⎢⎣

⎡⋅

−+⋅

−⋅⋅⋅= −−

PDbPDbMPDN

RRPDN

RNLGDEADRWA

5.115.21999.0

1115.12 11

PD

LGD

EAD

EL LGDEADPD ⋅⋅

EC

IRBA



Regulatory Requirements: Basel II RWA Calculation under IRB Advanced Approach

2model internal s'DB II Basel RR =

Basel II underlying model is a single global factor with identical weight 1 for all counterparts

Parameter R reflects the asset correlation between counterparts being a function of PD (R decreases with increasing PD – differing by asset class)

In the limit of reducing DB’s factor model to a single factor model, relation between the Basel II defined asset correlation R and the R2 parameter used in DB’s capital model:

Regulatory capital for credit risk = 8%* RWA*SF + Shortfall

formula displayed is valid for large corporates, banks, sovereigns

( ) ( ) ( ) ( )( ) ⎥

⎥⎦

⎤

⎢⎢⎣

⎡

⋅−⋅−+

⋅⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎥⎦

⎤⎢⎣

⎡⋅

−+⋅

−⋅⋅⋅= −−

PDbPDbM

PDNR

RPDN

RNLGDEADRWA

5.115.21

999.011

15.12 11

Exposure at Default

Loss GivenDefault

Probability ofDefault

Maturity B2 parameter(set by Regulators)

2model internal s'DB II Basel RR =



IRB AA: Regulatory Capital Calculation for Credit Risk

EL is removed from RWA calculation– Banks have to compare EL with the

total amount of provisions that they have made

– Shortfall amounts are deducted from Tier I and II capital

– Introduction of scaling factor

Regulatory capital reduction (increase) for loans with maturity under (above) 2.5 years depending on the creditworthiness of the customer

Regulatory capital reduction for SMEs(corporates with annual sales up to EUR 50mn) by a firm-size adjustment

Maturity Adjustments

50,00%

60,00%

70,00%

80,00%

90,00%

100,00%

110,00%

120,00%

130,00%

140,00%

150,00%

160,00%

170,00%

180,00%

190,00%

200,00%

1 1,25 1,5 1,75 2 2,25 2,5 2,75 3 3,25 3,5 3,75 4 4,25 4,5 4,75 5

Maturity

AA A

BBB BB

B CCC

CC

Rating

0.00%

100.00%

200.00%

300.00%

400.00%

500.00%

600.00%

0.03%

5.03%

10.03

%

15.03

%

20.03

%

25.03

%

30.03

%

35.03

%

40.03

%

45.03

%

50.03

%

55.03

%

60.03

%

65.03

%

70.03

%

75.03

%

80.03

%

85.03

%

90.03

%

95.03

%

PD

Ris

k w

eigh

t

Large_Corporate_Banks_Sovereign_with_EL Large_Corporate_Banks_Sovereign_without_EL

Basel II Capital requirement= IRB AA Capital

+ EL + provisions



Agenda







Basel II

Single factor model for different asset classes (corporates, sovereigns, retail, SME’s)

“One size fits all” model

Capital allocated to each borrower in isolation

Capital allocation is given by a function of : – PD, LGD, EAD, Maturity– Customer type (-> asset correlation)

Limited recognition of diversification,e.g. no diversification betweencorporate and retail portfolios

Increased procyclicality, e.g., systematic amplification of the economic cycle

Internal model

Multi - factor model (countries & industries)

Competition of different modeling approaches

Capital allocated to each borrower reflects risks across the whole portfolio

Capital allocation is the result of a default simulation based on:– PD, LGD, EAD, Maturity– Correlation with country & industry factors

Full recognition of diversification according to country/industry correlation

Penalties for sector or name concentration

Economic Capital vs Basel II Regulatory Capital - Credit Risk

Risk sensitive capital allocation, i.e. increased capital assignment upon credit downgrade



Dual Management of Regulatory and Economic Capital

Assumptions cause RC to Be too crude a risk measure

Exceed EC almost surely

=> Bank is managed via EC subject to RC constraint

Implications for – Transaction pricing – Risk assessment – Planning– Performance dilution

Procyclicality



Convergence of Regulatory and Economic Capital

RC and EC Gap reconciliation? Examples for Alignment Potential– Asset correlation parameter R: replace PD by size dependency– Diversification: Introduce a basic correlation model across geographical regions and

customer types– Maturity adjustment: mitigate its conservative effect on long term transactions– Confidence Level: give regulatory bodies more flexibility

Economic & Regulatory Capital

Christian DuesterbergRCM Risk Analytics & Instruments

Basel II and Financial Stability SeminarBali, 21 September 2006

economic & regulatory capital · rcm – rai · christian duesterberg · page 23 risk &...

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