Integrating Economic Capital, Regulatory Capital and ......2013/10/21 · Integrating Economic...

Integrating Economic Capital, Regulatory Capital and Regulatory Stress Testing in Decision Making

October 2013 Amnon Levy, Managing Director, Head of Portfolio Research

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2

Agenda

1. Context

2. Current State of Portfolio Management

3. Unified Measures

4. Stress Testing in an Economic Capital Framework

5. Recap


Context 1

Economic Capital (EC), Regulatory Capital (RegC) and Regulatory Stress Tests (RST)

4

EC is a measure of economic risk associated with a portfolio

» Accounts for diversification and concentration risks

» Provides insights allowing optimized risk-return profiles, facilitate strategic planning

and limit setting, as well as define risk appetite

» Provides a foundation for return-to-risk measures such as RORAC, Sharpe Ratio and

Vasicek Ratio to rank instruments

RegC and RST, when binding, results in tangible costs

» Additional capital is needed for new investments

» Changes in portfolio composition can require drastic action

» Sale of business units

» Access capital markets at unfavorable terms


5

Should RegC replace EC in asset selection?

» With the advent of Basel III, financial institutions face RegC constraints that are

increasingly impacting investment plans

» In such environments should an institution replace EC with RegC in RORAC style

decision rules?

How should RST enter into decision making?

Is there a need for unified measures?

» RegC and RST are risk measures

» do not account for concentration or diversification effects

» are associated with tangible costs

» EC does account for diversification, concentration effects, and other economic risks

EC, RegC and RST should all influence decision making

Strategic Questions


Current State of Credit Portfolio Management 2


Traditional Measures for Asset Selection

7

Using traditional measures that accounts for EC but not RegC,

The asset should be purchased as long as:

, ,

,

, ,

, ,

,

, ,

, ,

, , ,

, ,

, or

, or

j t P t

j t

j t P t

j t P t

j t

j t P t

j t P t

j t D t D t

j t P t

ES ESSR

RC

ES ESVR

CR CR

ES ESRORAC r r

CR CR


Motivation Behind Asset Selection Based on Traditional Measures

8

A financial institution maximizes the utility function of its stakeholders

C can be thought of as the dividend policy

Overarching structure is same as that which underpins

» CAPM in portfolio selection

» Black-Scholes style pricing

» NPV capital budgeting using a project‟s

2

0

, , , 1 1 , , ,

max

. .

(1 )

t

t t

t

t j t j t i t t D t i t i t t

j j

U C E C bC

s t

C P CF N D r P N D


Unified Measures 3


Introducing the Regulatory Capital Constraint

10

When RegC is binding, an institution faces a tangible cost, which can be

considered as an additional constraint in the optimization problem:

2

0

, , , 1 1 , , ,

, , ,

max

. .

(1 ) , and

Book Equity

t

t t

t


j j

t j t t j t j t

j j

U C E C bC

s t

C P CF N D r P N D

and

N D N RWC


Introducing the Stress Testing Constraint

11

When binding, an institution faces a tangible cost, which can be

considered as an additional constraint in the optimization problem:

2

0

, , , 1 1 , , ,

, , , , , ,

, ,

max

. .

(1 ) , and

Equity

t

t t

t


j j

t stress j t Liquid t stress j t stress j t Liquid t stress Liquid t t stress

j j

j t j t stress Liqu

j

U C E C bC

s t

C P CF N D r P N D

and

N N EL N EL N D

N RWC N

, ,id t stress Liquid t stressRWC


Asset Selection with RegC or RST Constraint

12

The agent should purchase assets as long as:

,

, ,. ,

,

. , , j t

j t P tj t P t

j t p

j t j t D t adjustment

ES ESSR SR

RC

where

ES r r f

Only the numerator is affected

by the RegC constraint

RegC-adjusted ES is similar to

traditional ES but the cost of

debt is multiplied by an

adjustment factor.


0.00%

0.02%

0.04%

0.06%

0.08%

0.10%

0.12%

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

RegC

Dif

fere

nce

Be

twe

en

ES

and

Re

gC

Ad

just

ed

ES

13

Impact of the RegC Constraint on ES

The impact on ES as a

function of RegC varies, in

part, because of the role

of price in the adjustment


5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

35.00%

5.00% 10.00% 15.00% 20.00% 25.00% 30.00% 35.00%

Traditional RORAC

Re

gC A

dju

ste

d R

OR

AC

Correlation = 0.874

14

Impact of the RegC Constraint on RORAC

Impact on RORAC can

exceed 50%


Stress testing in an EC framework 4


RiskFrontier framework with the GCorr Macro model

1-RSQ

Draws of systematic

credit risk factors φCR1, φCR2,…

Joint distribution with

correlation matrix Σ

Credit portfolio loss distribution

on a horizon

Draws of asset returns (credit quality changes)

RSQ

PD, LGD, EAD, Credit Migration

Correlations of GCorr systematic

factors and standard normal macroeconomic factors (φMV):

Σ GCorr

φCR φMV

φ C

R

φM

V

Scenario for

macroeconomic

variables (MV) →

conditional loss

distribution.

Draws of borrower

specific credit risk factors EL given a

macroeconomic shock

Range of losses given a

macroeconomic shock

Mapping between

φMV and

macroeconomic

variables (MV)

GCorr Macro Model


What is the impact of an oil price drop on a credit portfolio loss distribution?

Conditional distribution of φUS,Oil, given φ∆OilPrice Conditional loss distribution, given φ∆OilPrice

A large credit portfolio of homogenous exposures to the U.S.

“Oil, Gas, and Coal Expl/Prod” industry

» Input parameters: PD=1%, RSQ=20%, LGD=100%, EAD=1.

Oil Price drops by 2

standard deviations


standard deviations

E[L]=1% Unconditional

distr.

Unconditional

distr.


What is the impact of an oil price drop on a credit portfolio loss distribution?

Conditional distribution of φUS,Oil, given φ∆OilPrice Conditional loss distribution, given φ∆OilPrice

Conditional expected loss:

1

OilPr iceOilPr ice

2

N (PD) ρ RSQE L | N

1 ρ RSQ

A large credit portfolio of homogenous exposures to the U.S.

“Oil, Gas, and Coal Expl/Prod” industry

» Input parameters: PD=1%, RSQ=20%, LGD=100%, EAD=1.


standard deviations

E[L| φ∆OilPrice]

=2.3%

Conditional distr.

Mean=–0.82

Std=0.91


standard deviations

E[L]=1% Unconditional

distr.

Conditional distr.

Unconditional

distr.

Terminology: conditional expected loss,

given a macroeconomic scenario, will

be also called stressed expected loss.


Two ways of using the GCorr Macro model within the RiskFrontier framework:

Analytical method

• Calculating stressed expected loss using

formulas, which can be evaluated analytically,

without a Monte Carlo simulation.

– The formulas are based on the GCorr

Macro model.

• The formulas account only for losses due to

defaults, not due to deteriorating credit quality of

counterparties.

• The method is simpler and the calculation faster

than in the case of the simulation approach.

• The method allows for a CCAR-style analysis.

Simulation approach

• Running the Monte Carlo simulation in

RiskFrontier with the GCorr Macro model.

• Using the Monte Carlo simulation output for

various analyses of credit portfolio losses.

• In addition to calculation of the stressed

expected loss, the method allows for:

– further insights into relationships between

losses and macroeconomic variables.

– determining the full conditional loss

distribution.

– reverse stress testing.

• Accounting not only for defaults, but also for

losses due to credit quality deterioration.

• The method takes advantage of the RiskFrontier

capability to value various credit risk exposures.

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Running RiskFrontier, including the simulation, with the GCorr Macro model

Mapping between standard normal

macroeconomic factors and

macroeconomic variables MV.

GCorr

Matrix

rC and rI φMV

r C a

nd

rI

φM

V

Inputs

Expanded covariance matrix

RiskFrontier

Monte Carlo simulation engine

Trial Simulated

macroeconomic factors

Simulated GCorr systematic credit risk factors

Portfolio Loss

1 φMV1, φMV2, … φ1, φ2, … LTrial 1

2 φMV1, φMV2, … φ1, φ2, … LTrial 2

… … … …

Output of Monte Carlo simulation

Conversion to observable macroeconomic

variables MV1, MV2,… using mappings

Output

Analysis of relationships between portfolio losses

and macroeconomic variables across trials

Losses can account

for credit quality

deterioration.


How do correlations vary across U.S. industries?

Correlations

scaled by -1

» Box plots characterizing distribution of correlations between the 61 U.S. custom indexes

and select macroeconomic variables

'OIL, GAS & COAL EXPL/PROD'

'MINING'

'STEEL & METAL PRODUCTS'

'FURNITURE & APPLIANCES'

'CONSTRUCTION MATERIALS„

…

'REAL ESTATE'

'STEEL & METAL PRODUCTS'

'CHEMICALS'

'MINING'

'BUSINESS PRODUCTS WHSL'

'COMPUTER HARDWARE'

'SEMICONDUCTORS'

'COMPUTER SOFTWARE'

'TELEPHONE'

'UTILITIES, ELECTRIC'

'INSURANCE - PROP/CAS/HEALTH'

'INSURANCE - LIFE'

'BANKS AND S&LS„

Patterns resulting from a strong interest rate component in asset returns, attributable to financial leverage

Correlations

scaled by -1

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» IACPM portfolio – 3000 reference entities distributed across 7 developed countries and

60 industries.

» Running simulation engine, which generates draws of systematic factors as well as

macroeconomic standard normal shocks (φMV).

– Each trial → credit portfolio loss and a macroeconomic shock.

» Example: impact of two macroeconomic variables on the portfolio

Conditional expected loss given

the macroeconomic standard

normal shock φ∆S&P500.

How credit portfolio losses depend on various macroeconomic variables…

Losses more strongly associated with

macroeconomic shocks φ∆S&P500 than φ∆OilPrice.

One trial – portfolio loss versus a

draw of the macroeconomic

standard normal shock φ ∆S&P500.

Conversion to observable stock market

returns using a mapping


CCAR: stressed expected losses over multiple periods in the future

» Stressed expected losses over future periods:

Analysis

date Q1 Q2 Q3 Q4

Scenario Scenario Scenariok,1 k,1 k,1PD LGD EL




Stressed Expected

Loss

Q1 Q2 Q3 Q4


Quarterly FDIC C&I loan performance indicator for all FDIC-insured institutions

4Net Charge - offs

Avg Outstanding

Two periods of high losses:

• Dot-com bust recession

• Financial crisis

Time series pattern: Does GCorr Macro imply higher than average losses

during recessions and lower than average losses during periods of

economic growth?


Historical time series patterns in losses produced by the GCorr Macro model

9–quarter cumulative stressed expected losses.

Why 9–quarters? → CCAR time horizon

» Variables used in the scenario: unemployment rate, Baa yield, Stock market return, VIX.

Stressed expected losses increase above the unconditional expected losses during the dot-

com recession and the financial crisis.

Why are losses higher during the financial crisis? The financial crisis saw larger quarterly

shocks to the stock market and unemployment rate than the dot-com recession.

GCorr Macro

Stressed expected loss over the

9–quarter horizon t→t+9.

Both PD and LGD are stressed.

Unconditional expected loss over

the 9–quarter horizon t→t+9


Recap 5


» EC, RegC and RST should all influence decision making

» We design decision making variables that bring the three together using a broadly

accepted economic framework

– Accounts for risks related to concentration and diversification

– Accounts for tangible costs related to RegC and RST

» Link stress testing and EC under a single model

– Introduce GCorr Macro which unifies credit factors and macroeconomic variables

– Allows for CCAR/DFAST-style stress testing

– Provides insights on the extent to which scenarios span portfolio risk

– Reverse stress testing

– Risk integration

Recap


Amnon Levy

Managing Director

Head of Portfolio Research

Moody's Analytics Quantitative

Research

415.874.6279 tel

415.297.3503 mobile

[email protected]

Moody's Analytics

405 Howard Street,

Suite 300

San Francisco, CA 94105

www.moodysanalytics.com

moodysanaltyics.com


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Integrating Economic Capital, Regulatory Capital and ......2013/10/21 · Integrating Economic...

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