integrating economic capital, regulatory capital and ......2013/10/21 · integrating economic...
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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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Agenda
1. Context
2. Current State of Portfolio Management
3. Unified Measures
4. Stress Testing in an Economic Capital Framework
5. Recap
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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
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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
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Current State of Credit Portfolio Management 2
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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
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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
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Unified Measures 3
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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
t j t j t i t t D t i t i 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
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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
t j t j t i t t D t i t i 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
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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.
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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
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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
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Impact of the RegC Constraint on RORAC
Impact on RORAC can
exceed 50%
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Stress testing in an EC framework 4
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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
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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
Oil Price drops by 2
standard deviations
E[L]=1% Unconditional
distr.
Unconditional
distr.
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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.
Oil Price drops by 2
standard deviations
E[L| φ∆OilPrice]
=2.3%
Conditional distr.
Mean=–0.82
Std=0.91
Oil Price drops by 2
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.
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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.
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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
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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
Scenario Scenario Scenariok,2 k,2 k,2PD LGD EL
Scenario Scenario Scenariok,3 k,3 k,3PD LGD EL
Scenario Scenario Scenariok,4 k,4 k,4PD LGD EL
Stressed Expected
Loss
Q1 Q2 Q3 Q4
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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?
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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
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Recap 5
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» 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
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Amnon Levy
Managing Director
Head of Portfolio Research
Moody's Analytics Quantitative
Research
415.874.6279 tel
415.297.3503 mobile
Moody's Analytics
405 Howard Street,
Suite 300
San Francisco, CA 94105
www.moodysanalytics.com
moodysanaltyics.com
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29
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