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Monetary Policy and
Financial Distress:
Incorporating Financial Risk into
Monetary Policy Models
Dale Gray (IMF)
Leonardo Luna (BCCh)
Jorge Restrepo (BCCh)
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BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
Index
 Motivation
 Contingent Claims Analysis (CCA)
 Empirical Evidence
 The Model
 Impulse Responses
 Efficiency Frontiers
 Results, Conclusions & Next Steps
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BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
Motivation
 The integration of the financial sector vulnerability
into macroeconomic models is an area of important
and growing interest for policymakers.
 This paper analyze the explicit inclusion of credit
risk/financial fragility indicator in the Monetary
Policy Rate (MPR) Reaction Function.
 The main question is: Should a financial fragility
indicator be included in monetary policy models? In
particular, should it be explicitly included in the
reaction function?
 Or, should the central bank react only indirectly
through reacting to its effects on inflation and
output gap?
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BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
Motivation
 The
economy (interest rates) and the
financial sector (assets and liabilities) affect
each other, as evidences the US economy
over the past year.
 This paper uses contingent claims analysis
(CCA) tools, developed in finance, to
estimate the risk of default in the banking
sector as proxy for financial sector
vulnerability.
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BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
Literature
 Gray, D., Merton, R. C., Bodie, Z. (2006). “A New
Framework
for
Analyzing
and
Managing
Macrofinancial Risks of an Economy,” NBER paper
#12637 and Harvard Business School Working
Paper #07-026, October.
 Gray, D., C. Echeverria, L. Luna, (2006) “A measure
of default risk in the Chilean banking system”,
Financial Stability Report Second Half 2006, Central
Bank of Chile.
 Gray, D. and J. Walsh (2007) “Factor Model for
Stress-testing with a Contingent Claims Model of
the Chilean Banking System.” IMF Working Paper
05/155. (Washington: International Monetary
Fund).
 Gray, D. and S. Malone (2008) Macrofinancial Risk
Analysis. Wiley Finance, UK.
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BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
Contingent Claims Analysis
 Modern finance theory is used to combine
forward-looking market prices (e.g. equity
prices) and balance sheet data to “calibrate”
the implicit value of the assets and asset
volatility (Merton,1974).
 Liabilities derive their value from assets,
which are stochastic.
 The “calibrated” CCA model is used to
calculate credit risk indicators, such as
distance-to-distress, default probabilities,
expected losses on debt (implicit put
option), credit spreads, value of risk debt.
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BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
Contingent Claims Analysis
 Banks lend to households, companies, and
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the government. Households own equity,
government guarantees bank deposits.
 Interlinked
CCA
balance
sheets
for
corporates,
households,
banks
and
government can be constructed.
 Risky debt of firms is an asset of the banks.
Gov. contingent liabilities to banks are
modeled as an implicit put option (Merton
1977).
 This model does not include corporate &
households.
BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
Interlinked CCA
 Interlinked
CCA risk-adjusted balance
sheets are a useful tool for understanding:
 Financial accelerator mechanisms – increased bank
deposits, increased lending to corporate and
households, higher investment and consumption
leading to higher GDP.
 Credit
risk transmission – slower GDP, lower
corporate and household assets, lower value of risky
debt (from larger implicit put options/spreads), lower
bank assets, higher credit risk in banks (e.g. lower
distance-to-distress), higher contingent liabilities of
government.
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BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
CCA Credit Risk Measures
Asset
Value
Exp. asset
value path
Distribution of Asset Value
Distance to
Distress:
standard
deviations asset
value is from
debt distress
barrier
V0
Distress Barrier
or promised payments
Probability of Default
T
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BANCO CENTRAL DE CHILE
Time
28 DE MAYO DE 2008
CCA Core Concept
Equity
or Jr
Claims
Assets
Risky
Debt
• Value of liabilities derived
from value of assets.
• Liabilities have different
seniority.
• Randomness in asset value.
 Assets = Equity + Risky Debt


10
Loss
=
Equity + Default-Free Debt – Expected
= Implicit Call Option + Default-Free Debt
- Implicit Put Option
BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
Calibrate (Unobservable) Market Value
of Asset and Implied Asset Volatility
 INPUTS
 Value and
Volatility of
Market
Capitalization, E
 Debt Distress
Barrier B (from
Book Value)
 Time Horizon
USING TWO EQUATIONS WITH
TWO UNKNOWNS
 rt
1
2
E  A N (d )  Be N (d )
E E  A A N (d1 )
Gives:
Implied Asset Value A and
Asset Volatility
A
Distance-to-Distress
Default Probabilities
Spreads & Risk Indicators
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BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
CCA Model Indicators
 Distance to Default (DTD)
ln( A / D)  (r   / 2)
d2 
A t
2
A
 Probability of Default (PD)
PD  N (d2 ), where N : normal distributi on fn
 Credit Spread from Put Option
 rt
s  1 T ln( 1  PUT / De )
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BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
Chilean Banking System
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DTD of Banking System
Output Gap
10
8
6
4
2
1997M01
0
1999M01
-2
2001M01
2003M01
2005M01
2007M01
-4
-6
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28 DE MAYO DE 2008
DTD in GDP Growth for Chile
yt  c  1rt 1   2 dtdt 1   3et 1   4 yt 1   t
Sample: 1998 2007 (monthly)
Included observations: 106 after adjustments
Variable
Coefficient
C
R(-1)
DLOG(E(-1))
DLOG(DTD(-1))
DLOG(Y(-1))
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
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0.011
-0.001
0.046
0.012
0.463
0.574
0.557
0.008
0.007
358.890
1.912
Std. Error
t-Statistic
0.002
0.000
0.019
0.003
0.074
4.830
-3.723
2.438
3.551
6.283
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
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Prob.
0.000
0.000
0.017
0.001
0.000
0.009
0.013
-6.677
-6.552
34.036
0.000
28 DE MAYO DE 2008
DTD in Output Gap for Chile
gapt  c  1dtdt 1   2 et 1   4 gapt 1   t
Sample (adjusted): 1998M02 2007M02
Included observations: 109 after adjustments
Variable
Coefficient
C
DLOG(TCR(-3),0,3)
LOG(DTDS(-1))
YGAP(-1)
YGAP(-3)
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
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-1.736
4.134
0.934
0.513
0.225
0.661
0.648
0.712
52.766
-115.126
1.842
Std. Error
0.470
1.639
0.256
0.082
0.072
t-Statistic
-3.691
2.522
3.653
6.275
3.113
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
BANCO CENTRAL DE CHILE
Prob.
0.000
0.013
0.000
0.000
0.002
-0.035
1.201
2.204
2.328
50.695
0.000
28 DE MAYO DE 2008
CCA Applied to Chilean Banking
System

GDP is affected by financial stability in the
banking system.

Financial distress in banks and bank’s
borrowers reduces lending as borrower’s
credit risk increases, which reduces
investment and consumption affecting GDP.

There are a number of different financial
stability credit risk indicators.
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BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
CCA Applied to Chilean Banking
System
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
This study uses the distance-to-distress
for the banking system (dtd for each
mayor public traded bank, weighted by the
bank’s implied assets).

Chile’s estimation of the output gap shows
that a credit risk indicator (distance to
default) is significant and has a positive
effect on the output gap.
BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
Monetary Policy Model
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
The primary tool for macroeconomic
management is the interest rates set by
the Central Bank.

Simple monetary policy models are widely
used by Central Banks to understand
macroeconomic
and
interest
rate
relationships as well as to forecast.

Traditionally, central banks (models) target
inflation and GDP-gap.
BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
Monetary Policy Model

This paper uses a simple five equation monetary
policy model, with two modules:
Macro Monetary Policy Module.
2. CCA Financial System Module.
1.
19

This model begins by including the financial
stability credit risk indicator (banking system
distance to distress) in the output gap equation.

The model is calibrated with
parameters (instead of estimated).
BANCO CENTRAL DE CHILE
reasonable
28 DE MAYO DE 2008
Monetary Policy Model
 GDP Gap:
yt  1 yt 1   2 (rsd ,t  L   t  L )  3 X S ,t  L   4 dtdt  1,t
or
yt  yt *   4 dtdt  1,t
 Traditional Taylor Rule:
rsd ,t  rd ,t 1  (1   ) ( (
e
t ,t T
  )  (1   ) yt )   4,t
T
 Taylor Rule with Financial Stability Indicator:
rsd ,t  rd ,t 1  (1   ) ( ( te,t T   T )  (1   ) yt *)
 10dtdt   4,t
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BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
Monetary Policy Model
21

Thus the model includes a GDP-gap equation
and a Taylor Rule equation which includes
financial stability indicator.

The remaining three equations are for inflation,
exchange rate, and the yield curve.

The model was also run with a exchange rate
equation (interest parity condition) that
includes the financial fragility indicator (dtdarbitrage, country risk premium).
BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
Monetary Policy Model
 Inflation:
 t  5 t 1  6 yt  7 te,t T  8X S ,t  9 sLCD   2,t
 Exchange Rate:
X S ,t  11 X S ,t 1  12rsd ,t  13rsf ,t  14 st ,t T  15dtd   5,t
 Yield Curve:
Rt  16 Rt  17 ( Rt 1  Rt )
 18 ( Rt 1  Rt ) t 1  19 (rt 1  rt )t   2,t
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BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
CCA Endogeneity
 DTD and GDP-gap affect each other.
 In order to include this into the model, we define
one last equation where the value of the equity
depends on the GDP-gap.
Et  Et 1  yt
 This beta is a macro factor.
 The model is also run without this effect.
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BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
Impulse Response Function (IRF)
 IR is the standard tool to analyze the behavior
of a model (we are not presenting standard
deviations).
 The model needs to be solved using the
Gauss-Seidel (GS) algorithm and Fair-Taylor
(FT) for calculating the expectations.
 Starting from a fix value (zero), it iterates until a
the solution is achieved.
 This solve the Macro Model and also the asset’s
level & volatility.
 So, for each period of time, the model solves a
system of equations for the current and expected
value of the main variables (FT).
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BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
Impulse Responses
 The




25
impulse responses are obtained using
Winsolve.
In each case a response of GDP, inflation, exchange
rate, r (MPR) and R are shown for a shock of 100 bp
in each variable.
In addition, the response of the CCA (DTD)
variables is shown.
The basic model is the classic Taylor Rule
(theta=0.5, rho=0.6 & gamma =0.6).
We added a reaction of the monetary policy to the
DTD, with a coefficient equal to 0.5.
BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
Shock to inflation
1.2%
1.0%
0.8%
dp
y
e
r
rl
ldtd
0.6%
0.4%
0.2%
0.0%
200004
-0.2%
200204
200404
200604
200804
-0.4%
-0.6%
26
BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
201004
Shock to output gap
1.2%
1.0%
dp
y
e
0.8%
r
rl
ldtd
0.6%
0.4%
0.2%
0.0%
200004
-0.2%
200204
200404
200604
200804
-0.4%
-0.6%
-0.8%
27
BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
201004
Shock to real exchange rate
1.2%
dp
y
e
r
rl
ldtd
1.0%
0.8%
0.6%
0.4%
0.2%
0.0%
200004
200204
200404
200604
200804
-0.2%
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BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
201004
Shock to real short interest rate
1.5%
1.0%
dp
y
e
r
rl
ldtd
0.5%
0.0%
200004
200204
200404
200604
200804
-0.5%
-1.0%
-1.5%
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BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
201004
Shock to real long interest rate
1.5%
1.0%
dp
y
e
r
rl
ldtd
0.5%
0.0%
200004
200204
200404
200604
200804
-0.5%
-1.0%
30
BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
201004
Shock to distance to default
2.0%
dp
y
e
r
rl
ldtd
1.5%
1.0%
0.5%
0.0%
200004
200204
200404
200604
200804
-0.5%
-1.0%
-1.5%
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BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
201004
Impulse Response Conclusions
 The
model works as expected:
magnitudes seem reasonable.
signs
and
 There is high interaction of macro variables, but
they do not affect very much DTD.
 DTD have a high impact on MPR, R and Output-
Gap.
 Real exchange rate could be unstable for some
specifications of the model.
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BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
Efficiency Frontiers
 Different
stochastic simulated scenarios are
solved, for different monetary policy rules.
 MPR that reacts to Financial Fragility (DTD) is
compared with the Non-Policy case.
 A variance-covariance matrix is set, given the
standard error from the regression and some
judgment (for simplicity we set all the standard
deviations to 1bp).
 Each set of monetary rules is solved for
different values of gamma: the relative reaction
to inflation and GDP (output gap).
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BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
Efficiency Frontiers
 This process generates a frontier for the steady




34
state volatility of GDP and inflation.
A base scenario is set where there is no reaction of
the monetary policy to DTD, but GDP and exchange
rate still react to it.
Shocks to DTD could be understood as shocks to
risk appetite.
Starting from a Base Model a higher reaction to
DTD and lower endogeneity are tested.
Then
several
features
are
turned
off
simultaneously.
BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
Efficiency Frontiers: Base Model
3.5%
Output volatility
3.0%
2.5%
2.0%
1.5%
No Policy
MPR to DTD
1.0%
1.0%
1.5%
2.0%
2.5%
3.0%
Inflation volatility
35
BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
Higher reaction to DTD in MPR
3.5%
Output volatility
3.0%
2.5%
2.0%
1.5%
No Policy
MPR to DTD
1.0%
1.0%
1.5%
2.0%
2.5%
3.0%
Inflation volatility
36
BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
Smaller GDP effect on bank’s
equity (endogeneity)
3.5%
Output volatility
3.0%
2.5%
2.0%
1.5%
No Policy
MPR to DTD
1.0%
1.0%
1.5%
2.0%
2.5%
3.0%
Inflation volatility
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BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
Efficiency Frontiers
 In what follows, some characteristics of the
based model are changed:
 Lower endogeneity (LE).
 LE + no effect of DTD in exchange rate (EE).
 LE+EE+lower pass-through of the nominal
exchange rate to inflation.
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BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
Previous +: no effect of DTD in
real exchange rate
3.5%
Output volatility
3.0%
2.5%
2.0%
No Policy
1.5%
MPR to DTD
1.0%
1.0%
1.5%
2.0%
2.5%
3.0%
Inflation volatility
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BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
Previous +: Lower pass-through
3.5%
Output volatility
3.0%
2.5%
2.0%
No Policy
1.5%
MPR to DTD
1.0%
1.0%
1.5%
2.0%
2.5%
3.0%
Inflation volatility
40
BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
The model is robust to:
 Leads in the real exchange rate (forward
looking).
 Sign of the real exchange rate in the output
gap.
 Magnitude of the reaction of MPR to output
gap and inflation.
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BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
The model changes with
 The degree of arbitrage to DTD in the real
exchange rate (↑Effect → ↓Frontier).
 Magnitude of the reaction of the MPR to DTD
(↑Effect → ↓Frontier).
 Magnitude of the Pass- through reaction of
MPR to output gap and inflation (↑Effect →
↓Frontier).
 Endogenity of the value of the equity to
movements of the output gap (↑Effect →
↓Frontier).
42
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28 DE MAYO DE 2008
Results and Conclusions
 A simple, but powerful model for monetary




43
policy. The model has the main variables
analyzed by policymakers, but is small
enough to understand it easily.
Empirical evidence supports the model.
IRF in accordance with theory.
Robust efficient frontier, but there is a trade
off in the results.
A stronger reaction to DTD reduces inflation
volatility but increases output volatility.
BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
Next Steps / To Follow
 Combinations
of financial scenarios
normal, fragility) should be incorporated.
(strong,
 Changes in the dynamic of the macro model should
be tested (maybe move to DGE).
 More realistic Variance-Covariance matrix.
 Look for empirical evidence in other countries and
comparison of the model with other economies.
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Monetary Policy and
Financial Distress:
Incorporating Financial Risk into
Monetary Policy Models
(ANNEX)
Dale Gray (IMF)
Leonardo Luna (BCCh)
Jorge Restrepo (BCCh)
45
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28 DE MAYO DE 2008
CCA Model




Prob( At  Bt )  Prob A0 exp   A   A2 / 2 t   A t   Bt = Prob   d 2,  
Distributions of Asset Value at T
Asset Value
Expected Asset
Drift of μ
A0
Drift of r
Promised Payments: Bt
“Actual “
Probability
of Default
“Risk-Adjusted “ Probability
of Default
Time
T
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28 DE MAYO DE 2008
After Calibration Several Types of Risk
Indicators are Derived
 Distance to Distress (number of standard
deviations of asset value from distress)
 Default Probability
 Risk Neutral Default Probability = N(- d2)
 Estimated Actual Default Probability =
N(- d2 -λ)
 The market price of risk is λ, λ=(u-r)/σ
 Model Spread, s, in basis points
 Implicit Put Option (Expected Loss) and Value
of Risky Debt (Default-free value of debt –
expected loss)
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BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008
Monetary Policy and
Financial Distress:
Incorporating Financial Risk into
Monetary Policy Models
Dale Gray (IMF)
Leonardo Luna (BCCh)
Jorge Restrepo (BCCh)
48
BANCO CENTRAL DE CHILE
28 DE MAYO DE 2008