1 b a n c o c e n t r a l d e c h i l e 28 de mayo de 2008 monetary policy and financial distress:...

B A N C O C E N T R A L D E C H I L E 28 DE MAYO DE 20081

Monetary Policy and Financial Distress:

Incorporating Financial Risk into Monetary Policy Models

Dale Gray (IMF)Leonardo Luna (BCCh)Jorge Restrepo (BCCh)

2 B A N C O C E N T R A L D E C H I L E 28 DE MAYO DE 2008

Index

Motivation Contingent Claims Analysis (CCA) Empirical Evidence The Model

Impulse Responses Efficiency Frontiers

Results, Conclusions & Next Steps


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?


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.


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.


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.


Contingent Claims Analysis Banks lend to households, companies, and

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.


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.


CCA Credit Risk Measures

Asset Value

Exp. asset Distribution of Asset Valuevalue path

Distress Barrier or promised payments

V0

Time

Probability of Default

T

Distance toDistress: standard

deviations asset value is from debt distress

barrier


CCA Core Concept

Assets = Equity + Risky Debt = Equity + Default-Free Debt –

Expected Loss = Implicit Call Option + Default-Free

Debt - Implicit Put Option

Assets

Equity or Jr Claims

Risky Debt

• Value of liabilities derived from value of assets.

• Liabilities have different seniority.

• Randomness in asset value.


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

Gives:Implied Asset Value A and

Asset Volatility A

Distance-to-DistressDefault ProbabilitiesSpreads & Risk Indicators

)()( 21 dNBedNAE rt)( 1dNAE AE


CCA Model Indicators

Distance to Default (DTD)

Probability of Default (PD)

Credit Spread from Put Option

t

rDAd

A

A

)2/()/ln( 2

2

fnon distributi normal: where),( 2 NdNPD

)/1ln(1 rtDePUTTs


Chilean Banking System

-6

-4

-2

0

2

4

6

8

10

12

1997M01 1999M01 2001M01 2003M01 2005M01 2007M01

DTD of Banking System

Output Gap


DTD in GDP Growth for Chile

tttttt yedtdrcy 14131211 Sample: 1998 2007 (monthly)

Included observations: 106 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

C 0.011 0.002 4.830 0.000R(-1) -0.001 0.000 -3.723 0.000DLOG(E(-1)) 0.046 0.019 2.438 0.017DLOG(DTD(-1)) 0.012 0.003 3.551 0.001DLOG(Y(-1)) 0.463 0.074 6.283 0.000

R-squared 0.574 Mean dependent var 0.009Adjusted R-squared 0.557 S.D. dependent var 0.013S.E. of regression 0.008 Akaike info criterion -6.677Sum squared resid 0.007 Schwarz criterion -6.552Log likelihood 358.890 F-statistic 34.036Durbin-Watson stat 1.912 Prob(F-statistic) 0.000


DTD in Output Gap for Chile

ttttt gapedtdcgap 141211 Sample (adjusted): 1998M02 2007M02Included observations: 109 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

C -1.736 0.470 -3.691 0.000DLOG(TCR(-3),0,3) 4.134 1.639 2.522 0.013LOG(DTDS(-1)) 0.934 0.256 3.653 0.000YGAP(-1) 0.513 0.082 6.275 0.000YGAP(-3) 0.225 0.072 3.113 0.002

R-squared 0.661 Mean dependent var -0.035Adjusted R-squared 0.648 S.D. dependent var 1.201S.E. of regression 0.712 Akaike info criterion 2.204Sum squared resid 52.766 Schwarz criterion 2.328Log likelihood -115.126 F-statistic 50.695Durbin-Watson stat 1.842 Prob(F-statistic) 0.000


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.


CCA Applied to Chilean Banking System

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.


Monetary Policy Model

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.



This paper uses a simple five equation monetary policy model, with two modules:

1. Macro Monetary Policy Module.2. CCA Financial System Module.

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 reasonable parameters (instead of estimated).



GDP Gap:

Traditional Taylor Rule:

Taylor Rule with Financial Stability Indicator:

tttt

ttLtSLtLtsdtt

dtdyyor

dtdXryy

,14

,14,3,211

*

)(

ttTe

Ttttdtsd yrr ,4,1,, ))1()(()1(

tt

tTe

Ttttdtsd

dtd

yrr

,410

,1,, *))1()(()1(



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 (dtd- arbitrage, country risk premium).



Inflation:

Exchange Rate:

Yield Curve:

ttttttt

tttt

rrRR

RRRR

,21191118

11716

)()(

)(

tTtttsftsdtStS dtdsrrXX ,515,14,13,121,11,

tLCDtSeTttttt sXy ,29,8,7615


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.

This beta is a macro factor.

The model is also run without this effect.

ttt yEE 1


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).


Impulse Responses

The 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.


Shock to inflation

-0.6%

-0.4%

-0.2%

0.0%

0.2%

0.4%

0.6%

0.8%

1.0%

1.2%

200004 200204 200404 200604 200804 201004

dp y e

r rl ldtd


Shock to output gap

-0.8%

-0.6%

-0.4%

-0.2%

0.0%

0.2%

0.4%

0.6%

0.8%

1.0%

1.2%

200004 200204 200404 200604 200804 201004

dp y e

r rl ldtd


Shock to real exchange rate

-0.2%

0.0%

0.2%

0.4%

0.6%

0.8%

1.0%

1.2%

200004 200204 200404 200604 200804 201004

dp y e

r rl ldtd


Shock to real short interest rate

-1.5%

-1.0%

-0.5%

0.0%

0.5%

1.0%

1.5%

200004 200204 200404 200604 200804 201004

dp y e

r rl ldtd


Shock to real long interest rate

-1.0%

-0.5%

0.0%

0.5%

1.0%

1.5%

200004 200204 200404 200604 200804 201004

dp y e

r rl ldtd


Shock to distance to default

-1.5%

-1.0%

-0.5%

0.0%

0.5%

1.0%

1.5%

2.0%

200004 200204 200404 200604 200804 201004

dp y e

r rl ldtd


Impulse Response Conclusions

The model works as expected: signs and magnitudes seem reasonable.

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.


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).



This process generates a frontier for the steady 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.


Efficiency Frontiers: Base Model

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

1.0% 1.5% 2.0% 2.5% 3.0%

Inflation volatility

Ou

tpu

t v

ola

tilit

y

No Policy

MPR to DTD


Higher reaction to DTD in MPR

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

1.0% 1.5% 2.0% 2.5% 3.0%


Ou

tpu

t v

ola

tilit

y

No Policy

MPR to DTD


Smaller GDP effect on bank’s equity (endogeneity)

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

1.0% 1.5% 2.0% 2.5% 3.0%


Ou

tpu

t v

ola

tilit

y

No Policy

MPR to DTD



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.


Previous +: no effect of DTD in real exchange rate

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

1.0% 1.5% 2.0% 2.5% 3.0%


Ou

tpu

t v

ola

tilit

y

No Policy

MPR to DTD


Previous +: Lower pass-through

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

1.0% 1.5% 2.0% 2.5% 3.0%


Ou

tpu

t v

ola

tilit

y

No Policy

MPR to DTD


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.


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).


Results and Conclusions

A simple, but powerful model for monetary 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.


Next Steps / To Follow

Combinations of financial scenarios (strong, normal, fragility) should be incorporated.

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.




(ANNEX)



CCA Model

2

0 2,Prob( ) Prob exp = Prob/ 2t t A A A tA B A t t B d

Asset Value

Expected Asset

Distributions of Asset Value at T

Drift of μ

Promised Payments: Bt

A0

T Time

“Actual “ Probability of Default

Drift of r

“Risk-Adjusted “ Probability of Default


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)

1 b a n c o c e n t r a l d e c h i l e 28 de mayo de 2008 monetary policy and financial distress:...

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contingent claims model

financial sector assets

financial distress

risk of default

contingent liabilities

financial sector vulnerability