1. 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: Incorporating Financial Risk into Monetary Policy Models Dale Gray (IMF) Leonardo Luna (BCCh) Jorge Restrepo (BCCh)

2. 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

3. 3 B A N C O C E N T R A L D E C H I L E 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?

4. 4 B A N C O C E N T R A L D E C H I L E 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.

5. 5 B A N C O C E N T R A L D E C H I L E 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.

6. 6 B A N C O C E N T R A L D E C H I L E 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.

7. 7 B A N C O C E N T R A L D E C H I L E 28 DE MAYO DE 2008 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.

8. 8 B A N C O C E N T R A L D E C H I L E 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.

9. 9 B A N C O C E N T R A L D E C H I L E 28 DE MAYO DE 2008 CCA Credit Risk Measures Asset Value Exp. asset Distribution of Asset Value value path Distress Barrier or promised payments V 0 Time Probability of Default T Distance to Distress: standard deviations asset value is from debt distress barrier

10. 10 B A N C O C E N T R A L D E C H I L E 28 DE MAYO DE 2008 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.

11. 11 B A N C O C E N T R A L D E C H I L E 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 Gives: Implied Asset Value A and Asset Volatility  A Distance-to-Distress Default Probabilities Spreads & Risk Indicators

12. 12 B A N C O C E N T R A L D E C H I L E 28 DE MAYO DE 2008 CCA Model Indicators  Distance to Default (DTD)  Probability of Default (PD)  Credit Spread from Put Option

13. 13 B A N C O C E N T R A L D E C H I L E 28 DE MAYO DE 2008 Chilean Banking System

14. 14 B A N C O C E N T R A L D E C H I L E 28 DE MAYO DE 2008 DTD in GDP Growth for Chile Sample: 1998 2007 (monthly) Included observations: 106 after adjustments VariableCoefficientStd. Errort-StatisticProb. C 0.0110.0024.8300.000 R(-1) -0.0010.000-3.7230.000 DLOG(E(-1)) 0.0460.0192.4380.017 DLOG(DTD(-1)) 0.0120.0033.5510.001 DLOG(Y(-1)) 0.4630.0746.2830.000 R-squared 0.574 Mean dependent var 0.009 Adjusted R-squared 0.557 S.D. dependent var 0.013 S.E. of regression 0.008 Akaike info criterion -6.677 Sum squared resid 0.007 Schwarz criterion -6.552 Log likelihood 358.890 F-statistic 34.036 Durbin-Watson stat 1.912 Prob(F-statistic) 0.000

15. 15 B A N C O C E N T R A L D E C H I L E 28 DE MAYO DE 2008 DTD in Output Gap for Chile Sample (adjusted): 1998M02 2007M02 Included observations: 109 after adjustments VariableCoefficientStd. Errort-StatisticProb. C -1.7360.470-3.6910.000 DLOG(TCR(-3),0,3) 4.1341.6392.5220.013 LOG(DTDS(-1)) 0.9340.2563.6530.000 YGAP(-1) 0.5130.0826.2750.000 YGAP(-3) 0.2250.0723.1130.002 R-squared 0.661 Mean dependent var -0.035 Adjusted R-squared 0.648 S.D. dependent var 1.201 S.E. of regression 0.712 Akaike info criterion 2.204 Sum squared resid 52.766 Schwarz criterion 2.328 Log likelihood -115.126 F-statistic 50.695 Durbin-Watson stat 1.842 Prob(F-statistic) 0.000

16. 16 B A N C O C E N T R A L D E C H I L E 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.

17. 17 B A N C O C E N T R A L D E C H I L E 28 DE MAYO DE 2008 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.

18. 18 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 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.

19. 19 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 Model  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).

20. 20 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 Model  GDP Gap:  Traditional Taylor Rule:  Taylor Rule with Financial Stability Indicator:

21. 21 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 Model  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).

22. 22 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 Model  Inflation:  Exchange Rate:  Yield Curve:

23. 23 B A N C O C E N T R A L D E C H I L E 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.  This beta is a macro factor.  The model is also run without this effect.

24. 24 B A N C O C E N T R A L D E C H I L E 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).

25. 25 B A N C O C E N T R A L D E C H I L E 28 DE MAYO DE 2008 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.

26. 26 B A N C O C E N T R A L D E C H I L E 28 DE MAYO DE 2008 Shock to inflation

27. 27 B A N C O C E N T R A L D E C H I L E 28 DE MAYO DE 2008 Shock to output gap

28. 28 B A N C O C E N T R A L D E C H I L E 28 DE MAYO DE 2008 Shock to real exchange rate

29. 29 B A N C O C E N T R A L D E C H I L E 28 DE MAYO DE 2008 Shock to real short interest rate

30. 30 B A N C O C E N T R A L D E C H I L E 28 DE MAYO DE 2008 Shock to real long interest rate

31. 31 B A N C O C E N T R A L D E C H I L E 28 DE MAYO DE 2008 Shock to distance to default

32. 32 B A N C O C E N T R A L D E C H I L E 28 DE MAYO DE 2008 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.

33. 33 B A N C O C E N T R A L D E C H I L E 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).

34. 34 B A N C O C E N T R A L D E C H I L E 28 DE MAYO DE 2008 Efficiency Frontiers  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.

35. 35 B A N C O C E N T R A L D E C H I L E 28 DE MAYO DE 2008 Efficiency Frontiers: Base Model

36. 36 B A N C O C E N T R A L D E C H I L E 28 DE MAYO DE 2008 Higher reaction to DTD in MPR

37. 37 B A N C O C E N T R A L D E C H I L E 28 DE MAYO DE 2008 Smaller GDP effect on bank’s equity (endogeneity)

38. 38 B A N C O C E N T R A L D E C H I L E 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.

39. 39 B A N C O C E N T R A L D E C H I L E 28 DE MAYO DE 2008 Previous +: no effect of DTD in real exchange rate

40. 40 B A N C O C E N T R A L D E C H I L E 28 DE MAYO DE 2008 Previous +: Lower pass-through

41. 41 B A N C O C E N T R A L D E C H I L E 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.

42. 42 B A N C O C E N T R A L D E C H I L E 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).

43. 43 B A N C O C E N T R A L D E C H I L E 28 DE MAYO DE 2008 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.

44. 44 B A N C O C E N T R A L D E C H I L E 28 DE MAYO DE 2008 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.

45. 45 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: Incorporating Financial Risk into Monetary Policy Models (ANNEX) Dale Gray (IMF) Leonardo Luna (BCCh) Jorge Restrepo (BCCh)

46. 46 B A N C O C E N T R A L D E C H I L E 28 DE MAYO DE 2008 CCA Model Asset Value Expected Asset Distributions of Asset Value at T Drift of μ Promised Payments: B t A 0 T Time “Actual “ Probability of Default Drift of r “Risk-Adjusted “ Probability of Default

47. 47 B A N C O C E N T R A L D E C H I L E 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(- d 2 )  Estimated Actual Default Probability = N(- d 2 -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)

48. 48 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: Incorporating Financial Risk into Monetary Policy Models Dale Gray (IMF) Leonardo Luna (BCCh) Jorge Restrepo (BCCh)