Macrofinancial Risk Analysis Using Contingent Claims Analysis CCA

Macrofinancial Risk Analysis Using Contingent Claims Analysis (CCA) for Financial Stability, Linking Financial Sector to Monetary Policy Models Dale Gray Monetary and Capital Markets Department International Monetary Fund Dgray@imf. org The views expressed in this presentation are those of the author and should not be attributed to the International Monetary Fund, its Executive Board, or its management.

Outline n Contingent Claims Analysis (CCA) – CCA Framework and Models – Application to Financial Institutions • Recent Sub-prime Crisis • CCA for Icelandic Banks n n CCA Models Linked to Factor Models and Monetary Policy Models (application to Chile) Sovereign Economy-wide CCA Models Presentation based on ongoing research Dale Gray; and papers by Dale Gray, Robert C. Merton and Zvi Bodie in: (i) JOIM 2007, (ii) NBER 2007; and (iii) new book on Macrofinancial Risk Analysis (2008). 2

Macrofinancial Risk Analysis n n Framework integrates riskadjusted balance sheets using Contingent Claims Analysis (CCA) with macroeconomic and monetary policy models CCA models of financial institutions, corporates, and sovereigns are integrated together and with macroeconomic models 3

Linking CCA Balance Sheet Models to Macroeconomic Flows and Models n n Macroeconomic models geared to try to forecast the mean of macro variables (i. e. first moment) Finance measures risk from stochastic assets relative to threshold (second and third moments critical to risk indicators). CCA is an excellent tool for analyzing financial stability Time pattern of CCA risk indicators can be linked to macroeconomic variables and to monetary policy models 4

Core Concept: Merton Model/CCA for Firms and Banks Assets Equity or Jr Claims Risky Debt Assets = Equity + + • Value of liabilities derived from value of assets. • Liabilities have different seniority. • Randomness in asset value. Risky Debt Default-Free Debt – Expected Loss = Implicit Call Option + Default-Free Debt – Implicit Put Option 5

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 V 0 Distress Barrier or promised payments Probability of Default T Time 6

CCA models of the Financial Sector and links to Macro Models n Decomposing factors driving bank CDS spreads – Leverage, asset volatility, Global market risk appetite, loss given default – Implicit put options as a measure of risk n n n Linking credit risk indicators to macro models. Factor models of CCA asset and risk indicators for systemic stress testing and link to GDP growth Integrating financial sector with monetary policy models Analysis of non-linear risk transmission between key sectors in an economy-wide CCA balance sheet model 7

Calibrating Implied Assets and Asset Volatility Implied asset value and implied asset volatility calibrated from contingent claims analysis. n. Merton Model n. Moody’s-KMV for firms and financial institutions n. Merton-type CCA or hybrid models have been applied to corporates and financial institutions. Moody’s. KMV, Kamakura and others have applied these models for credit risk analysis to tens of thousands of firms and banks in over 50 countries around the world. n. MKMV provides daily output for 37 financial institutions in Sweden n. Calibration using equity options n. Another way to implement the Merton model is to use information from equity options (implied volatility and “skew”) to calculate credit risk and spreads in banks in US, Sweden and other countries. 8

Calibrate (Unobservable) Market Value of Asset and Implied Asset Volatility USING TWO EQUATIONS WITH TWO UNKNOWNS INPUTS Value and Volatility of Market Capitalization, E n Debt Distress Barrier B (from Book Value) n n Time Horizon Gives: Implied Asset Value A and Asset Volatility A Default Probabilities Spreads, Risk Indicators KMV maps risk indicators to actual default probabilities (EDFs) using historical default data 9

MKMV Key Drivers of Expected Default Frequency (EDF) and EDF Implied CDS spreads (EICDS) EDF Key Drivers are Market Leverage (default point divided by assets) and asset volatility Key Drivers of EICDS are Risk-Neutral EDF (from EDF, Market Sharpe Ratio (SR), correlation ρ) and Loss Given Default 10

What does CCA/MKMV Have to Say About Subprime Crisis? –First, See evolution of market CDS Spreads over the 2007 -2008 Crisis for Major US banks and Primary Dealers 11

Market Leverage Has Increased Implied Asset Volatility Has Increased 6/30/2007=100 12

Banks in Subprime Crisis – CCA/MKMV Implied Market Value of Assets, June 30, 2007=100 Assets increase Aug 2007 to early 2008 because of SIV etc. assets brought back on to balance sheets ? 13

EDF Has Increased EDF Implied CDS 14

Significantly Higher Market Sharpe Ratio since July 2007, with peaks on 3/27/08 and 8/6/08 Market Sharpe Ratio and other indicators show decreased risk appetite 15

Changes in Bank CDS due to Leverage, Volatility and Impact of Increase in Market Price of Risk as of March 20, 2008 (Lower Risk Appetite, Higher Correlation) With Subprime Exposure/Loss CDS January 2007 Without Subprime Loss 18 20 Increased Market Leverage +52 +45 Change in Volatility +41 +10 Market Price of Risk Increase (SR*ρ) +75 +70 190 bps 145 bps CDS March 2008 16

Icelandic banks and government– Questions and issues that CCA can help with What does the equity market vs the CDS market say about credit risk in Icelandic banks? What are implied asset and asset volatility and EDFs? How has the change in global market risk appetite affected CDS spreads in Iceland? What are the differences in credit risk from the equtiy market vs the CDS market? illiquidity of CDS? , What does this mean for the contingent liabilities of the Central Bank (liquidity support) and what does it mean for government? 17

Icelandic Banks CCA Using MKMV 18

Icelandic Banks CCA Using MKMV 19

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Iceland Banks CCA 21

Iceland Banks CCA 22

Issues regarding differences in information from CDS and Equity markets for Icelandic banks What does the equity market vs the CDS market say about credit risk in Icelandic banks? n n Take observed market CDS an get implicit Put option (PCDS) Then take equity information and get implicit Put Option (PEQ) What are the explanations for the differences? illiquidity of CDS? , illiquidity of equity? , other? What does this mean for the contingent liabilities of the Central Bank (liquidity support) and what does it mean for government? 23

CCA models of the Financial Sector and links to Macro Models n Decomposing factors driving bank CDS spreads – Leverage, asset volatility, Global market risk appetite, loss given default – Implicit put options n n n Linking credit risk indicators to macro models. Factor models of CCA asset and risk indicators for systemic stress testing and link to GDP growth Integrating financial sector with monetary policy models Analysis of non-linear risk transmission between key sectors in an economy-wide CCA balance sheet model 24

Bank-by-Bank CCA and Factor Models for Stress-Testing Proceedure: n Calibrate CCA model for each bank n Estimate factor model for bank return n Generate scenarios and carry out stress test to see impact on bank credit risk and on equity capital 25

EXAMPLE OF CHILE BANK FACTOR MODEL - Banks have Heterogeneous Response to Individual Factors; Stress testing can be with individual factors or with Four Principal Components Factors associated with different components of asset returns Factor 1 Factor 2 Factor 3 Factor 4 26

CCA models of the Financial Sector and links to Macro Models n Decomposing factors driving bank CDS spreads – Leverage, asset volatility, Global market risk appetite, loss given default – Implicit put options n n n Linking credit risk indicators to macro models. Factor models of CCA asset and risk indicators for systemic stress testing and link to GDP growth Integrating financial sector with monetary policy models Analysis of non-linear risk transmission between key sectors in an economy-wide CCA balance sheet model 27

CCA Risk Indicators in Monetary Policy Models The integration of the financial sector vulnerability into macroeconomic models is of keen interest for policymakers. Explicit inclusion of CCA sytemic credit risk/financial fragility indicator n Should a financial fragility indicator be included in monetary policy models? – Yes, at least in the GDP Output Gap equation n Should it be explicitly included in the reaction function? Or, should the central bank react only indirectly through reacting to its effects on output gap and inflation? – Depends 28

CCA Chilean Banking System Risk and Macro Effects GDP is affected by financial stability in the banking system via n n Financial accelerator links; Financial distress in banks and bank’s borrowers reduces lending as borrower’s credit risk increases, which reduces investment and consumption affecting GDP. 29

Chilean Banking System – CCA Distance-to. Distress (DTD) is Estimated for Banking System DTD has significant impact on Output Gap 30

DTD related to GDP Growth for Chile Sample: 1998 2007 (monthly) Included observations: 106 after adjustments Variable 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 Coefficient 0. 011 -0. 001 0. 046 0. 012 0. 463 0. 574 0. 557 0. 008 0. 007 358. 890 1. 912 Std. Error 0. 002 0. 000 0. 019 0. 003 0. 074 t-Statistic 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) Prob. 0. 000 0. 017 0. 001 0. 000 0. 009 0. 013 -6. 677 -6. 552 34. 036 0. 000 31

DTD related to Output Gap for Chile Sample (adjusted): 1998 M 02 2007 M 02 Included observations: 109 after adjustments Variable 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 Coefficient -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) Prob. 0. 000 0. 013 0. 000 0. 002 -0. 035 1. 201 2. 204 2. 328 50. 695 0. 000 32

Simple Five Equation Monetary Policy Model GDP Gap with Financial Sector DTD: Traditional Taylor Rule: Taylor Rule with Financial Stability Indicator: 33

Monetary Policy Model (cont. ) Inflation: Exchange Rate: Yield Curve: 34

Impulse Response Functions (IRF) with DTD in Monetary Policy Model IRF is the standard tool to analyze the behavior of a monetary model of this type (we are not presenting standard deviations). – For each period of time, the model solves a system of equations for the current and expected value of the main variables; – The model works as expected: signs and magnitudes seem reasonable; – Financial Sector Distance-to-Distress (DTD) has a significant impact on short and long term interest rates, ER, and Output-Gap. 35

Impulse Response: Shock to banking sector distance to default (DTD) 36

Efficiency Frontiers 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. 37

Efficiency Frontiers: Base Model if Monetary Policy Rate reacts to Financial Sector DTD 38

Results and Conclusions of Chile CCA-Monetary Policy Model Analysis A simple, but powerful model for monetary policy including financial sector risk indicator (DTD) Empirical evidence supports the model. DTD affects GDP growth and Output Gap Impulse Responses in accordance with theory. Robust efficient frontier, but there is a trade off in the results: A stronger reaction of policy interest rates to DTD reduces inflation volatility, but increases output volatility. More analysis is being carried out. 39

Unified Macrofinance Framework (Targets: GDP, Inflation, Financial System Credit Risk, Sovereign Credit Risk) Policies: Domestic and International Factors Sovereign CCA Model • Fiscal Policy • Debt Management • Reserves / SWF Interest Rate Term Structure Model Monetary Policy Model Financial CCA (Merton-STV) Model (s) Economic Capital Adequacy • Policy Rate CRI • Economic Capital Adequacy • Bank and Financial Sector Regulations 40

CCA Model of the Sovereign – Very Useful for Iceland n Sovereign Assets – Present value of primary fiscal surplus – Reserves – Minus contingent liabilities to banks and others n Sovereign Liabilities – Base money, foreign and local-currency debt – Model measures sovereign spreads Note exchange rate volatility and skew affects sovereign spreads 41

Sovereign, Bank, and Corporate Economy-wide CCA Sector Interlinked Balance Sheets Risky Debt = Default-free Value of Debt minus Expected Losses Corporate Sector Assets Equity Default-free Debt Value – Put Option Money & Sovereign Assets Local Currency Debt Expected losses in risky debt are implicit put options, contingent liabilities are implicit put options, equity and junior claims are implicit call options Equity Banking/ Financial Sector Assets Foreign Def-free Debt Value – Put Option Contingent Liab Deposits and Debt Value – Put Option See Annex Implicit Put Option 42

Economy-wide Interlinked CCA Balance Sheets with Assets, Junior Claims, Risky Debt and Cont. Liabilities 43 A=Assets, E=Jr. Claim, B=Def-free Debt, P=Put Options

Economy-wide CCA Balance Sheet Models Capture Non-linear Risk Transmission n Note that if asset volatility in CCA sector balance sheets is set to zero: – Implicit put options go to zero, – Macroeconomic accounting balance sheets and traditional flow-of-funds are the result – Measurement of (non-linear) risk transmission is not possible using macroeconomic flow or accounting frameworks n Interlinked implicit options result in compound options that exhibit highly nonlinear risk transmission, as seen a variety of financial crises 44

Summary use CCA models of the Financial Sector and links to Macro Models n Decomposing factors driving bank CDS spreads – Leverage, asset volatility, Global market risk appetite, loss given default – Implicit put options n n n Vulnerability and stress-testing Linking credit risk indicators to macro models. Factor models of CCA asset and risk indicators for systemic stress testing and link to GDP growth FX reserves “adequacy” for banking sector contingent liquidity and credit risks Integrating financial sector with monetary policy models Analysis of non-linear risk transmission between key sectors in an economy-wide CCA balance sheet model 45

Thank you, More information see: Papers by D. Gray, Robert C. Merton, Zvi Bodie: n NBER 12637 (2006) n NBER 13607 (2007) n Sovereign Credit Risk, JOIM v. 5, no. 4, Dec 2007 n CCA and the Subprime Crisis (Gray, Merton, Bodie forthcoming) IMF Working Papers: WP 05/155, 04/121, 07/233, Indonesia SIP (2006), Gray and Walsh (WP 08/89), Gray, Lim, Loukoianova, Malone (WP/08), IMF Staff Papers Gapen et. al v 55 #1 2008; Framework for Integrating Macroeconomics and Financial Sector Analysis by Gray, Karam, Malone, N’Diaye (forthcoming) Macrofinancial Risk Analysis, Gray and Malone (Wiley Finance book Foreword by Robert Merton) 202 -623 -6858 dgray@imf. org 46

Annex 1 - CCA Risk Indicators and Values Value of Risky Debt, D (B=distress barrier, P=implicit put option) D-to-D= Default Probability Risk Neutral DP Estimated Actual DP Credit Spreads 47

Annex 2 - Sovereign, Bank, and Corporate Economywide CCA Sector Interlinked Balance Sheets Risky Debt = Default-free Value of Debt minus Expected Losses Corporate Sector Assets Equity Default-free Debt Value – Put Option Money & Sovereign Assets Local Currency Debt Expected losses in risky debt are implicit put options, contingent liabilities are implicit put options, equity and junior claims are implicit call options Equity Banking/ Financial Sector Assets Foreign Def-free Debt Value – Put Option Contingent Liab Deposits and Debt Value – Put Option See Annex Implicit Put Option 48

Annex 4 – Aggregation of Credit Risk Indicators (CRIs) Tractable measures of system risk for use with macroeconomic models and for financial stability analysis the CCA credit risk indicators are: Weight the EDF or distance-to-distress for each institution by the implied assets of each bank/financial institution to get a system risk indicator. Use the median or 75% quartile EDF for the sub-sector or group, e. g. as calculated by MKMV. Composite spread or default probability for financial sector, corporate sector and households (if data is available). Weight of the volatility and/or skew from put option on equity of key financial institutions by the assets of the institution. Calculate an Nth to default indicator. Calculate the joint distribution of default probabilities in a portfolio of financial institutions. Tail risk dependence measure from equity options or implied assets is another indicator. 49