Systemic CCA A Model Approach to Systemic Risk

Transcription

1 Conference on Beyond the Financial Crisis: Systemic Risk, Spillovers and Regulation Dresden, October 2010 Andreas A Jobst International Monetary Fund Systemic CCA A Model Approach to Systemic Risk

2 Systemic Risk Conference Deutsche Bundesbank/TU Dresden Dresden October 28 29, 2010 Dale F. Gray and Andreas (Andy) Jobst Monetary and Capital Markets (MCM) Department IMF 1

3 Overview Systemic Risk Regulation Definition of CCA and Systemic CCA Some methodological issues Examples Other systemic risk measurement approaches 2

4 Systemic Risk: Current Regulatory Efforts current policy efforts aimed establishing regulatory framework that helps mitigate the risk from systemic linkages multi faceted approach comprising complementary measures in areas of regulatory policies, supervisory scope, and resolution arrangements is needed as part of a sustainable solution o o o o more stringent prudential standards, such as limits on funding liquidity and leverage and higher capital requirements as a way to limit the scale and scope of banking activities, a broader adoption of contingent capital initiatives, designing living wills and strengthening national and cross border (!) resolution processes for large complex financial institutions (LCFIs), incl. special resolution fund sponsored by taxes or levies on too big to fail (TBTF) firms. possibly in combination with the establishment of a specialized supervisor of systemically important firms o systemic risk charges (capital, tax, fees) 3

5 Challenges to Systemic Risk Measurement Method and Regulation o danger of underestimating practical problems of trying to apply systemic risk management approaches to a real life situation o complex modeling or stress testing risks losing transparency, and conclusions will be highly dependent on the assumptions used, and the availability of high quality real time data o complexity might also increase the scope for gaming by firms Policy o could create additional burden on the financial sector at a time when capital is scarce and credit supply is so much needed to sustain the recovery o careful implementation to ensure that availability of adequate credit to support the ongoing recovery is not impeded 4

6 Objectives of Systemic CCA 1. estimate risk adjusted (CCA) balance sheets for individual financial institutions and the dependence between them to estimate systemic tail risk (using a multivariate set up) expected losses 2. assess risk transfer to the government: measuring government contingent liabilities 3. identify the contribution of individual institutions to: o o system wide losses and contingent liabilities [solvency] systemic liquidity risk, as proxied by short term expected losses from the effective maturity mismatch after controlling for the maturity of off balance sheet hedging transactions 4. assess impact of actual and counterfactual financial sector stabilization measures (capital injections, liability guarantees, asset purchases, and/or other) 5

7 Systemic Tail Risk Models for Multiple Entities Accounting Balance Sheet Aggregate FSIs Interbank Exposures CDS/spread implied JPoD Network Merton-based Network Merton-type CCA Joint Risk Systemic CCA Lo Getmansky model Equity Joint Tail Risk (from returns or from option derived higher moments: SES, MES) Systemic Distress Insurance Premium Equity option implied joint risk Market Equitybased CoVaR CDS CoRisk CDS Joint Probability of Distress (JPoD) Source: Dale Gray and Andy Jobst forthcoming IMF WP Market Debt-based (CDS & bond spreads) 6

8 Core Concept of Contingent Claims Analysis (CCA): Asset Value and the Default Process Value of Assets / Liabilities Asset Volatility Distribution of market value of assets σ Distance to default (DD) in σ E[A T ] = μ X T Notional value of liabilities PD EDF TM t = 0 T = 1 year Time 7

9 Core Concept of CCA: Merton Model (1) Assets Equity Risky Debt uncertainty in asset value value of liabilities derived from asset value Assets = Equity + Risky Debt = Equity + Default Barrier Expected Loss = Implicit Call Option + Default Barrier Implicit Put Option = Implicit Call Option + Default Barrier Debt Guarantees (α*put Option) Net Risk ((1 α)*put Option) Equity can be valued as an implicit call option Expected losses can be valued 8 as an implicit put option 8

10 Core Concept of CCA: Merton Model (2) captures uncertainty about asset quality and the ability to absorb losses combines equity market and balance sheet information to infer asset dynamics and expected losses (EL) forward looking by construction, providing a consistent framework for estimating EL based on current market conditions rather than on historical experience (but assumptions, e.g., complete markets and a specific stochastic process) 9

11 Core Concept of CCA: Calibrating Implied Assets and Asset Volatility assets and asset volatility cannot be observed directly implied asset value and implied asset volatility can be calibrated from Merton type model using two equations and two unknowns or enhanced Merton type CCA models o implied assets as RND from equity call options o GEV and/or Gram Charlier OPT once the asset value and asset volatility are known, together with the default barrier, time horizon, and the discount rate r, the implicit put option P can be calculated value of risky debt D defined as implicit put option (=Expected Loss) for distress barrier B ( ) ( ) D Be P P Be N d A N d = rt rt =

12 Estimation of Contingent Liabilities (1) in recent crisis, spreads calculated from implicit equity put options are larger than observed market CDS spreads reflect impact of implicit and explicit government liability guarantees on expected losses (Gray, Merton and Bodie, 2008) combine implicit put options derived from equity and CDS to calculate the market s view of the government contingent liabilities 11

13 Estimation of Contingent Liabilities (2) government contingent liability = α*implicit put option derived from bank equity Assets = Implicit Call Option + [Default Free Debt (1 α)*implicit CDS Put Option] ( ( CDS )) ( ) P = 1 exp s 10,000 RMV RFV T Bexp rt α*implicit Put Option Value of 'put option' from CDS α =1 Value of put option from equity implicit put option (derived from equity): present value of expected losses implicit put option (implied by CDS spread): expected losses associated with default net of any financial guarantees as residual default risk on unsecured senior debt CDS spread RFV Value of put option on CDS = 1 exp T default barrier 10,000 RMV 12

14 United States: Financial Sector Alpha Value 80 Lehman Collapse Alpha value (sample median), 20 day moving average Feb 07 Mar 07 Apr 07 May 07 Jun 07 Jul 07 Aug 07 Sep 07 Oct 07 Nov 07 Dec 07 Jan 08 Feb 08 Mar 08 Apr 08 May 08 Jun 08 Jul 08 Aug 08 Sep 08 Oct 08 Nov 08 Dec 08 Jan 09 Feb 09 Mar 09 Apr 09 May 09 Jun 09 Jul 09 Aug 09 Sep 09 Oct 09 Nov 09 Dec 09 Jan 10 In percent

15 Estimation of Contingent Liabilities (3): Caveats CCA: high level balance sheet aggregates use of market values market perception o implied asset value and asset volatility based on equity prices o CDS spread methodology CCA based contingent liabilities: estimation of alpha value depends on a variety of assumptions that influence the assessment of government support due to distortions stemming from o modeling choice (and the breakdown of efficient asset pricing) o changes in market conditions, and o capital structure impact of crisis interventions, such as equity dilution 14

16 Modeling Systemic Risk from Expected Losses and Contingent Liabilities Systemic CCA how can we assess these contingent liabilities jointly? correlation becomes exceedingly unreliable during times of market stress examine higher moments and non linear measures of dependence to attribute greater attention to joint tail risks multivariate extreme value model of expected losses/contingent liabilities with time varying and non linear dependence (using Extreme Value Theory) estimate individual bank s contribution to systemic risk at different percentile levels (and at each point in time) 15

17 Systemic CCA Methodology (1): Summary (Gray and Jobst, 2010) estimate time varying, multivariate density of individual put option values by accounting for tail risk o combine individual marginal distributions of i.i.d. random series of put option values and their dependence structure o contrary to correlation analysis: captures non linear association between extreme realizations does not rely on the normality assumption in particular, shows whether extreme linkages indeed exist determine the contribution of each series at time t 16

18 Systemic CCA Methodology (2): Generalized Extreme Value Distribution (GEV) Definition Multivariate density with extreme value dependence (based on limit law for joint asymptotic tail behavior) of random vector X=(X 1,,X m ) (here: α P Fit, ) with marginal distributions Y=(y 1,,y m ) { } j j ( ) ( m exp ) ( ω ) G x = = y A t, μσξ,, 1 to derive any point estimate over estimation window τ at time t ˆ ξ ( ) 1 = ( ) = μ+ σ ˆ ξ ln a xˆ ˆ ˆ ta, Gt a ( ω) 1 A and calculate the average daily expected shortfall (ES) at 95% percentile (1 a) and contribution of specific institutions to risk (at different levels of statistical confidence) derived as the partial derivative. ( ) ES z z G a VaR 1 ta, = E τ τ t = tq, a 17

19 United States: Sum of Expected Losses (Implicit Put Options) and Contingent Liabilities (Alpha*Implicit Put Options) Compared to 50 th Percentile of Multivariate Distribution 1,500 Lehman Collapse In US dollar billions 1, Apr 07 May 07 Jun 07 Jul 07 Aug 07 Sep 07 Oct 07 Nov 07 Dec 07 Jan 08 Feb 08 Mar 08 Apr 08 May 08 Jun 08 Jul 08 Aug 08 Sep 08 Oct 08 Nov 08 Dec 08 Jan 09 Feb 09 Mar 09 Apr 09 May 09 Jun 09 Jul 09 Aug 09 Sep 09 Oct 09 Nov 09 Dec 09 Jan 10 Total Expected Losses (sum of individual put options) Total Cont. Liabilities (sum of ind. alpha*put option) Total Cont. Liabilities (GEV, 50th percentile), without GSEs Total Cont. Liabilities (GEV, 50th percentile), with GSEs Source: Staff estimates. 18

20 United States: Expected Shortfall (95 th Percentile) of Multivariate Distribution of Joint Contingent Liabilities Lehman Collapse Apr 07 May 07 Jun 07 Jul 07 Aug 07 Oct 07 Nov 07 Jan 08 Feb 08 Mar 08 Apr 08 Jun 08 Jul 08 Aug 08 Oct 08 Nov 08 Dec 08 Jan 09 Feb 09 Apr 09 May 09 Jun 09 Jul 09 Aug 09 Oct 09 Nov 09 Dec 09 Jan 10 In percent of GDP

21 United States: Groupwise Contributions to Systemic Risk from Contingent Liabilities Expected Shortfall (95 th Percentile) In percent of GDP Apr 07 May 07 Jun 07 Jul 07 Aug 07 Oct 07 Nov 07 Jan 08 Feb 08 Mar 08 Apr 08 Jun 08 Jul 08 Aug 08 Oct 08 Nov 08 Dec 08 Jan 09 Feb 09 Apr 09 May 09 Jun 09 Jul 09 Aug 09 Oct 09 Nov 09 Dec 09 Jan 10 Other financial institutions Insurance companies Banks Failed and bailed out institutions

22 United States: Groupwise Contributions to Systemic Risk Sample group Contribution to Systemic Risk from Contingent Liabilities Pre Crisis: July 1, 2007 Sept. 14, 2008 Crisis Period 1: Sept. 15 Dec. 31, 2008 (In percent) Crisis Period 2: Jan. 1 May 8, 2009 Crisis Period 3: May 11 Dec. 31, 2009 Banks Insurance companies Other, non bank financial institutions Failed or bailed out financial institutions Total Sample Period (April 1, 2007 Jan. 29, 2010) Relative Measure (In percent) Banks Insurance companies Other, non bank financial institutions Failed or bailedout financial institutions Contribution to Systemic Risk Share of Total Liabilities Share of Total Contingent Liabilities

23 Visualizing the Relation between Systemic CCA and Individual Risk (1) estimate of bivariate kernel density function (w/ empirical bandwidth) of individual contingent liabilities ( individual CCA) and individual contributions to systemic risk ( Systemic CCA) Systemic CCA estimated as expected shortfall at 95% percentile (3 month rolling est. window with daily updating), Sample: 01/02/ /20/2009 units of measure: o average individual cont. liabilities (y axis): average of alpha*put option values (x axis) 1 m m αit, PutEquity it, i= i o systemic risk from joint cont. liabilities (x axis): average individual contribution to Systemic CCA MC at, 22

24 Visualizing the Relation between Systemic CCA and Individual Risk (2) Bivariate Kernel Density Function* of average Contingent Liabilities (Individual CCA) average contribution to joint contingent liabilities (Systemic CCA) *Note: Kernel density estimation with Epanechnikov kernel and linear binning. 23

25 Some recent systemic risk measures, CoVaR and SES/MES, are much less informative than Systemic CCA Single Firm CoVaR = historical systemic risk conditional on high expected loss of individual bank MES = historical expected losses conditional on high systemic risk (plus leverage SES) CoVaR MES *Note: Kernel density estimation with Epanechnikov kernel and linear binning. 24 Source: Gray and Jobst (2010) 24

26 Empirical Example 1: Large U.S. Bank Bivariate Density of the Relative Contribution to Systemic Cont. Liabilities (In percent, x axis) and Total Individual Cont. Liabilities of Sample Banks (In percent, y axis) contributes somewhat more to systemic risk in distress 25

27 United States: Systemic Risk Charge Based on Systemic CCA estimated government contingent liabilities from the financial sector can deliver a fair value price of a systemic risk surcharge quantify the magnitude of risk transfer to the sovereign balance sheet using Systemic CCA model T 1 ( α () ()) 1 G ˆ a; t P, ξμσ, ˆ, ˆ E t ln 1 t t T m rt ( t) 10,000 T Be t j j where B represents the aggregate default barrier of all n institutions in the sample, r is the risk free rate, T is time horizon of the surcharge, and G(.) is the multivariate density function (with location, scale and shape parameters (μ,σ,ξ) underpinning point estimates under the Systemic CCA framework. 50 th percentile 95 th percentile Period US$ billion annual fee (basis points) US$ billion annual fee (basis points) Total: April 1, 2007 Jan. 29, Pre Crisis: July 1, 2007 Sept. 14, Crisis Period 1: Sept. 15 Dec. 31, Crisis Period 2: Jan. 1 May 8, Crisis Period 3: May 11 Dec. 31,

28 United States: Stress Tests Dynamic Factor Model macro financial linkages of contingent liabilities estimate of the joint historical sensitivity of monthly implicit put option values in a multivariate dynamic factor model with a set of macro variables (nominal and real GDP growth, real consumption, output gap, unemployment rate, housing prices, ROA in the banking sector, and the TED spread) as exogenous covariates in both the equations for the latent factors and the observable dependent variables each institution s contingent liabilities are forecasted under the baseline/adverse scenarios for each quarter until end

29 United States: Stress Tests Dynamic Factor Model (2) Systemic CCA of Financial Sector Average Systemic Risk from Expected Losses and Contingent Liabilities (In billion US dollars unless indicated otherwise) Forecasting Period, 2010 Q Q4 50 th percentile VaR (95%) ES (95%) Baseline Scenario Market Implied Contingent Liabilities Market Implied Expected Losses Adverse Scenario Market Implied Contingent Liabilities Market Implied Expected Losses

30 Concluding Remarks non trivial aggregation problem to capture entire financial sector, esp. in presence of: (1) heavy tails (non normality); (2) high volatility; and (3) non linear changes of asset values managing systemic risk from contingent liabilities is different from managing systemic risk from expected losses importance of cyclicality: individual contributions to systemic risk (esp. innovations ) are very dynamic, and controlling for interconnectedness is crucial Systemic CCA is very flexible (time, stat. confidence) and also performs well in non crisis periods 29

31 Future Work systemic liquidity risk: estimation of short term CCA with effective maturity mismatch metric scenario analysis: o factor model of bank asset returns individual CCA o sensitivity to B/S impact of government interventions on risk and contingent liabilities robustness: sensitivity analysis of CCA inputs, esp. alpha value structural model for Systemic CCA outputs 30

32 Discussion Points (1) availability and use of market and supervisory balance sheet data (esp. for liquidity stress tests) o Default barrier, (asset value and implied asset volatility for non listed) sample coverage macro financial specification for the Systemic CCA based framework estimation of implicit government support (and review of work completed in the context of the U.S. FSAP 2010)? 31

33 References Gray, Dale F. and Andreas A. Jobst, forthcoming, Systemic Contingent Claims Analysis (Systemic CCA) Estimating Potential Losses and Implicit Government Guarantees to Banks, Working Paper (Washington: International Monetary Fund)., forthcoming, Lessons from the Financial Crisis on Modeling Systemic and Sovereign Risk, in: Berd, Arthur (ed.) Lessons from the Financial Crisis (London: RISK Books)., 2010a, Using the CCA Framework to Estimate Potential Losses and Implicit Government Guarantees to the U.S. Financial Sector, United States: Publication of Financial Sector Assessment Program Documentation Technical Note on Stress Testing, Country Report No. 10/244 (July 30) (Washington: International Monetary Fund), pp , 2010b, New Directions in Financial Sector and Sovereign Risk Management, Journal of Investment Management, Vol. 8, No.1, pp , 2010c, Risk Transmission Between Sovereigns and Banks in Europe, Global Financial Stability Report, Chapter 1, October (Washington: International Monetary Fund), pp. 12, Gray, Dale F., Jobst, Andreas A. and Samuel Malone, 2010, Quantifying Systemic Risk and Reconceptualizing the Role of Finance for Economic Growth, Journal of Investment Management, Vol. 8, No.2, pp

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