Where the Risks Lie: A Survey on Systemic Risk

Transcription

1 S. Benoit a, J.-E. Colliard b, C. Hurlin c, C. Pérignon b a Université Paris-Dauphine b HEC Paris c Université d Orléans Conference: Risks, Extremes & Contagion

2 Motivation Microprudential Regulation vs. Macroprudential Regulation. Basel III calls for tighter supervision and extra capital requirement for the most Systemically Important Financial Institutions (SIFIs). Regulators need measures of systemic risk that are timely, capture well-identified economic mechanisms, and can be used as inputs for regulatory tools. Sylvain BENOIT - Univ. Paris-Dauphine 2/36

3 Motivation and contribution Cross-fertilization between regulation and academic research. Prolific research field at the crossroads of banking, macroeconomics, econometrics, network theory, mathematical finance, etc. Our angle differs from existing surveys (e.g. De Bandt, Hartmann and Peydro, 2012, Bisias et al., 2012) as we focus on matching (i) sources of systemic risk, (ii) regulatory tools, and (iii) systemic risk measures. Sylvain BENOIT - Univ. Paris-Dauphine 3/36

4 What is systemic risk? Definition (systemic risk) We define systemic risk as the risk that many market participants are simultaneously affected by severe losses, which then spread through the system. This definition can apply to a huge number of papers, of which we survey 220, published over the past 35 years. Sylvain BENOIT - Univ. Paris-Dauphine 4/36

5 Outline of the survey 1 Sources of systemic risk: (1) systemic risk-taking, (2) contagion, and (3) amplification mechanisms. 2 Regulation: tools proposed to mitigate systemic risk concerns. 3 Systemic risk measurement: (1) current methodology of the FSB to identify SIFIs, (2) measures specific to a given source of systemic risk, and (3) global measures. 4 Comparison of systemic risk measures: Derive popular systemic risk measures in a unified framework and study their added value compared to standard market risk measures. 5 Validation of systemic risk measures. Sylvain BENOIT - Univ. Paris-Dauphine 5/36

6 A Conceptual Framework Network Preview Framework Consider N financial institutions, each with a risk exposure x i. A proportion α i of the exposure concerns a systematic risk factor, while 1 α i concerns a risk factor idiosyncratic to i. Denote yi S = α i x i the systematic exposure and yi I = (1 α i ) x i the idiosyncratic exposure of institution i. We also denote y S = N i=1 y i S the cumulative exposure to systematic risk for all institutions. Sylvain BENOIT - Univ. Paris-Dauphine 6/36

7 A Conceptual Framework Network Preview Framework Financial institutions have direct links among each other (interbank loans or derivatives), given by a N N matrix B, whose elements b i,j denote how much i is exposed to j. The returns on the systematic and i s idiosyncratic factors are ρ S + ε S and ρ i + ε i, respectively, where ρ S and ρ i are constants, while ε S and all the ε i are i.i.d.with zero mean. Sylvain BENOIT - Univ. Paris-Dauphine 7/36

8 A Conceptual Framework Network Preview Framework Definition (benchmark payoff) We define the benchmark payoff ˆπ i as what i would receive if there were no other institutions in the system: ˆπ i = ˆπ i (y S i, y I i, ε S, ε i ) Example (benchmark payoff) For illustration, a simple specification could be: ˆπ i = (ρ S + ε S ) y S i + (ρ i + ε i ) y I i Sylvain BENOIT - Univ. Paris-Dauphine 8/36

9 A Conceptual Framework Network Preview Framework Definition (actual payoff) Denoting π i the actual payoff of i, E I, Y S, and Y I, the N 1 vectors of idiosyncratic shocks, systematic exposures, and idiosyncratic exposures, respectively, π i is given by: π i (Y S, Y I, B, ε S, E I ) Remark A defining characteristic of systemic risk is that: π i (Y S, Y I, B, ε S, E I ) ˆπ i (y S i, y I i, ε S, ε i ) Sylvain BENOIT - Univ. Paris-Dauphine 9/36

10 A Conceptual Framework Network Preview 1. Systemic risk-taking mechanisms Systemic risk-taking mechanisms study why financial institutions choose to be exposed to similar risks (high α i ) and why they take large risk exposures (large x i ), exposing themselves to default and their counterparts to contagion. Financial institutions take too much systemic risk if they endogenously choose a risk exposure x i and its systematic component α i x i that differ from their welfare-maximizing values. Sylvain BENOIT - Univ. Paris-Dauphine 10/36

11 A Conceptual Framework Network Preview 2. Contagion mechanisms Contagion mechanisms occur when losses in one financial institution spillover to other institutions that are linked with the first one. These mechanisms work through the matrix of links B. The payoffs of two institutions are positively correlated, even when there is no systematic shock: cov(π i, π j ε S = 0) > 0 Sylvain BENOIT - Univ. Paris-Dauphine 11/36

12 A Conceptual Framework Network Preview 3. Amplification mechanisms Amplification mechanisms explain why small shocks can turn into large losses if they affect simultaneously many institutions. The effect of a systematic shock ε S is greater when the cumulative exposure to this shock y S is larger: Example (deleveraging) 2 E(π i ) ε S y S > 0 A small negative shock ε S hits the institutions with a high y S i, they need to sell their assets and exert a price impact that worsens the losses to other market participants, and so on. Sylvain BENOIT - Univ. Paris-Dauphine 12/36

13 A Conceptual Framework Network Preview Systemic loops Systematic shock ε S αi y S i i defaults ε i bj,i System-wide losses αj y S j j defaults bk,i ε j Idiosyncratic shocks bk,j αk y S k k defaults ε k y S Amplification... Contagion The figure represents amplification mechanisms and contagion mechanisms. Each edge represents a risk transmission channel, whose strength is given by the label on the edge. For example, the sensitivity of j to system-wide losses is measured by α j, while j s contribution to system-wide losses depends on y S j Sylvain BENOIT - Univ. Paris-Dauphine 13/36

14 A Conceptual Framework Network Preview Synoptic table Sylvain BENOIT - Univ. Paris-Dauphine 14/36

15 A Conceptual Framework Network Preview Systemically important articles and their periphery Sylvain BENOIT - Univ. Paris-Dauphine 15/36

16 Regulation Academia Propositions Empirical Illustration Systemic risk measures We review a large number of measures, classified in three groups: 1 the one currently implemented by the regulators, 2 some structural measures that target a specific channel of transmission, 3 some global measures, potentially encompassing several/all channels of transmission. Sylvain BENOIT - Univ. Paris-Dauphine 16/36

17 Regulation Academia Propositions Empirical Illustration Regulatory approach The scoring methodology developed by the BCBS aggregates information about 5 categories of systemic importance: (i) size, (ii) interconnectedness, (iii) substitutability/financial institution infrastructure, (iv) complexity, (v) cross-jurisdictional activity. In order not to favor any particular facet of systemic risk, the BCBS aims to give the same importance to each input. This method is currently implemented to identify the SIFIs and allocate them in different buckets. Sylvain BENOIT - Univ. Paris-Dauphine 17/36

18 Regulation Academia Propositions Empirical Illustration Regulatory approach Let each bank i, for i = 1,..., N, be characterized by K inputs denoted x i1,..., x ik. Definition (systemic score) The systemic risk score for bank i, denoted S i, is then defined as a simple average of these K inputs: S i = 1 K where x ij = (1/F ) ( F f =1 X if / ) N i=1 X if corresponds to the category s score of input j for bank i. K j=1 x ij Sylvain BENOIT - Univ. Paris-Dauphine 18/36

19 Regulation Academia Propositions Empirical Illustration Regulatory approach An unintended consequence is that that the resulting systemic risk score will be mechanically dominated by the most volatile categories. Scores, ranking of banks, and extra capital buffers are driven by a subset of variables only. BCBS (2013): apply a cap on the substitutability category score because this category has too high an impact on the final score. Sylvain BENOIT - Univ. Paris-Dauphine 19/36

20 Regulation Academia Propositions Empirical Illustration Regulatory approach Solution (standardized score) One potential correction for the above-mentioned bias is to standardize by their volatility the variables that enter into the definition of the index S i = 1 K K j=1 x ij σ j where σ j corresponds to the cross-sectional variance of input j. Sylvain BENOIT - Univ. Paris-Dauphine 20/36

21 Regulation Academia Propositions Empirical Illustration G-SIBs as of November 2015 (work in progress) Sylvain BENOIT - Univ. Paris-Dauphine 21/36

22 Regulation Academia Propositions Empirical Illustration Literature Systemic risk measures proposed in the academia 1 Specific sources of systemic risk (contagion, bank runs, liquidity crises, etc.). This source-specific approach relies on qualitative models, which deliver predictions that can be confirmed by empirical analyses, often based on supervisory data (e.g. Greenwood, Landier and Thesmar, 2014). 2 Global measures of systemic risk (e.g. SRISK and CoVaR), potentially encompassing all the mechanisms studied in the other group of papers, often based on market data. Sylvain BENOIT - Univ. Paris-Dauphine 22/36

23 Regulation Academia Propositions Empirical Illustration Overview Global measures: Pros Easily computed in real-time using market data (see V-Lab). Could replace a host of complex macroprudential tools by a simple Pigouvian systemic risk tax. Sylvain BENOIT - Univ. Paris-Dauphine 23/36

24 Regulation Academia Propositions Empirical Illustration Overview Global measures: Pros Easily computed in real-time using market data (see V-Lab). Could replace a host of complex macroprudential tools by a simple Pigouvian systemic risk tax. Global measures: Cons Not completely transparent on the causes of systemic risk. May appear hazardous to base regulation on global measures without a clear understanding of the risks they capture and the ones they overlook. Strongly related to standard market risk measures. Sylvain BENOIT - Univ. Paris-Dauphine 23/36

25 Regulation Academia Propositions Empirical Illustration Marginal Expected Shortfall (MES) MES (Acharya et al., 2010; Brownlees and Engle, 2015) The MES is the expected equity loss per dollar invested in a particular financial institution if the overall market declines by at least its Value-at-Risk. MES it (α) = ES ( ) m,t(α) = E t 1 r it r mt < VaR mt (α). w it Sylvain BENOIT - Univ. Paris-Dauphine 24/36

26 Regulation Academia Propositions Empirical Illustration Systemic RISK (SRISK) SRISK (Acharya et al. 2012; Engle et al. 2014) The SRISK captures the expected capital shorfall of a firm given its book vaue of total liabilities and long-run MES. Required Capital Available Capital {}}{{}}{ SRISK it = max 0 ; k (D it + (1 LRMES it ) W it ) (1 LRMES it )W it, where SRISK it = max 0; k }{{} Prudential Cap. Ratio Liability {}}{ D it (1 k) W it }{{} Market Value (1 LRMES it ). Sylvain BENOIT - Univ. Paris-Dauphine 25/36

27 Regulation Academia Propositions Empirical Illustration CoVaR and CoVaR CoVaR (Adrian and Brunnermeier, 2014) The CoVaR is the Value-at-Risk of the market return given a specific event on the firm return. ( ) Pr r mt CoVaR m r it=var it (α) t r it = VaR it (α) = α. CoVaR The contribution of the institution to systemic risk, CoVaR, is the difference between its CoVaR and the CoVaR calculated at the median state. CoVaR it (α) = CoVaR m r it=var it (α) t CoVaR m r it=median(r it ) t. Sylvain BENOIT - Univ. Paris-Dauphine 26/36

28 Regulation Academia Propositions Empirical Illustration A unified framework Consider a bivariate GARCH process for the vector of demeaned returns r t = (r mt r it ): r t = H 1/2 t ν t where ν t = (ε mt ξ it ) is i.i.d. with E (ν t ) = 0 and E (ν t ν t) = I 2, and: ( σmt H t = 2 ) σ it σ mt ρ it σ it σ mt ρ it We assume that the innovations ε mt and ξ it are independently distributed at time t. σ 2 it Sylvain BENOIT - Univ. Paris-Dauphine 27/36

29 Regulation Academia Propositions Empirical Illustration Analytical form Proposition for MES The MES of a given financial institution i is proportional to its systematic risk, as measured by its conditional beta: MES it (α) = β it ES mt (α) where β it = ρ it σ it /σ mt denotes the time-varying beta of firm i and ES mt (α) = E t 1 (r mt r mt < C) denotes the expected shortfall of the market return. Sylvain BENOIT - Univ. Paris-Dauphine 28/36

30 Regulation Academia Propositions Empirical Illustration Analytical form Proposition for SRISK The SRISK can be expressed as a linear function of the liabilities, market capitalization and systematic risk: SRISK it max [0; k D it (1 k) W it exp (18 β it ES mt (α))]. as well as leverage of a given financial institution i: SRISK it max [0; [k (L it 1) + (1 k) exp (18 β it ES mt (α))] W it ]. Sylvain BENOIT - Univ. Paris-Dauphine 29/36

31 Regulation Academia Propositions Empirical Illustration Analytical form Proposition for CoVaR The CoVaR of a given financial institution i depends on its tail risk, as measured by its VaR: CoVaR it (α) = γ it [VaR it (α) VaR it (0.5)] where γ it = ρ it σ mt /σ it the linear projection coefficient of the market return on the firm return. If the marginal distribution of the firm return is symmetric around zero: CoVaR it (α) = γ it VaR it (α). Sylvain BENOIT - Univ. Paris-Dauphine 30/36

32 Regulation Academia Propositions Empirical Illustration Econometrics approaches Same estimation methods as in the original articles presenting the MES, SRISK and CoVaR. Same sample as in Acharya, Pedersen, Philippon, and Richardson (2010) as well as Brownlees and Engle (2015). This sample contains all US financial firms with a market capitalization greater than $5 billion as of end of June Sample period, January 3, December 31, Sylvain BENOIT - Univ. Paris-Dauphine 31/36

33 Regulation Academia Propositions Empirical Illustration MES cross-sectional analysis MES Beta Strong Relationship between MES and beta [MES it (α) = β it ES mt (α)] Sylvain BENOIT - Univ. Paris-Dauphine 32/36

34 Regulation Academia Propositions Empirical Illustration Standard risk or systemic risk? 100 Percentage of concordant pairs between MES and Beta 50 0 Jan00 Mar02 May04 Aug06 Oct08 Dec Percentage of concordant pairs between SRISK and Beta 50 0 Jan00 Mar02 May04 Aug06 Oct08 Dec Percentage of concordant pairs between SRISK and Leverage 50 0 Jan00 Mar02 May04 Aug06 Oct08 Dec Percentage of concordant pairs between SRISK and Liabilities 50 0 Jan00 Mar02 May04 Aug06 Oct08 Dec Percentage of concordant pairs between CoVaR and VaR Sylvain BENOIT - Univ. Paris-Dauphine 33/36

35 Regulation Academia Propositions Empirical Illustration CoVaR cross-sectional analysis CoVaR VaR CoVaR is not Equivalent to VaR in the Cross-Section [ CoVaR it (α) = γ i VaR it (α)] Sylvain BENOIT - Univ. Paris-Dauphine 34/36

36 Regulation Academia Propositions Empirical Illustration CoVaR time-series analysis 0.06 CoVaR VaR BAC CoVaR VaR Jan00 Mar02 May04 Aug06 Oct08 Dec10 CoVaR is Equivalent to VaR in Time Series [ CoVaR it (α) = γ i VaR it (α)] Sylvain BENOIT - Univ. Paris-Dauphine 35/36

37 Concluding remarks Many methodologies are now available to identify different sources of systemic risk and will produce new regulatory or policy tools. What is less clear however is how to link the measures produced by these tools to regulatory interventions. The quest for a global risk measure that encompasses different sources of systemic risk and yet produces a single/simple metric that can directly be used for regulation (tax or capital surcharge) is still ongoing. Could align systemic risk banks interests with social optimum. Reasons to remain optimist as more data are becoming available (Data Gaps Initiative). Sylvain BENOIT - Univ. Paris-Dauphine 36/36

38 Additional Explanations Systemic Risk Measures Time Profile SIFI or not SIFI? Linear Models Notation Firm and market returns We consider N firms and we denote by r it the return of firm i at time t. The market return is the value-weighted average of all firm returns: r mt = N w it r it i=1 where w it denotes the relative market capitalization of firm i. Sylvain BENOIT - Univ. Paris-Dauphine 37/36

39 Additional Explanations Systemic Risk Measures Time Profile SIFI or not SIFI? Linear Models Individual risk measures Value-at-Risk (VaR) The VaR at the α% level is the α% quantile of the return distribution (F ): Expected Shortfall (ES) VaR mt (α) = F 1 r mt (α) The ES at the α% level is the expected return in the worst α%, but it can be extended to the general case, in which the returns are beyond a given threshold C. Formally, the conditional ES of the system is defined as follows: ES m,t 1 (C) = E t 1 (r mt r mt < C) = N w i E t 1 (r it r mt < C). i=1 Sylvain BENOIT - Univ. Paris-Dauphine 38/36

40 Additional Explanations Systemic Risk Measures Time Profile SIFI or not SIFI? Linear Models Marginal Expected Shortfall (MES) MES (Acharya et al., 2010; Brownlees and Engle, 2015) The MES is the expected equity loss per dollar invested in a particular financial institution if the overall market declines by at least its Value-at-Risk. MES it (α) = ES ( ) m,t(α) = E t 1 r it r mt < VaR mt (α). w it Sylvain BENOIT - Univ. Paris-Dauphine 39/36

41 Additional Explanations Systemic Risk Measures Time Profile SIFI or not SIFI? Linear Models Systemic RISK (SRISK) SRISK (Acharya et al. 2012; Engle et al. (2014)) The SRISK captures the expected capital shorfall of a firm given its book vaue of total liabilities and long-run MES. Required Capital Available Capital {}}{{}}{ SRISK it = max 0 ; k (D it + (1 LRMES it ) W it ) (1 LRMES it )W it, where SRISK it = max 0; k }{{} Prudential Cap. Ratio Liability {}}{ D it (1 k) W it }{{} Market Value (1 LRMES it ). Sylvain BENOIT - Univ. Paris-Dauphine 40/36

42 Additional Explanations Systemic Risk Measures Time Profile SIFI or not SIFI? Linear Models CoVaR and CoVaR CoVaR (Adrian and Brunnermeier, 2014) The CoVaR is the Value-at-Risk of the market return given a specific event on the firm return. ( ) Pr r mt CoVaR m r it=var it (α) t r it = VaR it (α) = α. CoVaR The contribution of the institution to systemic risk, CoVaR, is the difference between its CoVaR and the CoVaR calculated at the median state. CoVaR it (α) = CoVaR m r it=var it (α) t CoVaR m r it=median(r it ) t. Sylvain BENOIT - Univ. Paris-Dauphine 41/36

43 Additional Explanations Systemic Risk Measures Time Profile SIFI or not SIFI? Linear Models Evolution of systemic risk measures (1) 0.3 MES CoVaR SRISK LEH x MES and CoVaR SRISK Jan00 Sep01 Jun03 Mar05 Dec06 Sep08 Sylvain BENOIT - Univ. Paris-Dauphine 42/36

44 Additional Explanations Systemic Risk Measures Time Profile SIFI or not SIFI? Linear Models Evolution of systemic risk measures (2) 6 5 MES CoVaR SRISK LEH Jan00 Sep01 Jun03 Mar05 Dec06 Sep08 Sylvain BENOIT - Univ. Paris-Dauphine 43/36

45 Additional Explanations Systemic Risk Measures Time Profile SIFI or not SIFI? Linear Models Ranking approach Systemic Risk Rankings: 12/31/2010 Rank MES SRISK CoVaR 1 MBI BAC HRB 2 AIG C MI 3 MI JPM BEN 4 CBG MS CIT 5 RF AIG WU 6 LM MET AIZ 7 JNS PRU AXP 8 HRB HIG JNS 9 BAC SLM NYB 10 UNM LNC MTB Sylvain BENOIT - Univ. Paris-Dauphine 44/36

46 Additional Explanations Systemic Risk Measures Time Profile SIFI or not SIFI? Linear Models Concordant pairs 100 Percentage of concordant pairs between MES and SRISK 50 0 Jan00 Mar02 May04 Aug06 Oct08 Dec Percentage of concordant pairs between SRISK and CoVaR 50 0 Jan00 Mar02 May04 Aug06 Oct08 Dec Percentage of concordant pairs between MES and CoVaR 50 0 Jan00 Mar02 May04 Aug06 Oct08 Dec10 Sylvain BENOIT - Univ. Paris-Dauphine 45/36

47 Additional Explanations Systemic Risk Measures Time Profile SIFI or not SIFI? Linear Models Regression analysis SRM i,t = a + b. X i,t + ɛ i,t SRM i,t MES SRISK CoVaR Dimension Cross-Section Cross-Section Time series X i,t beta LTQ VaR average R min R max R std R Sylvain BENOIT - Univ. Paris-Dauphine 46/36