Measuring Systemic Risk

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Measuring Systemic Risk

• Viral Acharya, Lasse Heje Pedersen,
• Thomas Philippon, and Matthew Richardson
• New York University Stern School of Business
• NBER, CEPR

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Motivation

• Systemic risk can be defined as
• joint distress of several financial institutions
• with externalities that disrupt the real economy
• The challenge is
• to use economic theory to find a measure of
  systemic risk
• that is useful in managing it
• and asses its empirical success

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Two approaches to regulation

• Traditional approach Firm-level risk management
• Goal Limit risk of collapse of each bank seen in
  isolation
• Requirement Detailed knowledge of activities
  inside the firm
• We advocate Systemic approach
• Goal Limit risk of collapse of the system
• Requirement Understand risks and externalities
  across firms

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Our results insights from economic theory

• Each financial institutions contribution to
  systemic crisis can measured as its systemic
  expected shortfall (SES)
• SES expected capital shortfall, conditional on
  a future crisis
• A financial institutions SES increases in
• its own leverage and risk
• the systems leverage and risk
• the tail dependence between the institution and
  the system
• the severity of the externality from a systemic
  crisis
• Managing systemic risk
• Incentives can be aligned by imposing a tax or
  mandatory insurance based SES adjusted for the
  cost of capital

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Our results empirical implementation

• Empirical methodology
• we provide a very simple of estimating SES
• Institutions ex-ante SESs
• predict their losses during the subprime crisis
• with more explanatory power than measures of
  idiosyncratic risk
• SES in the cross-section
• higher for securities dealers and brokers every
  year 1963-2008
• higher for larger institutions that tend to be
  more levered
• SES in the time series
• higher during periods of macroeconomic stress,
  especially for securities dealers and brokers

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Related literature

• Incentive to take correlated risk
• Acharya (2001, 2009), Acharya and Yorulmazer
  (2007)
• Externalities
• Liquidity spirals (Brunnermeier and Pedersen
  (2009), Pedersen (2009))
• Bank runs (Diamond and Dybvig (1983), Allen and
  Gale)
• Debt market freezes (Acharya, Gale, and
  Yorulmazer (08), He and Xiong (2009))
• Tightening risk management (Garleanu and Pedersen
  (2007))
• Contingent claims analysis
• Lehar (2005), Gray, Merton, and Bodie (2008),
  Gray and Jobst (2009)
• Statistical measures
• Huang, Zhou, and Zhu (2009), Adrian and
  Brunnermeier (2009)
• Other proposals
• Kashyap, Rajan, and Stein (2008), Wall (1989),
  Doherty and Harrington (1997), Flannery (2005),
  squam lake, NYU book (chapter 13),

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Outline of the rest of the talk

• Theory
• Managing risk within and across banks
• Economic model of systemic risk
• Empirics
• Methodology
• Findings
• Implemention
• Practical considerations and policy issues
• Conclusion

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Managing risk within and across banks

• Standard measures of risk within banks
• Value at risk Pr ( R - VaR ) a
• Expected shortfall ES - E( R R - VaR )
• Banks consists of several units i1,, I of size
  yi
• Return of bank is R ?i yi ri
• Expected shortfall ES - ?i yi E( ri R -
  VaR )
• Risk contribution of unit i Marginal expected
  shortfall (MES)
• We can re-interpret this as each banks
  contributions to the risk of overall banking
  system The loss of bank i when overall banking
  is in trouble
• Question what is the economic rationale for
  looking at these measures?

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Economic model

• Banks b1,,B choose at time 0
• initial capital w0
• exposures x(x1,,xS) to all assets, which yield
  returns r (r1,,rS)
• to maximize their objective function
• given
• cost of raising capital c
• tax tb
• the evolution of capital

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Economic model, continued

• Regulator cares about
• aggregate outcome, including
• externality, proportional to e
• times the aggregate bank capital shortfall below
  cutoff
• insured default losses with the government cost
  of capital cg

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Efficient tax of systemic risk contribution

• Proposition 1. The regulator can achieve an
  efficient outcome with the tax t DESSES, where
  DES is a banks expected default loss and SES is
  its systemic expected shortfall
• A banks systemic expected shortfall is larger
  if
• the externality is more severe (e)
• the bank takes a larger exposure (xs) in an asset
  s that experiences loses when other banks are in
  trouble
• the bank raises less capital initially (w0)
• other banks are riskier
• the banks cost of capital c is lower.

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The importance of MES and leverage

• Proposition 2. With wbz ab, where z is the
  target capital ratio, the systemic expected
  shortfall in percent of a banks initial capital,
  SES can be written as
• It increases in
• the banks MES and
• its leverage lb 1 w0b / ab

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The importance of comovement

• Proposition 3. If the payoffs are jointly Normal,
  then the percent systemic expected shortfall is
• which increases in
• the banks volatility sb
• its correlation to the aggregate system ?b
• the banks leverage lb
• the system volatility s
• the system leverage L
• and decreases in the expected returns of the bank
  µb and the system µ

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Empirical methodology

• MES
• Very simple non-parametric estimation
• find the 5 worst days for the market
• compute each institutions return on these days
• Parametric
• SES, scaled
• 60/1.4 scales to consider a crisis with a 60
  drop, rather than the 1.4 drop over the ex ante
  estimation period
• Data CRSP and COMPUSTAT

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Descriptive statistics
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Predicting contribution to systemic crisis
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Predicting systemic risk SES
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Predicting systemic risk MES
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Predicting systemic risk market beta
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Predicting systemic risk ES
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Types of institutions
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Institution-type fixed effects
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Determinants of systemic risk within institution
types
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Time-series determinants of systemic risk
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Time-series determinants of systemic risk
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Robustness
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Robustness different estimation period
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Implementation Our proposal

• SES signals institutions likely to contribute to
  aggregate crises
• Three approaches to limit systemic risk
• Systemic Capital Requirement
• Capital requirement proportional to estimated
  systemic risk
• Systemic Fees (FDIC-style)
• Fees proportional to estimated systemic risk
• Create systemic fund
• Private/public systemic insurance

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Our systemic insurance proposal

• Compulsory insurance against own losses during
  crisis
• Payment goes to systemic fund, not the bank
  itself
• Insurance from government, prices from the market
• Say 5 cents from private 95 cents from the
  government
• Analogy to terrorism reinsurance by the
  government (TRIA, 2002)
• Advantages of private/public proposal
• A market-based estimate of the contribution to
  crises and externalities
• Private sector has incentives to be forward
  looking
• Gives bank an incentive to be less systemic and
  more transparent
• to lower their insurance payments

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Conclusion

• Economic model of systemic risk gives rise to SES
• Systemic expected shortfall (SES)
• Measures each financial institutions
  contribution to systemic crisis
• Increases in leverage, risk, comovement, tail
  dependence
• An SES tax/insurance incentivizes banks to
  contribute less to crisis
• Empirically
• Ex ante SES predicts ex post crisis loses
• We analyze its cross-sectional and time series
  properties