taking the risk out of systemic risk measurement
TRANSCRIPT
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The Search for Systemic Risk
The search for systemic risk measures is allabout big business
It focuses on big complex financial businesses
It is a big business opportunityfor financialeconomists
But has it really identified systemic risk?
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There are BigRisksin the continued use of scurrently popular systemic risk measures
Should government require a mandatory warning label?
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We Focus on Two MeasuresCoVaR and MES (akaSES & SRISK)
CoVaR Conditional Value at Risk
The value at risk of a conditional stock return distribution
Adrian and Brunnermeier, (2011) CoVaR, FRB of New York. Staff Report N
MES Marginal Expected Shortfall
The expected shortfall of a conditional stock return distribution Acharya, Engle, and Richardson, (2012). Capital Shortfall: A New Approach
and Regulating Systemic Risks, The American Economic Review102, 59-64
Acharya, Pedersen, Philippon, and Richardson, (2010). Measuring SystemiTechnical report, Department of Finance, NYU Stern School of Business.
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Warning!
CoVaR and MES
Confound systemic and systematicrisk
Firms with large systematic risk components have large CoVaRs an
They diagnose systemic risk without a proper hypothesis tes
Literature argues that firms that failed or needed govt assistance financial crisis had large CoVaRs or MESs prior to the crisis
Concludes large CoVaR or MES for a large financial institution==systemic ris
But the literature has no formal hypothesis tests!
CoVaR and MES measures can be calculated for all firms
Real-side firms can have larger CoVaRs and MESs
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CoVaR, MES and Systematic iskCross section of CRSP stock returns
Run regression on MES on MM
Run regression of CoVaR on Ma
Large Beta, Large market correlatio
= Large (negative) MES,
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Contribution to the systemic risk literatu
We introduce a proper null hypothesis Stock returns are Gaussian
This allows us to:
Separate systemic risk from systematic risk
Formulate a classical hypothesis tests for presence of systemic risk
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Stock returns and tail dependence
Gaussian returns --independent in the tails of the distribution & Very large/small realization in one dimension does not increase the prob
very large/small realization in the other dimension
If returns are Gaussian, there is no systemic risk
Systemic risk hypothesis-> stock returns have left-tail dependenc
When financial firms suffer large losses, there is a higher probability tha
(financial and real) will suffer large losses With systemic risk, returns are not Gaussian
How large must tail dependence estimates be before we can rejehypothesis of no tail dependence?
Need a proper statistical test
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Our test strategy uses 2 estimators
Gaussian (parametric) estimators CoVaR and MES are calculated from sample estimates of the mean, std d
These estimates do not allow tail dependence
Unbiased and efficient if Gaussian null hypothesis is true
Biased if alternative hypothesis is true
Nonparameteric estimators CoVaR is estimated using quantile regression focusing on the 1% quanti
The 1% quantile of the CRSP equal-weight market portfolio conditional on stocits 1 percent quantile
MES is estimated as the average stock return on days when the market rpercent left-hand tail
If null is true, nonparametric estimators are unbiased but not efficient
If alternative is true, nonparametric estimators are still unbiased
The nonparametric estimators can produce much larger negative CoVaRestimates if there is tail dependence in returns
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CoVaR Sampling Distribution 2
Correlation .05 Sigma i=.004
Mean Std. Dev. Q05 Q95
CoVar -.0005 .0016 -.003 .002
PCoVar -.0005 .0004 -.001 .0002
Correlation .288 Rank
Correlation.2567
Low Correlation Example
Nonparametric
Parametric
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Test Statistics Our tests evaluate the difference between two estimators
Nonparametric estimate-Parametric estimate
CoVaR Quantile regression CoVaR estimate-Gaussian CoVaR estimate
MES Selected sample average MES estimate-Gaussian estimate
Both estimators are unbiased under the null
If Null is true, parametric is most efficient estimator
The differencing controls for systematic risk
We scale these differences to remove idiosyncratic risk depende CoVaR difference is scaled by Gaussian CoVaR estimate
MES is scaled by estimate of stock idiosyncratic standard deviation
Correlation remains as a nuisance parameter
We calculate critical values for these test statistics using Monte C
simulations
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Test Statistic Critical valuesSample size =5
.about 2 yea
25,000 Monte
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Apply test to CRSP daily returns: 2006-2Table 6: Industry Representation in Sample
Financials
Depository Institutions 380
Insurance 139
Other Financial 101
Broker Dealers 55
Non-financials
Manufacturing 1,324
Services 626
Transportation, Communication, Utilities 317
Retail Trade 224
Mining 144
Wholesale Trade 110
Construction 42
Public Administration 13
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Results
Lots of firm returns reject the null Many more rejections are nonfinancial than financial
MES and CoVaR often disagree about which firms are potensystemic
MES test rejects the null much more frequently than CoVaR test
Some summary pictures of results by industry.
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Banks (Depository Institutions)
Rejection region
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Insurance Industry
Rejection region
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Retail Trade
Rejection region
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Manufacturing
Rejection region
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CoVaR and MESOften Identify
Different Firms as
Systemic
Top 25 BHCs Systemic Risk Measures 2006-2007 by Market Cap in 2006
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Top 25 BHCs Systemic Risk Measures 2006 2007 by Market Cap in 2006
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Summary & Conclusion
Our contribution is to introduce a null hypothesis into syste
modeling Removes systematic risk contamination in systemic risk measure
Needed to for classical hypothesis tests (much needed in this litera
Tests must be improvedviolations may not indicate system
The Null hypothesis is too restrictive
Many data generating processes could lead to rejection, even if thallow for tail dependence and systemic risk
Can test idea can be extended to systemic risk measures basCDS-spreads?