taking the risk out of systemic risk measurement

8/13/2019 Taking the risk out of systemic risk measurement

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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?

taking the risk out of systemic risk measurement

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