Risk-neutral systemic risk indicators Malz Slides.pdf · 2014-04-29 · Risk-neutral systemic risk indicators Construction Risk-neutral probability of large loss 2006–2014 2006

Risk-neutral systemic risk indicatorsIAQF/Thalesians Seminar Series

Allan Malz

Federal Reserve Bank of New York

April 28, 2014

Risk-neutral systemic risk indicators

Outline

Overview

Construction

Results

Assessment

Issues

Working paper available at

http://www.newyorkfed.org/research/staff_reports/sr607.pdf

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The views expressed in these lectures are my own and are not necessarily reflective ofviews at the Federal Reserve Bank of New York or of the Federal Reserve System. Anyerrors or omissions are my responsibility.

http://www.newyorkfed.org/research/staff_reports/sr607.pdf


Overview

Systemic risk and systemic risk indicators

• Systemic risk a financial stability concept• Risk of a systemic event severely impairing financial system• Symptoms include impairment of payment system, sudden stop

of credit extension, asset fire sales• Capture underlying phenomena: impact of large common

shock, fragility, contagion, connectedness and linkages,leverage

• Search for measures, (leading) indicators• Likelihood of systemic event• Are specific institutions systemically important, large

contributors to systemic risk?

• Balance sheet focus: risk of loss of assets, debt, equity

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Overview

Summary of our approach

• Represent systemic risk as market risk of a portfolio oflarge-bank stocks

• Version of CoVaR , SES , MES and DIP based on derivativesprices

• But uses firms’ market values, not liabilities or asset values, asexposure/loss metric

• Requires only contemporaneously observed market data, nohistorical data

• Can be computed daily using only that day’s data

• Risk-neutral, so contains risk premiums

• Option-Based Systemic Expected Shortfall Statistics(OBSESS)

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Construction

Overview of construction of indicators

• 3 building blocks• Option-based risk-neutral probability distributions• Option-based equity implied return correlation• Copula model to tie risk-neutral distributions together and

generate simulations

• 8 U.S. banks listed as global systemically important financialinstitutions (G-SIFIs) by Financial Stability Board (FSB)

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Construction

Risk-neutral distributions

• Data: Bloomberg implied volatility datasets• Three-month single-stock and index options

• Volatility smile interpolation• Cubic spline with clamped endpoints• In moneyness-volatility space• Differencing→risk-neutral CDF and PDF

• OBSESS not dependent on this particular data or RNPDFestimation technique

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Construction

Risk-neutral densities of major U.S. financial firms

0.4 0.6 0.8 1.0 1.2 1.40.00.51.01.52.02.53.0

JPM

0.4 0.6 0.8 1.0 1.2 1.40.00.51.01.52.02.53.0

WFC

0.4 0.6 0.8 1.0 1.2 1.40.0

0.5

1.0

1.5

2.0

2.5

BAC

0.4 0.6 0.8 1.0 1.2 1.40.0

0.5

1.0

1.5

2.0

2.5

C

0.4 0.6 0.8 1.0 1.2 1.40.00.51.01.52.02.53.03.5

GS

0.4 0.6 0.8 1.0 1.2 1.40.00.51.01.52.02.53.0

BK

0.4 0.6 0.8 1.0 1.2 1.40.00.51.01.52.02.53.0

STT

0.4 0.6 0.8 1.0 1.2 1.40.00.51.01.52.02.53.0

MS

Density of the ratio of the stock price three months hence to the current outright forward price, Feb. 11, 2011.The forward price is computed using the 3-month T-bill yield and a trailing dividend yield. Points represent theobserved implied volatilities.

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Construction

Risk-neutral probability of large loss 2006–2014

2006 2008 2010 2012 20140.0

0.1

0.2

0.3

0.4

0.5

JPM

2006 2008 2010 2012 20140.00.10.20.30.40.5

WFC

2006 2008 2010 2012 20140.00.10.20.30.40.50.6

BAC

2006 2008 2010 2012 20140.00.10.20.30.40.50.60.7

C

2006 2008 2010 2012 20140.00.10.20.30.40.5

GS

2006 2008 2010 2012 20140.0

0.1

0.2

0.3

0.4

BK

2006 2008 2010 2012 20140.00.10.20.30.40.5

STT

2006 2008 2010 2012 20140.00.10.20.30.40.50.60.7

MS

Risk-neutral cumulative probability of a decline in equity value in excess of 25 percent over the subsequent threemonths, daily, Jan. 4, 2006 to Apr. 23, 2014. Vertical grid lines: first volatility event of the crisis (27 Feb. 2007),BNP Paribas redemption halt (09Aug07), Bear Stearns run (14Mar08), Lehman bankruptcy (16Sep08), first Greekbailout request (23Apr10), U.S. debt ceiling deal (31Jul2011), Joint Economic Committee testimony (22May2013).

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Construction

Equity implied correlation

• Risk-neutral implied correlation of banks’ stock returns

• Estimates from index and constituent vols• All ATM and of same 3-month tenor

• KBW Bank Sector Index (ticker BKX)• Overlap with but not identical to the list of G-SIFIs (GS, MS

not in BKX)• Few other sources of market data on correlation

• Constant pairwise correlation�, but new estimate each day�• Contrast to S&P corr: decline post-Lehman

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Construction

Risk-neutral BKX implied correlation 2006–2014

2006 2008 2010 2012 2014

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Three-month, daily, Jan. 4, 2006 to Apr. 23, 2014. Vertical grid lines: first volatility event of the crisis (27 Feb.2007), BNP Paribas redemption halt (09Aug07), Bear Stearns run (14Mar08), Lehman bankruptcy (16Sep08), firstGreek bailout request (23Apr10), U.S. debt ceiling deal (31Jul2011), Joint Economic Committee testimony(22May2013).

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Construction

Computing the indicators via a copula model

• Why a copula model?• Joint (and portfolio) return distribution unknown• But marginal distributions known: RNPDFs, updated daily• As well as correlation matrix, updated daily• But all off-diagonal elements equal

• Normal copula; but can use other copula models, e.g.t-copula

• Doesn’t assume returns multivariate normal• Rather, “normal z ’s” corresponding to probabilities

corresponding to returns are multivariate normal• Fat-tailed marginals (RNPDFs) generate tail dependence

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Results

From simulation results to indicators

• Daily simulation procedure• Draw from multivariate correlated normal• Map to firms’ equity returns via RNPDFs (can incorporate

CDS-based risk-neutral default probability)• Raw results: 10 000 simulations of each firm’s equity return

• Sort and otherwise manipulate to get• Portfolio returns by cap-weighting within each simulation• Simulated returns sorted by order statistics of any firm’s or

portfolio’s simulated returns• Unconditional or conditional risk metrics• Probability of loss of given size, quantiles, VaR, expected

shortfall at given confidence level

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Results

Unconditional systemic risk measures

• Definition of systemic risk event: portfolio loss of givenseverity or low probability

• E.g. firm or portfolio loss ≥ 25 percent over subsequent 3months

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Results

Probability of a systemic risk event 2006–2014

2006 2008 2010 2012 2014

0.0

0.1

0.2

0.3

0.4

Systemic risk event: 3-month decline in 8-bank equity portfolio value in excess of 25 percent. Black plot: OBSESSportfolio-based systemic risk probability, blue plot: SPX index-based probability, orange plot: BKX index-basedprobability. Daily, Jan. 4, 2006 to Apr. 23, 2014. Vertical grid lines: first volatility event of the crisis (27 Feb.2007), BNP Paribas redemption halt (09Aug07), Bear Stearns run (14Mar08), Lehman bankruptcy (16Sep08), firstGreek bailout request (23Apr10), U.S. debt ceiling deal (31Jul2011), Joint Economic Committee testimony(22May2013).

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Results

Conditioning from individual bank to portfolio

• “Conditional systemic event probability,” probability ofsystemic risk event conditional on individual FI experiencingextreme loss

• Varies more over time than across firms; why?• Should be high for large firm when systemic risk is high, since

much dependence of other banks on its financial health(“contagion”)

• Should be high for small, relatively non-fragile firm whensystemic risk is high, since only very severe shock associatedwith conditioning event

• Can also compute system expected shortfall conditional onindividual FI experiencing loss ≥ given quantile

• Analogue to CoVaR

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Results

Conditional systemic event probability 2006–2014

2006 2008 2010 2012 20140.0

0.2

0.4

0.6

0.8

JPM

2006 2008 2010 2012 20140.00.20.40.60.81.0

WFC

2006 2008 2010 2012 20140.00.20.40.60.81.0

BAC

2006 2008 2010 2012 20140.0

0.2

0.4

0.6

0.8

C

2006 2008 2010 2012 20140.0

0.2

0.4

0.6

0.8

GS

2006 2008 2010 2012 20140.0

0.2

0.4

0.6

0.8

BK

2006 2008 2010 2012 20140.00.20.40.60.81.0

STT

2006 2008 2010 2012 20140.0

0.2

0.4

0.6

0.8

MS

Conditioning event is a 25 percent market capitalization loss of the firm over the subsequent three months.Systemic risk event is a 25 percent market capitalization loss of the portfolio over the subsequent three months.Daily, Jan. 4, 2006 to Apr. 23, 2014. Vertical grid lines: first volatility event of the crisis (27 Feb. 2007), BNPParibas redemption halt (09Aug07), Bear Stearns run (14Mar08), Lehman bankruptcy (16Sep08), first Greekbailout request (23Apr10), U.S. debt ceiling deal (31Jul2011), Joint Economic Committee testimony (22May2013).

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Results

Conditioning from portfolio to individual bank

• “Conditional expected shortfall”: firm’s expected shortfall,conditional on systemic event

• “Conditional expected shortfall ratio”: divide by portfolioexpected shortfall

• Is conditional expected shortfall over- or underproportional tofirm’s market cap?

• Too-big-to-fail indicator?

• Probability, VaR or expected shortfall of bank experiencingextreme firm loss conditional on systemic risk event

• Analogues to:• DIP (but equity rather than liabilities)• SES (but conditioning on FI portfolio loss, not overall stock

market)

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Results

Conditional expected shortfall ratios 2006–2014

2006 2008 2010 2012 20140.850.900.951.001.051.101.151.20

JPM

2006 2008 2010 2012 20140.70.80.91.01.11.2

WFC

2006 2008 2010 2012 20140.80.91.01.11.21.31.4

BAC

2006 2008 2010 2012 2014

0.91.01.11.21.3

C

2006 2008 2010 2012 2014

0.70.80.91.01.11.21.31.4

GS

2006 2008 2010 2012 2014

0.7

0.8

0.9

1.0

1.1

BK

2006 2008 2010 2012 20140.70.80.91.01.11.2

STT

2006 2008 2010 2012 2014

0.91.01.11.21.31.4

MS

Ratio of conditional expected shortfall of the firm to the system expected shortfall, both at a 5 percent confidencelevel. Conditioning event is a 25 percent market capitalization loss of the 8-firm portfolio over the next threemonths. Daily, Jan. 4, 2006 to Apr. 23, 2014. Vertical grid lines: first volatility event of the crisis (27 Feb. 2007),BNP Paribas redemption halt (09Aug07), Bear Stearns run (14Mar08), Lehman bankruptcy (16Sep08), first Greekbailout request (23Apr10), U.S. debt ceiling deal (31Jul2011), Joint Economic Committee testimony (22May2013).

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Assessment

How do we validate OBSESS?

• Predictive power: second half of 2008

• Comparison with other approaches (using larger portfolio)• CCAR results as “fundamentals-based” or “real-world”

estimate of losses• Compare with another, similar systemic risk measure, marginal

expected shortfall (MES), defined as the loss a firm wouldsuffer in the event of a 2 percent decline in the broader equitymarket.

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Assessment

Conditional expected shortfall and crisis losses

JPMJPM

WFCWFC

BACBAC

CC

GSGS

BKBKSTTSTT

MSMS

0.15 0.16 0.17 0.18 0.19 0.20

0.2

0.4

0.6

0.8

Values on x-axis: firms’ conditional expected shortfall at the 95 percent level (ratio to market capitalization) onJuly 3, 2008. Values on the y-axis are realized equity market losses between July 3 and Dec. 31, 2008.

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Assessment

Conditional expected shortfall and stress test results

JPMJPMWFCWFC

BACBACCC

GSGS

USBUSB

COFCOF

METMET

MSMS

AXPAXPBKBK

PNCPNC

STTSTT

BBTBBT

STISTI

FITBFITB

RFRFKEYKEY

0.26 0.28 0.30 0.32 0.34 0.36 0.38

�0.2

0.0

0.2

0.4

0.6

Values on x-axis: firm’s average conditional expected shortfall at the 95 percent level (ratio to marketcapitalization) between Feb. 10 and Mar. 8, 2012. Values on y-axis: (−1×) the ratio of each firm’s Net Incomebefore Taxes, Table 4 of CCAR 2012 documentation, to average market capitalization between Feb. 10 and Mar.8, 2012.

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Assessment

Conditional expected shortfall and V-Lab marginalexpected shortfall

JPMJPMWFCWFC

BACBAC

CC

GSGS

USBUSB

COFCOF METMET

MSMS

AXPAXP

BKBK

PNCPNC

STTSTT

BBTBBT

STISTIFITBFITB RFRF

KEYKEY

0.26 0.28 0.30 0.32 0.34 0.36 0.382

3

4

5

6

Values on x-axis: firm’s average conditional expected shortfall at the 95 percent level (ratio to marketcapitalization), Apr. 2-30, 2012. Values on y-axis: MES for Apr. 30, 2012 fromhttp://vlab.stern.nyu.edu/analysis/RISK.USFIN-MR.MES .

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http://vlab.stern.nyu.edu/analysis/RISK.USFIN-MR.MES


Issues

Issues• Great hopes placed in systemic risk indicators

• But was problem really lack of data?• Do OBSESS have predictive value?

• Challenge of measuring predictive power of tail probabilitymeasures

• Can we identify the real-world distribution component ofOBSESS?

• And if not, how are they useful?• Use as benchmark

• Nice to have something sensitive other than CDS• Point of comparison to analogues based on historical data and

fundamentals

• Market-based cross-sectional systemic risk measuresconsistent with macro prudential approach to regulation

• But based on a particular view of causes of financial crises?• Contagion, externalities, common shocks/canary in the coal

mine?23/24


Appendix

Appendix: banks included in OBSESS

Ticker Name Market cap (Dec. 2011) Share of totalG-SIFIs

WFC Wells Fargo & Co 137.0 18.6JPM JPMorgan Chase & Co 121.2 16.4C Citigroup Inc 76.1 10.3BAC Bank of America Corp 52.7 7.1GS Goldman Sachs Group Inc 46.0 6.2MS Morgan Stanley 28.9 3.9BK Bank of New York Mellon Corp 23.2 3.1STT State Street Corp 19.7 2.7

other SCAP/CCAR banksAXP American Express Co 54.5 7.4USB US Bancorp 49.6 6.7MET MetLife Inc 32.0 4.3PNC PNC Financial Services Group 29.0 3.9COF Capital One Financial Corp 19.9 2.7BBT BB&T Corp 16.8 2.3FITB Fifth Third Bancorp 11.1 1.5STI SunTrust Banks Inc 8.8 1.2KEY KeyCorp 6.8 0.9RF Regions Financial Corp 5.0 0.7

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Documents

Risk-neutral systemic risk indicators Malz Slides.pdf · 2014-04-29 · Risk-neutral systemic risk indicators Construction Risk-neutral probability of large loss 2006–2014 2006