Risk-neutral systemic risk indicators
IAQF/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
The views expressed in these lectures are my own and are not necessarily reflective of
views at the Federal Reserve Bank of New York or of the Federal Reserve System. Any
errors or omissions are my responsibility.
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Risk-neutral systemic risk indicators
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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Risk-neutral systemic risk indicators
Overview
Summary of our approach
• Represent systemic risk as market risk of a portfolio of
large-bank stocks
• Version of CoVaR, SES, MES and DIP based on derivatives
prices
• But uses firms’ market values, not liabilities or asset values, as
exposure/loss metric
• Requires only contemporaneously observed market data, no
historical 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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Risk-neutral systemic risk indicators
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 financial
institutions (G-SIFIs) by Financial Stability Board (FSB)
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Risk-neutral systemic risk indicators
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 RNPDF
estimation technique
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Risk-neutral systemic risk indicators
Construction
Risk-neutral densities of major U.S. financial firms
JPM
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0.4
0.6
0.8
1.0
WFC
1.2
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0.4
1.4
2.0
1.5
1.0
0.5
0.6
0.8
C
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0.4
2.0
1.5
1.0
0.5
0.6
0.8
1.0
1.0
1.2
0.0
0.4
1.4
0.6
0.8
GS
2.5
0.0
0.4
BAC
2.5
1.2
1.4
0.6
0.8
1.0
1.2
1.4
STT
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0.4
0.6
0.8
1.0
1.0
1.2
1.4
1.2
1.4
BK
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0.4
0.6
1.2
1.4
0.8
1.0
MS
1.2
1.4
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0.4
0.6
0.8
1.0
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 the
observed implied volatilities.
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Risk-neutral systemic risk indicators
Construction
Risk-neutral probability of large loss 2006–2014
JPM
WFC
BAC
0.5
0.5
0.4
0.3
0.2
0.1
0.0
2006
0.4
0.3
0.2
0.1
0.0
2006
2008
2010
2012
2014
2008
C
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
2006
2008
2010
2010
2012
0.6
0.5
0.4
0.3
0.2
0.1
0.0
2006
2014
2008
GS
2012
0.5
0.4
0.3
0.2
0.1
0.0
2006
2014
2008
2010
2012
2014
2012
2014
BK
0.4
0.3
0.2
0.1
2008
2010
2012
0.0
2006
2014
STT
0.5
0.4
0.3
0.2
0.1
0.0
2006
2010
2008
2010
MS
2012
2014
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
2006
2008
2010
2012
2014
Risk-neutral cumulative probability of a decline in equity value in excess of 25 percent 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),
BNP Paribas redemption halt (09Aug07), Bear Stearns run (14Mar08), Lehman bankruptcy (16Sep08), first Greek
bailout request (23Apr10), U.S. debt ceiling deal (31Jul2011), Joint Economic Committee testimony (22May2013).
8/24
Risk-neutral systemic risk indicators
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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Risk-neutral systemic risk indicators
Construction
Risk-neutral BKX implied correlation 2006–2014
1.0
0.9
0.8
0.7
0.6
0.5
0.4
2006
2008
2010
2012
2014
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), first
Greek bailout request (23Apr10), U.S. debt ceiling deal (31Jul2011), Joint Economic Committee testimony
(22May2013).
10/24
Risk-neutral systemic risk indicators
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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Risk-neutral systemic risk indicators
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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Risk-neutral systemic risk indicators
Results
Unconditional systemic risk measures
• Definition of systemic risk event: portfolio loss of given
severity or low probability
• E.g. firm or portfolio loss ≥ 25 percent over subsequent 3
months
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Risk-neutral systemic risk indicators
Results
Probability of a systemic risk event 2006–2014
0.4
0.3
0.2
0.1
0.0
2006
2008
2010
2012
2014
Systemic risk event: 3-month decline in 8-bank equity portfolio value in excess of 25 percent. Black plot: OBSESS
portfolio-based systemic risk probability, blue plot: SPX index-based probability, orange plot: BKX index-based
probability. 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
Greek bailout request (23Apr10), U.S. debt ceiling deal (31Jul2011), Joint Economic Committee testimony
(22May2013).
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Risk-neutral systemic risk indicators
Results
Conditioning from individual bank to portfolio
• “Conditional systemic event probability,” probability of
systemic risk event conditional on individual FI experiencing
extreme 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 when
systemic risk is high, since only very severe shock associated
with conditioning event
• Can also compute system expected shortfall conditional on
individual FI experiencing loss ≥ given quantile
• Analogue to CoVaR
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Risk-neutral systemic risk indicators
Results
Conditional systemic event probability 2006–2014
JPM
WFC
1.0
0.8
0.6
0.4
0.2
0.0
2006
0.8
0.6
0.4
0.2
0.0
2006
2008
2010
2012
2014
2008
C
2010
BAC
2012
1.0
0.8
0.6
0.4
0.2
0.0
2006
2014
0.8
0.8
0.6
0.6
0.6
0.4
0.4
0.4
0.2
0.2
0.0
2006
0.0
2006
2010
2012
2014
2012
2014
2012
2014
0.2
2008
2010
2012
0.0
2006
2014
STT
1.0
0.8
0.6
0.4
0.2
0.0
2006
2010
BK
0.8
2008
2008
GS
2008
2010
MS
0.8
0.6
0.4
0.2
2008
2010
2012
2014
0.0
2006
2008
2010
2012
2014
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), BNP
Paribas redemption halt (09Aug07), Bear Stearns run (14Mar08), Lehman bankruptcy (16Sep08), first Greek
bailout request (23Apr10), U.S. debt ceiling deal (31Jul2011), Joint Economic Committee testimony (22May2013).
16/24
Risk-neutral systemic risk indicators
Results
Conditioning from portfolio to individual bank
• “Conditional expected shortfall”: firm’s expected shortfall,
conditional on systemic event
• “Conditional expected shortfall ratio”: divide by portfolio
expected shortfall
• Is conditional expected shortfall over- or underproportional to
firm’s market cap?
• Too-big-to-fail indicator?
• Probability, VaR or expected shortfall of bank experiencing
extreme 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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Risk-neutral systemic risk indicators
Results
Conditional expected shortfall ratios 2006–2014
JPM
1.20
1.15
1.10
1.05
1.00
0.95
0.90
0.85
2006
2008
2010
WFC
2012
1.2
1.1
1.0
0.9
0.8
0.7
2006
2014
2008
C
2008
2010
2012
2014
2008
GS
1.4
1.3
1.2
1.1
1.0
0.9
0.8
0.7
2006
1.3
1.2
1.1
1.0
0.9
2006
2010
BAC
1.4
1.3
1.2
1.1
1.0
0.9
0.8
2006
2012
2014
2012
2014
2012
2014
BK
1.1
1.0
0.9
0.8
0.7
2008
2010
2012
2014
2006
STT
1.2
1.1
1.0
0.9
0.8
0.7
2006
2010
2008
2010
MS
1.4
1.3
1.2
1.1
1.0
0.9
2008
2010
2012
2014
2006
2008
2010
2012
2014
Ratio of conditional expected shortfall of the firm to the system expected shortfall, both at a 5 percent confidence
level. Conditioning event is a 25 percent market capitalization loss of the 8-firm portfolio over the next three
months. 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 Greek
bailout request (23Apr10), U.S. debt ceiling deal (31Jul2011), Joint Economic Committee testimony (22May2013).
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Risk-neutral systemic risk indicators
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 would
suffer in the event of a 2 percent decline in the broader equity
market.
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Risk-neutral systemic risk indicators
Assessment
Conditional expected shortfall and crisis losses
C
0.8
MS
BAC
GS
0.6
0.4
STT
JPM
BK
0.2
WFC
0.15
0.16
0.17
0.18
0.19
0.20
Values on x-axis: firms’ conditional expected shortfall at the 95 percent level (ratio to market capitalization) on
July 3, 2008. Values on the y-axis are realized equity market losses between July 3 and Dec. 31, 2008.
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Risk-neutral systemic risk indicators
Assessment
Conditional expected shortfall and stress test results
MS
BAC
0.6
STI
0.4
KEY
GS
MET
PNC
0.2
BBT
USB
0.0
C
RF
COF
JPM
WFC
FITB
STT
AXP
0.2
BK
0.26
0.28
0.30
0.32
0.34
0.36
0.38
Values on x-axis: firm’s average conditional expected shortfall at the 95 percent level (ratio to market
capitalization) between Feb. 10 and Mar. 8, 2012. Values on y-axis: (−1×) the ratio of each firm’s Net Income
before Taxes, Table 4 of CCAR 2012 documentation, to average market capitalization between Feb. 10 and Mar.
8, 2012.
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Risk-neutral systemic risk indicators
Assessment
Conditional expected shortfall and V-Lab marginal
expected shortfall
MS
6
C
5
BK
FITB
GS
STI
STT
COFKEY
JPM MET
WFC
4
3
BAC
RF
BBT
AXP
PNC
USB
2
0.26
0.28
0.30
0.32
0.34
0.36
0.38
Values on x-axis: firm’s average conditional expected shortfall at the 95 percent level (ratio to market
capitalization), Apr. 2-30, 2012. Values on y-axis: MES for Apr. 30, 2012 from
http://vlab.stern.nyu.edu/analysis/RISK.USFIN-MR.MES .
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Risk-neutral systemic risk indicators
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 probability
measures
• Can we identify the real-world distribution component of
OBSESS?
• 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 measures
consistent 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?
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Risk-neutral systemic risk indicators
Appendix
Appendix: banks included in OBSESS
Ticker
WFC
JPM
C
BAC
GS
MS
BK
STT
AXP
USB
MET
PNC
COF
BBT
FITB
STI
KEY
RF
Name
Market cap (Dec. 2011)
G-SIFIs
Wells Fargo & Co
137.0
JPMorgan Chase & Co
121.2
Citigroup Inc
76.1
Bank of America Corp
52.7
Goldman Sachs Group Inc
46.0
Morgan Stanley
28.9
Bank of New York Mellon Corp
23.2
State Street Corp
19.7
other SCAP/CCAR banks
American Express Co
54.5
US Bancorp
49.6
MetLife Inc
32.0
PNC Financial Services Group
29.0
Capital One Financial Corp
19.9
BB&T Corp
16.8
Fifth Third Bancorp
11.1
SunTrust Banks Inc
8.8
KeyCorp
6.8
Regions Financial Corp
5.0
Share of total
18.6
16.4
10.3
7.1
6.2
3.9
3.1
2.7
7.4
6.7
4.3
3.9
2.7
2.3
1.5
1.2
0.9
0.7
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