Weak

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Weak Strong Systemic Fragility

• Casper G. de Vries
• Erasmus University Rotterdam
• Tinbergen Institute

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Contents

• Current Credit Crisis
• Fat Tails
• Multivariate Fat Tails
• Systemic Risk Measure
• Bank Networks
• Hedge Fund Application
• Estimation
• Conclusion

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Banks Systemic Risk

• A Reality Check

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Current Crisis Aspects

• History Savings glut Low interest produced
  Credit binge big time
• Basel I stimulates Conduits formation to shift
  mortgages off-balance repackaging of risk
• Interest rate tightening triggers mortgage
  failures Basel II 2008 start brings on-balance
  fears
• Asymmetric information about conduits, non-market
  over the counter instruments, turns money market
  into market for lemons

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Two Crucial Crisis Features

• I/ Asymmetric Information
• II/ Interconnectedness of Banks and other Vehicles

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I/ The Asymmetric Information Problem

• The Old Lady meets the Old Maid, or

Payoff if win W
Probability to win 3/4
Payoff if loose -L
Probability to loose 1/4
Willingness to play if not dealt the old maid if
3/4W-1/4Lgt0
Thus play if W/Lgt1/3
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The Old Lady meets the Old Maid
Probability to win 3/4
Payoff if win W
autarky
Payoff if loose -L
Probability to loose 1/4
Willingness to play if not dealt the old maid if
3/4W-1/4Lgt0
Subprime woes lead to risk reassessment such that
L increased and W/Llt1/3
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II/ Bank Network System

• Banks are highly interconnected
• directly
• Syndicated Loans
• Conduits
• Interbank Money Market
• indirectly
• Macro interest rate risk
• Macro gdp risk

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Fat versus Normal2 Features

• Univariate More than normal outliers along the
  axes
• Multivariate Extremes occur jointly along the
  diagonal, systemic risk is of higher order than
  if normal (market speak market stress increases
  correlation)

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Basel Motivation

• Systemic Risk of banks is important due to the
  externality to the entire economy
• Motive for Basle Accords why banks are stronger
  regulated than insurers (Solvency)
• Surprise is micro orientation of Basle II, rather
  than macro approach
• Improper information to supervisor
  overregulation or too little?

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Fat Tails
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Normal versus Fat Tail
Normal
Fat
Ratios
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Multivariate Fat Tails
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Of Larger Order Than
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Feller Theorem
Consider two independent Pareto distributed
random variables X and Y
Their joint probability is
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Of Equal Order as
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Conclude

• With linear dependence, as between portfolios and
  balance sheets, the probability of a joint
  failure is
• Of smaller order than the individual failure
  probabilities in case of the normal, hence
  systemic risk is unimportant
• Of the same order in case of fat tails, hence
  systemic risk is important

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Systemic Risk Measure
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Systemic Risk Measure

• Like marginal risk measure VaR
• Desire a scale for measuring the potential
  Systemic Risk

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PrMingts
1 PrMingts / PrMaxgts 1
PrMaxgts
Given that there is a bank failing, what is the
probability the other bank fails as well?

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Answers Differ Radically
Question If bank exposures are linear in the
risk factors, and banks have some of these
factors in common, then what is the expected
number of failures given that there is a failure?

• Normal
• Zero

• Fat Tails
• Positive

Note to see something under normality, we need a
finer risk measure like the Trace of the
covariance matrix / the Tawn measure
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• Note Plus Shape is due to the Outliers
• Under normal, just get a Circular cloud

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• Consider Bank versus Market Neutral Hedge Fund
• Bank is Long in both X and Y
• Bank portfolio return XY
• Hedge fund is long in X, short in Y
• Hedge fund portfolio return X-Y

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Systemic Risk Measure

• Do not know where systemic failure sets in
• Take limits
• Evaluate in limit and extrapolate back
• Construct Multivariate VaR, in terms of Failure
  Probability, rather than loss quantile
• Conditional Failure Measure
• Given that one bank fails, Probability the other
  banks fail

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Y
PrMingts
X
1 PrMingts / PrMaxgts 1
Y
PrMaxgts
X
Systemic Risk Measure
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(1-a)RaQ
PrMingts
Normal Case
aR(1-a)Q
1 PrMingts / PrMaxgts 1
(1-a)RaQ
PrMaxgts
Q
aR(1-a)Q
R
1
1
Q
R
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Ledford-Tawn measure

• Need fine measure in case of normality since
• Use instead

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Portfolios composed of indepedent returns R and Q
aR(1-a)Q
(1-a)RaQ
Q
s/(1-a)
R
s/a
(1-a)RaQs
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(1-a)RaQ
PrMingts
Fat Tail Case
aR(1-a)Q
1 PrMingts / PrMaxgts 1
(1-a)RaQ
PrMaxgts
Q
aR(1-a)Q
R
1
gt 1
Q
R
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Systemic risk with fat tails

• Since numerator and denominator are of the same
  order in case of fat tails, the measure
• Is appropriate

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Bank Network System

• Syndicated Loans
• Conduits
• Interbank Money Market
• 4 Banks with 4 Projects
• Each Project Divisible into 4 Parts

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Bank Networks
Banks are circles. Arrows indicate transfer of
part of- project, loan etc.
autarky
Wheel 1
Wheel 2
Full Diversification
Star
Cycle
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Bank Networks
1/2
1/4
Wheel 1
Wheel 2
autarky
1/4
1/4
1/4
1/4
1/4
1/4
1/4
Full Diversification
Cycle
Star
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Systemic Risk, normal
E1, T1/4
E1, T2/5
E1, T1/2
E4, T1
E1, T2/3
E1, T11/20
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Systemic Risk, fat tails, 3
E1
E11/27
E11
E11/4
E13
E13/41
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Conclude

• Pattern of Systemic Risk under fat tails differs
  from normal based covariance intuition
• Too much Diversification hurts Systemic Risk
  (slicing and dicing convexifies the exposures)

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Banks Hedge Funds

• application

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Cross plot Insurers versus Banks
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Cross plot Hedge Funds vs. Banks
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Cross plot Banks vs. HFR Equity Market Neutral
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Cross plot Banks vs. HFR Fixed Income High Yield
Index
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CAPM Explanation
Banks
Hedge Funds
Corr(B1B2,B1-B2)0
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Banks Hedge Funds

• Banks are MORE Risky than Hedge Funds
• Little Systemic Risk effects of hedge funds for
  the Banking Sector
• If anything, hedge funds are grasshoppers wearing
  the bolder hat that provides the protection

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Multivariate Estimation

• Count Measure

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PrMingts
1 PrMingts / PrMaxgts 1
PrMaxgts

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Correlated Normal
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Correlated Student-t
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Bank Data ABNAMRO ING
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Interpretation

• 1 in 3 times one bank fails, the other bank
  fails as well

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Estimated failure measureBanks and Insurers
(bivariate normal)
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Estimated failure measureBanks and Insurers
across EU
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Four Conclusions

• Asymmetric Information, market trade or OTC
• Linear dependence and normal risk cannot produce
  systemic risk
• Linear dependence and fat tails imply that
  systemic risk is always there
• Need for systemic risk scale like Richter scale,
  in order to impute correct capital requirements
  and signal potential stress

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Thank You, Until the next Crisis!

• Check Eurointelligence, EMUMonitor

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Technical Appendix
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Fat Tail versus Normal

• Some further results

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Y
PrMingts
X
1 PrMingts / PrMaxgts 1
Y
PrMaxgts
X
Systemic Risk Measure
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Portfolios composed of indepedent returns R and Q
aR(1-a)Q
(1-a)RaQ
Q
s/(1-a)
R
s/a
(1-a)RaQs
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(1-a)RaQ
PrMingts
Fat Tail Case
aR(1-a)Q
1 PrMingts / PrMaxgts 1
(1-a)RaQ
PrMaxgts
Q
aR(1-a)Q
R
1
gt 1
Q
R
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(1-a)RaQ
PrMingts
Normal Case
aR(1-a)Q
1 PrMingts / PrMaxgts 1
(1-a)RaQ
PrMaxgts
Q
aR(1-a)Q
R
1
1
Q
R
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Normal Details
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Fat Tail Details
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Conduit Runs

• Bank Return X Market Risk M Interest Rate Risk
  R Idiosyncratic Risk E
• Bank 1
• Bank 2
• If
• Systemic Risk (expected number of joint
  failures)