weak & strong systemic fragility casper g. de vries erasmus university rotterdam & tinbergen...
TRANSCRIPT
Weak & Strong Systemic Fragility
Casper G. de Vries
Erasmus University Rotterdam
& Tinbergen Institute
Contents
• Current Credit Crisis• Fat Tails• Multivariate Fat Tails• Systemic Risk Measure• Bank Networks• Hedge Fund Application• Estimation• Conclusion
Banks & Systemic Risk
A Reality Check
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
Two Crucial Crisis Features
• I/ Asymmetric Information
• II/ Interconnectedness of Banks and other Vehicles
I/ The Asymmetric Information Problem
• The Old Lady meets the Old Maid, or …
Payoff if win: W
Payoff if loose: -L
Willingness to play if not dealt the old maid if: 3/4W-1/4L>0
Probability to win: 3/4
Probability to loose: 1/4
Thus play if: W/L>1/3
The Old Lady meets the Old Maid
Payoff if win: W
Payoff if loose: -L
Willingness to play if not dealt the old maid if: 3/4W-1/4L>0
Probability to win: 3/4
Probability to loose: 1/4
Subprime woes lead to risk reassessment such that L increased and: W/L<1/3
autarky
II/ Bank Network System
Banks are highly interconnected:directly• Syndicated Loans• Conduits• Interbank Money Marketindirectly• Macro interest rate risk• Macro gdp risk
daily returns 1991-2003
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2
ING
AB
NA
MR
O
simulated normal returns
-0.2
0
0.2
-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2
Fat versus Normal:2 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)
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?
Fat Tails
Normal versus Fat Tail
2/2
2
11}Pr{ ses
sY
ssX }Pr{
01
2/2
s
e s
Normal
Fat
Ratios
2/
1
2se
s
Multivariate Fat Tails
Normal
Normal
Sum / Fractal Nature (square root rule)
with n
Rate Declines with Sum
2/2
2
11}Pr{ se
ssY
nsn
ii e
s
nsY 2/
1
2
2
1}Pr{
n
s
ndn
ssnd
ndsYdn
ii 22
1
log
]2
2logloglog2
1[
log/}Pr{log2
2
1
4/21
2
2
12}2
Pr{}2Pr{}Pr{ ses
sYsYsYY
Portfolio X+Y composed of indepedent normal returns X and YPortfolio failure probability is of lower order than marginal failure probabilities
X+Y
2s
2s
s
s)exp(
2
1
2
1}2Pr{ 2s
ssYX
portfolio failure probability
)2
1exp(
2
11}Pr{ 2ss
sX
marginal failure probability
Of Larger Order Than
Feller Theorem
ssXP 1}{ ssYP 1}{
ssssssYsXP 2121)1)(1(},{ 2
Consider two independent Pareto distributed random variables X and Y
Their joint probability is
ssX }Pr{
Fat Tail
Pareto
Sum / Fractal Nature
with n
Rate Independent of Summation
ssX }Pr{
ssXX 2}Pr{ 21
nssXn
ii }Pr{
1
1log
]log[loglog/}Pr{log
1
nd
sndndsXd
n
ii
Portfolio X+Y composed of independent fat tailed returns X and YMarginal and portfolio failure probabilities are of the same order
X+Y
2s
2s
s
s
ssYX 12}2Pr{
Marginal failure probability
ssX }Pr{
Portfolio failure probability
Of Equal Order as
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
Systemic Risk Measure
Systemic Risk Measure
• Like marginal risk measure VaR
• Desire a scale for measuring the potential Systemic Risk
1 + Pr{Min>s} / Pr{Max>s} = 1 +
Pr{Max>s}
Pr{Min>s}
Given that there is a bank failing, what is the probability the other bank fails as well?
Answers Differ Radically
• Normal• Zero
• Fat Tails• Positive
Question: If bank exposures are linear in the risk factors, andbanks have some of these factors in common, then what is theexpected number of failures given that there is a failure?
Note: to see something under normality, we need a finer risk measure like the Trace of the covariance matrix / the Tawn measure
x
y
-10 0 10 20
-15
-10
-50
51
0
Student-t (3 df.) independent asset returns
• Note Plus Shape + is due to the Outliers
• Under normal, just get a Circular cloud
• Consider Bank versus Market Neutral Hedge Fund
• Bank is Long in both X and Y
• Bank portfolio return X+Y
• Hedge fund is long in X, short in Y
• Hedge fund portfolio return X-Y
x - y
y +
x
-4 -2 0 2 4
-4-2
02
4Normal independent portfolio returns
x + y
x -
y
-10 0 10 20
-10
01
02
0Student-t (3 df.) non-correlated portfolio returns
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
1 + Pr{Min>s} / Pr{Max>s} = 1 +
Pr{Max>s}
Pr{Min>s}
X
X
Y
Y
Systemic Risk Measure:
}),(Pr{
}),(Pr{1
},Pr{1
}Pr{}Pr{
sYXMax
sYXMin
sYsX
sYsX
1 + Pr{Min>s} / Pr{Max>s} = 1 +
Pr{Max>s}
Pr{Min>s}
= 1+
Normal Case
= 1
R
Q
R
Q
aR+(1-a)Q
aR+(1-a)Q
(1-a)R+aQ
(1-a)R+aQ
Ledford-Tawn measure
Need fine measure in case of normality since
Use instead
1}),(Pr{
}),(Pr{1
},Pr{1
}Pr{}Pr{
sYXMax
sYXMin
sYsX
sYsX
},Pr{log
}Pr{log}Pr{loglim2
1
sYsX
sYsXs
Portfolios composed of indepedent returns R and Q
aR+(1-a)Q
(1-a)R+aQ
s/a
s/(1-a)
R
Q
(1-a)R+aQ=s
1 + Pr{Min>s} / Pr{Max>s} = 1 +
Pr{Max>s}
Pr{Min>s}
= 1+
Fat Tail Case
> 1
Q
R
R
Q
aR+(1-a)Q
aR+(1-a)Q
(1-a)R+aQ
(1-a)R+aQ
Systemic risk with fat tails
Since numerator and denominator are of the same order in case of fat tails, the measure
Is appropriate
}),(Pr{
}),(Pr{1
},Pr{1
}Pr{}Pr{
sYXMax
sYXMin
sYsX
sYsX
Bank Network System
• Syndicated Loans
• Conduits
• Interbank Money Market
• 4 Banks with 4 Projects
• Each Project Divisible into 4 Parts
Bank Networks
autarky Wheel 1 Wheel 2
Star Full DiversificationCycle
Banks are circles. Arrows indicate transfer of –part of- project, loan etc.
Bank Networks
autarky Wheel 1 Wheel 2
Star Full DiversificationCycle
1/4
1/4
1/4
1/4
1/4
1/4
1/4 1/4
1/2
Systemic Risk, normal
E=1, T=1/4 E=1, T=2/5 E=1, T=1/2
E=1, T=11/20 E=1, T=2/3 E=4, T=1
Systemic Risk, fat tails, =3
E=1 E=1+1/27 E=1+1
E=1+3/41 E=1+1/4 E=1+3
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)
Banks & Hedge Funds
application
Cross plot Insurers versus Banks
stock price in %
0
50
100
150
200
250
300
350
400
450
500n
ov-9
4
no
v-9
5
no
v-9
6
no
v-9
7
no
v-9
8
no
v-9
9
no
v-0
0
no
v-0
1
no
v-0
2
no
v-0
3
no
v-0
4
no
v-0
5
no
v-0
6
bank
tremont
Monthly Returns 1994-2007
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
-0.3 -0.2 -0.1 0 0.1 0.2 0.3
EU Banks Index
Trem
ont D
edic
ated
Sho
rt B
ias
x + 2 * y
x -
2 *
y
-10 0 10 20
-10
01
0Student-t (3 df.) long versus dedicated short bias
2 * y + x
x -
2 *
y
-6 -4 -2 0 2 4 6
-50
5
Normal long versus dedicated short bias
Monthly Returns 1994-2007
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
EU Banks index
AB
NA
MR
O
Monthly Returns 1994-2007
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
-0.3 -0.2 -0.1 0 0.1 0.2 0.3
EU Banks Index
Trem
ont H
edge
Fun
d In
dex
Cross plot Hedge Funds vs. Banks
Cross plot Banks vs. HFR Equity Market Neutral
Cross plot Banks vs. HFR Fixed Income High Yield Index
CAPM Explanation
Hedge Funds
Banks11 bRB 22 bRB
2121 2 bRBB
2121 BB
Corr(B1+B2,B1-B2)=0
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
Multivariate Estimation
Count Measure
1 + Pr{Min>s} / Pr{Max>s} = 1 +
Pr{Max>s}
Pr{Min>s}
rr
0 100 200 300 400 500
0.0
0.2
0.4
0.6
Correlated Normal
Correlated Student-trr
0 100 200 300 400 500
0.0
0.2
0.4
0.6
Bank Data: ABNAMRO & INGrr
0 100 200 300 400 500
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Interpretation
1 in 3 times one bank ‘fails’, the other bank fails as well
Estimated failure measureBanks and Insurers (bivariate normal)
0.01330.0063Insurer
0.00630.0082Bank
InsurerBank
Mean
0.01330.0063Insurer
0.00630.0082Bank
InsurerBank
Mean
Estimated failure measureBanks and Insurers across EU
0.1070.0690.11700.0744Insurer
0.0690.0950.07440.1038Bank
InsurerBankInsurerBank
MedianMean
0.1070.0690.11700.0744Insurer
0.0690.0950.07440.1038Bank
InsurerBankInsurerBank
MedianMean
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
Thank You, Until the next Crisis!
Check Eurointelligence, EMUMonitor
Technical Appendix
Fat Tail versus Normal
Some further results
1 + Pr{Min>s} / Pr{Max>s} = 1 +
Pr{Max>s}
Pr{Min>s}
X
X
Y
Y
Systemic Risk Measure:
}),(Pr{
}),(Pr{1
},Pr{1
}Pr{}Pr{
sYXMax
sYXMin
sYsX
sYsX
Portfolios composed of indepedent returns R and Q
aR+(1-a)Q
(1-a)R+aQ
s/a
s/(1-a)
R
Q
(1-a)R+aQ=s
1 + Pr{Min>s} / Pr{Max>s} = 1 +
Pr{Max>s}
Pr{Min>s}
= 1+
Fat Tail Case
> 1
Q
R
R
Q
aR+(1-a)Q
aR+(1-a)Q
(1-a)R+aQ
(1-a)R+aQ
1 + Pr{Min>s} / Pr{Max>s} = 1 +
Pr{Max>s}
Pr{Min>s}
= 1+
Normal Case
= 1
R
Q
R
Q
aR+(1-a)Q
aR+(1-a)Q
(1-a)R+aQ
(1-a)R+aQ
Normal Details
))1(2
1exp(
2
1)1(})1({})1({
}{}],[{
)exp(2
12/1}2/1{}2{
}2{}],[{
22
22222
2
aa
s
s
aasRaaPsQaaRP
SXPsYXMaxP
ss
sRPsQRP
sYXPsYXMinP
01
1
2/1
1
2
1exp
2
1
}{
}],[{22
22
aa
aa
sXP
sYXMinP
Fat Tail Details
a
ssYXMinP
12}],[{
a
ssYXMaxP 2}],[{
11
1}{
}{1
a
a
sMaxP
sMinP
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):
1111 ERMX
2222 ERMX ssEPsRPsMP }{}{}{
2
21}1|{
2121
2121
kkE