Risk Spillovers among Financial Institutionsmarkus/research/papers/risk...1 Risk Spillovers among...
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Risk Spillovers
among Financial Institutions
Tobias Adrian and Markus K. Brunnermeier
Federal Reserve Bank of New York and Princeton University
NBER Risk of Financial Institutions
Cambridge, 10 July 2008
The views expressed in this paper are those of the authors and do not necessarily represent
those of the Federal Reserve Bank of New York or the Federal Reserve System
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Motivation
“Risk spillovers” across financial institutions Commercial banks, Investment banks, Hedge fund styles
Why do risk spillovers matter? Financial stability Central banks
Counterparty credit risk management Dealers and banks
Portfolio management Fund-of-Funds
Risk spillovers in crisis: 87 crash, Asian financial crisis, LTCM crisis, Bear Stearns crisis
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Measuring Risk Spillovers
Our proposal: CoVaR
VaR conditional that others are in distress
CoVaR is based on quantile regressions
Focus on tails
Data efficient
Simple
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Overview
1. Quantile regressions – refresher
2. Spillover risk – CoVaR
3. Offloading spillover risk with factors
4. Incentives to offload
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Quantile Regressions – A Refresher
OLS regression: min sum of squared residuals:
2arg minOLS
t t ty x
Quantile regression: min weighted absolute values:
if 0argmin
1 if 0
t t t tq
t
t t t t
q y x y x
q y x y x
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-10
-50
5
-10 -5 0 5 10CS/Tremont Hedge Fund Index
Fixed Income Arbitrage 50%-Sensitivity
5%-Sensitivity 1%-Sensitivity
q-Sensitivities
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Quantiles and Value-at-Risk
Quantile regressions give an estimate of the quantile q of y
as a linear function of x:
-1ˆ | |q y q qy x F q x x
where F-1(q|x) is the inverse CDF conditional on x.
So F-1(q|x) = q% Value-at-Risk conditional on x.
Note our sign convention!
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CoVaR – measure of risk spillover
ˆˆ ˆi ij ij j
q q qR R
Return Ri depends on return Rj for quantile q:
Definition: We denote the CoVaRij, the VaR of style i
conditional on the (unconditional) VaR of style j by:
ˆˆ|ij i j ij ij j
q q q q qCoVaR VaR VaR VaR
Conditioning shifts
mean contagion effect
variance
lower
increase due to heteroskedasticity + tail behavior
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-10
-50
5
-10 -5 0 5 10CS/Tremont Hedge Fund Index
Fixed Income Arbitrage 50%-Sensitivity
5%-Sensitivity 1%-Sensitivity
q-Sensitivities
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Data
CRSP equity returns 1986/4-2008/3
Five commercial banks Bank of America, Citibank, J. P. Morgan Chase, Wachovia, Wells Fargo
Five investment banks Bear Stearns, Goldman Sachs, Lehman Brothers, Merrill Lynch, Morgan Stanley
CSFB/Tremont hedge fund strategies 1994/1-2008/05 Long/Short Equity, Global Macro, Event Driven, Fixed Income Arbitrage, Multi-
Strategy, Emerging Markets, Equity Market Neutral, Convertible Arbitrage,
Managed Futures, Dedicated Short Bias
Commercial bank and security broker dealer industry
portfolios from Ken French 1926/7-2007/3
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Result 1a: CoVaRs > VaR
5%-VaR
CB IB HF CB IB HF
Commercial Banks (CB) -12.23 43 29 18 -12.85 5.01 3.73 0.94
Investment Banks (IB) -13.69 45 24 61 -7.86 5.03 3.14 4.13
Ten Hedge Fund Styles (HF) -2.40 27 23 48 -9.24 1.40 1.13 2.84
5%-VaR
CB IB HF CB IB HF
Commercial Bank Portfolio (CB) -10.13 . 42.64 . -17.84 . 6.15 .
Security Broker Dealer Portfolio (IB) -11.83 37.44 . . -17.37 5.06 . .
5%-CoVaR / 5%-VaR
Panel A: Institutions
Panel B: Portfolios 1926-2008
percent icrease
percent increase t-stats
5%-CoVaR / 5%-VaR
t-stats
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Result 1b: Quantile-CoVaRs > OLS-CoVaRs
CB IB HF CB IB HF
Commercial Banks (CB) 18 4 10 2.64 0.53 0.71
Investment Banks (IB) 15 12 32 1.91 1.83 2.57
CSFB/Tremont Hedge Fund Styles (HF) 21 17 34 1.22 0.99 2.48
CB IB CB IB
Commercial Bank Portfolio (CB) . 16 . 2.29
Security Broker Dealer Portfolio (IB) 11 . 1.35 .
Panel A: Institutions
5%-CoVaR / OLS-CoVaR
percent increase t-stats
Panel B: Portfolios 1926-2008
percent increase t-stats
5%-CoVaR / OLS-CoVaR
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Result 2:
HF-VaR predict I-Bank’s-CoVaR
5%-VaR
CB IB HF CB IB HF
Commercial Banks (CB) -13.90 -3 -2 -16 -8.58 -0.61 -0.17 -1.02
Investment Banks (IB) -15.09 4 5 32 -4.27 0.49 0.68 2.83
Ten Hedge Fund Styles (HF) -3.30 -2 2 3 -6.57 -0.28 0.23 0.41
5%-VaR
CB IB CB IB
Commercial Bank Portfolio (CB) -11.49 . 4 -11.00 . 0.72
Security Broker Dealer Portfolio (IB) -13.78 -7 . -12.16 -1.61 .
5%-CoVaR / 5%-VaR
t-stats
t-statspercent increase
Panel A: Institutions
percent increase
Panel B: Portfolios 1926-2008
5%-CoVaR / 5%-VaR
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Overview
1. Quantile regressions – refresher
2. Spillover risk – CoVaR
3. Offloading spillover risk with factors
4. Incentives to offload
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6-Risk Factor Pricing Model
Factors: Interpretation:
Repo - 3 Month Treasury : “Flight to Quality”
10 Year - 3 Month Treasury Return: “Business Cycle”
Moody's BAA - 10 Year Treasury Return: “Credit Indicator”
CRSP Market Excess Return: “Equity Market Risk”
VIX Straddle Excess Return: “Volatility Exposure”
Variance Swap Return: “Variation in Price of Risk”
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Offloaded Returns
All factors are excess returns
We can offload systematic risk
CoVaR of offloaded returns
Offloaded Return = i i i i
q q qi R X res
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Result 3a: 5%-offloaded returns
CoVaRs ~ VaRs
5%-VaR
CB IB HF CB IB HF
Commercial Banks (CB) -7.86 30 3 -8 -33.45 3.54 0.31 -0.93
Investment Banks (IB) -10.28 3 14 0 -60.95 0.39 1.76 -0.03
Ten Hedge Fund Styles (HF) -2.36 1 1 10 -35.25 0.14 0.08 1.61
t-stats
5%-CoVaR / 5%-VaR
percent increase
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Result 3b: Offloaded Returns:
Quantile CoVaRs ~ OLS VaRs
CB IB HF CB IB HF
Commercial Banks (CB) -7 -20 -2 -0.92 -2.80 -0.11
Investment Banks (IB) -14 1 -1 -1.14 0.10 -0.07
CSFB/Tremont Hedge Fund
Styles (HF) 3 2 -2 0.33 0.20 -0.20
t-stats
5%-CoVaR / OLS-CoVaR
percent increase
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0
.02
.04
.06
.08
-30 -20 -10 0 10 20
Commercial Banks
0
.02
.04
.06
.08
-40 -20 0 20 40
Investment Banks
0
.05
.1.1
5.2
.25
-10 -5 0 5 10
CS/Tremont Hedge Fund Index
Figure 1: Kernel Densities of Total and 5%-Offloaded Returns
• Hedging reduces left tail
• But average returns decrease
• Incentives to hedge spillover risk
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q-Sensitivities:
Total and Offloaded ReturnsFigure 2: Average q-Sensitivities by Quantiles
10%
15%
20%
25%
30%
35%
40%
45%
50%
5% 15% 25% 35% 45% 55% 65% 75% 85% 95%Quantiles
Average Sensitivities of Total Returns
Averag Sensitivities of OLS Offloaded Returns
Average Sensitivities of 5% Offloaded Returns
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Related Literature
Dependence / contagion:Boyson, Stahel, Stulz (2008), Chan, Getmansky, Haas, Lo (2006), Adrian (2007), Forbes, Rigobon (2002)
Hedge fund tail risk: Asness, Krail, Liew (2001), Agarwal & Naik (2004), Bali, Gokcan, Liang (2007), Liang & Park (2007), Bondarenko (2004)
Pricing factors:Fung and Hsieh (2001, 2002, 2003), Hasanhodzic & Lo (2007)
Finance applications of quantile regressions:Bassett and Chen (2001), Chernozhukov and Umantsev (2001)
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Summary
Institutions have incentives to hold tail risk
Holding tail risk increases returns
There is spillover of tail risk among hedge funds and
among banks, as well as between hedge funds and
banks (contemporaneous and lagged)
The increase in CoVaR relative to VaR can be
offloaded with liquid, tradable risk factors
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Robustness Analysis
Alternative measure of tail risk:
1%-CoVaR and Expected Shortfall
Alternative measure of sensitivities:
GARCH variances
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Robustness check:
1%-CoVaR and Expected shortfall
1%-VaR
Panel A: 1%-CoVaR CB IB CB IB
Commercial Bank Portfolio (CB) -21.46 . 23 -9.06 . 1.89
Security Broker Dealer Portfolio (IB) -22.46 38 . -9.30 3.44 .
5%-ES
Panel B: 5%-Expected Shortfall CB IB CB IB
Commercial Bank Portfolio (CB) -13.67 . 40 -13.98 . 6.74
Security Broker Dealer Portfolio (IB) -16.01 37 . -14.63 5.95 .
percent icrease t-stats
percent icrease
1%-CoVaR / 1%-VaR
t-stats
5%-CoES / 5%-ES
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Figure 3: Average GARCH Covariances over Time
0
5
10
15
20
25
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
Total Returns
5% Offloaded Returns