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Macroeconomic Framework for Quantifying Systemic Discussion by Tobias Adrian

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Macroeconomic Framework for Quantifying Systemic Discussion by Tobias Adrian
Macroeconomic Framework for Quantifying Systemic
Risk by Zhiguo He and Arvind Krishnamurthy
Discussion by Tobias Adrian
Federal Reserve Bank of New York
The New Normal for Monetary Policy, FRBSF, March 27, 2015
The views expressed here are those of the author and do not necessarily reflect those
of the Federal Reserve Bank of New York or the Federal Reserve System
Tobias Adrian FRBNY
Macro of Systemic Risk
March 2015
1
Overview
Overview
I
Contribution of the paper
1. He-Krishnamurthy have been pioneering macro-finance models with
intermediaries, building a coherent framework over the years
2. The current paper is applying this framework to study systemic risk
I
Review
1. The model
2. The quantitative results
I
My comments
1. Funds and banks
2. Stress testing
Tobias Adrian FRBNY
Macro of Systemic Risk
March 2015
2
Review of the Paper
Households and Production
I
Households
"Z
E
0
I
+∞
e −(ρt)
(cty )1−φ (cth )φ
1−γ
1−γ
#
dt
Production
Yt = AKt
dKt /Kt = it − δdt + σdZt
κ
Φ (it , Kt ) = it Kt + (it − δ)2 Kt
2
I
Price of capital qt , price of housing Pt
Tobias Adrian FRBNY
Macro of Systemic Risk
March 2015
3
Review of the Paper
Intermediaries
I
Mean-variance preferences, equity capacity constraint Et ≤ εt
E [dRt − rt dt] +
Tobias Adrian FRBNY
m
V [dRt ]
2
Macro of Systemic Risk
s.t.
dεt
= mdRt
εt
March 2015
4
Model
Review of the Paper
me is continuous and indexed by t. The economy has two types of capital: productive capital
Intermediaries
and housing capital H. We assume that housing is in fixed supply and normalize H ≡ 1.
denote by Pt the price of a unit of housing, and qt the price of a unit of capital; both will be
I
Mean-variance preferences, equity capacity constraint Et ≤ εt
ogenously determined in equilibrium. The numeraire is the consumption good. There are
dεt
m
ee types of agents: equity
households,
V [dR ] and
s.t.bankers. =
E [dR
− r dt]debt
+ households,
t
'
Loans to Capital
Producers it
&
t
$
t
2
εt
Et ≡ Aggregate bank capital capacity
%
6
Intermediary
Sector
Household Sector
Financial Wealth
Wt = qt Kt + pt H
Capital qt Kt
Equity Et
Housing Pt H
HH
(1 − λ)Wt
No constraint
Debt Wt − Et λWt
Tobias Adrian FRBNY
mdRt
HH
Y
H Et ≤ Et
Constraint:
H
Figure 1: Model Schematic
Macro of Systemic Risk
March 2015
4
Review of the Paper
Amplification: Model and Data
Matching
Data:Data(L)
Data(L)
and
Model(R)
Matching
Data:
and
Model(R)
(b) Data
(a) Model
!"
!"
!"
!"
Note:
model
does
poorly
many
standard
macro
calibration
targets
(e.g
Note:
TheThe
model
does
poorly
on on
many
standard
macro
calibration
targets
(e.g.,
no
labor)
labor)
I no
Strong
amplification
effects when the capital constraint binds
Model
does
in capturing
non-linearity
a select set
of economic
measur
does
wellwell
in capturing
in ainselect
economic
measures
I Model
Captures
joint
dynamics
ofnon-linearity
intermediary
equity, set
landofprices,
spreads
... We
have
to argue
metric
a good
... We
willwill
have
to argue
thatthat
ourour
metric
is aisgood
oneone
Tobias Adrian FRBNY
Macro of Systemic Risk
March 2015
5
ults(1): State variable is et = Et /Kt
Review of the Paper
Intermediary Wealth Share e = E /K as Key State Variable
Sharpe ratio
interest rate
8
0.1
6
0.05
4
0
2
−0.05
0
0
5
10
15
20
−0.1
0
q(e), capital price
5
10
15
20
investment I/K
1.05
0.105
0.1
1
0.095
0.09
0.95
0
I
5
10
15
scaled intermediary reputation e
20
0.085
0
5
10
15
scaled intermediary reputation e
20
Leverage inversely related e
Capital constraint binds for e < 0.435
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Systemic risk when capital constraint binds and leverage shoots up
Tobias Adrian FRBNY
Macro of Systemic Risk
March 2015
6
Review of the Paper
Key Assumption: Capital Constraint is Mutual Fund
Flow-Performance Chevalier-Ellison 1997
risk taking by mutal funds
1179
Fig. 2.—Flow-performance relationship f̂ for old funds (age . 10) with 90 percent
I
bands.
Skin inconfidence
the game
constraint is key amplification mechanism
I
Generates strongly countercyclical leverage
We report estimates of the other parameters of the model obtained from the subsamples of young and old funds in columns 1
and 2, respectively, of table 2. To interpret the age category–specific
Tobias Adrian FRBNY
Macro of Systemic Risk
March 2015
7
Comments
Comments
1. Funds and banks
2. Stress testing
Tobias Adrian FRBNY
Macro of Systemic Risk
March 2015
8
Comment 1: Funds and Banks
Countercyclial Net Equity Issuance of Banks
300
Billions USD
200
100
0
-100
1985q1
1990q1
1995q1
2000q1
I
Huge issuance in the depth of the crisis
I
Same is true for dealers
Tobias Adrian FRBNY
Macro of Systemic Risk
2005q1
2010q1
2015q1
March 2015
9
Comment 1: Funds and Banks
Countercyclical e = E /K for Banks
Bank Equity/Nonfinancial Equity
Detrended Commerical Bank Equity Ratio
.02
.02
.018
.018
.016
.016
.014
.014
.012
1980q1
I
.012
1990q1
2000q1
2010q1
Ratio of commercial bank equity to nonfinanical equity declines
during expansions and rises sharply during downturns
Tobias Adrian FRBNY
Macro of Systemic Risk
March 2015
10
Comment 1: Funds and Banks
Procyclical Book Leverage of Banks
Detrended Book Leverage
14
12
10
8
1980q1
I
1985q1
1990q1
1995q1
2000q1
2005q1
2010q1
2015q1
Countercyclical equity results in procyclical leverage
Tobias Adrian FRBNY
Macro of Systemic Risk
March 2015
11
Comment 1: Funds and Banks
Procyclical Book Leverage of Banks
14
17
Leverage
12
16.8
10
16.6
8
1980q1
I
1985q1
1990q1
1995q1
2000q1
2005q1
2010q1
Detrended Log Assets
Detrended Book Leverage
Log Assets
16.4
2015q1
Adrian-Shin 2008, 2010, 2014
Tobias Adrian FRBNY
Macro of Systemic Risk
March 2015
12
Comment 1: Funds and Banks
Procyclical Book Leverage of Banks
14
17
Detrended Leverage
Detrended Log Assets
16.9
12
16.8
11
Detrended Log Assets
Detrended Book Leverage
13
16.7
10
2005q1
Tobias Adrian FRBNY
2006q1
2007q1
2008q1
Macro of Systemic Risk
2009q1
16.6
2010q1
March 2015
13
Comment 1: Funds and Banks
Procyclical Book Leverage of Broker-Dealers
20
Detrended Book Leverage
16.6
Detrended Log Assets
16.4
16
16.2
14
Detrended Log Assets
Detrended Book Leverage
18
16
12
15.8
1980q1
Tobias Adrian FRBNY
1985q1
1990q1
1995q1
2000q1
2005q1
Macro of Systemic Risk
2010q1
2015q1
March 2015
14
Comment 1: Funds and Banks
Procyclical Equity of He-Krishnamurthy
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Data strongly supports this for mutual funds
40
20
20
10
0
0
-20
-10
-40
-20
US Equity Funds
Dow Jones Industrial Average Return (Y/Y)
Countercyclical leverage is due to procyclical equity flows
US Equity Funds: Net Cash Inflow (Bil.$)
I
DJIA
-60
2000m1
Tobias Adrian FRBNY
2005m1
2010m1
Macro of Systemic Risk
-30
2015m1
March 2015
15
Comment 1: Funds and Banks
Reconciling Cyclicality of Leverage
Adrian-Boyarchenko 2013
πbt wht
Cbt bht
Households
Invest in risk-free debt,
non-bank financial sector and bank financial
sector
Banks
Create new capital; financed by debt issuance
to the households
πft wht
πft wht dRtf
Funds
Hold existing capital; financed by profit
sharing contracts with
households
Φ (it ) kt
At kt
T. Adrian, N. Boyarchenko
Tobias Adrian FRBNY
Producers
A-K production technology; financed by
financial sector
Intermediary Balance Sheets
Macro of Systemic Risk
At kht
6
March 2015
16
Comment 1: Funds and Banks
Leverage Growth and Financial Sector Asset Growth
(d) Data
.5
Bank sector
Bank sector
Nonbank financial sector
Nonbank financial sector
-.2
-.1
0
-.4 -.3 -.2 -.1
Cross-correlation
.2
.3
.1
Cross-correlation
0 .1 .2 .3 .4
.5
.4
.6
.7
(c) Model
-10
-5
Tobias Adrian FRBNY
0
Lag (quarters)
5
10
-10
Macro of Systemic Risk
-5
0
Lag (quarters)
5
March 2015
10
17
Comment 1: Funds and Banks
Funds and Banks
He-Krishnamurthy matches the fund sector well
I
Modeling the bank sector requires different constraints
I
This explains procyclicality of financial sector assets
1
3Q
Q
1
20
1
1
Q
03
20
08
1
Macro of Systemic Risk
20
1
Q
98
Q
19
1
93
19
1
88
Q
Q
19
1
Q
78
19
83
Q
19
73
68
19
Tobias Adrian FRBNY
19
Q
1
1
0
5
10
15
I
March 2015
18
Comment 2: Stress Testing
Stress Testing in He-Krishnamurthy
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Stress test scenario is mapped into underlying shock to capital
I
Stress test assumptions similar to CCAR
I
I
6 quarters of adverse shocks to equity
Cumulatively -30% return on equity
I
Probability of crisis calculated via simulation
I
Model captures feedback effects
Tobias Adrian FRBNY
Macro of Systemic Risk
March 2015
19
Comment 2: Stress Testing
Probability of Crisis in He-Krishnamurthy
ng e
=1.27
Probability of capital constraint being binding: hitting e
distress
crisis
=0.4354
1
0.9
0.8
in next 2 years
in next 5 years
in next 10 years
0.7
0.6
0.5
0.4
0.3
0.2
0.1
1.8
2
2.2
2.4
0
0.4
0.6
0.8
1
1.2
1.4
1.6
starting value e
1.8
2
2.2
2.4
init
I
What if capital regulation would be based to stress tests?
ck to e.
Tobias Adrian FRBNY
Macro of Systemic Risk
March 2015
20
Comment 2: Stress Testing
Stress Test based Capital Regulation
I
Consider a forward-looking capital constraint
Z
τD
max Et
{i,β,k}
e
−ρ(s−t)
wt (i, β, k) ds
t
s.t.
s
θt−1 ≥ ϑ
Z
T
Et
t
2
σk,s
ds
I
“Choose optimal capital plan”
I
While VaR constraint is proportional to contemporaneous risk, CCAR
makes capital proportional to forward looking risk
I
Equilibrium dynamics change
I
Adrian-Boyarchenko 2012 conjecture that this mitigates procyclicality
Tobias Adrian FRBNY
Macro of Systemic Risk
March 2015
21
Conclusion
Conclusion
I
He and Krishnamurthy have pioneered models of financial
intermediation within a macro context
I
Contribution of this paper is to consider systemic risk
I
My comments
1. The theory models fund sector, not banking
I
I
Banks exhibit procyclical leverage (Adrian-Shin)
Risk based capital constraints can explain procyclicality
(Adrian-Boyarchenko)
2. How do stress tests influence equilibrium outcomes?
I
I
Impact of stress tests on equilibrium outcomes is not modeled
Conjecture that CCAR mitigates procyclicality
Tobias Adrian FRBNY
Macro of Systemic Risk
March 2015
22
Appendix
Countercyclical Dealer Equity
Broker-Dealer Equity Ratio
15
15
10
10
5
5
0
1980q1
Tobias Adrian FRBNY
1985q1
1990q1
1995q1
2000q1
2005q1
Macro of Systemic Risk
2010q1
0
2015q1
March 2015
23
Appendix
Book Leverage is Procyclical
Market Leverage is Countercyclical
JPM, BoA, C
JPM, BoA, C
20
10
5
0
-5
-20
-10
0
10
Quarterly Book Leverage Growth (%)
Tobias Adrian FRBNY
β = .448
t-stat = 105.703
R2 = .301
20
Quarterly Enterprise Value Growth (%)
Quarterly Asset Growth (%)
15
15
10
5
0
-5
-100
Macro of Systemic Risk
-50
0
50
Quarterly Market Leverage Growth (%)
β = -.064
t-stat = -134.906
R2 = .073
100
March 2015
24
Appendix
Market Leverage moves with Book-to-Market
60
40
40
20
20
0
0
-20
-20
Quarterly Book/Market Growth (%)
Quarterly Market Leverage Growth (%)
-40
1985q1
1990q1
1995q1
2000q1
Date
2005q1
2010q1
Quarterly Market Leverage Growth (%)
Quarterly Book/Market Growth (%)
Commerical Banks
60
-40
2015q1
I
The book-to-market ratio is outside of the control of banks
I
Banks manage accounting based ROE and book leverage
Tobias Adrian FRBNY
Macro of Systemic Risk
March 2015
25
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