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Cross-Border Banking and Global Liquidity
Valentina Bruno
Hyun Song Shin
November 2014
Cross-Border Banking and Global Liquidity
1
“Global Liquidity”
• Global factor associated with credit availability and compressed risk
premiums
• Strong cross-border element
• BIS (CGFS “Landau report” 2011), Rey (2013, 2014)
Cross-Border Banking and Global Liquidity
Global Liquidity: Two Phases
• First Phase of Global Liquidity (2003 - 2008)
—
—
—
—
Bank-driven
Key theme is leverage
Main actors: global banks intermediating US dollar credit
Global factor is leverage of global banks
• Second Phase of Global Liquidity (2010 - )
— Bond market-driven
— Key theme is search for yield
— Main actors: Asset managers with global reach
This paper is about the First Phase
2
Cross-Border Banking and Global Liquidity
“Triple Coincidence”
• Boundary of national income area
• Boundary defining decision-making unit with coherent preferences
— Consumption and savings decisions (e.g. “global savings glut”)
— Portfolio choice decisions (e.g. preference for “safe assets”)
• Boundary defining currency area
— Exchange rate as relative price level
3
Cross-Border Banking and Global Liquidity
“Economic territory” 1
Output 1
4
“Economic territory” 2
Output 2
Figure 1. Boundary for national income accounting defines “economic terriroty”
Cross-Border Banking and Global Liquidity
Economic territory 1
A
L
5
Economic territory 2
A
L
Figure 2. Boundary for national income accounting defines decision-making unit
Cross-Border Banking and Global Liquidity
Economic territory 1
(USD)
A
USD
6
Economic territory 2
(JPY)
L
A
L
USD
JPY
JPY
Figure 3. Boundary for national income accounting defines exchange rates as relative prices across boundary
Cross-Border Banking and Global Liquidity
7
2008Q1
20.0 Trillion
Other
dollars
Swiss Franc
15.0
Yen
Sterling
10.0
Euro
US dollar
5.0
Assets
0.0
-5.0
Liabilities
-10.0
-15.0
2012-Q2
2010-Q4
2009-Q2
2007-Q4
2006-Q2
2004-Q4
2003-Q2
2001-Q4
2000-Q2
1998-Q4
1997-Q2
1995-Q4
1994-Q2
1992-Q4
1991-Q2
1989-Q4
1988-Q2
1986-Q4
1985-Q2
1983-Q4
1982-Q2
1980-Q4
1979-Q2
1977-Q4
-20.0
Figure 4. Foreign currency claims and liabilities of BIS reporting banks (Source: BIS Locational statistics
5A)
Cross-Border Banking and Global Liquidity
8
Trillion dollars
Net interoffice assets
Borrowings from others
Cash assets
Large time deposits
Securities
Borrowings from banks in U.S.
Loans and leases
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
23-Nov-11
11-May-11
27-Oct-10
14-Apr-10
30-Sep-09
18-Mar-09
03-Sep-08
20-Feb-08
08-Aug-07
24-Jan-07
12-Jul-06
28-Dec-05
15-Jun-05
01-Dec-04
19-May-04
05-Nov-03
23-Apr-03
09-Oct-02
27-Mar-02
12-Sep-01
28-Feb-01
16-Aug-00
02-Feb-00
21-Jul-99
06-Jan-99
-2.0
Figure 5. Assets and liabilities of foreign banks in the U.S. (Source: Federal Reserve H8 weekly series on
assets and liabilities of foreign-related institutions)
Billion dollars
Cross-Border Banking and Global Liquidity
9
800
600
400
Net interoffice assets of foreign banks in US
200
0
-200
30-Nov-11
03-Nov-10
07-Oct-09
10-Sep-08
15-Aug-07
19-Jul-06
22-Jun-05
26-May-04
30-Apr-03
03-Apr-02
07-Mar-01
09-Feb-00
13-Jan-99
17-Dec-97
20-Nov-96
25-Oct-95
28-Sep-94
01-Sep-93
05-Aug-92
10-Jul-91
13-Jun-90
17-May-89
20-Apr-88
-400
Figure 6. Net interoffice assets of foreign banks in U.S. given by negative of Federal Reserve weekly H8 series
on “net due to related foreign offices of foreign-related institutions”
Cross-Border Banking and Global Liquidity
(%)
10
90
80
Asia
70
60
United States
50
40
Other Europe
30
20
Other euro area
10
2011 H1
2010 H2
2010 H1
2009 H2
2009 H1
2008 H2
2008 H1
2007 H2
2007 H1
2006 H2
0
Belgium, Italy,
Spain, Portugal,
Ireland, Greece
Figure 7. Amount owed by banks to US prime money market funds (% of total), based on top 10 prime
MMFs, representing $755 bn of $1.66 trn total prime MMF assets (Source: IMF GFSR Sept 2011, data
from Fitch).
Cross-Border Banking and Global Liquidity
11
US Dollar Intermediation
Local
corporate
A
Regional
Bank
L
A
L
Stage 3
Local
USD
currency
Global Bank
A
L
Stage 1
Stage 2
USD
USD
USD
Figure 8. Cross-border bank lending in US Dollars
USD
Wholesale
Funding
Market
Cross-Border Banking and Global Liquidity
12
Where to draw the boundary?
The balance sheet chain is consistent with many variants with different
placement of the border:
• The local bank can be within the border (say, branch of foreign-owned
bank)
• The local bank can be in a neighbouring jurisdiction
• The asset side of the global bank could be in a regional financial centre
(Hong Kong or Singapore, say)
• The liabilities side of the global bank could in the United States
• What of the European headquarters? Where does it fit in the picture?
Cross-Border Banking and Global Liquidity
13
US dollar depreciation and global lending boom
Local
corporate
A
Regional
Bank
L
A
L
USD
USD
Stage 3
Local
USD
currency
Global Bank
A
L
USD
USD
Stage 1
Stage 2
Wholesale
Funding
Market
• Local currency appreciation strengthens borrower balance sheet
• Creates slack in lending capacity of local banks; creates slack in global
bank lending capacity; local and global banks drive credit boom
• Higher interest rate differential vis-à-vis the dollar amplifies boom
Cross-Border Banking and Global Liquidity
14
500
Dec 2008
450
Ireland
400
Spain
350
Turkey
300
Australia
250
South Korea
200
Chile
Mar 2003 =100
150
Brazil
100
South Africa
50
Dec.2011
Mar.2011
Jun.2010
Sep.2009
Dec.2008
Mar.2008
Jun.2007
Sep.2006
Dec.2005
Mar.2005
Jun.2004
Sep.2003
Dec.2002
Mar.2002
Jun.2001
Sep.2000
Dec.1999
Mar.1999
0
Figure 9. Cross-border claims (loans and deposits) of BIS reporting banks on counterparties listed on right
(Source: BIS locational banking statistics Table 7A)
Cross-Border Banking and Global Liquidity
15
3,000
2,500
2,000
Latvia
1,500
Lithuania
1,000
Estonia
500
Iceland
100
Dec.2011
Mar.2011
Jun.2010
Sep.2009
Dec.2008
Mar.2008
Jun.2007
Sep.2006
Dec.2005
Mar.2005
Jun.2004
Sep.2003
Dec.2002
Mar.2002
Jun.2001
Sep.2000
Dec.1999
Mar.1999
0
Figure 10. Cross-border claims (loans and deposits) of BIS reporting banks on counterparties listed on right
(Source: BIS locational banking statistics Table 7A)
Cross-Border Banking and Global Liquidity
16
Cross-border Liabilities by Counterparty (Developed Countries)
40.0
Trillion US dollars
Trillion US dollars
Categories of Cross-border Liabilities by Counterparty (All countries)
45.0
Non-bank to Non-bank
35.0
Non-bank to Bank
30.0
Bank to Non-bank
25.0
45.0
40.0
Non-bank to Non-bank
35.0
Non-bank to Bank
30.0
Bank to Non-bank
25.0
Bank to Bank
20.0
20.0
15.0
15.0
10.0
10.0
5.0
5.0
0.0
0.0
Bank to Bank
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
Figure 11. Cross-border liabilities by type of counterparty. Left panel shows cross-border debt liabilities
by pairwise classification of borrower and lender. “Bank to bank” refers to cross-border claims of banks on
other banks (BIS banking statistics table 7A minus 7B). “Bank to non-bank” refers to cross-border claims of
banks on non-banks (BIS table 7B). Claims of non-banks are from BIS international debt security statistics,
tables 11A and 11B). The right panel shows cross-border debt liabilities of developed countries according to
BIS classification.
Cross-Border Banking and Global Liquidity
17
Bank to Bank Liabilities as Percentage of Private Credit
Percent of Private Credit
Percent of GDP
Bank to Bank Liabilities as Percentage of GDP
40%
All
35%
Developed
30%
Developing
25%
20%
25%
All
Developed
20%
Developing
15%
10%
15%
10%
5%
5%
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
0%
1995
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
0%
Figure 12. Cross-border bank-to-bank liabilities. Left panel shows cross-border bank-to-bank debt
liabilities as percentage of GDP of the recipient economy. The right panel shows cross-border bank-to-bank
debt liabilities as percentage of total private credit in recipient economy. Cross-border bank-to-bank liabilities
are from the BIS banking statistics (table 7A minus 7B). GDP and private credit data are from the World
Bank.
Cross-Border Banking and Global Liquidity
18
Timeline for borrower
Exchange rate
Exchange rate
Loan
granted
Loan
repaid
θ0
θ1
1
Cross-Border Banking and Global Liquidity
19
Borrowers
Many potential borrowers indexed by j;
borrowing at rate r
purchase asset for 1 dollar by
Effort cost ej , distributed in the population according to H (.)
θt is exchange rate (increase in θt is appreciation of local currency). θ̄1 is
date 0 expected value of θ1
Dollar value of project at date 1 is
θ1V1 = exp µ θ̄1
s2
− + sWj
2
Wj is a standard normal, µ (·) is increasing function of θ̄1
(1)
Cross-Border Banking and Global Liquidity
20
Project
value
Density of
θ1V1
1+ r
1
Asset cost
(= loan amount)
0
0
default probability
t
1
Figure 13. The borrower defaults when θ1 V1 falls short of the notional debt 1 + r. The effect of a currency
appreciation is to shift the outcome density upward, lowering the default probability.
Cross-Border Banking and Global Liquidity
21
Borrower j with effort cost ej undertakes the project if
E (max {0, θ1V1 − (1 + r)}) − ej ≥ 0
(2)
Denote by e∗ (r) the threshold effort cost level where (2) holds with equality
when the loan rate is r.
Loan demand is
Cd (r) = H (e∗ (r))
• decreasing in borrowing rate r and
• increasing in expected appreciation of local currency θ̄1
(3)
Cross-Border Banking and Global Liquidity
22
Borrower defaults when θ1V1 < 1 + r. Probability of default viewed from
date 0 is
2
Prob (θ1V1 < 1 + r) = Prob Wj <
ln(1/(1+r))+µ− s2
−
s
= Φ (−dj )
where dj is distance to default:
dj =
− ln (1 + r) + µ θ̄1 −
s
Probability of default is falling in θ̄1
s2
2
Cross-Border Banking and Global Liquidity
23
Vasicek (2002):
Wj =
√
ρY +
1 − ρXj
Borrower j repays the loan when Zj ≥ 0, where Zj is the random variable:
Zj
√
ρY + 1 − ρXj
√
= −Φ−1 (ε) + ρY + 1 − ρXj
= dj +
Realized value of assets at date 1
w (Y ) ≡ (1 + r) C · Pr (Zj ≥ 0|Y )
√
= (1 + r) C · Pr
ρY + 1 − ρXj ≥ Φ−1 (ε) |Y
= (1 + r) C · Φ
Y
√
ρ−Φ−1(ε)
√
1−ρ
Cross-Border Banking and Global Liquidity
24
12
15
ρ = 0.3
ε = 0.2
8
density over realized assets
density over realized assets
10
ε = 0.1
6
4
ε = 0.2
2
0
12
ρ = 0.01
9
6
ρ = 0.1
3
ε = 0.3
0
0.2
ρ = 0.3
0.4
0.6
z
0.8
1
0
0
0.2
0.4
0.6
0.8
1
z
Figure 14. The two charts plot the densities over realized assets when C (1 + r) = 1. The left hand
charts plots the density over asset realizations of the bank when ρ = 0.1 and ε is varied from 0.1 to 0.3.
The right hand chart plots the asset realization density when ε = 0.2 and ρ varies from 0.01 to 0.3.
Cross-Border Banking and Global Liquidity
Mode 1: Increased leverage due to equity buyback
A
L
A
L
25
Mode 2: Increased leverage due to fall in asset value
A
A
Assets
Debt
Debt
A
Equity
Assets Equity
Assets
Debt
L
L
L
Equity
Equity
Assets
A
L
Equity
Mode 3: Increase borrowing to fund asset growth
Debt
Equity
Assets
Debt
Assets
Debt
Figure 15. Three modes of leveraging up: Mode 1 is through an equity buyback through a debt issue.
Mode 2 is through a dividend financed by asset sale. Mode 3 is through increased borrowing to fund new
assets. In each case the grey area indicates balance sheet component that is held fixed
Cross-Border Banking and Global Liquidity
26
BNP Paribas: annual change in assets, equity and debt
(1999 - 2010)
500
y = 1.0051x - 6.2
R2 = 0.9987
Change in equity and debt
(billion euros)
400
300
Debt
Change
200
100
Equity
Change
0
-100
-200
-200
-100
0
100
200
300
400
500
Asset change (billion euros)
Figure 16. BNP Paribas: annual change in assets, equity and debt (1999-2010) (Source: Bankscope)
Cross-Border Banking and Global Liquidity
27
Societe Generale: annual changes in assets, equity and debt
(1999 - 2010)
Annual change in equity and debt
(billion euros)
300
250
y = 0.996x - 3.15
R2 = 0.9985
200
150
Debt
change
100
50
Equity
change
0
-50
-100
-150
-200
-100
0
100
200
300
Annual asset change (billion euros)
Figure 17. Société Générale: annual change in assets, equity and debt (1999-2010) (Source: Bankscope)
Cross-Border Banking and Global Liquidity
28
Credit Supply by Banks
• Book equity is given
• Credit supply is
Equity × Leverage
So theory of leverage is theory of credit supply
• ⇒ Credit supply (hence, capital flows, interbank runs) depend on risk
conditions
Cross-Border Banking and Global Liquidity
29
Assets or Enterprise Value?
Enterprise value is defined as
Enterprise value = market capitalization + debt
• Enterprise value addresses how much a bank is worth
• Total assets address how much a bank lends
Here, we focus on total assets, as we are interested in cross-border lending
Cross-Border Banking and Global Liquidity
30
Determinants of Regional Bank Lending
Risk-neutral regional banks with fixed ER
Choice variable is C (equivalently, L or leverage)
Banks maximize expected value of book equity:
Equity value = Asset value − Debt value
=
Asset value − Notional debt + Option value of default
Contracting problem with moral hazard (Adrian and Shin (2014))
Leverage is constrained by creditors
Cross-Border Banking and Global Liquidity
31
Notation
Bank
E
1+ r
C
1+ f
L
Cross-Border Banking and Global Liquidity
32
Moral Hazard Problem
• Good portfolio: probability of default ε and correlation ρ > 0
• Bad portfolio: probability of default ε + k (k > 0) correlation ρ′ > ρ
(higher option value of limited liability)
Good portfolio realized value:
wG (Y ) = (1 + r) C · Pr
= (1 + r) C · Φ
√
ρY +
Y
1 − ρXj ≥ Φ−1 (ε) |Y
√
ρ−Φ−1(ε)
√
1−ρ
(4)
Cross-Border Banking and Global Liquidity
33
Normalized asset realization ŵG (Y ) ≡ wG (Y ) / (1 + r) C has c.d.f.
FG (z) = Pr (ŵG ≤ z)
−1
= Pr Y ≤ ŵG
(z)
−1
(z)
= Φ ŵG
= Φ
√
Φ−1(ε)+ 1−ρΦ−1(z)
√
ρ
(5)
Bad portfolio ŵB (Y ) ≡ wB (Y ) / (1 + r) C has c.d.f.
FB (z) = Φ
−1
Φ
√ ′ −1
(ε+k)+ 1−ρ Φ (z)
√ ′
ρ
(6)
Cross-Border Banking and Global Liquidity
34
ϕ is notional debt ratio of the bank:
ϕ = (1 + f ) L/ (1 + r) C
(7)
• ϕ is the default point of the bank as a proportion of its notional assets
• strike price of the embedded put option arising from limited liability
Risk-neutral bank chooses ϕ to maximize:
E (ŵ) − [ϕ − π (ϕ)]
(8)
subject to incentive compatibility constraint
EG (ŵ) − [ϕ − π G (ϕ)] ≥ EB (ŵ) − [ϕ − π B (ϕ)]
(9)
Cross-Border Banking and Global Liquidity
35
or
∆π (ϕ) ≤ k
(10)
Lemma 1. There is a unique ϕ that solves ∆π (ϕ) = k.
1
1
EB (wˆ ) = 1 − ε − k
FB
FG
FG
FB
∆π (ϕ )
0
0
ϕ
0
1
0
1
Cross-Border Banking and Global Liquidity
36
Digression on Options and Outcome Distribution
p(z −3)
p(z −3)
p(z −2)
p(z −3)
p(z −2)
p(z −1)
z −2
z −1
L z −3
z
Outcome space is {0, 1, 2, · · · , Z}.
p (s) is price of Arrow-Debreu contingent claim at outcome s
Cross-Border Banking and Global Liquidity
37
Put option with strike price z has price
p (z − 1) + 2p (z − 2) + 3p (z − 3) + · · · + zp (0)
First difference in option prices is c.d.f.
π (z) − π (z − 1) = p (z − 1) + 2p (z − 2) + 3p (z − 3) + · · · + zp (0)
−p (z − 2) − 2p (z − 3) − · · · − (z − 1) p (0)
= p (z − 1) + p (z − 2) + p (z − 3) + · · · + p (0)
Second difference in option prices is (state price) density
In general, state price density is second derivative of option price w.r.t.
strike price (Breeden and Litzenberger (Journal of Finance, 1978)).
Cross-Border Banking and Global Liquidity
38
ϕ
Given risk-neutrality, ∆π (ϕ) = 0 [FB (s) − FG (s)] ds. Since FG (z) cuts
FB (z) once from below, ∆π (ϕ) is single-peaked. In particular,
1
lim ∆π (ϕ) =
ϕ→1
[FB (s) − FG (s)] ds
0
1
1
[1 − FG (s)] ds −
=
0
1
=
0
0
[1 − FB (s)] ds
1
sFG (s) ds −
sFB (s) ds = k
(11)
0
so that ∆π (ϕ) approaches k from above as ϕ → 1. Since ϕ < 1 for any
bank with positive notional equity, we have a unique solution to ∆π (ϕ) = k
Cross-Border Banking and Global Liquidity
39
Default Probability of Regional Banks
Under incentive compatibility constraint, probability of default by the bank
is
α = FG (ϕ)
so that
α=Φ
Φ
−1
√
(ε) + 1 − ρΦ−1 (ϕ)
√
ρ
(12)
Since ϕ is uniquely solved by Lemma 1, and ε and ρ are parameters of the
contracting problem, α is also uniquely defined.
From the point of view of global banks, the regional banks are borrowers
with default probability α, and same apparatus can be applied once more
Cross-Border Banking and Global Liquidity
40
Double-decker model of Global Liquidity
Global Bank
Regional Bank
ER
1+ r
C
EG
1+ f
L
L
Figure 18. Regional and global bank balance sheets
1+ i
M
Cross-Border Banking and Global Liquidity
41
Borrowers
in A
Banks
in A
Borrowers
in B
Banks
in B
Global
Banks
Wholesale
Funding
Market
Banks
in C
Borrowers
in C
Figure 19. Topography of global liquidity
Cross-Border Banking and Global Liquidity
42
Borrowers
in A
Banks
in A
Borrowers
in B
Banks
in B
Global
Banks
Wholesale
Funding
Market
Banks
in C
Borrowers
in C
Figure 20. Topography of global liquidity
Cross-Border Banking and Global Liquidity
43
Regional
bank in k
Diversified loan portfolio
across regional banks
Diversified loan portfolio from region k
j
Borrower j
in region k
Borrowers
Regions
k
Figure 21. Global and regional banks
Global
bank
Cross-Border Banking and Global Liquidity
44
Global, Regional and Idiosyncratic Risk Factors
−1
Zkj ≡ −Φ
Yk =
√
(ε) + ρYk +
βG +
1 − ρXkj
1 − βRk
(13)
(14)
Global bank has a fully-diversified portfolio across regions. Regional bank
k defaults when ŵG (Yk ) < ϕ, or
Yk < ŵ
−1
(ϕ) =
√
Φ−1(ε)+ 1−ρΦ−1(ϕ)
√
ρ
= Φ−1 (α)
(15)
Equivalently, regional bank k defaults when ξ k < 0, where ξ k is the random
Cross-Border Banking and Global Liquidity
45
variable:
ξ k ≡ −Φ−1 (α) + Yk
= −Φ−1 (α) +
βG +
1 − βRk
(16)
Global bank asset realization is deterministic function of global risk factor
G only
w (G) = (1 + f ) L · Pr (ξ k ≥ 0|G)
= (1 + f ) L · Pr Rk ≥
= (1 + f ) L · Φ
√
Φ−1 (α)−G β
√
1−β
√
G β−Φ−1 (α)
√
1−β
G
(17)
Cross-Border Banking and Global Liquidity
46
Normalized asset realization is ŵ (G) = w (G) / (1 + f ) L with c.d.f.
F (z) = Φ ŵ−1 (z)
√
1 − βΦ−1 (z) + Φ−1 (α)
√
= Φ
β
(18)
Global bank contracting problem.
• Good portfolio has loans with default probability α but β = 0
• Bad portfolio probability of default α + h, with h > 0, and β ′ > 0.
wB (G) = (1 + f ) L · Φ
√
G
β ′ −Φ−1 (α+h)
√
1−β ′
(19)
Cross-Border Banking and Global Liquidity
47
Normalized ŵB (G) ≡ wB (G) / (1 + f ) L with c.d.f.
FB (z) = Φ
√
Φ−1 (α+h)+ 1−βΦ−1 (z)
√
β
(20)
Outcome distribution of the good portfolio is
FG (z) =
0
1
if z < 1 − α
if z ≥ 1 − α
(21)
Notional debt ratio ψ = (1 + i) M/ (1 + f ) L.
Bank maximizes
E (ŵ) − [ψ − π (ψ)]
(22)
Cross-Border Banking and Global Liquidity
48
subject to incentive compatibility constraint
EG (ŵ) − [ψ − π G (ψ)] ≥ EB (ŵ) − [ψ − π B (ψ)]
(23)
∆π (ψ) ≤ h
(24)
or
Lemma 2. There is a unique ψ that solves ∆π (ψ) = h, where ψ < 1 − α.
(debt issued by global bank is risk-free)
Cross-Border Banking and Global Liquidity
49
Closed Form Solution
Market clearing for L
ER
EG
=
1+f 1
1+f
·
−
1
1
−
1+r ϕ
1+i ψ
Private credit
C=
EG + ER
1 − 1+r
1+i ϕψ
Aggregate bank capital (regional + global)
Total private
=
credit
regional
global
1 − spread ×
×
leverage
leverage
Cross-Border Banking and Global Liquidity
50
Equilibrium stock of cross-border lending L
L=
EG + ER · 1+r
1+i ϕψ
1 − 1+r
1+i ϕψ
Global and weighted regional bank capital
Total cross=
border lending
regional
global
1 − spread ×
×
leverage
leverage
Cross-Border Banking and Global Liquidity
51
r
1+ f
ϕ −1
C (r )
ε / (1 − ε )
0
E
1−
Credit
Supply
ϕ
(1 − ε )(1 + f )
Figure 22. Credit supply curve of local bank. Equilibrium in loan market is obtained by crossing supply and
demand for loans. Equilibrium loan amount is increasing in expected appreciation θ̄ 1/θ 0. But lending rate
r could go either way.
Cross-Border Banking and Global Liquidity
52
θ0
Net dollar
demand
in local
spot market
− C (θ0 , θ1 )
D (θ0 , θ1 )
θ1
θ0
Corporate borrowers’
dollar demand on
date 0 spot market
− Q0
0
Others’ dollar demand
on date 0 spot market
Q0
Figure 23. Model is closed by determining date 0 exchange rate θ0 . Fix θ̄ 1. The banks supply L dollars in
spot market, while non-banks demand D dollars in spot market. θ0 clears the spot market at date 0.
Cross-Border Banking and Global Liquidity
53
Comparative Statics
Global factors EG and ψ
∆L ≃
∂L
∂L
∆EG +
∆ψ
∂EG
∂ψ
=
1
∆EG +
1 − ϕψ
(1 − ϕψ) ERϕ − (EG + ERϕψ) (−ϕ)
=
ϕ
1
∆EG + C
∆ψ
1 − ϕψ
1 − ϕψ
2
(1 − ϕψ)
∆ψ
Banking sector capital flows (i) increase with ∆EG (ii) increase with bank
leverage (iii) increase in change in bank leverage
Cross-Border Banking and Global Liquidity
54
Proposition 1. The model has a unique solution.
regions is
EG + ER
C=
1 − 1+r
1+i ϕψ
Total credit in the
(25)
and total cross-border lending is
L=
EG + ER · 1+r
1+i ϕψ
1 − 1+r
1+i ϕψ
(26)
where i is the risk-free US dollar interest rate.
(Geanakoplos (2009) and Fostel and Geanakoplos (2012): default does not
happen precisely because the contract addresses the possibility of default)
Cross-Border Banking and Global Liquidity
55
B (ε , ϕ ,ψ ) = 0
1
ψ
A
B (ε ′, ϕ ,ψ ) = 0
h
0
0
ϕ
1
Figure 24. Risk capacity of global banking system. This figure shows the impact of increased default
risk from ε to ε′ on the leverage of global and regional banks.
Cross-Border Banking and Global Liquidity
56
Corollary 1. US dollar appreciation is associated with deleveraging
somewhere in the global banking system
Corollary 2. Greater fundamental risk is associated with deleveraging
somewhere in the global banking system
Corollary 3. Cross-border lending is increasing in global banks’ leverage,
growth in global banks’ leverage, and growth in global banks’ equity.
Corollary 4. Cross-border lending is increasing in local banks’ leverage,
growth in local banks’ leverage, and growth of local banks’ equity.
Corollary 5. Cross-border lending is increasing in the spread between local
lending rate r and money market rate i.
Cross-Border Banking and Global Liquidity
57
Empirical Counterparts
35.0
Leverage ( =(total liabilities + equity)/equity)
2007Q2
30.0
25.0
20.0
15.0
2009Q1
10.0
2012Q1
2011Q1
2010Q1
2009Q1
2008Q1
2007Q1
2006Q1
2005Q1
2004Q1
2003Q1
2002Q1
2001Q1
2000Q1
1999Q1
1998Q1
1997Q1
1996Q1
1995Q1
1994Q1
1993Q1
1992Q1
1991Q1
1990Q1
5.0
Figure 25. Leverage of US Securities broker dealer sector (Source: Federal Reserve Flow of Funds)
Cross-Border Banking and Global Liquidity
58
500
Dec 2008
450
Ireland
400
Spain
350
Turkey
300
Australia
250
South Korea
200
Chile
Mar 2003 =100
150
Brazil
100
South Africa
50
Dec.2011
Mar.2011
Jun.2010
Sep.2009
Dec.2008
Mar.2008
Jun.2007
Sep.2006
Dec.2005
Mar.2005
Jun.2004
Sep.2003
Dec.2002
Mar.2002
Jun.2001
Sep.2000
Dec.1999
Mar.1999
0
Figure 26. Cross-border claims (loans and deposits) of BIS reporting banks on counterparties listed on right
(Source: BIS locational banking statistics Table 7A)
Cross-Border Banking and Global Liquidity
59
Sample
Sample of 46 countries with largest foreign bank penetration (Claessens,
van Horen, Gurcanlar and Mercado (2008))
Argentina, Australia, Austria, Belgium, Brazil, Bulgaria, Canada, Chile,
Cyprus, Czech Republic, Denmark, Egypt, Estonia, Finland, France,
Germany, Greece, Hungary, Iceland, Indonesia, Ireland, Israel, Italy, Japan,
Latvia, Lithuania, Malaysia, Malta, Mexico, Netherlands, Norway, Poland,
Portugal, Romania, Russia, Slovakia, Slovenia, South Korea, Spain, Sweden,
Switzerland, Thailand, Turkey, Ukraine, United Kingdom and Uruguay.
Cross-Border Banking and Global Liquidity
60
Summary Statistics
Variable
Dependent Variable
∆Loan
Global Variables
∆Interoffice
VIX
BD Leverage
∆Equity
Local Variables
∆RER
∆M2
GDP growth
Debt to GDP
Inflation
Stock volatility
Bank ROA
Frequency
Obs
Mean
Std. Dev.
Min
Max
Quarter
2944
0.025
0.090
-0.172
0.240
Quarter
Quarter
Quarter
Annual
64
64
64
14
0.087
3.045
0.203
0.131
0.515
0.347
0.046
0.219
-1.362
2.433
0.124
-0.266
1.908
3.787
0.304
0.697
Quarter
Annual
Annual
Annual
Annual
Annual
Annual
2942
532
532
532
532
465
465
-0.002
0.135
0.080
0.517
0.046
3.213
0.007
0.068
0.152
0.078
0.284
0.054
0.425
0.011
-0.510
-0.253
-0.208
0.067
-0.004
2.195
-0.041
1.030
1.413
0.607
1.272
0.365
4.705
0.026
Cross-Border Banking and Global Liquidity
Global Leverage
Local Leverage
1
0.0043***
[0.000]
-0.2191
[0.160]
Global Equity Growth
61
2
0.0346***
[0.002]
1.5900***
[0.000]
Local Equity Growth
Global Leverage Growth
Local Leverage Growth
∆RER
∆M2
∆GDP
∆Debt/GDP
Inflation
∆Interest Spread
Constant
Observations
R-squared
# Countries
3
-0.2204***
[0.000]
0.0837**
[0.015]
0.1464*
[0.067]
-0.0988***
[0.005]
-0.4083***
[0.002]
0.0212
[0.527]
1,872
0.086
46
-0.1841***
[0.002]
0.1014***
[0.001]
0.1457*
[0.060]
-0.0695***
[0.007]
-0.3117**
[0.016]
0.0368***
[0.006]
2,192
0.072
46
0.1746***
[0.000]
0.016
[0.526]
-0.2100***
[0.000]
0.1005**
[0.015]
0.3690***
[0.000]
-0.1089***
[0.005]
-0.4648***
[0.005]
0.0712***
[0.001]
1,676
0.076
46
4
0.0038***
[0.000]
-0.083
[0.545]
-0.0224
[0.136]
1.9706***
[0.000]
0.1203***
[0.002]
0.0265
[0.294]
-0.1858***
[0.000]
0.0783**
[0.014]
0.0347
[0.687]
-0.0471
[0.215]
-0.1458
[0.378]
-0.024
[0.530]
1,672
0.102
46
5
0.0038***
[0.001]
0.0296***
[0.000]
2,459
0.001
45
6
0.0033***
[0.006]
-0.1488
[0.372]
-0.0234
[0.173]
2.2129***
[0.001]
0.1518***
[0.002]
0.034
[0.293]
-0.1320**
[0.022]
0.0879**
[0.015]
-0.0042
[0.965]
-0.0829*
[0.056]
-0.2115
[0.243]
0.0233
[0.919]
0.0188
[0.665]
1,266
0.090
41
Cross-Border Banking and Global Liquidity
63
Leverage and VIX
35.0
BD leverage
30.0
25.0
20.0
15.0
10.0
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
3.6
3.8
4.0
log_vix(-1)
Figure 27. Scatter chart of broker-dealer leverage and lagged log VIX
Cross-Border Banking and Global Liquidity
VIX(-1)
64
1
2
-5.797***
-3.100***
[0.000]
[0.008]
Post-crisis dummy
-5.865***
[0.000]
Constant
Observations
2
R
2
Adjusted R
37.907***
31.188***
[0.000]
[0.000]
64
64
0.20
0.471
0.187
0.453
Cross-Border Banking and Global Liquidity
VIX
0.25
70
0.20
60
0.15
50
0.10
0.05
40
0.00
30
-0.05
VIX Index
(average over quarter)
Banking Sector Capital Flows (year on year growth of
external claims of BIS-reporting banks)
Banking sector capital flows
65
20
-0.10
10
-0.15
Sep-11
Dec-10
Mar-10
Jun-09
Sep-08
Dec-07
Mar-07
Jun-06
Sep-05
Dec-04
Mar-04
Jun-03
Sep-02
Dec-01
Mar-01
Jun-00
Sep-99
Dec-98
Mar-98
Jun-97
Sep-96
-0.20
0
Figure 28. This figure plots cross-border banking sector capital flows as year-on-year growth in external
claims of BIS-reporting banks (Table 7A). The VIX series is the quarterly average of CBOE VIX index.
Cross-Border Banking and Global Liquidity
Global Leverage
1
0.0099***
[0.000]
Global Leverage growth
Global Equity growth
Local Leverage
-0.1806
[0.719]
Local Leverage growth
Local Equity growth
∆RER
∆Interest Spread
Loans growth
q−1
-0.2041***
[0.001]
-0.1273***
[0.002]
66
2
0.0052**
[0.048]
0.0314
[0.558]
0.0769**
[0.048]
-0.7089
[0.249]
0.1581**
[0.024]
1.8395
[0.265]
-0.2360***
[0.005]
0.4618
[0.683]
-0.0903
[0.119]
Mk Global Leverage
3
0.0040***
[0.000]
4
5
0.0039***
[0.000]
6
0.0073***
[0.000]
7
0.0031***
[0.001]
-0.2169
[0.147]
-0.1419
[0.381]
-0.2335
[0.126]
-0.1995
[0.275]
-0.1823
[0.131]
-0.2180***
[0.000]
-0.1960***
[0.000]
-0.2193***
[0.000]
-0.2515***
[0.000]
-0.1977***
[0.000]
Y
1,356
0.057
45
-0.0527***
[0.000]
Y
1,872
0.102
46
0.0021
[0.186]
VIX
-0.0514***
[0.000]
Interoffice Growth
0.0139***
[0.009]
Domestic Crisis
Additional controls
Observations
R-squared
# Countries
Y
1,872
Y
1,266
46
41
Y
1,872
0.088
46
Y
1,872
0.085
46
Y
1,872
0.09
46
Cross-Border Banking and Global Liquidity
Robustness Analysis
• Crisis period dummy
— Effect is larger during crisis period
— But also at work during non-crisis periods
• Developing country dummy
— No difference between developing and developed economies
— Europe effect?
68