Banks’Risk Exposures

Banks’Risk Exposures
Juliane Begenau
Stanford
Monika Piazzesi
Stanford & NBER
Martin Schneider
Stanford & NBER
Cambridge Oct 11, 2013
Begenau, Piazzesi, Schneider ()
Cambridge Oct 11, 2013
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Modern Bank Balance Sheet, JP Morgan Chase 2011
Total assets/liabilities: $2.3 Trillion
Assets
Cash
Securities
Loans
Fed funds + Repos
Trading assets
Other assets
Liabilities
6%
16%
31%
17%
20%
10%
Equity
Deposits
Other borrowed money
Fed funds + Repos
Trading liabilities
Other liabilities
8%
50%
15%
10%
6%
11%
Derivatives: $60 Trillion Notionals of Swaps
Begenau, Piazzesi, Schneider ()
Cambridge Oct 11, 2013
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Portfolio approach to measuring risk exposure
Many positions: how to compress & compare?
Basic idea: represent as simple portfolios
I statistical evidence: cross section of bonds driven by “few shocks”
! can replicate any …xed income position by portfolio of “few bonds”
Portfolios = additive measure of risk & exposure, comparable
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across positions (do derivative holdings hedge other business?)
across institutions (systemic risk?)
to simple portfolios implied by economic models
Begenau, Piazzesi, Schneider ()
Cambridge Oct 11, 2013
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Ingredients
Valuation model
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parsimonious representation of cross section of bonds
allow for interest rate and credit risk
can depend on calendar time; cross sectional …t is key
this paper: one shock = shift in level of BB bond yield
Bank data requirements
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maturity & credit risk by position ! payment streams
detailed data on loans & securities ! apply valuation model directly
coarser data (e.g. derivatives) ! estimate positions …rst
Results for large US banks
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traditional business = long bonds …nanced by short debt
interest rate derivatives often do not hedge traditional business
similar exposures to aggregate risk across banks
Begenau, Piazzesi, Schneider ()
Cambridge Oct 11, 2013
4 / 32
Related literature
Bank regulation (Basel II):
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separately consider credit & market risk
credit risk: default probabilities from credit ratings
or internal statistical models
capital requirements for di¤erent positions
look at positions one by one
Measures of exposure
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regress stock returns on risk factor, e.g. interest rates
Flannery-James 84, Venkatachalam 96, Hirtle 97,
English, van den Heuvel, Zakrajsek 12, Landier, Sraer & Thesmar 13...
stress tests: Brunnermeier-Gorton-Krishnamurthy 12, Du¢ e 12
Measures of tail risk (VaR etc.)
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Acharya-Pederson-Philippon-Richardson 10, Kelly-Lustig-van
Nieuwerburgh 11
Bank position data
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derivatives: Gorton-Rosen 95, Stulz et al. 08, Hirtle 08
crisis: Adrian & Shin 08, Shin 11, He & Krishnamurthy 11
Begenau, Piazzesi, Schneider ()
Cambridge Oct 11, 2013
5 / 32
Outline
Replication with spanning securities
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bond/debt positions t simple portfolios in a few bonds
One factor model of bond values
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…t to bonds with & without credit risk
Replication of loans, securities & deposits
Interest rate swaps
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de…nitions and data
estimation of replicating portfolio
Example results for large US banks
Begenau, Piazzesi, Schneider ()
Cambridge Oct 11, 2013
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Replication with spanning securities
Factor structure with normal shocks
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consider payo¤ stream with value π (ft , t )
factors ft = µ (ft , t ) + σt εt , εt v N (0, IK K )
Change in value of payo¤ stream π between t and t + 1
π ( ft + 1 , t + 1 )
π (ft , t ) t atπ + btπ εt +1
form replicating portfolio from K + 1 spanning securities
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always include θ 1t one period bonds ( = cash) with price e it
use θ̂ t other securities, e.g. longer bonds
choose θ 1t , θ̂ t to match change in value π for all εt +1 :
0
θ 1t θ̂ t
e
it i
t
ât
0
b̂t
1
ε t +1
=
atπ btπ
1
ε t +1
.
no arbitrage: value of replicating portfolio at t = value π (ft , t )
Begenau, Piazzesi, Schneider ()
Cambridge Oct 11, 2013
7 / 32
Implementation with one factor
single factor ft = credit risky short rate (BB rating)
to relate value of other payo¤ streams π to f , estimate joint
distribution of risky & riskless yields
pricing kernel
Mt +1 = exp ( δ0
δ1 ft
λt εt +1 + Jensen term)
= l0 + l1 ft
λt
riskless zero coupon bond prices as functions of ft
h
i
(n )
(n 1 )
(0 )
Pt
= Et Mt +1 Pt +1 , Pt = 1
(n )
Pt
= exp (An + Bn ft )
…nd Bn < 0 (high interest rates, low prices)
also λt < 0 so Et [excess return on n period bond] = Bn
Begenau, Piazzesi, Schneider ()
1 σλt
>0
Cambridge Oct 11, 2013
8 / 32
Credit risk
risky bonds default; recovery value proportional to price
payo¤ per dollar invested
∆t +1 = exp
λ̃t
d0
d1 ft
λ̃t
λt εt +1 + Jensen term
= l̃0 + l̃1 ft
risky zero coupon prices
(n )
P̃t
(n )
P̃t
h
(n
= Et Mt +1 ∆t +1 P̃t
= exp Ãn + B̃n ft
1)
i
,
(0 )
P̃t
=1
spreads
ı̃t
it = d0 + d1 ft
estimation …nds
I d > 0 spreads high when credit risk is high
1
I B̃n < 0 (high interest rates or default risk, low prices)
I λ̃t > λt low payo¤ when credit risk ε
t +1 high
I Et [excess return] = B̃
λ̃t λt λt > 0
n 1σ
Begenau, Piazzesi, Schneider ()
Cambridge Oct 11, 2013
9 / 32
Replication with one factor
Change in bond value π t = π (ft , t )
π t +1
Cash
πt
πt
µt
|{z}
expected return
µ t = it ,
+ σ t ε t +1
|{z}
volatility
σt = 0
Represent other bond π̃ t = π̃ (ft , t ) as simple portfolio
et εt +1 ) = ω t π t (µt + σt εt +1 ) + Kt it
et + σ
π̃ t (µ
π = value of 5-year riskless bond
Simple portfolios = holdings ω t of 5-year riskless bond & cash Kt
Portfolio weight on 5-year bond increasing in maturity, risk of π̃
2 year Treasury: 40% 5-year bond, 60% cash
10 year Treasury: 140% 5-year bond, 40% cash
10 year BBB corporate bond: 180% 5-year bond, 80% cash
Begenau, Piazzesi, Schneider ()
Cambridge Oct 11, 2013
10 / 32
Outline
Basic replication argument
I
bond/debt positions t simple portfolios in a few bonds
One factor model of bond values
I
…t to bonds with & without credit risk
Replication of loans, securities, deposits
Interest rate swaps
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de…nitions and data
estimation of replicating portfolio
Example results for large US banks
Begenau, Piazzesi, Schneider ()
Cambridge Oct 11, 2013
11 / 32
From regulatory data to simple portfolios
Quarterly Call report data on bank balance sheets
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loans: book value, maturity, credit quality
securities: fair values, maturity, credit quality
cash, deposits & fed funds
Loans
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start from data on book value & interest rates
derive stream of promises = bundle of (risky) zero coupon bonds
replicate with simple portfolio as above
Securities
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observe fair values by maturity & issuer (private, government)
use public, private bond prices to compute simple portfolio
bonds held for trading: rough assumptions on maturity
Deposits & money market funds
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mostly short term ( = cash)
Represent as simple portfolios in 5-year bond & cash
Begenau, Piazzesi, Schneider ()
Cambridge Oct 11, 2013
12 / 32
JP Morgan Chase: simple portfolio holdings
2
1.5
cash, old FI
5 year, old FI
Trillions $US
1
0.5
0
-0.5
-1
-1.5
96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11
Begenau, Piazzesi, Schneider ()
Cambridge Oct 11, 2013
13 / 32
Outline
Basic replication argument
I
bond/debt positions t simple portfolios in a few bonds
One factor model of bond values
I
…t to bonds with & without credit risk
Replication of loans, securities & deposits
Interest rate swaps
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de…nitions and data
estimation of replicating portfolio
Example results for large US banks
Begenau, Piazzesi, Schneider ()
Cambridge Oct 11, 2013
14 / 32
Notionals of Interest Rate Derivatives of US Banks
160
140
Trillions $US
120
100
80
60
40
all contracts
swaps
20
1995
Begenau, Piazzesi, Schneider ()
2000
2005
2010
Cambridge Oct 11, 2013
15 / 32
Swap payo¤s
Counterparties swap …xed vs ‡oating payments ∝ notional value N
Payments, Example: 1-Year Swap, Notional = $1
0.5
Fixed
s
s
s
s
0
R(1,2)
-0.5
R(0,1)
Floating
0
1
R(2,3)
R(3,4)
2
3
time (in quarters)
4
5
Direction of position: pay-…xed swap or pay-‡oating swap
“…xed leg” := …xed payments + N at maturity; value falls w/ rates
"‡oating leg": = ‡oating payments + N at maturity; value = N
Begenau, Piazzesi, Schneider ()
Cambridge Oct 11, 2013
16 / 32
Valuation of swaps
(m )
Discount …xed leg payo¤s w/ bond price Pt
(m )
value of …xed leg = N s Ct
(m )
, annuity price Ct
(m )
+ Pt
Direction: d = 1 for pay …xed, 1 for pay ‡oating
Fair value of individual swap position (d, m, s )
N d
1
(m )
s Ct
(m )
+ Pt
=: N d Ft (s, m)
Inception date: swap rate set s.t. Ft (s, m ) = 0
After inception date
I pay …xed swap gains , rates increase
I pay ‡oating swap gains , rates fall
Fair value of bank’s swap book
FVt =
∑
Ntd ,m,s dt Ft (s, m )
d ,m,s
Begenau, Piazzesi, Schneider ()
Cambridge Oct 11, 2013
17 / 32
Data & institutional detail
Call report derivatives data
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notionals
positive & negative fair values (marked to market)
"for trading" vs "not for trading"
maturity buckets
Intermediation
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large interdealer positions
dealers incorporate bid-ask spread into swap rates
data: bid-ask spreads (Bloomberg),
net credit exposure (recent call reports)
subtract rents from intermediation from fair values,
derive net notionals from trading on own account
Unknown: directions of trade, locked in swap rates
Begenau, Piazzesi, Schneider ()
Cambridge Oct 11, 2013
18 / 32
Concentrated Holdings of Interest Rate Derivatives
160
140
for trading
not for trading
top 3 dealers
Trillions $US
120
100
80
60
40
20
1995
Begenau, Piazzesi, Schneider ()
2000
2005
2010
Cambridge Oct 11, 2013
19 / 32
Data & institutional detail
Call report derivatives data
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notionals
positive & negative fair values (marked to market)
"for trading" vs "not for trading"
maturity buckets
Intermediation
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large interdealer positions
dealers incorporate bid-ask spread into swap rates
data: bid-ask spreads (Bloomberg),
net credit exposure (recent call reports)
subtract rents from intermediation from fair values,
derive net notionals from trading on own account
Unknown: directions of trade, locked in swap rates
Begenau, Piazzesi, Schneider ()
Cambridge Oct 11, 2013
20 / 32
Gains from trade on own account
Observation equation for "multiple" = fair value per dollar notional:
µt = dt Ft (s̄t , m̄t ) + εt
Data
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fair values (exclude intermediation rents)
net notionals
m̄t = average maturity
bond prices contained in Ft
Estimation
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prior over unknown sequence (dt , s̄t )
measurement error ε N 0, σ2ε
Begenau, Piazzesi, Schneider ()
Cambridge Oct 11, 2013
21 / 32
Identi…cation
Observation equation for fair value per dollar notional:
µt = dt Ft (s̄t , m̄t ) + εt
For each direction dt , can …nd swap rate to exactly match µt
For example, positive gains µt > 0 require
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pay …xed dt > 0 & low locked-in rate s t than current rate st
pay ‡oating dt < 0 & high locked-in rate s̄t than current rate st
Which is more plausible? Look at swap rate history!
Begenau, Piazzesi, Schneider ()
Cambridge Oct 11, 2013
22 / 32
Estimation details
Fix var (εt ) = var (µt ) /10
Compare two priors over sequence (dt , s̄t )
1. Simple date-by-date approach
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Pr (dt = 1) = 12
prior over swap rate = empirical distribution over last 10 years
Begenau, Piazzesi, Schneider ()
Cambridge Oct 11, 2013
23 / 32
JP Morgan Chase: swap position
multiple µ (%)
notionals
t
4
$ trillions
60
2
40
0
20
-2
0
1995
2000
2005
2010
1995
2000
2005
2010
avg maturity swap rate (% p.a.)
6
4
2
2000
Begenau, Piazzesi, Schneider ()
2005
2010
Cambridge Oct 11, 2013
24 / 32
JP Morgan Chase: swap position
multiple µ (%)
notionals
t
4
$ trillions
60
2
40
0
20
-2
0
1995
2000
2005
2010
1995
2000
2005
2010
posterior Pr(pay fixed) avg maturity swap rate (% p.a.)
1
7
6
5
0.5
4
3
2
0
1995
1
2000
Begenau, Piazzesi, Schneider ()
2005
2010
curr.
fix
float
2000
2005
2010
Cambridge Oct 11, 2013
25 / 32
JPMorgan Chase: swap position
multiple µ (%)
$ trillions
notionals
t
4
60
2
40
0
20
data
es tim ate
-2
0
1995
2000
2005
2010
posterior Pr(pay fixed)
1
1995
2000
2005
2010
avg maturity swap rate (% p.a.)
7
6
5
0.5
4
3
2
0
1995
1
2000
Begenau, Piazzesi, Schneider ()
2005
2010
curr.
fix
float
2000
2005
2010
Cambridge Oct 11, 2013
26 / 32
Estimation details
Fix var (εt ) = var (µt ) /10
Compare two priors over sequence (dt , s̄t )
1. Simple date-by-date approach
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Pr (dt = 1) = 12
prior over swap rate = empirical distribution over last 10 years
2. “Dynamic trading prior”
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symmetric 2 state Markov chain for dt with prob of ‡ipping φ = .1
draw s0 from empirical distribution
update swap rate conditional on evolution of dt and notionals
a. increase exposure, same direction
adjust swap rate proportionally to share of new swaps
b. decrease exposure, same direction
swap rate unchanged
c. switch direction
o¤set existing swaps & initial new position at current rate
Begenau, Piazzesi, Schneider ()
Cambridge Oct 11, 2013
27 / 32
JPMorgan Chase: swap position
multiple µ (%)
notionals
t
$ trillions
6
60
4
40
2
0
20
data
es tim ate
-2
0
1995
2000
2005
2010
1995
2000
2005
2010
posterior Pr(pay fixed) avg maturity swap rate (% p.a.)
1
7
6
5
0.5
4
3
2
0
1995
1
2000
Begenau, Piazzesi, Schneider ()
2005
2010
curr.
fix
float
2000
2005
2010
Cambridge Oct 11, 2013
28 / 32
JP Morgan Chase: replicating portfolios
2
1.5
cash, old FI
5 year, old FI
Trillions $US
1
0.5
0
-0.5
-1
-1.5
96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11
Begenau, Piazzesi, Schneider ()
Cambridge Oct 11, 2013
29 / 32
JP Morgan Chase: replicating portfolios
6
Trillions $US
4
cash, old FI
5 year, old FI
cash, deriv
5 year, deriv
2
0
-2
-4
96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11
Begenau, Piazzesi, Schneider ()
Cambridge Oct 11, 2013
30 / 32
5
cash
5 year
0
-5
1995
2000
WELLS FARGO & COMPANY
Trillions $US
Trillions $US
JPMORGAN CHASE & CO.
2005
2010
1
0
-1
1995
4
2
0
-2
-4
1995
2005
2010
CITIGROUP INC.
Trillions $US
Trillions $US
BANK OF AMERICA CORPORATION
2000
2
1
0
-1
-2
2000
Begenau, Piazzesi, Schneider ()
2005
2010
2000
2005
2010
Cambridge Oct 11, 2013
31 / 32
Summary
Portfolio methodology to both measure and represent
exposures in bank positions
Results for top dealer banks
Derivatives often increase exposure to interest rate risk.
Possible models of banks
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risk averse agents who use derivatives to insure (no!)
agents who insure others
(bond funds? foreigners? those who don’t expect bailouts?)
Next step: models with heterogeneous institutions,
informed by position data represented as portfolios...
Begenau, Piazzesi, Schneider ()
Cambridge Oct 11, 2013
32 / 32