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Banks’Risk Exposures
Juliane Begenau Monika Piazzesi Martin SchneiderStanford Stanford & NBER Stanford & NBER
Cambridge Oct 11, 2013
Begenau, Piazzesi, Schneider () Cambridge Oct 11, 2013 1 / 32
Modern Bank Balance Sheet, JP Morgan Chase 2011
Total assets/liabilities: $2.3 Trillion
Assets Liabilities
Cash 6% Equity 8%Securities 16% Deposits 50%Loans 31% Other borrowed money 15%Fed funds + Repos 17% Fed funds + Repos 10%Trading assets 20% Trading liabilities 6%Other assets 10% Other liabilities 11%
Derivatives: $60 Trillion Notionals of Swaps
Begenau, Piazzesi, Schneider () Cambridge Oct 11, 2013 2 / 32
Portfolio approach to measuring risk exposure
Many positions: how to compress & compare?
Basic idea: represent as simple portfoliosI statistical evidence: cross section of bonds driven by “few shocks”→ can replicate any fixed income position by portfolio of “few bonds”
Portfolios = additive measure of risk & exposure, comparableI across positions (do derivative holdings hedge other business?)I across institutions (systemic risk?)I to simple portfolios implied by economic models
Begenau, Piazzesi, Schneider () Cambridge Oct 11, 2013 3 / 32
Ingredients
Valuation modelI parsimonious representation of cross section of bondsI allow for interest rate and credit riskI can depend on calendar time; cross sectional fit is keyI this paper: one shock = shift in level of BB bond yield
Bank data requirementsI maturity & credit risk by position → payment streamsI detailed data on loans & securities → apply valuation model directlyI coarser data (e.g. derivatives) → estimate positions first
Results for large US banksI traditional business = long bonds financed by short debtI interest rate derivatives often do not hedge traditional businessI similar exposures to aggregate risk across banks
Begenau, Piazzesi, Schneider () Cambridge Oct 11, 2013 4 / 32
Related literatureBank regulation (Basel II):
I separately consider credit & market riskI credit risk: default probabilities from credit ratingsor internal statistical models
I capital requirements for different positionsI look at positions one by one
Measures of exposureI regress stock returns on risk factor, e.g. interest ratesFlannery-James 84, Venkatachalam 96, Hirtle 97,English, van den Heuvel, Zakrajsek 12, Landier, Sraer & Thesmar 13...
I stress tests: Brunnermeier-Gorton-Krishnamurthy 12, Duffi e 12
Measures of tail risk (VaR etc.)I Acharya-Pederson-Philippon-Richardson 10, Kelly-Lustig-vanNieuwerburgh 11
Bank position dataI derivatives: Gorton-Rosen 95, Stulz et al. 08, Hirtle 08I crisis: Adrian & Shin 08, Shin 11, He & Krishnamurthy 11
Begenau, Piazzesi, Schneider () Cambridge Oct 11, 2013 5 / 32
Outline
Replication with spanning securitiesI bond/debt positions ≈ simple portfolios in a few bonds
One factor model of bond valuesI fit to bonds with & without credit risk
Replication of loans, securities & deposits
Interest rate swapsI definitions and dataI estimation of replicating portfolio
Example results for large US banks
Begenau, Piazzesi, Schneider () Cambridge Oct 11, 2013 6 / 32
Replication with spanning securities
Factor structure with normal shocksI consider payoff stream with value π (ft , t)I factors ft = µ (ft , t) + σt εt , εt v N (0, IK×K )
Change in value of payoff stream π between t and t + 1
π (ft+1, t + 1)− π (ft , t) ≈ aπt + b
πt εt+1
form replicating portfolio from K + 1 spanning securitiesI always include θ1t one period bonds ( = cash) with price e
−itI use θt other securities, e.g. longer bonds
choose θ1t , θt to match change in value π for all εt+1:(θ1t θ
′t
)( e−it it 0at bt
)(1
εt+1
)=(aπt bπ
t
) ( 1εt+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 payoff streams π to f , estimate jointdistribution of risky & riskless yields
pricing kernel
Mt+1 = exp (−δ0 − δ1ft − λt εt+1 + Jensen term)
λt = l0 + l1ft
riskless zero coupon bond prices as functions of ft
P (n)t = Et[Mt+1P
(n−1)t+1
], P (0)t = 1
P (n)t = exp (An + Bnft )
find Bn < 0 (high interest rates, low prices)
also λt < 0 so Et [excess return on n period bond] = Bn−1σλt > 0
Begenau, Piazzesi, Schneider () Cambridge Oct 11, 2013 8 / 32
Credit riskrisky bonds default; recovery value proportional to pricepayoff per dollar invested
∆t+1 = exp(−d0 − d1ft −
(λt − λt
)εt+1 + Jensen term
)λt = l0 + l1ft
risky zero coupon prices
P (n)t = Et[Mt+1∆t+1P
(n−1)t
], P (0)t = 1
P (n)t = exp(An + Bnft
)spreads
ıt − it = d0 + d1ftestimation finds
I d1 > 0 spreads high when credit risk is highI Bn < 0 (high interest rates or default risk, low prices)I λt > λt low payoff when credit risk εt+1 highI Et [excess return] =
(Bn−1σ−
(λt − λt
))λt > 0
Begenau, Piazzesi, Schneider () Cambridge Oct 11, 2013 9 / 32
Replication with one factorChange in bond value πt = π (ft , t)
πt+1 − πt ≈ πt
(µt︸︷︷︸ + σt︸︷︷︸ εt+1
)expected return volatility
Cashµt = it , σt = 0
Represent other bond πt = π(ft , t) as simple portfolio
πt (µt + σt εt+1) = ωt πt (µt + σt εt+1) +Kt it
π = value of 5-year riskless bondSimple portfolios = holdings ωt of 5-year riskless bond & cash KtPortfolio weight on 5-year bond increasing in maturity, risk of π2 year Treasury: 40% 5-year bond, 60% cash10 year Treasury: 140% 5-year bond, −40% cash10 year BBB corporate bond: 180% 5-year bond, −80% cash
Begenau, Piazzesi, Schneider () Cambridge Oct 11, 2013 10 / 32
Outline
Basic replication argumentI bond/debt positions ≈ simple portfolios in a few bonds
One factor model of bond valuesI fit to bonds with & without credit risk
Replication of loans, securities, deposits
Interest rate swapsI definitions and dataI 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 sheetsI loans: book value, maturity, credit qualityI securities: fair values, maturity, credit qualityI cash, deposits & fed funds
LoansI start from data on book value & interest ratesI derive stream of promises = bundle of (risky) zero coupon bondsI replicate with simple portfolio as above
SecuritiesI observe fair values by maturity & issuer (private, government)I use public, private bond prices to compute simple portfolioI bonds held for trading: rough assumptions on maturity
Deposits & money market fundsI 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
96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 111.5
1
0.5
0
0.5
1
1.5
2Tr
illion
s $U
Scash, old FI5 year, old FI
Begenau, Piazzesi, Schneider () Cambridge Oct 11, 2013 13 / 32
Outline
Basic replication argumentI bond/debt positions ≈ simple portfolios in a few bonds
One factor model of bond valuesI fit to bonds with & without credit risk
Replication of loans, securities & deposits
Interest rate swapsI definitions and dataI 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
1995 2000 2005 2010
20
40
60
80
100
120
140
160Tr
illion
s $U
S
all contractsswaps
Begenau, Piazzesi, Schneider () Cambridge Oct 11, 2013 15 / 32
Swap payoffs
Counterparties swap fixed vs floating payments ∝ notional value N
0 1 2 3 4 5
0.5
0
0.5s s s s
R(0,1)
R(1,2) R(2,3)
R(3,4)
Fixed
Floating
Payments, Example: 1Year Swap, Notional = $1
time (in quarters)
Direction of position: pay-fixed swap or pay-floating swap
“fixed leg” := fixed payments + N at maturity; value falls w/ rates
"floating leg": = floating payments + N at maturity; value = N
Begenau, Piazzesi, Schneider () Cambridge Oct 11, 2013 16 / 32
Valuation of swapsDiscount fixed leg payoffs w/ bond price P (m)t , annuity price C (m)t
value of fixed leg = N(s C (m)t + P (m)t
)Direction: d = 1 for pay fixed, −1 for pay floatingFair value of individual swap position (d ,m, s)
N d(1−
(s C (m)t + P (m)t
))=: N d Ft (s,m)
Inception date: swap rate set s.t. Ft (s,m) = 0After inception date
I pay fixed swap gains ⇔ rates increaseI pay floating swap gains ⇔ rates fall
Fair value of bank’s swap book
FVt = ∑d ,m,s
Nd ,m,st dt Ft (s,m)
Begenau, Piazzesi, Schneider () Cambridge Oct 11, 2013 17 / 32
Data & institutional detail
Call report derivatives dataI notionalsI positive & negative fair values (marked to market)I "for trading" vs "not for trading"I maturity buckets
IntermediationI large interdealer positionsI dealers incorporate bid-ask spread into swap ratesI data: bid-ask spreads (Bloomberg),
net credit exposure (recent call reports)I 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
1995 2000 2005 2010
20
40
60
80
100
120
140
160Tr
illion
s $U
Sfor tradingnot for tradingtop 3 dealers
Begenau, Piazzesi, Schneider () Cambridge Oct 11, 2013 19 / 32
Data & institutional detail
Call report derivatives dataI notionalsI positive & negative fair values (marked to market)I "for trading" vs "not for trading"I maturity buckets
IntermediationI large interdealer positionsI dealers incorporate bid-ask spread into swap ratesI data: bid-ask spreads (Bloomberg),
net credit exposure (recent call reports)I subtract rents from intermediation from fair values,derive net notionals from trading on own account
Unknown: directions of trade, locked in swap rates
Begenau, Piazzesi, Schneider () Cambridge Oct 11, 2013 20 / 32
Gains from trade on own account
Observation equation for "multiple" = fair value per dollar notional:
µt = dt Ft (st , mt ) + εt
DataI fair values (exclude intermediation rents)I net notionalsI mt = average maturityI bond prices contained in Ft
EstimationI prior over unknown sequence (dt , st )I measurement error ε ∼ N
(0, σ2ε
)
Begenau, Piazzesi, Schneider () Cambridge Oct 11, 2013 21 / 32
Identification
Observation equation for fair value per dollar notional:
µt = dt Ft (st , mt ) + εt
For each direction dt , can find swap rate to exactly match µtFor example, positive gains µt > 0 require
I pay fixed dt > 0 & low locked-in rate st than current rate stI pay floating dt < 0 & high locked-in rate st than current rate st
Which is more plausible? Look at swap rate history!
Begenau, Piazzesi, Schneider () Cambridge Oct 11, 2013 22 / 32
Estimation details
Fix var (εt ) = var (µt ) /10Compare two priors over sequence (dt , st )
1. Simple date-by-date approachI Pr (dt = 1) = 1
2I prior over swap rate = empirical distribution over last 10 years
Begenau, Piazzesi, Schneider () Cambridge Oct 11, 2013 23 / 32
JP Morgan Chase: swap position
1995 2000 2005 20100
20
40
60
notionals$
trillio
ns
1995 2000 2005 2010
2
0
2
4
multiple µt (%)
2000 2005 2010
2
4
6
avg maturity swap rate (% p.a.)
Begenau, Piazzesi, Schneider () Cambridge Oct 11, 2013 24 / 32
JP Morgan Chase: swap position
1995 2000 2005 20100
20
40
60
notionals$
trillio
ns
1995 2000 2005 2010
2
0
2
4
multiple µt (%)
1995 2000 2005 20100
0.5
1posterior Pr(pay fixed)
2000 2005 2010
1
2
3
4
5
6
7
avg maturity swap rate (% p.a.)
curr.fixfloat
Begenau, Piazzesi, Schneider () Cambridge Oct 11, 2013 25 / 32
JPMorgan Chase: swap position
1995 2000 2005 20100
20
40
60
notionals$
trillio
ns
1995 2000 2005 20100
0.5
1posterior Pr(pay fixed)
2000 2005 2010
1
2
3
4
5
6
7
avg maturity swap rate (% p.a.)
curr.fixfloat
1995 2000 2005 2010
2
0
2
4
multiple µt (%)
dataestimate
Begenau, Piazzesi, Schneider () Cambridge Oct 11, 2013 26 / 32
Estimation details
Fix var (εt ) = var (µt ) /10Compare two priors over sequence (dt , st )
1. Simple date-by-date approachI Pr (dt = 1) = 1
2I prior over swap rate = empirical distribution over last 10 years
2. “Dynamic trading prior”I symmetric 2 state Markov chain for dt with prob of flipping φ = .1I draw s0 from empirical distributionI update swap rate conditional on evolution of dt and notionals
a. increase exposure, same directionadjust swap rate proportionally to share of new swaps
b. decrease exposure, same directionswap rate unchanged
c. switch directionoffset existing swaps & initial new position at current rate
Begenau, Piazzesi, Schneider () Cambridge Oct 11, 2013 27 / 32
JPMorgan Chase: swap position
1995 2000 2005 20100
20
40
60
notionals$
trillio
ns
1995 2000 2005 20100
0.5
1posterior Pr(pay fixed)
2000 2005 2010
1
2
3
4
5
6
7
avg maturity swap rate (% p.a.)
curr.fixfloat
1995 2000 2005 2010
2
0
2
4
6
multiple µt (%)
dataestim ate
Begenau, Piazzesi, Schneider () Cambridge Oct 11, 2013 28 / 32
JP Morgan Chase: replicating portfolios
96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 111.5
1
0.5
0
0.5
1
1.5
2Tr
illion
s $U
Scash, old FI5 year, old FI
Begenau, Piazzesi, Schneider () Cambridge Oct 11, 2013 29 / 32
JP Morgan Chase: replicating portfolios
96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11
4
2
0
2
4
6Tr
illion
s $U
Scash, old FI5 year, old FIcash, deriv5 year, deriv
Begenau, Piazzesi, Schneider () Cambridge Oct 11, 2013 30 / 32
1995 2000 2005 20105
0
5
Trill
ions
$U
SJPMORGAN CHASE & CO.
cash5 year
1995 2000 2005 2010
1
0
1
Trill
ions
$U
S
WELLS FARGO & COMPANY
1995 2000 2005 20104
2
0
2
4
Trill
ions
$U
S
BANK OF AMERICA CORPORATION
2000 2005 201021
012
Trill
ions
$U
S
CITIGROUP INC.
Begenau, Piazzesi, Schneider () Cambridge Oct 11, 2013 31 / 32
Summary
Portfolio methodology to both measure and representexposures in bank positions
Results for top dealer banksDerivatives often increase exposure to interest rate risk.
Possible models of banksI risk averse agents who use derivatives to insure (no!)I 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