banks™risk exposures · portfolio weight on 5-year bond increasing in maturity, risk of p˜ 2...

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


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


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


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


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


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)


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


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


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


Outline

Basic replication argumentI bond/debt positions ≈ simple portfolios in a few bonds


Replication of loans, securities, deposits




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


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


Outline

Basic replication argumentI bond/debt positions ≈ simple portfolios in a few bonds


Replication of loans, securities & deposits




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


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


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)


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


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


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


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

)


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!


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


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.)


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


curr.fixfloat


JPMorgan Chase: swap position

1995 2000 2005 20100

20

40

60

notionals$

trillio

ns

1995 2000 2005 20100

0.5


2000 2005 2010

1

2

3

4

5

6

7


curr.fixfloat

1995 2000 2005 2010

2

0

2

4

multiple µt (%)

dataestimate


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


JPMorgan Chase: swap position

1995 2000 2005 20100

20

40

60

notionals$

trillio

ns

1995 2000 2005 20100

0.5


2000 2005 2010

1

2

3

4

5

6

7


curr.fixfloat

1995 2000 2005 2010

2

0

2

4

6

multiple µt (%)

dataestim ate


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


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


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.


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...


banks™risk exposures · portfolio weight on 5-year bond increasing in maturity, risk of p˜ 2...

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