Banks Risk Exposures

Transcription

1 Banks Risk Exposures Juliane Begenau Monika Piazzesi Martin Schneider Stanford Stanford & NBER Stanford & NBER Cambridge Oct 11, 213 Begenau, Piazzesi, Schneider () Cambridge Oct 11, / 32

2 Modern Bank Balance Sheet, JP Morgan Chase 211 Total assets/liabilities: $2.3 Trillion Assets Liabilities Cash 6% Equity 8% Securities 16% Deposits 5% Loans 31% Other borrowed money 15% Fed funds + Repos 17% Fed funds + Repos 1% Trading assets 2% Trading liabilities 6% Other assets 1% Other liabilities 11% Derivatives: $6 Trillion Notionals of Swaps Begenau, Piazzesi, Schneider () Cambridge Oct 11, / 32

3 Portfolio approach to measuring risk exposure Many positions: how to compress & compare? Basic idea: represent as simple portfolios 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, comparable 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, / 32

4 Ingredients Valuation model parsimonious representation of cross section of bonds allow for interest rate and credit risk can depend on calendar time; cross sectional fit is key this paper: one shock = shift in level of BB bond yield Bank data requirements maturity & credit risk by position payment streams detailed data on loans & securities apply valuation model directly coarser data (e.g. derivatives) estimate positions first Results for large US banks traditional business = long bonds financed 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, / 32

5 Related literature Bank regulation (Basel II): separately consider credit & market risk credit risk: default probabilities from credit ratings or internal statistical models capital requirements for different positions look at positions one by one Measures of exposure 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 stress tests: Brunnermeier-Gorton-Krishnamurthy 12, Duffi e 12 Measures of tail risk (VaR etc.) Acharya-Pederson-Philippon-Richardson 1, Kelly-Lustig-van Nieuwerburgh 11 Bank position data derivatives: Gorton-Rosen 95, Stulz et al. 8, Hirtle 8 crisis: Adrian & Shin 8, Shin 11, He & Krishnamurthy 11 Begenau, Piazzesi, Schneider () Cambridge Oct 11, / 32

6 Outline Replication with spanning securities bond/debt positions simple portfolios in a few bonds One factor model of bond values fit to bonds with & without credit risk Replication of loans, securities & deposits Interest rate swaps definitions and data estimation of replicating portfolio Example results for large US banks Begenau, Piazzesi, Schneider () Cambridge Oct 11, / 32

7 Replication with spanning securities Factor structure with normal shocks consider payoff stream with value π (f t, t) factors f t = µ (f t, t) + σ t ε t, ε t N (, I K K ) Change in value of payoff stream π between t and t + 1 π (f t+1, t + 1) π (f t, t) a π t + b π t ε t+1 form replicating portfolio from K + 1 spanning securities always include θ 1 t one period bonds ( = cash) with price e i t use ˆθ t other securities, e.g. longer bonds choose θ 1 t, ˆθ t to match change in value π for all ε t+1 : ( θ 1 t ˆθ ) ( e i ) ( ) t i t 1 t = ( at â t ˆb t ε π b π ) ( 1 t t+1 ε t+1 no arbitrage: value of replicating portfolio at t = value π (f t, t) ). Begenau, Piazzesi, Schneider () Cambridge Oct 11, / 32

8 Implementation with one factor single factor f t = credit risky short rate (BB rating) to relate value of other payoff streams π to f, estimate joint distribution of risky & riskless yields pricing kernel M t+1 = exp ( δ δ 1 f t λ t ε t+1 + Jensen term) λ t = l + l 1 f t riskless zero coupon bond prices as functions of f t [ ] P (n) t = E t M t+1 P (n 1), P () t = 1 t+1 P (n) t = exp (A n + B n f t ) find B n < (high interest rates, low prices) also λ t < so E t [excess return on n period bond] = B n 1 σλ t > Begenau, Piazzesi, Schneider () Cambridge Oct 11, / 32

9 Credit risk risky bonds default; recovery value proportional to price payoff per dollar invested t+1 = exp ( d d 1 f t ( ) λ t λ t εt+1 + Jensen term ) λ t = l + l 1 f t risky zero coupon prices [ ] P (n) t = E t M t+1 t+1 P (n 1) t, P () t = 1 P (n) t = exp ( ) Ã n + B n f t spreads ĩ t i t = d + d 1 f t estimation finds d 1 > spreads high when credit risk is high B n < (high interest rates or default risk, low prices) λ t > λ t low payoff when credit risk ε t+1 high E t [excess return] = ( B n 1 σ ( )) λ t λ t λt > Begenau, Piazzesi, Schneider () Cambridge Oct 11, / 32

10 Replication with one factor Change in bond value π t = π (f t, t) ( π t+1 π t π t µ }{{} t expected return Cash µ t = i t, σ t = + σ t }{{} ε t+1 volatility Represent other bond π t = π(f t, t) as simple portfolio π t ( µ t + σ t ε t+1 ) = ω t π t ) (µ t + σ t ε t+1 ) + K t i t π = value of 5-year riskless bond Simple portfolios = holdings ω t of 5-year riskless bond & cash K t Portfolio weight on 5-year bond increasing in maturity, risk of π 2 year Treasury: 4% 5-year bond, 6% cash 1 year Treasury: 14% 5-year bond, 4% cash 1 year BBB corporate bond: 18% 5-year bond, 8% cash Begenau, Piazzesi, Schneider () Cambridge Oct 11, / 32

11 Outline Basic replication argument bond/debt positions simple portfolios in a few bonds One factor model of bond values fit to bonds with & without credit risk Replication of loans, securities, deposits Interest rate swaps definitions and data estimation of replicating portfolio Example results for large US banks Begenau, Piazzesi, Schneider () Cambridge Oct 11, / 32

12 From regulatory data to simple portfolios Quarterly Call report data on bank balance sheets Loans loans: book value, maturity, credit quality securities: fair values, maturity, credit quality cash, deposits & fed funds 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 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 mostly short term ( = cash) Represent as simple portfolios in 5-year bond & cash Begenau, Piazzesi, Schneider () Cambridge Oct 11, / 32

13 Trillions $US JP Morgan Chase: simple portfolio holdings cash, old FI 5 year, old FI Begenau, Piazzesi, Schneider () Cambridge Oct 11, / 32

14 Outline Basic replication argument bond/debt positions simple portfolios in a few bonds One factor model of bond values fit to bonds with & without credit risk Replication of loans, securities & deposits Interest rate swaps definitions and data estimation of replicating portfolio Example results for large US banks Begenau, Piazzesi, Schneider () Cambridge Oct 11, / 32

15 Trillions $US Notionals of Interest Rate Derivatives of US Banks all contracts swaps Begenau, Piazzesi, Schneider () Cambridge Oct 11, / 32

16 Swap payoffs Counterparties swap fixed vs floating payments notional value N Payments, Example: 1 Year Swap, Notional = $1.5 Fixed s s s s R(2,3) R(1,2).5 R(3,4) R(,1) Floating 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, / 32

17 Valuation of swaps Discount fixed leg payoffs w/ bond price P (m), annuity price C (m) value of fixed leg = N t ( s C (m) t + P (m) t Direction: d = 1 for pay fixed, 1 for pay floating Fair value of individual swap position (d, m, s) ( ( )) N d 1 s C (m) t + P (m) t =: N d F t (s, m) Inception date: swap rate set s.t. F t (s, m) = After inception date pay fixed swap gains rates increase pay floating swap gains rates fall Fair value of bank s swap book FV t = Nt d,m,s d t F t (s, m) d,m,s ) t Begenau, Piazzesi, Schneider () Cambridge Oct 11, / 32

18 Data & institutional detail Call report derivatives data notionals positive & negative fair values (marked to market) "for trading" vs "not for trading" maturity buckets Intermediation 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, / 32

19 Trillions $US Concentrated Holdings of Interest Rate Derivatives for trading not for trading top 3 dealers Begenau, Piazzesi, Schneider () Cambridge Oct 11, / 32

20 Data & institutional detail Call report derivatives data notionals positive & negative fair values (marked to market) "for trading" vs "not for trading" maturity buckets Intermediation 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, / 32

21 Gains from trade on own account Observation equation for "multiple" = fair value per dollar notional: µ t = d t F t ( s t, m t ) + ε t Data fair values (exclude intermediation rents) net notionals m t = average maturity bond prices contained in F t Estimation prior over unknown sequence (d t, s t ) measurement error ε N (, σ 2 ) ε Begenau, Piazzesi, Schneider () Cambridge Oct 11, / 32

22 Identification Observation equation for fair value per dollar notional: µ t = d t F t ( s t, m t ) + ε t For each direction d t, can find swap rate to exactly match µ t For example, positive gains µ t > require pay fixed d t > & low locked-in rate s t than current rate s t pay floating d t < & high locked-in rate s t than current rate s t Which is more plausible? Look at swap rate history! Begenau, Piazzesi, Schneider () Cambridge Oct 11, / 32

23 Estimation details Fix var (ε t ) = var (µ t ) /1 Compare two priors over sequence (d t, s t ) 1. Simple date-by-date approach Pr (d t = 1) = 1 2 prior over swap rate = empirical distribution over last 1 years Begenau, Piazzesi, Schneider () Cambridge Oct 11, / 32

24 $ trillions JP Morgan Chase: swap position notionals multiple µ t (%) avg maturity swap rate (% p.a.) Begenau, Piazzesi, Schneider () Cambridge Oct 11, / 32

25 $ trillions JP Morgan Chase: swap position notionals multiple µ t (%) posterior Pr(pay fixed) avg maturity swap rate (% p.a.) curr. fix float Begenau, Piazzesi, Schneider () Cambridge Oct 11, / 32

26 $ trillions JPMorgan Chase: swap position notionals multiple µ t (%) posterior Pr(pay fixed) avg maturity swap rate (% p.a.) curr. fix float data estim ate Begenau, Piazzesi, Schneider () Cambridge Oct 11, / 32

27 Estimation details Fix var (ε t ) = var (µ t ) /1 Compare two priors over sequence (d t, s t ) 1. Simple date-by-date approach Pr (d t = 1) = 1 2 prior over swap rate = empirical distribution over last 1 years 2. Dynamic trading prior symmetric 2 state Markov chain for d t with prob of flipping φ =.1 draw s from empirical distribution update swap rate conditional on evolution of d t 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 offset existing swaps & initial new position at current rate Begenau, Piazzesi, Schneider () Cambridge Oct 11, / 32

28 $ trillions JPMorgan Chase: swap position notionals 6 multiple µ t (%) posterior Pr(pay fixed) avg maturity swap rate (% p.a.) 7 data estim ate curr. fix float Begenau, Piazzesi, Schneider () Cambridge Oct 11, / 32

29 Trillions $US JP Morgan Chase: replicating portfolios cash, old FI 5 year, old FI Begenau, Piazzesi, Schneider () Cambridge Oct 11, / 32

30 Trillions $US JP Morgan Chase: replicating portfolios 6 4 cash, old FI 5 year, old FI cash, deriv 5 year, deriv Begenau, Piazzesi, Schneider () Cambridge Oct 11, / 32

31 Trillions $US Trillions $US Trillions $US Trillions $US 5 JPMORGAN CHASE & CO. cash 5 year WELLS FARGO & COMPANY BANK OF AMERICA CORPORATION CITIGROUP INC Begenau, Piazzesi, Schneider () Cambridge Oct 11, / 32

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 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, / 32