Price contagion through balance sheet linkages

Transcription

1 Price conagion hrough balance shee linkages Agosino Capponi Deparmen of Indusrial Engineering and Operaions Research Columbia Universiy Join work wih M. Larsson Workshop on Sysemic Risk in Financial Markes Universiy of Hannover December 9, 2015

2 Talk Ouline 1 Inroducion 2 The Model 3 Asse prices 4 Sysemicness of leverage argeing 5 The nework of asse prices 6 Policy implicaions and concluding remarks

3 Sysemic Risk Sysemically imporan insiuions can conaminae ohers and spiral ino shocks desabilizing he financial sysem. Curren lieraure has pu forward wo main approaches for modeling sysemic risk: Boom-up approach: Model linkages arising when financial eniies are conneced via direc bilaeral exposures Ofen used owards descripive characerisics of sysem via simulaion wih lile analyical resuls Top-down approach: Global indicaors of sysemic risk and conribuion of each financial insiuion Granulariy of sysem no as fine compared o boom-up, bu generally leads o more analyically racable predicions

4 Top-down approach Spread of disress across eniies capured by sysemic risk measures. Noiceable conribuions include: Adrian and Brunnermeier (2001): CoVar relaes sysemic risk conribuion of an eniy o value a risk of he overall sysem Acharaya e al. (2012): sysemic expeced shorfall index o measure expeced amoun of undercapializaion under sysemic evens Brownless and Engle (2014): SRISK o measure expeced capial shorfall under prolonged period of marke disress

5 Balance shee conagion vs Nework Models Nework sudies assume asse prices fixed a heir book values: balance shees only ake his a defaul evens. Empirical evidence suggess ha financial insiuions reac o asse price changes by acively managing heir balance shees. Disress propagaion: forced sales of illiquid asses may depress prices, and promp financial disress a oher banks wih similar holdings. Adrian and Shin (2008): if he domino model of financial conagion were he relevan one, defauls on producs such as subprime morgages would have had a much smaller impac.

6 Our conribuion Top-down model aiming a quanifying price linkages arising when firms, holding similar asses on heir balance shees, manage heir leverage raios o conform wih pre-specified arge levels. Relaed conribuions include: Shleifer and Vishny (2011): how asse fire sales lead o downward spirals or cascades in asse prices Brunnermier and Pedersen (2009): ineracion of marke and funding liquidiy Greenwood, Landier and Thesmar (2014): how disribuion of bank leverage and risk exposures lead o formaion of sysemic risk Con e al (2015): fire sales and amplificaion effecs arising when banks need o mainain minimal leverage requiremens

7 Moivaing Evidence Empirical sudies indicae ha banks acively manage leverage Gropp and Heider (2010) find ha banks adjus oward heir arge leverages a fas speeds Berger e al. (2008) find ha poorly capialized banks adjus oward heir arges more quickly han well capialized banks Adrian and Shin (2008, 2010) find ha commercial banks rack heir leverage raios, while invesmen banks even have procyclical leverage Adrian and Shin (2010): micro-foundaion of leverage procyclicaliy driven by value a risk

8 6 Adrian and Shin (2010) Leverage Growh (Percen Quarerly) Toal Asse Growh (Percen Quarerly) Toal Asse Growh (Percen Quarerly) Leverage Growh (Percen Quarerly) 40 rowh (Percen Quarerly) Toal Asse Growh (Percen Quarerly) Leverage Growh (Percen Quarerly)

9 Marke Paricipans and Asses Marke divided ino wo secors: Banking: commercial and invesmen banks. Non-banking: muual, money marke and pension funds, insurances. Banks manage heir leverage raios o conform wih a pre-specified arge level Non-banking secor is no subjec o sringen leverage managemen

10 The Banking secor Balance shee managemen Sae of each bank described by is balance shee which consiss of asses, equiy and deb. Banks manage heir capial srucure by buying and selling asses, and by increasing or reducing heir level of deb. Banks do no raise new equiy capial in response o a posiive or negaive shock o he asse value.

11 The Banking secor Adrian, Colla and Shin (2012) 300 Invesmen Banks (1994Q1-2011Q2) 800 Commercial Banks (Call Repors) 1984Q1-2010Q2 Change in Equiy & Changes in Deb (Billions) y = x y = x Equiy Deb Change in Asses (Billions) Change in Equiy & Changes in Deb (Billions) 600 y = x y = x Equiy -400 Deb Change in Asses (Billions) Figure 3. Scaer char of {( )} and {( )} for changes in asses, equiy and deb of US invesmen bank secor consising of Bear Searns, Goldman Sachs, Lehman Brohers, Merrill Lynch and Morgan Sanley beween Q1:1994 and Q2:2011 (Source: SEC 10Q filings). Figure 4. Scaer char of {( )} and {( )} for changes in asses, equiy and deb of US commercial bank secor a beween Q1:1984 and Q2:2010 (Source: FDIC call repors). 2.3 Focus on Banking Secor We are sill lef wih a broader heoreical quesion of wha makes he banking secor so special. In Kashyap, Sein and Wilcox (1993), he shock envisaged was a moneary ighening ha hi he banking secor specifically hrough igher reserve requiremens ha led o a shrinking of bank balance shees. However, he downurn in was {( )} is close o zero. 1 Commercial banks show a similar paern o invesmen banks. Figure 4 is he analogous scaer plo of he quarerly change in oal asses of he US commercial bank secor which plos {( )} and {( )} using he FDIC Call Repors. The sample period is beween Q1:1984 and Q2:2010. We see essenially he same paern as

12 The Banking secor Asses of banking secor K ypes of asses. Marke prices a denoed by P k : P = (P 1 P 2 P K ) The aggregae supply of each asse is fixed and given by Q o = (Qo 1 Qo) K N banks. Holdings of bank i are given by Q i = (Q 1i Q 2i Q Ki ). Marke value of he i:h bank s holdings of asse k is A ki = P k Q ki. Then A i = (A 1i A 2i A Ki ).

13 The Banking secor Deb of banking secor Deb of bank i a ime is D i. Key behavioral assumpion: each bank i racks a fixed arge leverage λ i This yields he leverage equaion: D i 1 A i D i = λ i Ineres rae r = 0 o simplify exposiion

14 The Banking secor Bank s operaions Each bank receives revenues R i, ne of operaing coss and dividends, over each ime inerval [, + ] Cash flows resul from (i) operaing revenues (ii) increase or reducion in deb used by he bank o eiher purchase more asses or liquidae par of is curren holdings. Cash flow allocaion sraegy α i = (α 1i α Ki ), α ki > 0 wih K k=1 αki = 1

15 The Banking secor Cash flow equaion The fundamenal cash flow equaion is P+ k Qki = α ki ( R i + D) i LHS: amoun invesed by bank i in asse k a + RHS: proceeds from operaing revenues and deb issuance in ime inerval [, + ]

16 The Banking secor The demand curve Combining leverage raio and cash flow equaion leads o Q ki = αki P+ k ( λ i Q i P + (1 + λ i ) R i In he absence of revenue shocks and if P h = 0 for h k ) Q ki Q ki = λ i α ki P k P k +

17 The Banking secor Upward sloping demand Q ki Q ki = λ i α ki P k P k + λ i α ki can be inerpreed as price elasiciy. Suppose he price of one uni of he k-h asse rises from o +. The firm increases is deb level o rack leverage raio, The firm invess he raised capial by purchasing asse unis.

18 The Non-banking secor Non-banking demand Non-bank insiuions also rade in he available asses k, nb Non-banking secor holds a quaniy Q of asse k a, k, nb A = P k k, nb Q The incremenal demand is given by k, nb Q = γ k P+ k Q k, nb ( Z k P k ) where Z k are asse-specific demand shocks

19 The Non-banking secor Downward-sloping demand Assume no leverage raio rackers. Marke clearing leads o asse price dynamics P k = Z k. Relaionship beween price and demand condiional on Z k = 0 given by k, nb Q k, nb Q = γ k P k P k + γ k > 0: elasiciy of nonbanking demand for asse k

20 Noaions and Definiions Given vecors u = (u 1 u n ) and v = (v 1 v n ) The componenwise produc is u v = (u 1 v 1 u n v n ) The componenwise raio is ( u v = u1 v 1 ) u n v n Diag(u) is he diagonal marix wih u on he diagonal.

21 Sysemicness marix The sysemicness marix S is given by S = N i=1 α i γ A nb λ i A i Is componenwise form is S kl = N i=1 α ki λ i A li γ k A k, nb Key deerminan for excess price correlaion induced by he leverage argeing banks.

22 Graph based inerpreaion Sysemicness marix S kl = N i=1 αki weighed adjacency marix of nework: λ i A li k, nb γ k A inerpreed as Direced edge from node l o node k wih weigh S kl. Reurn shock o asse l of size y l propagaes along he edge (l, k) and resuls in a shock o asse k of size y k = S kl The shock y k forces furher leverage adjusmens, causing reurn shocks o oher asses, and so on. y l

23 Marke dynamics Proposiion The cash flow equaion, leverage equaion, he non-banking demand funcion, and marke clearing imply P P = (I S ) 1 [ ] Z N α i + P γ A nb (1 + λ i ) R i i=1 }{{} vecor of iniial aggregae reurn shocks ( ) A i = Q i P + α i λ i Q i P + (1 + λ i ) R i ) A nb = Q nb (γ Z (γ 1) P assuming ha he marix inverse exiss.

24 Sysemic Risk Suppose all eigenvalues of S are less han one. Then P P = [ I + S + S 2 + S ] Y Direc impac: firs erm I in he power series expansion Indirec effec: Suppose negaive shock occurs. Term S corresponds o firs round of deleveraging. Term S 2 corresponds o a second round of deleveraging. Each round impacs prices and oal realized reurn is he aggregae oucome of his process

25 Specral Radius The specral radius of he sysemicness marix The specral radius ρ(s ), S = N i=1 λ γ A nb i A i, is he aggregae level of vulnerabiliy in he sysem Proposiion Assume all asse holdings and all cash flow allocaion weighs α ki are nonnegaive. We have he bounds α i max k=1,...,k N i=1 λ iα ki A ki k, nb γ k A ρ(s ) N i=1 max λ iα ki 1 A i k=1,...,k k, nb γ k A

26 Specral Radius Upper bound of specral radius The upper bound is given by N i=1 max λ iα ki 1 A i k=1,...,k k, nb γ k A Quanifies he size of leverage argeing banks relaive o he size of he nonbanking secor, as measured by elasiciy-weighed asses. When nonbanking secor is large, ρ(s ) is small, and he impac on realized reurns is moderae.

27 Specral Radius Lower bound of specral radius The lower bound is given by max k=1,...,k N i=1 λ iα ki A ki k, nb γ k A Numeraor only involves he banks holdings of he k:h asse If he nonbanking secor is small in relaive erms, ρ(s ) is large, causing srong impac on realized reurns

28 Cash Flow Allocaion Sraegies Fixed relaive exposure sraegy Relaive exposure sraegy is given by α ki = A ki /(1 A i ). Upper bound on he specral radius given by ρ(s ) max k=1,...,k N i=1 λ ia ki γ k A k, nb Exisence of an asse class for which holdings of highly levered banks are large relaively o he nonbanking secor desabilizes sysem. Relaion o illiquidiy concenraion measure by Duare and Eisenbach (2013).

29 Cash Flow Allocaion Sraegies Liquidiy based sraegy I Banks sell (buy) he mos liquid asses when here is a need o delever (lever up) α ki = γ ka k, nb K l=1 γ l, nb la Specral radius equals is upper bound, i.e. ρ(s ) = N i=1 λ i1 A i K k=1 γ k, nb ka

30 Cash Flow Allocaion Sraegies Liquidiy based sraegy II Specral radius only depends on he relaive aggregae size of he banking and he nonbanking secors. Exisence of an asse class for which price elasiciy is high and for which he nonbanking secor is large relaive o he banking secor, would be enough o sabilize he sysem Severe deleveraging needs can be absorbed by he nonbanking secor. The remaining, poenially illiquid, asses are no subjeced o fire sales.

31 Cash Flow Allocaion Sraegies Liquidiy based sraegy III Proposiion Assume all asse holdings are nonnegaive. Then N i=1 λ i1 A i K k=1 γ k, nb ka }{{} liquidiy based max N i=1 λ ia ki k, nb k=1,...,k γ k A }{{} fixed exposure

32 One-sep impac of shocks Deleveraging aciviies of bank i conribues o one-sep propagaion of shocks from asse l o asse k: α ki λ i A li γ k A k, nb Toal one-sep reurn impac caused by bank i: λ i 1 A i K k=1 α ki γ k A 1 k, nb Sronges one-sep sysemic impac by large banks ha are highly levered and allocae heir cash flows o illiquid asses

33 Aggregae impac of shocks One-sep reurn impacs give an incomplee view of he sysemic properies of he banking secor. Aggregae impac on reurn of asse k due o a shock in asse l given by (I S ) 1 = I + S + S 2 + Can higher-order effecs beyond he one-sep impac be negleced?

34 Illusraive Example I Three asses (K = 3) and wo banks (N = 2). Boh banks rack he same deb-over-equiy leverage raio λ = 9. Curren asses and fixed relaive exposure sraegies given by Banking Secor Non-Banking Secor A 1 = A 2 = α 1 = α 2 = γ A nb =

35 Illusraive Example II Sysemicness marix becomes S = , ρ(s ) = 0.97 S 3,1 = 0, bu he (3, 1) enry of (I S ) 1 is A shock o asse 1 has a sizable impac on he reurn of asse 3, even hough he one-sep effec is zero!

36 Asse growh and exreme sensiive regime Numerical seup R i N (0, 0.1), Z k N (0, 0.1) Iniial aggregae size of banking secor is 8% of he nonbanking secor N = K = 2 and P 1 0 = P2 0 = 1. λ 1 = λ 2 = 10 and γ 1 = γ 2 = 9

37 Asse growh and exreme sensiive regime Sable realizaion Fixed relaive exposure sraegy Values Sysemicness Marix Specral Radius Upper bound Lower bound Time (Years) Asse Values Asses A 11 +A 12 A 21 +A 22 A 1,nb A 2,nb Time (Years) Values Relaive Price Changes P 1 /P 1 P 2 /P Time (Years)

38 Asse growh and exreme sensiive regime Unsable realizaion Liquidiy based sraegy 0.7 Sysemicness Marix 10 Asses 0.02 Relaive Price Changes Values Specral Radius Lower bound Asse Values A +A A +A 1,nb A 2,nb A Values P 1 /P 1 P 2 /P Time (Years) Time (Years) Time (Years) Fixed relaive exposure sraegy 1.4 Sysemicness Marix 14 Asses 0.04 Relaive Price Changes Values Specral Radius Upper bound Lower bound Asse Values A +A A +A 1,nb A 2,nb A Values P 1 /P 1 P 2 /P Time (Years) Time (Years) Time (Years)

39 Conclusions Policies suggesions? Specral radius of sysemicness marix characerizes sabiliy of price dynamics in presence of leverage argeing banks Sabiliy improves if (i) he banking secor is small, (ii) he nonbanking secor is large, (iii) nonbanking demand is highly elasic, (iv) arge leverage is low, or (v) banks assign low allocaion weighs o illiquid asses. Can we creae incenives for banks o operae more closely o a liquidiy-based sraegy? Newly imposed Basel III liquidiy requiremens feaure such a mechanism: liquidiy coverage raio.

40 Conclusions Conclusions Empirical evidence suggess ha banks end o acively manage heir leverage raio. Key oucome: leverage racking behavior may be desabilizing, causing asse prices o become highly correlaed, and sensiive o shocks. In normal imes, he downward-sloping demand curve of he nonbanking secor exers a sabilizing force on asse prices. Afer susained periods of growh in he banking secor, his force may no longer be sufficien o keep prices sable. Suppor policies creaing incenives for sraegies wih higher exposure o liquid, raher han illiquid, asses.

41 Conclusions Reference Agosino Capponi and Marin Larsson. Price conagion hrough balance shee linkages. Review of Asse Pricing Sudies, Forhcoming.