Working Paper Broker-dealer risk appetite and commodity returns

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1 econsor Der Open-Access-Publikaionsserver der ZBW Leibniz-Informaionszenrum Wirschaf The Open Access Publicaion Server of he ZBW Leibniz Informaion Cenre for Economics Eula, Erkko Working Paper Broker-dealer risk appeie and commodiy reurns Saff Repor, Federal Reserve Bank of New York, No. 406 Provided in Cooperaion wih: Federal Reserve Bank of New York Suggesed Ciaion: Eula, Erkko (2010) : Broker-dealer risk appeie and commodiy reurns, Saff Repor, Federal Reserve Bank of New York, No. 406 This Version is available a: hp://hdl.handle.ne/10419/60961 Nuzungsbedingungen: Die ZBW räum Ihnen als Nuzerin/Nuzer das unengelliche, räumlich unbeschränke und zeilich auf die Dauer des Schuzrechs beschränke einfache Rech ein, das ausgewähle Werk im Rahmen der uner hp://www.econsor.eu/dspace/nuzungsbedingungen nachzulesenden vollsändigen Nuzungsbedingungen zu vervielfäligen, mi denen die Nuzerin/der Nuzer sich durch die erse Nuzung einversanden erklär. Terms of use: The ZBW grans you, he user, he non-exclusive righ o use he seleced work free of charge, erriorially unresriced and wihin he ime limi of he erm of he propery righs according o he erms specified a hp://www.econsor.eu/dspace/nuzungsbedingungen By he firs use of he seleced work he user agrees and declares o comply wih hese erms of use. zbw Leibniz-Informaionszenrum Wirschaf Leibniz Informaion Cenre for Economics

2 Federal Reserve Bank of New York Saff Repors Broker-Dealer Risk Appeie and Commodiy Reurns Erkko Eula Saff Repor no. 406 November 2009 Revised March 2010 This paper presens preliminary findings and is being disribued o economiss and oher ineresed readers solely o simulae discussion and elici commens. The views expressed in he paper are hose of he auhor and are no necessarily reflecive of views a he Federal Reserve Bank of New York or he Federal Reserve Sysem. Any errors or omissions are he responsibiliy of he auhor.

3 Broker-Dealer Risk Appeie and Commodiy Reurns Erkko Eula Federal Reserve Bank of New York Saff Repors, no. 406 November 2009; revised March 2010 JEL classificaion: G10, G12, G13, G24 Absrac This paper shows ha he risk-bearing capaciy of U.S. securiies brokers and dealers is a srong deerminan of risk premia in commodiy markes. Commodiy derivaives are he principal insrumen used by producers and consumers of commodiies o hedge agains commodiy price risk. Broker-dealers play an imporan role in his hedging process because commodiy derivaives are raded primarily over he couner. I capure he limis of arbirage in his marke in a simple asse-pricing model where producers and consumers of commodiies share risk wih broker-dealers who are subjec o funding consrains. In equilibrium, he price of aggregae commodiy risk decreases in he relaive leverage of he broker-dealer secor. I esimae he model in he cross-secion of commodiies and find srong empirical suppor for is predicions. Flucuaions in riskbearing capaciy have paricularly srong forecasing power for energy reurns, boh in sample and ou of sample. Key words: asse pricing, financial inermediaries, commodiy prices, fuures markes, risk appeie Eula: Federal Reserve Bank of New York ( This paper was published as Chaper 1 of he auhor s 2009 Ph.D. disseraion a Harvard Universiy. The auhor hanks advisors John Campbell, Kenneh Rogoff, Andrei Shleifer, and Jeremy Sein, as well as Viral Acharya, Tobias Adrian, Yacov Amihud, Alvaro Carea, Richard Crump, Darrell Duffie, Emmanuel Farhi, Xavier Gabaix, Gary Goron, Robin Greenwood, Ravi Jagannahan, Owen Lamon, Lasse Pedersen, Chrisopher Polk, Erns Schaumburg, Hyun Song Shin, Erik Safford, and Moohiro Yogo for heir commens, suppor, and advice. The auhor also hanks seminar paricipans a Harvard Universiy, New York Universiy s Sern School of Business, Universiy Carlos III, and he Federal Reserve Bank of New York. The views expressed in his paper are hose of he auhor and do no necessarily reflec he posiion of he Federal Reserve Bank of New York or he Federal Reserve Sysem.

4 1. Inroducion This paper shows ha he risk-bearing capaciy of U.S. securiies brokers and dealers is a srong deerminan of risk premia in commodiy markes. Commodiy relaed derivaives are he principal means by which producers and consumers of commodiies hedge he price risk of heir physical posiions. This risk is ofen ermed non-markeable as ransacion coss make he rading of physical commodiies unaracive o nancial invesors. Since he majoriy of commodiy derivaives are bilaeral over-he-couner (OTC) conracs beween a clien and a nancial inermediary, broker-dealers play a key role in he hedging process. I capure he limis of arbirage (Shleifer and Vishny, 1997) in his marke by deriving a simple asse pricing model where producers and consumers of commodiies share risk wih broker-dealers who are subjec o funding consrains. In equilibrium, he price of aggregae commodiy risk decreases in he relaive leverage of he broker-dealer secor. I esimae he model in he cross-secion of individual commodiies and nd srong empirical suppor for is predicions. Flucuaions in risk-bearing capaciy have paricularly srong forecasing power for energy reurns, boh in-sample and ou-of-sample. Broker-dealers are leveraged nancial insiuions, such as invesmen banks, who buy and sell securiies for a fee, hold an invenory of securiies for resale, or do boh. 1 They are disinguished from oher invesor classes by heir acive, pro-cyclical managemen of leverage: Adrian and Shin (2008a) documen ha expansions in broker-dealer asses are accompanied by increases in leverage as broker-dealers ake advanage of greaer balance shee capaciy. Conversely, conracions in broker-dealer asses are accompanied by decreases in leverage as risk consrains ighen. Consequenly, o an ouside observer, i would appear ha he risk-bearing capaciy, or e ecive risk aversion, of broker-dealers changes wih marke oucomes. The lieraure on limis of arbirage and is applicaions o seg- 1 Guide o he Flow of Funds Accouns, Board of Governors of he Federal Reserve (2000) 1

5 mened markes suggess ha he pricing implicaions of ime-varying e ecive risk aversion are larges when broker-dealers are predominanly on one side of he marke. 2 Following his lieraure, I argue ha he e ecive risk aversion of brokerdealers deermines risk premia in commodiy derivaives because broker-dealers are, o a large exen, he marginal invesor on he speculaive side of he marke. The imporance of broker-dealers sems from he high degree of inermediaion required o funnel nancial invesor capial ino commodiies. Unlike socks, bonds and oher securiies, he rading of many physical commodiies involves signi can ransporaion and sorage coss as well as possible informaional asymmeries (such as qualiy concerns), which discourage nancial invesors from engaging in physical commodiy ransacions in he markeplace. To bypass hese marke imperfecions, commodiy price risk can be securiized and raded via derivaives ha reference physical commodiies. A brief overview of his marke is provided below Marke for Commodiy Derivaives There are wo broad caegories of commodiy derivaives: exchange-raded derivaives and OTC derivaives. Exchange-raded derivaives include fuures and opions raded in exchanges such as he New York Mercanile Exchange and Chicago Mercanile Exchange. While in principle any invesor can buy or sell hese securiies, he large noional sizes of fuures conracs and he perceived riskiness of commodiies have radiionally discouraged reail and insiuional invesors alike. Only recenly have invesable commodiy indexes and exchange raded funds made he asse class more accessible o a broader class of invesors. 3 Despie his de- 2 Gromb and Vayanos (2010) provide an excellen survey of he heoreical lieraure on limis of arbirage. An example of a siuaion where nancial inermediaries are predominanly on one side of he marke is provided by Froo (1999) who sudies he pricing of caasrophe insurance. 3 Tang and Xiong (2010) examine he nancializaion process of commodiies precipiaed by he rapid growh of index invesmen o he commodiies markes since he early 2000s. 2

6 velopmen, he exchange-raded marke sill represens less han 10% of he oal marke for commodiy derivaives: A he peak of he June 2008 boom, he Commodiy Fuures Trading Commission (2008) esimaed he oal noional value of all commodiy fuures and opions ousanding in U.S. exchanges o be $946 billion, which is approximaely 85% of all exchange-raded commodiy derivaives ousanding worldwide (Bank for Inernaional Selemens, 2008). A he same ime, he Bank for Inernaional Selemens esimaed he oal noional value of all OTC commodiy derivaives ousanding worldwide o be $13.2 rillion. Unlike sandardized conracs raded in exchanges, OTC derivaives (such as forwards, swaps, and opions) are ailored o sui he needs of individual invesors. In OTC ransacions cliens bargain direcly wih broker-dealers who are he marke makers in hese derivaives. Upon reaching an agreemen, he broker-dealer may hold he commodiy risk on is rading book unil i receives an o seing OTC posiion, or i may hedge is ne exposure using an exchange-raded derivaive or anoher OTC conrac. In addiion o he price risk associaed wih pure marke making, mos commodiy raders ake on commodiy risk by choosing no o hedge heir books or by holding enirely speculaive posiions. Some larger broker-dealers even speculae by holding ourigh posiions in physical commodiies. The overwhelming size of he OTC marke relaive o he exchange-raded marke highlighs he imporance of broker-dealer capial for he funcioning of commodiy derivaives markes. As such, he premium ha hedgers are required o pay for insurance agains commodiy price risk is likely o be a eced by he e ecive risk aversion of broker-dealers. To he exen ha hedgers demand for insurance is independen of broker-dealers risk consrains, broker-dealers e ecive risk aversion can be expeced o impac he equilibrium reurns on commodiy derivaives. 4 Absence of arbirage across derivaives markes implies ha he risk 4 Grossman and Miller (1988) emphasize ha hedgers also have a srong preference for immediacy in hedging ransacions. This furher increases heir vulnerabiliy o shifs in broker- 3

7 premia of OTC ransacions are also incorporaed in he reurns on exchangeraded derivaives Theoreical and Empirical Sraegy I formalize he link beween broker-dealer risk-bearing capaciy and securiy risk premia by deriving a simple asse pricing model where risk-consrained brokerdealers provide insurance o households who wish o hedge heir posiions in physical commodiies. Broker-dealer leverage is limied by a value-a-risk (VaR) consrain, which caps he probabiliy of insolvency. 6 In equilibrium, he required reurn on a securiy depends on is comovemen wih he marke porfolio, bu also on is residual comovemen wih he aggregae porfolio of physical commodiies. I refer o he laer as he aggregae non-markeable porfolio. Thus, here is an addiional sysemaic risk facor he reurn on he aggregae non-markeable porfolio which deermines securiy reurns in addiion o he marke risk facor. The premium per uni of non-markeable risk is pinned down by he economy s e ecive risk aversion. I show ha he e ecive risk aversion varies over ime wih he ighness of broker-dealers risk consrains and i can be expressed as a funcion of aggregae balance shee componens of broker-dealers and households. This innovaion allows me o esimae he model using aggregae balance shee daa from he Federal Reserve s Flow of Funds Accouns. The model predics ha, conrolling for marke risk, he measure of e ecive risk aversion forecass reurns on securiies ha co-move wih he aggregae non-markeable porfolio. Since he marke risk adjused reurns of di eren securiies load di erenly on he non-markeable risk facor, he model also delivers a cross-secional predicion for he magniude and direcion of he forecasing dealers e ecive risk aversion. 5 Due o poor availabiliy of OTC forwards daa, he empirical secion uses daa on fuures conracs. 6 Adrian and Shin (2008c) provide a micro foundaion for his consrain from a moral hazard problem beween borrowers and lenders. 4

8 relaionship. The empirical secion of he paper ess hese predicions for 14 commodiy fuures, wo invesable commodiy indexes, and oher securiies Relaed Lieraure This paper builds on wo broad srands of lieraure: he lieraure on nancial marke fricions and asse prices as well as he exensive lieraure on he deerminans of commodiy prices. The idea ha he risk-bearing capaciy of arbirageurs is limied and has consequences for asse prices originaes in he work on limis of arbirage pioneered by Shleifer and Vishny (1997). Gromb and Vayanos (2002) and Brunnermeier and Pedersen (2009) are among he rs o relae arbirageurs inabiliy o exploi price di erences o endogenous balance shee consrains. The speci c funding consrains analyzed in his paper build on he work of Adrian and Shin (2008a,b,c) who demonsrae ha he acive managemen of nancial inermediary balance shees generaes procyclical leverage, which has consequences for asse prices. My nding ha he risk-bearing capaciy of broker-dealers deermines risk premia in commodiy markes is mos similar in spiri o he nding of Adrian, Eula and Shin (2009) ha ucuaions in shor-erm U.S. dollar funding liquidiy deermine risk premia in foreign exchange markes, and o he nding of Adrian and Shin (2008a) ha ucuaions in shor-erm funding liquidiy forecas changes in he VIX risk premium. The view ha balance shee consrains in uence risk premia receives srong suppor in he evens of he nancial marke urmoil, which show how he ighening of nancial inermediary funding consrains may lead o subsanial sysemaic asse pricing consequences. The lieraure on he deerminans of expeced commodiy reurns can be roughly divided ino wo groups. The rs group uses he CAPM o argue ha he expeced reurn on commodiy holdings is compensaion for sysemaic risk. Early sudies include Black (1976) and Breeden (1980) who explain he variaion 5

9 in fuures prices by sysemaic risk ha sems from changes in economic sae variables. Tess of hese models nd scan evidence in he daa, as shown by Jagannahan (1985) and a number of oher sudies. More recenly, Bessembinder and Chan (1992) nd ha he same variables ha forecas marke reurns e.g., dividend yield, ineres rae, and yield spread also forecas commodiy reurns. This suggess ha ime-varying risk premia in commodiies could be driven by macro-economic forces ha deermine asse allocaion. Goron and Rouwenhors (2006) argue ha commodiy fuures, as an asse class, provide a risk-reurn pro le ha is comparable o ha of equiies. The second group of sudies argues ha he expeced reurn of holding commodiies is driven largely by commodiy-speci c facors. Mos relevan for he presen paper are he sudies ha nd addiional forecasabiliy of commodiy fuures reurns using he ne posiions of hedgers in he fuures marke, which is known as hedging pressure. The idea of hedging pressure daes back o Keynes (1930) whose heory of normal backwardaion argues ha producers shor fuures o hedge heir iniially long posiions in he underlying physical commodiy. Goron, Hayashi and Rouwenhors (2007) provide a comprehensive review of he lieraure and show ha while he direcion of ne hedging is consisen wih Keynes hedging pressure hypohesis, commodiy-speci c hedging pressures do no have signi can forecasing abiliy for fuures reurns. Models ha allow boh sysemaic and commodiy-speci c predicors of fuures prices include Soll (1979) and Hirschleifer (1988, 1989). Empirical evidence for he combined role of commodiy-speci c hedging pressure and sysemaic risk include Carer, Rausser and Schmid (1992), Bessembinder (1992), and de Roon, Nijman and Veld (2000). Hong and Yogo (2009) show ha he aggregae fuures basis explains as much of he variaion in expeced reurns as sysemaic predicors. The curren paper conribues o he rs group of commodiy sudies by demonsraing ha, for a se of commodiies, a signi can porion of he ime- 6

10 variaion in expeced reurns can be aribued o ime-variaion in U.S. brokerdealer risk appeie. The paper s argumen for why broker-dealer risk appeie maers for expeced commodiy reurns builds on he second group of sudies: broker-dealers have an imporan role in providing insurance o producers and consumers of commodiies who wish o hedge heir posiions in he underlying commodiies. Anson (2002) and Erb and Harvey (2006) sugges ha fuures sraegies ha engage in such insurance provision have earned posiive excess reurns. The resuls in his paper are also nicely consisen wih he recen nding of Acharya, Lochsoer and Ramadorai (2009) ha he risk appeie of oil and gas producers, as proxied by heir defaul risk, forecass fuure reurns on hese commodiies. The auhors build on my resuls o show ha boh broker-dealer risk-bearing capaciy and producer defaul risk forecas commodiy reurns. My heoreical framework combines insighs from he commodiy pricing model of de Roon, Nijman and Veld (2000) and he asse pricing model of Danielsson, Shin and Zigrand (2008). In he laer model, he risk appeie of arbirageurs shifs endogenously wih balance shee consrains ha ucuae wih marke oucomes, generaing endogenous risk. The balance shee consrains are imposed by a conracing seing of Adrian and Shin (2008c), which yields a value-a-risk rule. In addiion o he lieraure on limis of arbirage, he model has similariies wih he large behavioral nance lieraure on noise rader risk (e.g. DeLong, Shleifer, Summers and Waldmann, 1990; Barberis, Shleifer and Vishny, 1998; Hong and Sein, 1999), and marke making (e.g. Grossman and Miller, 1988; Kyle, 1985). I is also consisen wih Du e and Srulovici s (2009) model of limied capial mobiliy where higher coss of inermediaion increase reurn volailiy and prolong emporary risk premia. Overall, he disinguishing feaure of he curren heoreical framework is is abiliy o generae ime-varying e ecive risk aversion wihou resricive assumpions on he behavior of passive raders. By focusing on he acions of risk-consrained nancial insiuions, he model is also disincly 7

11 di eren from he consumpion-based models ha generae ime-varying risk aversion hrough, for insance, habi formaion (Campbell and Cochrane, 1999; Chan and Kogan, 2002). The ouline of he paper is as follows. Secion 2 develops a simple heoreical model, which inroduces risk-consrained broker-dealers in an equilibrium pricing model for commodiies. Secion 3 esimaes he model in he daa and conducs robusness checks. Secion 4 digs deeper ino energy commodiies and o ers a discussion of he 2008 run-up in energy prices. Secion 5 concludes. 2. Theoreical Framework As discussed above, here is an exensive lieraure ha relaes commodiy risk premia o wo componens: sysemaic markeable risk and commodiy-speci c hedging pressure. 7 The laer arises from risks ha agens canno, or do no wan o, rade because of marke fricions such as ransacion coss or informaional asymmeries. Following his lieraure, consider an economy wih markeable asses A, forwards conracs F, and non-markeable asses N. Le he respecive vecors of excess reurns be denoed by r A +1, r F +1, and r N +1. The non-markeable asses may serve as he underlying value of he forwards conracs and can also coincide wih some of he markeable asses. While he non-markeable asses by de niion do no ener he marke porfolio, hey may in uence porfolio choice. Suppose here are wo ypes of agens in he economy: funding consrained broker-dealers and risk averse households. The porfolio of agen j consiss of posiions in markeable asses! j A;, forwards!j F;, and non-markeable asses qj : r j +1 =! j0 A ra +1 +! j0 F rf +1 + q j0 r N +1: Each posiion is expressed as a fracion of he agen s nancial wealh, e j. 7 For insance, de Roon, Nijman and Veld (2000). 8

12 2.1. Funding Consrained Broker-Dealers Suppose broker-dealers (bd) are risk neural bu subjec o risk consrains, which ensure ha each dealer s equiy is su cienly large o cover heir Value a e bd Risk (V ar ). 8 Broker-dealers rade only markeable securiies. Tha is, hey end o shy away from direc purchases and sales of physical commodiies because of aforemenioned coss associaed wih such ransacions. Thus, he reurn on broker-dealer equiy derives from posiions in markeable asses and forwards: r bd +1 =! bd0 A;r A +1 +! bd0 F;r F +1: Each broker-dealer chooses is porfolio o maximize expeced reurn on equiy, subjec o he VaR consrain, max! bd A; ;!bd F; E r+1 bd s:: V ar e bd : By risk neuraliy, he risk consrain binds wih equaliy, deermining he leverage q of he dealer s porfolio. If V ar is some muliple of equiy volailiy q e bd V ar r+1 bd, he consrain becomes V ar r+1 bd 1. The Lagrangian is: L = E 0, De ne r +1 = r A +1; r+1 F! bd q V ar r+1 bd = 1 r+1 bd o obain he FOC: qv ar r+1 bd 1 : (2.1) =! bd A; ;!bd F; 0, and use he binding VaR consrain! bd = 1 [V ar (r +1 )] 1 E (r +1 ) : (2.2) This characerizes he broker-dealer s opimal porfolio choice. Noe ha equaion (2:2) is idenical o he sandard mean-variance choice bu wih he risk-aversion parameer replaced by, he Lagrange muliplier 8 My formulaion follows Danielsson, Shin and Zigrand (2009) who sudy his opimizaion problem in anoher conex. 9

13 associaed wih he risk consrain scaled by he consan. broker-dealers are risk-neural bu behave as if hey were risk-averse. In oher words, As he risk consrain binds harder, he shadow price increases, and leverage mus be reduced. The scaled Lagrange muliplier measures he e ecive risk aversion of broker-dealers. Plugging he broker-dealers porfolio choice (2:2) in he binding VaR consrain, one obains: q = E (r +1 ) 0 [V ar (r +1 )] 1 E (r +1 ): Tha is, he Lagrange muliplier associaed wih he risk consrain is proporional o he generalized Sharpe raio for he se of risky securiies raded in he marke as a whole Risk Averse Households Suppose he res of he invesors are risk averse households (hh). They rade o mean agains variance in he porfolio reurn, which depends on he reurns on markeable asses, forwards, and non-markeable asses: r+1 hh =! hh0 A;r A +1 +! hh0 F; r F +1 + q hh0 r N +1: Households choose posiions in markeable securiies o solve: De ning! hh max! hh A; ;!hh F; E r+1 hh 2 V ar r hh +1 : =! hh A; ;!hh F; 0, one obains he opimal porfolio choice:! hh = 1 [V ar (r +1 )] 1 E (r +1 ) Cov r +1 ; r+1 N q hh : (2.3) 10

14 2.3. Marke Porfolio Since forwards conracs are in zero ne supply, marke clearing implies: 0! M = M A; C A = e hh! hh e bd +ehh A; e bd ebd +ehh! bd A; 1 C A ; (2.4) If he marke porfolio is e cien in he sense ha i sais es he FOCs (2:2) and (2:3) for ;,, q hh, e hh and e bd, one obains: E (r +1 ) = M Cov r +1 ; r+1 M + Cov r +1 ; r N +1 q M ; (2.5) where r+1 M =! M0 r +1 is he reurn on he marke porfolio, 1 M = e bd e hh + e hh 1 + e bd e bd + e hh 1 (2.6) is he inverse of he economy s e ecive risk aversion, and q M = e bd e hh + e hh q hh (2.7) is he vecor of aggregae non-markeable posiions in he economy. Noe ha he aggregaes in (2:6) and (2:7) are wealh-weighed combinaions of he wo invesor groups respecive variables Equilibrium Reurns Leing i = Cov(ri +1 ;rm +1) denoe securiy i s bea wih he porfolio of markeable V ar (r M +1) asses, he expression (2:5) for equilibrium reurns can be rewrien as: E r+1 i = i E r+1 M + Cov r+1; i r+1 N q M i Cov r+1; M r N +1 q M + Cov r+1 i i r+1; M r+1 NM = i E r M +1 M M : (2.8) 11

15 The second line de nes: r NM +1 = r N0 +1q M ; (2.9) which is inerpreed as he excess reurn on he aggregae producion-weighed porfolio of N on-m arkeable securiies. Here non-markeable securiies are physical commodiies, and hence r NM +1 is he excess spo reurn on a porfolio of commodiies weighed by world producion values. The equilibrium of he model is summarized in: Proposiion 1 (Equilibrium Reurns). The risk premium of securiy i depends on is comovemen wih he aggregae porfolio of markeable asses and is comovemen wih he aggregae porfolio of non-markeable asses: E r+1 i {z } Securiy Risk Premium = i E r+1 M {z } Compensaion for Sysemaic Markeable Risk + i M {z } Compensaion for Sysemaic Non-Markeable Risk ; (2.10) where i = Cov r+1; i r+1 M =V ar r+1 M is he securiy s marke bea and i = Cov r+1 i r+1; M r+1 NM is he covariance of he securiy s risk-adjused reurn wih he aggregae non-markeable porfolio. The risk premium per a uni of i is he expeced reurn on he porfolio of markeable asses, E r+1 M. The risk premium per a uni of i is he economy s e ecive risk aversion, M. Imporanly, he compensaion for sysemaic non-markeable risk varies across securiies, as summarised in he following corollary: Corollary 1 (Cross-Secional Predicion). The risk premium of securiy i increases in e ecive risk aversion if is risk-adjused reurn covaries posiively wih he porfolio of non-markeable asses, i > 0. Conversely, he risk premium of securiy i decreases in e ecive risk aversion if is risk-adjused reurn covaries negaively wih he porfolio of non-markeable asses, i < 0. Sricly speaking (2:10) prices only securiies markeable asses and forwards. However, i is possible ha e cien invenory managemen (basis arbirage) by 12

16 holders of physical commodiies keeps he excess reurns on some cash commodiies close o he reurns on he corresponding nearby forwards conracs. 9 Hence, he equilibrium pricing predicions of he model may carry over o some spo reurns Empirical Implemenaion Proposiion 1 saes ha securiy risk premia are deermined by wo sysemaic risk componens: one ha sems from aggregae markeable risk and anoher ha sems from aggregae non-markeable risk. I can es he empirical validiy of he proposiion by esimaing (2:10) for individual securiies reurns. To do his, I assume consan condiional variances and covariances, replace he expecaions in by realizaions, and add a consan o obain: r+1 i = i + i r+1 M + i M + i +1; (2.11) where i +1 r+1 i E r+1j1; i r+1; M M is he predicion error. Since he e ecive risk aversion M is no direcly observable in he daa, he nex sep is o express i as a funcion of observable variables. Sar by rewriing (2:6) as M = 1 + ebd 1 e hh M : (2.12) In order o obain an expression for M, plug he equilibrium expressions (2:5) and (2:9) in he broker-dealer s FOC (2:2):! bd = M [V ar (r +1 )] 1 Cov r +1 ; r+1 M + Cov r +1 ; r+1 NM : Using he de niion of he marke porfolio and de ning h [V ar (r +1 )] he above simpli es o:! bd 9 See, for insance, Acharya, Lochsoer and Ramadorai (2009). = M! M + h ; (2.13) 1 Cov r +1 ; r+1 NM, 13

17 where vecor h capures he ne shor open ineres of households. To see his, noe ha households collecively wish o shor h i e bd + e hh dollars worh of markeable securiy i o hedge he price risk ha sems from heir aggregae holdings of non-markeable securiies. 10 Equaion (2:13) saes ha broker-dealers ful ll a fracion M of his open ineres. Noe ha h i is loosely relaed o he noion of hedging pressure, which is commonly de ned as he ne shor open ineres of hedgers divided by he oal open ineres of hedgers. Summing (2:13) over individual securiies posiions, one obains: M = Pi!bd i; P i!m i; + P i h i; : (2.14) By balance shee ideniy, he value of risky securiies holdings of invesor j mus equal he value of equiy plus he value of deb: e j X! j i; = ej + deb j ; i which implies ha one can de ne he nancial leverage of broker-dealers and households as: lev j 1 + debj e j = X i and he aggregae nancial leverage is given by:! j i; ; j 2 fbd; hhg ; lev M 1 + debbd e bd + deb hh + e hh = X i! M i;: Using his noaion, subsiue (2:14) ino (2:12) o obain: M = 1 + ebd lev bd 1 e hh lev M + P i h : (2.15) i; Since he focus of his paper is he broker-dealer secor, no he hedging decisions of producers and consumers of commodiies, I will assume ha he aggregae 10 Since he ne supply of hedging posiions is zero, hese posiions are no par of he marke porfolio. 14

18 ne open ineres of hedgers is consan over ime, P i h i; = H, such ha: M = 1 + ebd lev bd 1 : (2.16) e hh lev M + H Equaion (2:16) saes ha he ime-variaion in e ecive risk aversion can be explained by he produc of wo erms: he rs erm is he fracion of brokerdealer equiy relaive o household equiy; he second erm is he fracion of broker-dealer nancial leverage relaive o he nancial leverage of he marke plus a consan. In he absence of broker-dealers e bd = 0, he e ecive risk aversion is consan and given by. Normalizing he consans = 1 and H = 0, equaion (2:16) moivaes he following empirical proxy for e ecive risk aversion: ^ M = 1 + Broker-Dealer Equiy Broker-Dealer Leverage 1 : (2.17) Household Equiy Marke Leverage Time-Series I employ (2:17) s measure of e ecive risk aversion in (2:11) o obain he imeseries regression: r i +1 = i + i r M +1 + i^m + i +1; (2.18) where r i +1 is he excess reurn on securiy i, and r M +1 is he excess reurn on he marke. This is he main regression speci caion o be esimaed in Secion 3.2. A poenial cavea of he measure of e ecive risk aversion in (2:17) is he implici assumpion ha one can always infer broker-dealers risk-bearing capaciy from heir level of leverage. In realiy, however, his assumpion may no hold. For insance, i is conceivable ha here are fricions in he marke ha do no allow broker-dealers o adjus leverage insananeously in response o changes in risk consrains. One such poenial fricion is marke illiquidiy, which limis he broker-dealer s abiliy o rapidly buy and sell large quaniies of securiies in he markeplace. In he presence of such fricions, igher risk consrains may coincide wih high bu decreasing leverage as broker-dealers srive o decrease he 15

19 size of heir balance shees. Similarly, more permissive funding condiions may coincide wih low bu increasing leverage as broker-dealers look for ways o pu heir increased balance shee capaciy o work. Thus, i is possible ha one may no be able o accuraely infer he level of e ecive risk aversion from he levels of balance shee variables. Ye, one migh be able o capure changes in e ecive risk aversion, or a leas he direcion of hese changes, from observable balance shee dynamics. To invesigae his possibiliy, Secion 3.2 also implemens he following speci caion: r+1 i = i + i r+1 M + i ^ M + i +1; (2.19) where ^ M = ^ M ^ M 1 is he rs di erence in (2:17) Cross-Secion In order o es he cross-secional predicion of he model (Corollary 1), I compue he model-prediced loadings on M indexes by: for individual commodiy derivaives and Model i = Cov r+1 i i r+1; M r+1 NM ; (2.20) where i is he OLS esimae of securiy i s marke bea, r M +1 is he marke excess reurn, and r NM +1 is he excess reurn on he GSCI Spo index, which weighs commodiies by heir respecive world producion quaniies. 11 I hen compare hese model-prediced loadings Model i o he OLS esimaes of i obained from (2:18) : The resuls are analyzed in Secion Empirical Resuls The previous secion provided a simple heoreical jusi caion for he link beween he ighness of broker-dealer risk consrains and he economy s e ecive 11 Recall ha he weighs of he non-markeable porfolio r+1 NM are given by he vecor of aggregae non-markeable posiions q M in he economy. 16

20 risk aversion, M. The analysis also demonsraed how o consruc an empirical proxy for e ecive risk aversion using daa on he aggregae balance shee componens of broker-dealers and households. In his secion, I follow hese insrucions o invesigae he exen o which he heoreical predicions of he model hold in he daa. The baseline regressions cover he ime period Q3/1990-Q4/2007, he beginning of which was seleced based on daa availabiliy. The ime period Q1/2008-Q3/2009, which includes he 2008 run-up and crash in crude oil prices as well as he dramaic conracion in broker-dealer balance shees, is sudied separaely a he end of he secion Daa The empirical analysis focuses on he fuures and spo reurns of four energy commodiies (crude oil, heaing oil, gasoline and naural gas), four meals (copper, silver, plainum, gold), and six agriculural commodiies (sugar, coon, corn, soybeans, cocoa, and whea). 12 The individual commodiies were seleced based on heir respecive world producion quaniies and he liquidiy of fuures conracs. I also use daa on wo invesable commodiy fuures indexes (S&P Goldman Sachs Commodiy Index and Dow Jones-UBS Commodiy Index). The price daa on individual commodiies and commodiy indexes are obained from Bloomberg and Daasream. Excess spo reurns are generaed by subracing he 3-Monh Treasury Bill rae from he oal quarerly reurns. Since posiions in fuures conracs are pure bes in he sense ha hey require no invesmen oulays, excess fuures reurns are given simply by percenage price changes. To ensure liquidiy, I compue quarerly reurns from rolling fron-monh conracs Due o poor availabiliy of daa on OTC forwards, I use daa on fuures conracs insead. By absence of arbirage, fuures reurns can be expeced o re ec he risk premia of OTC conracs. 13 The one-monh excess reurn a he end of monh is given by F ;T F 1;T 1; 17

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