Repurchase Agreements, Collateral Re-Use and Intermediation

Transcription

1 Repurchae Agreement, Collateral Re-Ue and Intermediation Piero Gottardi Vincent Maurin Cyril Monnet EUI, EUI, Bern Rome TV, Feb. 26, 2016 Gottardi, Maurin, Monnet (EUI, EUI, Bern) Repo Rome TV, Feb. 26, / 27

2 Motivation: Importance of Repo Repo: ale of an aet combined with a forward contract (to repurchae of the aet) di erence from collateralized loan: pledged collateral (re-ue) repo lender obtain right to Repo received coniderable attention ince the crii: extenively ued by market maker, dealer bank,... to get fund, acquire ecuritie, get afe return on cah. Growing body of work on repo, but till ome important quetion to anwer... Gottardi, Maurin, Monnet (EUI, EUI, Bern) Repo Rome TV, Feb. 26, / 27

3 Repo: Important iue 1. Repo v. Sale : you could ell the aet pot to obtain fund.! Obtain le cah than with a pot ale if haircut>0... Haircut = pot price - repo price! Commit to a future repurchae price. 3/35

4 Repo: Important iue 1. Repo v. Sale : you could ell the aet pot to obtain fund.! Obtain le cah than with a pot ale if haircut>0... Haircut = pot price - repo price! Commit to a future repurchae price. 2. What determine haircut?! Some empirical evidence that haircut increae with counterparty or aet rik...! but haircut are a puzzle (GM, JFE 2012). 3/35

5 Repo: Haircut index Figure: Haircut index (bilateral repo). Source : GM, JFE /35

6 Repo: Some Iue 3. Why repo and not collateralized lending?! Lender acquire ownerhip of the collateral. 5/35

7 Repo: Some Iue 3. Why repo and not collateralized lending?! Lender acquire ownerhip of the collateral. I Acquiring ownerhip mean you can re-ue the aet!! Allow collateral to circulate (Singh 2010, 2011,..).! Allow agent to intermediate repo: Dealer lend to a Hedge Fund and borrow from a Mutual Fund. Bilateral v. Tri-party egment of the market. 5/35

8 Repo: Some Iue 3. Why repo and not collateralized lending?! Lender acquire ownerhip of the collateral. I Acquiring ownerhip mean you can re-ue the aet!! Allow collateral to circulate (Singh 2010, 2011,..).! Allow agent to intermediate repo: Dealer lend to a Hedge Fund and borrow from a Mutual Fund. Bilateral v. Tri-party egment of the market. I Du e & Skeel (2012) and Infante (2013) analyze ale of collateral but focu on the conequence upon default. 5/35

9 Thi paper I Model: Agent 1 with a riky aet want to get fund from rik avere agent 2. With limited commitment, he need to ue the aet.! Can do pot trade, collateralized borrowing, repo. 6/35

10 Thi paper I Model: Agent 1 with a riky aet want to get fund from rik avere agent 2. With limited commitment, he need to ue the aet.! Can do pot trade, collateralized borrowing, repo. I Equilibrium repo trade-o : 1. Borrowing need 2. Hedging need of the lender. Wary of price rik of reelling. 6/35

11 Thi paper I Model: Agent 1 with a riky aet want to get fund from rik avere agent 2. With limited commitment, he need to ue the aet.! Can do pot trade, collateralized borrowing, repo. I Equilibrium repo trade-o : 1. Borrowing need 2. Hedging need of the lender. Wary of price rik of reelling. I Haircut increae with aet rik and counterparty rik and afer aet command a higher liquidity premium. 6/35

12 Thi paper I Model: Agent 1 with a riky aet want to get fund from rik avere agent 2. With limited commitment, he need to ue the aet.! Can do pot trade, collateralized borrowing, repo. I Equilibrium repo trade-o : 1. Borrowing need 2. Hedging need of the lender. Wary of price rik of reelling. I Haircut increae with aet rik and counterparty rik and afer aet command a higher liquidity premium. I We how that collateral re-ue: 1. Help agent reach firt bet through collateral multiplier e ect. 2. Generate endogenou intermediation. 6/35

13 Outline Introduction The Model Equilibrium Repo Equilibrium Comparative Static: Haircut Aet re-ue Re-ue and Collateral Supply Re-ue and Intermediation 7/35

14 Environment I 1 perihable conumption good and 2 agent i 2{1, 2}. I 3period:t =1, 2, 3 I Supply a of an aet with payo G on [, ] in period 3.! Payo known in period 2. I Endowment: Agent 1 : (!,!,!), a0 1 = a, Agent 2 : (!,!, 0), a0 2 =0 I Preference over conumption (c 1, c 2, c 3 ): v 1 (c 1, c 2, c 3 )=c 1 + (c 2 + c 3 ), < 1 v 2 (c 1, c 2, c 3 )=c 1 + u(c 2 ) with u concave atifying Inada condition. I Aumption : u 0 (!) >. Gain from trade. 8/35

15 Firt-Bet Allocation Period 1 Period 2 Period 3 known realized (!, a)!! Agent 1 c1 1 c2 1 c3 1 (c2, 2!) c2, 2! Agent 2 (!, 0)! c 2 1 u(c 2 2 ) I Firt bet allocation: u 0 (c 2 2, )=. I Implementation: Agent 1 borrow (c 2 2,!) atrater =1/ 1. 9/35

16 Limited Commitment I Limited commitment: need to ue the aet to trade.! Spot ale or collaterized borrowing. I FB allocation never attainable under pot trade which generate price reelling rik for agent / 35

17 Limited Commitment I Limited commitment: need to ue the aet to trade.! Spot ale or collaterized borrowing. I FB allocation never attainable under pot trade which generate price reelling rik for agent 2. I Agent 2 would purchae the aet in t =1andreellint = 2. I Agent 1 i the only one to hold the aet after t =2 Spot price p 2 () = = MWP of Agent 1! Agent 2 i rik-avere. Dilike the price rik. I Alternatively, you can ue repo. 10 / 35

18 Repurchae contract I Definition: ArepoF = { p()} 2[, ] i an agreement to repurchae the aet at price p() intate of period 2. I Repo F traded competitively at price p F in t = / 35

19 Repurchae contract I Definition: ArepoF = { p()} 2[, ] i an agreement to repurchae the aet at price p() intate of period 2. I Repo F traded competitively at price p F in t = 1. I Sell 1 contract F borrow p F with repayment chedule { p()}.! Amount a F old = collateral pledged. 11 / 35

20 Repurchae contract I Definition: ArepoF = { p()} 2[, ] i an agreement to repurchae the aet at price p() intate of period 2. I Repo F traded competitively at price p F in t = 1. I Sell 1 contract F borrow p F with repayment chedule { p()}.! Amount a F old = collateral pledged. I Default in tate : collateral lo+ penalty p()a F with 2 [0, 1]. No default p()a F apple ( p())a F p() apple (1) I Set of feaible repo: F = {F (1) hold}! No lo of generality in focuing on default free contract. 11 / 35

21 Equilibrium Selection of Repo I We olve for a competitive equilibrium where agent may trade pot and any repo F 2F. I Equilibrium elect the repo contract() that agent actually trade. All contract (even non-traded one) in F are priced in equilibrium. I Gue and Verify : In equilibrium, agent only trade one contract. 12 / 35

22 Conumer Problem I Let F = { p()} be that repo contract. I a i t: pot poition of agent i in period t. a i F : repo poition (period 1). ai F apple 0: eller. I Agent i problem max v i (c1, i c2, i c3) i ct i,ai t,ai F ubject to c i 1 =! p 1 (a i 1 a i 0) p F a i F 0 c i 2() =! + (a i 2 a i 1)+ p()a i F 0 c i 3() =1 {i=1}! + a i 2 a i 1 0 i 1 (No hort ale) a i 1 + a i F 0 i 1 (Collateral Contraint) 13 / 35

23 Equilibrium Repo Propoition In equilibrium, agent only trade repo: a 2 1 =0=a a 1 1 Define := (a,, ) a the olution to u 0! + a = = u 0 (c2, ) 2 The (eentially) unique equilibrium repo i F = { p()} where: i) If > (a low) ii) If 2 [, ] (a intermediate): p() = p() = ( if apple if > iii) If apple, p() = p i contant and p 2 [ /(), /()] 14 / 35

24 Equilibrium Repo: Borrowing v. Hedging Motive p() 15 / 35

25 Equilibrium Repo: Borrowing v. Hedging Motive p() Borrowing Motive c 2 2 () < c2 2, Hedging Motive c 2 2 () =c2 2, 15 / 35

26 Intuition I Intermediate Region : p() = ( if apple if > I FB allocation c 2 2 () =c2 2, uch that u0 (c 2 2, )= I Feaible repo p ) c2 2 () apple! + a/(). I When apple, hit the no default contraint p() =/(1! Borrowing Motive. ). I When >, you can have c 2 2 () =c2 2,.! Hedging Motive: Flat part in the repo contract. 16 / 35

27 Graphic Argument I p optimal contract among p 2F : E[( p() p()(u 0 (c 2 2 ()) )] 0 p() u 0 (c 2 2 ()) ŝ 17 / 35

28 Graphic Argument I p optimal contract among p 2F : E[( p() p()(u 0 (c 2 2 ()) )] 0 p() u 0 (c 2 2 ()) ŝ 17 / 35

29 Graphic Argument I p optimal contract among p 2F : E[( p() p()(u 0 (c 2 2 ()) )] 0 p() u 0 (c 2 2 ()) ŝ 17 / 35

30 Graphic Argument I p optimal contract among p 2F : E[( p() p()(u 0 (c 2 2 ()) )] 0 p() u 0 (c 2 2 ()) ŝ 17 / 35

31 Graphic Argument I p optimal contract among p 2F : E[( p() p()(u 0 (c 2 2 ()) )] 0 p() u 0 (c 2 2 ()) ŝ 17 / 35

32 Haircut I The haircut i the di erence between the pot and the repo price: H = p 1 p F = (E[] E[ p()]) p() + 18 / 35

33 Haircut I The haircut i the di erence between the pot and the repo price: H = p 1 p F = (E[] E[ p()]) p() + I Aet i carce = high: can have negative haircut.! Documented for ome ecuritie: on the run treaurie, collateral on pecial (cf. Vayano & Weill 2008). 18 / 35

34 Haircut - Pledgeability : I Haircut H = E[ p()] I Comparative Static: change from L to H > L :betterborrower. p() L L L L 19 / 35

35 Haircut - Pledgeability : I Haircut H = E[ p()] I Comparative Static: change from L to H > L :betterborrower. p() H L H H H I Agent with H can borrow more: H&! High quality counterpartie face lower haircut. 19 / 35

36 Aet Rik I Introduce two aet with perfectly correlated payo.! Safe aet pay.! Riky aet i mean-preerving pread of afe aet. riky = ( afe E[]) + E[], > 1 I We can apply the previou analyi with thee two aet. 20 / 35

37 Aet Rik I Introduce two aet with perfectly correlated payo.! Safe aet pay.! Riky aet i mean-preerving pread of afe aet. riky = ( afe E[]) + E[], > 1 I We can apply the previou analyi with thee two aet. I Claim : riky aet ha a higher haircut and a lower liquidity premium (LP) where LP = p 1 E[] I Rikier aet i wore collateral.! Can borrow le per unit of aet : higher haircut.! Le deirable than afe aet : lower liquidity premium. 20 / 35

38 Outline Introduction The Model Equilibrium Repo Equilibrium Comparative Static: Haircut Aet re-ue Re-ue and Collateral Supply Re-ue and Intermediation 21 / 35

39 Collateral re-ue I So far, repo = collateralized loan.! Main di erence: collateral i old in a repo: lender can re-ue it.! Propoition 1 (a low): Agent 1 want to buy to pledge more! I Agent 2 become owner of fraction 2 2 [0, 1] of collateral pledged. Legal Definition 22 / 35

40 Collateral re-ue I So far, repo = collateralized loan.! Main di erence: collateral i old in a repo: lender can re-ue it.! Propoition 1 (a low): Agent 1 want to buy to pledge more! I Agent 2 become owner of fraction 2 2 [0, 1] of collateral pledged. Legal Definition I When pledging a F, Agent 1 lend 2 a F unit of aet Agent 2.! I lender implicit promie to return 2 a F credible? I We treat lender default default in a ymmetric way and how the lender no default contraint doe not bind in equilibrium. Lender Default 22 / 35

41 Re-ue: Sequential proce I How much can you pledge with collateral re-ue?! Illutration a a equential proce. A1 a A2 Collateral Segregated 0 Figure: Re-ue and Pledgeability: Step 0 23 / 35

42 Re-ue: Sequential proce I How much can you pledge with collateral re-ue?! Illutration a a equential proce. A1 Pledge a ae[]/() A2 2 a (1 2 )a Collateral Segregated (1 2 )a Figure: Re-ue and Pledgeability: Step 1 23 / 35

43 Re-ue: Sequential proce I How much can you pledge with collateral re-ue?! Illutration a a equential proce. A1 Pledge 2 a 2 ae[]/() A2 2 2 a 2 (1 2 )a Collateral Segregated (1 2 )+ 2 (1 2 ) a Sell 2 a 2 ae[] Figure: Re-ue and Pledgeability: Step 2 I At tep n, agent 1 can pledge (in expected term) an additional: 2 ae[] n 1 23 / 35

44 Re-ue: Sequential proce I How much can you pledge with collateral re-ue?! Illutration a a equential proce. A1 Pledge 2 a A2 2 (1 2 )a Collateral Segregated 2 ae[]/() (1 2 )+ 2 (1 2 ) a Sell 2 a 2 ae[] Figure: Re-ue and Pledgeability: Step 2 I At tep n, agent 1 can pledge (in expected term) an additional: 2 ae[] n 1 I In the model, imultaneou trade with a conolidated collateral contraint. Detail 23 / 35

45 Equilibrium Repo: Re-ue Propoition Define ( ) := (a,, ) a the olution to u 0! + a ( ) 1 apple 1 = The equilibrium repo contract with re-ue i ( if < ( ) p(, )= ( ) + ( ( )) if ( ) If ( ) > a 1 1 = a 1 F = 1 1 a, a1 2 = 1 a, a2 F = a 1 F 24 / 35

46 Equilibrium Repo: Re-ue Propoition Define ( ) := (a,, ) a the olution to u 0! + a ( ) 1 apple 1 = The equilibrium repo contract with re-ue i ( if < ( ) p(, )= ( ) + ( ( )) if ( ) If ( ) > a 1 1 = a 1 F = 1 1 a, a1 2 = 1 a, a2 F = a 1 F Corollary: 1 () ( ) = (0) 1 There exit uch that if 2, equilibriumallocationifb. 24 / 35

47 Re-ue: Multiplier E ect I From Propoition 2: apple u 0! + a ( ) 1 1 I Ultimate quantity of collateral available i = a 0 =! Oberve that k(0, )=1forall 1 () a 1 {z } Collateral Multiplier k(, )! No multiplier e ect without ome commitment (Maurin, 2015). I Period 2 allocation (c2 1(), c2 2 ()) with aet a and re-ue i the ame than with aet a 0 and re-ue 0 25 / 35

48 Re-ue and Intermediation I Re-ue alo helpful to intermediate: Cah Cah Hedge Fund Dealer MMF Aet Aet re-ue Repo 1 Repo 2 I Dealer lend on bilateral repo market and borrow on the tri-party repo market. Why doe the Hedge Fund not borrow directly from the MMF. I i jut regulation? I We provide an explanation with di erence in counterparty quality.! Endogenou intermediation through better borrower. 26 / 35

49 Extending the model: 3 agent type I Let u have 2 type 1 agent:! Agent 1L : a0 L = a, L, L v L (c 1, c 2, c 3 )=c 1 + L (c 2 + c 3 )! Agent 1H; a0 H =0, H L, H H: v H (c 1, c 2, c 3 )=c 1 + H (c 2 + c 3 ) 27 / 35

50 Extending the model: 3 agent type I Let u have 2 type 1 agent:! Agent 1L : a0 L = a, L, L v L (c 1, c 2, c 3 )=c 1 + L (c 2 + c 3 )! Agent 1H; a0 H =0, H L, H H: v H (c 1, c 2, c 3 )=c 1 + H (c 2 + c 3 ) I For thi preentation, only agent 1H can re-ue collateral: L = 2 =0 I 1H i till a borrower with repect to 2 L apple H < u 0 (!) 27 / 35

51 Intermediation Equilibrium: Conjecture I Intermediation + Aet circulation in background. Segregate (1 H )a Sell (1 ) H a Pledge a Pledge H a A1L A1H A2 p LH p H2 I 1H mut be indi erent between red and green: Z 1 h i p H2 () u 0 c2 2 () H df () = ( H L) L H (1 H )( L ) I 1H lend b LH to 1L and borrow b H2 from 2. b LH (1 H )+b H2 = a 28 / 35

52 Intermediation Equilibrium I 1H more patient, better counterparty: L < H, L < H. Propoition If H L and a apple ā, the only contract traded in equilibrium are : 1. Arepo p LH where 1L borrow from 1H p LH () = L 2. Arepo p H2 where 1H borrow from 2 I Importantly, 1L and 2 do not trade directly but 1H intermediate. Benchmark cae 29 / 35

53 Intermediation Equilibrium: Intuition I Why doe 1L not trade with 2?! He ha the aet and higher gain from trade with 2: u 0 (!) L.! But L i low : cannot pledge much period 1 income. I 1H intermediate for 1L with hi higher borrowing capacity H > L. I Condition for intermediation: Let H 1 be the hadow price of the collateral contraint for 1H (1 H ) H 1 {z } Intermediation Cot apple E ( p H2 () p LH ()) u 0 (c2 2 ()) H {z } Intermediation Benefit 30 / 35

54 Intermediation Equilibrium: Interpretation I Intermediation valuable for non-trutworthy borrower: Cah Cah Hedge Fund L Aet Dealer H Aet re-ue MMF Bilateral Repo Tri-Party Repo I With partial commitment, counterparty and aet quality mixed.! Intermediation make the collateral more acceptable to MMF.. 31 / 35

55 Concluion I We preented a imple model of repurchae agreement :! Equilibrium repo among contract with limited commitment.! Haircut increae with aet rik and counterparty rik. I Repo are an e cient way of uing aet for borrowing/lending:! Equilibrium contract trade o borrowing/hedging motive.! Selling collateral allow for aet circulation/intermediation. I What next?! Collateral Tranformation.! Central Bank Policy : E ect of an aet purchae on repo.. 32 / 35

56 Trading Surplu I Net trading urplu S i = v i eq(c i 1, ci 2, ci 3 ) v i aut. I Agent 1 enjoy the liquidity premium on hi aet holding: S 1 = 1 1a = E[ p()(u 0 (c 2 2 () )]a An increae in the aet upply = = Z Agent 2 get hedging: appleu 0! u 00! + a a dg() Back to Preentation 32 / 35

57 Lender Default I Let now 2 be the reliability of agent 2. I Lender default : loe payment p()a F +penalty 2 2 a F.! No (lender) default if: p()a F 2 ( 2 )a F p() 2 ( 2 ) (2) I For a given { p()}, (2) give the maximal feaible 2. I In equilibrium, agent trade { p()} uch that (2) hold for 2 =0 and 2 = 1. Back to Preentation 32 / 35

58 Collateral Contraint with Re-ue I Repo F : ditinguih long af i,+ 0v.hortaF i, 0 poition. I Agent 1 (Borrower): a1 1 af 1,! Collateral contraint unchanged. I Agent 2 (Lender): a af 2,+ 0! Agent can re-ue (ell) 2 af 2,+ with... agent 1 I Agent 1 ha more aet to borrow by market clearing a1 2 + a2 2 = a Back to Preentation 32 / 35

59 3agent:Benchmarkcae1 I Identical Agent : L = H and L = H I Equilibrium:! 1L borrow a with contract p L2 with agent 2 ( p L2 () = if apple if >! 1H tay inactive I 1H would like to borrow from 2 a well but a H 1 = / 35

60 3agent:Benchmarkcae2 I Gain from trade: L = H, L < H. I Equilibrium:! 1L borrow b L2 with contract p L2 from agent 2 ( p L2 () = if apple (b L2, a, L ) (b L2,a, L ) if > (b L2, a, L )! 1H borrow b LH from 1H with contract p LH () =/( L ) I Equilibrium condition Agent 1L olve a portfolio allocation problem: a =(1 H )b LH + b L2 Mut be indi erent between borrowing from 1H and 2. I Importantly 1H and 2 do not trade! Back to Preentation 34 / 35

61 Definiton : Source ICMA I Repurchae agreement: In a repo, one party ell an aet (uually fixed-income ecuritie) to another party at one price at the tart of the tranaction and commit to repurchae the fungible aet from the econd party at a di erent price at a future date. I Lender Right: In Europe, repo tranfer legal title to collateral from the eller to the buyer by mean of an outright ale. [Under New York law], collateral i pledged but exempted from certain proviion of the US Bankruptcy Code that normally apply to pledge, in particular, the automatic tay on enforcement of collateral in the event of inolvency. In addition, unlike in traditional pledge, the pledgee/buyer in a US repo i given a general right of ue of collateral. Conequently, the reulting right are deemed to be much the ame a thoe achieved by an outright ale. Back to Preentation 35 / 35