Repurchase Agreements, Collateral Re-Use and Intermediation

Repurchase Agreements, Collateral Re-Use and Intermediation

Piero Gottardi Vincent Maurin Cyril Monnet

EUI, EUI, Bern

Rome TV, Feb. 26, 2016

Motivation: Importance of Repos

Repo:

sale of an asset combined with a forward contract (to repurchase of the asset)

di§erence from collateralized loans: repo lender obtains right to pledged collateral (re-use)

Repos received considerable attention since the crisis:

extensively used by market makers, dealer banks, ... to get funds, acquire securities, get safe return on cash.

Growing body of works on repo, but still some important questions to

answer ...

Repos: Important issues

1. Repos vs. Sales : you could sell the asset spot to obtain funds.

!Obtain less cash than with a spot sale if haircut>0...

Haircut = spot price - repo price

!Commit to a future repurchase price.

2. What determines haircuts?

!Some empirical evidence that haircuts increase with counterparty or asset risk...

!but“haircuts are a puzzle” (GM, JFE 2012).

Repos: Important issues

1. Repos vs. Sales : you could sell the asset spot to obtain funds.

!Obtain less cash than with a spot sale if haircut>0...

Haircut = spot price - repo price

!Commit to a future repurchase price.

2. What determines haircuts?

!Some empirical evidence that haircuts increase with counterparty or asset risk...

!but“haircuts are a puzzle”(GM, JFE 2012).

Repos: Haircuts index

Figure:Haircut index (bilateral repo). Source : GM, JFE 2012

Repo: Some Issues

3. Why repos and not collateralized lending ?

!Lender acquires ownership of the collateral.

I Acquiring ownership means you can re-use the asset!

!Allows collateral to circulate (Singh 2010, 2011,..).

!Allows agents to intermediate repo:

Dealers lend to a Hedge Fund and borrows from a Mutual Fund. Bilateral vs. Tri-party segments of the market.

I Duffie & Skeel (2012) and Infante (2013) analyze sale of collateral but focus on the consequence upon default.

Repo: Some Issues

3. Why repos and not collateralized lending ?

!Lender acquires ownership of the collateral.

I Acquiring ownership means you can re-use the asset!

!Allows collateral to circulate (Singh 2010, 2011,..).

!Allows agents to intermediate repo:

Dealers lend to a Hedge Fund and borrows from a Mutual Fund.

Bilateral vs. Tri-party segments of the market.

I Duffie & Skeel (2012) and Infante (2013) analyze sale of collateral but focus on the consequence upon default.

Repo: Some Issues

3. Why repos and not collateralized lending ?

!Lender acquires ownership of the collateral.

I Acquiring ownership means you can re-use the asset!

!Allows collateral to circulate (Singh 2010, 2011,..).

!Allows agents to intermediate repo:

Dealers lend to a Hedge Fund and borrows from a Mutual Fund.

Bilateral vs. Tri-party segments of the market.

I Duffie & Skeel (2012) and Infante (2013) analyze sale of collateral but focus on the consequence upon default.

This paper

I Model: Agent 1 with a risky asset wants to get funds from risk averse agent 2. With limited commitment, he needs to use the asset.

!Can do spot trade, collateralized borrowing, repos.

I Equilibrium repo trades-o↵: 1. Borrowing needs

2. Hedging needs of the lender. Wary of price risk of reselling.

I Haircuts increase with asset risk and counterparty risk and safer assets command a higher liquidity premium.

I We show that collateral re-use:

1. Help agents reach first best through collateral multiplier e↵ect. 2. Generates endogenous intermediation.

This paper

I Model: Agent 1 with a risky asset wants to get funds from risk averse agent 2. With limited commitment, he needs to use the asset.

!Can do spot trade, collateralized borrowing, repos.

I Equilibrium repo trades-o↵:

1. Borrowing needs

2. Hedging needs of the lender. Wary of price risk of reselling.

I Haircuts increase with asset risk and counterparty risk and safer assets command a higher liquidity premium.

I We show that collateral re-use:

1. Help agents reach first best through collateral multiplier e↵ect. 2. Generates endogenous intermediation.

This paper

I Model: Agent 1 with a risky asset wants to get funds from risk averse agent 2. With limited commitment, he needs to use the asset.

!Can do spot trade, collateralized borrowing, repos.

I Equilibrium repo trades-o↵:

1. Borrowing needs

2. Hedging needs of the lender. Wary of price risk of reselling.

I Haircuts increase with asset risk and counterparty risk and safer assets command a higher liquidity premium.

I We show that collateral re-use:

1. Help agents reach first best through collateral multiplier e↵ect. 2. Generates endogenous intermediation.

This paper

I Model: Agent 1 with a risky asset wants to get funds from risk averse agent 2. With limited commitment, he needs to use the asset.

!Can do spot trade, collateralized borrowing, repos.

I Equilibrium repo trades-o↵:

1. Borrowing needs

2. Hedging needs of the lender. Wary of price risk of reselling.

I Haircuts increase with asset risk and counterparty risk and safer assets command a higher liquidity premium.

I We show that collateral re-use:

1. Help agents reach first best through collateral multiplier e↵ect.

2. Generates endogenous intermediation.

Outline

Introduction The Model

Equilibrium

Repo Equilibrium

Comparative Statics: Haircuts

Asset re-use

Re-use and Collateral Supply Re-use and Intermediation

Environment

I 1 perishable consumption good and 2 agentsi2{1,2}.

I 3 periods : t = 1,2,3

I Supplya of an asset with payo↵s⇠G on [s,¯s] in period 3.

!Payo↵s known in period 2.

I Endowments:

Agent 1 : (!,!,!), a¹₀=a, Agent 2 : (!,!,0), a²₀= 0

I Preferences over consumption (c₁,c₂,c₃):

v¹(c₁,c₂,c₃) =c₁+ (c₂+c₃), <1 v²(c1,c2,c3) =c1+u(c2)

withu concave satisfying Inada condition.

I Assumption : u⁰(!)> . Gains from trade.

First-Best Allocation

Period 1 Period 2 Period 3

s known s realized

Agent 1 (!,a) ! !

c₁¹ c₂¹ c₃¹

Agent 2 (!,0) !

c₁² u(c₂²)

(c_2,²_⇤ !) c_2,²_⇤ !

I First best allocation: u⁰(c_2,²_⇤) = .

I Implementation: Agent 1 borrows (c_2,²_⇤ !) at rater = 1/ 1.

Limited Commitment

I Limited commitment: need to use the asset to trade.

!Spot sale or collaterized borrowing.

I FB allocation never attainable under spot trades which generate price reselling risk for agent 2.

I Agent 2 would purchase the asset int = 1 and resell int = 2.

I Agent 1 is the only one to hold the asset aftert = 2 Spot price p₂(s) =s= MWP of Agent 1

!Agent 2 is risk-averse. Dislikes the price risk.

I Alternatively, you can use repos.

Limited Commitment

I Limited commitment: need to use the asset to trade.

!Spot sale or collaterized borrowing.

I FB allocation never attainable under spot trades which generate price reselling risk for agent 2.

I Agent 2 would purchase the asset int = 1 and resell int = 2.

I Agent 1 is the only one to hold the asset aftert = 2 Spot price p2(s) =s= MWP of Agent 1

!Agent 2 is risk-averse. Dislikes the price risk.

I Alternatively, you can use repos.

Repurchase contract

I Definition: A repoF ={p(s)¯ }s2[s,¯s] is an agreement to repurchase the asset at price ¯p(s) in states of period 2.

I RepoF traded competitively at pricepF int = 1.

I Sell 1 contract F ⇠borrowpF with repayment schedule{p(s)¯ }s.

!AmountaF sold = collateral pledged.

I Default in state s: collateral loss+ penalty✓p(s)a¯ _F with✓2[0,1]. No default ✓p(s)a¯ _F (s p(s))a¯ _F

¯

p(s) s

1 ✓ (1)

I Set of feasible repos: F ={F|(1) holds}

!No loss of generality in focusing on default free contracts.

Repurchase contract

I Definition: A repoF ={p(s)¯ }s2[s,¯s] is an agreement to repurchase the asset at price ¯p(s) in states of period 2.

I RepoF traded competitively at pricepF int = 1.

I Sell 1 contractF ⇠borrowpF with repayment schedule{p(s)¯ }s.

!AmountaF sold = collateral pledged.

I Default in state s: collateral loss+ penalty✓p(s)a¯ _F with✓2[0,1]. No default ✓p(s)a¯ _F (s p(s))a¯ _F

¯

p(s) s

1 ✓ (1)

I Set of feasible repos: F ={F|(1) holds}

!No loss of generality in focusing on default free contracts.

Repurchase contract

I Definition: A repoF ={p(s)¯ }s2[s,¯s] is an agreement to repurchase the asset at price ¯p(s) in states of period 2.

I RepoF traded competitively at pricepF int = 1.

I Sell 1 contractF ⇠borrowpF with repayment schedule{p(s)¯ }s.

!AmountaF sold = collateral pledged.

I Default in state s: collateral loss+ penalty✓p(s)a¯ _F with✓2[0,1].

No default ✓p(s)a¯ _F (s p(s))a¯ _F

¯

p(s) s

1 ✓ (1)

I Set of feasible repos: F ={F|(1) holds}

!No loss of generality in focusing on default free contracts.

Equilibrium Selection of Repos

I We solve for a competitive equilibrium where agents may trade spot and any repoF 2F.

I Equilibrium selects the repo contract(s) that agents actually trade.

All contracts (even non-traded ones) in F are priced in equilibrium.

I Guess and Verify : In equilibrium, agents only trade one contract.

Consumer Problem

I Let F={p(s)¯ }^s be that repo contract.

I aⁱ_t: spot position of agenti in periodt. aⁱ_F: repo position (period 1). a_Fⁱ 0: seller.

I Agent i problem max

c_tⁱ,aⁱ_t,aⁱ_Fvⁱ(c₁ⁱ,c₂ⁱ,c₃ⁱ)

subject to c₁ⁱ =! p₁(a₁ⁱ a₀ⁱ) p_Faⁱ_F 0 c₂ⁱ(s) =!+s(a₂ⁱ aⁱ₁) + ¯p(s)aⁱ_F 0 c₃ⁱ(s) =1_{i=1}!+aⁱ₂s

aⁱ₁ 0 ⇠₁ⁱ (No short sale) aⁱ₁+aⁱ_F 0 ⌘₁ⁱ (Collateral Constraint)

Equilibrium Repo

Proposition

In equilibrium, agents only trade repo:

a²1= 0 =a a1¹

Defines^⇤:=s^⇤(a,✓, )as the solution to u⁰

✓

!+ s^⇤ 1 ✓a

◆

= =u⁰(c_2,⇤² ) The (essentially) unique equilibrium repo isF ={p(s¯ )}^s where:

i) Ifs^⇤>s¯(a low)

¯

p(s) = s

1 ✓

ii) Ifs^⇤2[s,s¯](a intermediate):

¯ p(s) =

( _s

1 ✓ if s s^⇤

s^⇤

1 ✓ if s >s^⇤

iii) Ifs^⇤s,p(s) = ¯¯ p is constant andp¯2[s^⇤/(1 ✓),s/(1 ✓)]

Equilibrium Repo: Borrowing vs. Hedging Motive

¯ p(s)

s s

s^⇤ 1 ✓

¯ s s

s 1 ✓

Borrowing Motive c₂²(s)<c_2,²_⇤

Hedging Motive c₂²(s) =c_2,²_⇤

15 / 35

Equilibrium Repo: Borrowing vs. Hedging Motive

¯ p(s)

s s

s^⇤ 1 ✓

¯ s s

s 1 ✓

Borrowing Motive c₂²(s)<c_2,²_⇤

Hedging Motive c₂²(s) =c_2,²_⇤

15 / 35

Intuition

I Intermediate Region :

¯ p(s) =

( _s

1 ✓ if ss^⇤

s^⇤

1 ✓ if s>s^⇤

I FB allocationc₂²(s) =c_2,⇤² such that u⁰(c_2,⇤² ) =

I Feasible repo ¯p)c₂²(s)!+as/(1 ✓).

I When ss^⇤, hit the no default constraint ¯p(s) =s/(1 ✓).

!Borrowing Motive.

I When s>s^⇤, you can havec₂²(s) =c_2,²_⇤.

!Hedging Motive: Flat part in the repo contract.

Graphic Argument

I p¯optimal contract among ˜p2F : E[( ¯p(s) p(s˜ )(u⁰(c2²(s)) )] 0

s

¯ p(s)

s s^⇤

s^⇤ 1 ✓

¯ s

s 1 ✓

s u⁰(c₂²(s))

s s^⇤ ˆs s¯

Graphic Argument

I p¯optimal contract among ˜p2F : E[( ¯p(s) p(s˜ )(u⁰(c2²(s)) )] 0

s

¯ p(s)

s s^⇤

s^⇤ 1 ✓

¯ s

s 1 ✓

s u⁰(c₂²(s))

s s^⇤ ˆs s¯

Graphic Argument

I p¯optimal contract among ˜p2F : E[( ¯p(s) p(s˜ )(u⁰(c2²(s)) )] 0

s

¯ p(s)

s s^⇤

s^⇤ 1 ✓

¯ s

s 1 ✓

s u⁰(c₂²(s))

s s^⇤ ˆs s¯

Graphic Argument

I p¯optimal contract among ˜p2F : E[( ¯p(s) p(s˜ )(u⁰(c2²(s)) )] 0

s

¯ p(s)

s s^⇤

s^⇤ 1 ✓

¯ s

s 1 ✓

s u⁰(c₂²(s))

s s^⇤ ˆs s¯

Graphic Argument

I p¯optimal contract among ˜p2F : E[( ¯p(s) p(s˜ )(u⁰(c2²(s)) )] 0

s

¯ p(s)

s s^⇤

s^⇤ 1 ✓

¯ s

s 1 ✓

s u⁰(c₂²(s))

s s^⇤ ˆs s¯

Haircuts

I The haircut is the di↵erence between the spot and the repo price:

H=p1 pF = (E[s] E[ ¯p(s)])

s

¯ p(s)

s s^⇤

s^⇤ 1 ✓

¯ s +

s

s 1 ✓

I Asset is scarce =s^⇤ high: can have negative haircut.

!Documented for some securities: on the run treasuries, collateral

“on special” (cf. Vayanos & Weill 2008).

Haircuts

I The haircut is the di↵erence between the spot and the repo price:

H=p1 pF = (E[s] E[ ¯p(s)])

s

¯ p(s)

s s^⇤

s^⇤ 1 ✓

¯ s +

s

s 1 ✓

I Asset is scarce =s^⇤ high: can have negative haircut.

!Documented for some securities: on the run treasuries, collateral

“on special” (cf. Vayanos & Weill 2008).

Haircuts - Pledgeability : ✓

I Haircut H= E[s p(s)]¯

I Comparative Statics: change from✓_L to✓_H>✓_L : better borrower.

s

¯ p(s)

s s¯

s

s 1 ✓L

s_L^⇤

s^⇤_L 1 ✓L

I Agent with ✓H can borrow more: H&

!High quality counterparties face lower haircut.

Haircuts - Pledgeability : ✓

I Haircut H= E[s p(s)]¯

I Comparative Statics: change from✓_L to✓_H>✓_L : better borrower.

s

¯ p(s)

s ¯s

s

s 1 ✓L s

1 ✓H

s_H^⇤

s^⇤_H 1 ✓H

I Agent with✓H can borrow more: H&

!High quality counterparties face lower haircut.

Asset Risk

I Introduce two assets with perfectly correlated payo↵s.

!Safe asset pays s.

!Risky asset is mean-preserving spread of safe asset.

s_risky =↵(s_safe E[s]) +E[s], ↵>1

I We can apply the previous analysis with these two assets.

I Claim: risky asset has a higher haircut and a lower liquidity premium (LP) where

LP=p₁ E[s]

I Riskier asset is worse collateral.

!Can borrow less per unit of asset : higher haircut.

!Less desirable than safe asset : lower liquidity premium.

Asset Risk

I Introduce two assets with perfectly correlated payo↵s.

!Safe asset pays s.

!Risky asset is mean-preserving spread of safe asset.

s_risky =↵(s_safe E[s]) +E[s], ↵>1

I We can apply the previous analysis with these two assets.

I Claim: risky asset has a higher haircut and a lower liquidity premium (LP) where

LP=p₁ E[s]

I Riskier asset is worse collateral.

!Can borrow less per unit of asset : higher haircut.

!Less desirable than safe asset : lower liquidity premium.

Outline

Introduction The Model

Equilibrium

Repo Equilibrium

Comparative Statics: Haircuts

Asset re-use

Re-use and Collateral Supply Re-use and Intermediation

Collateral re-use

I So far, repo = collateralized loan.

!Main di↵erence: collateral is sold in a repo: lender can re-use it.

!Proposition 1 (alow): Agent 1 wants to buy to pledge more!

I Agent 2 becomes owner of fraction ⌫22[0,1] of collateral pledged.

Legal Definition

I When pledgingaF, Agent 1 lends⌫2aF units of asset Agent 2.

!Is lender implicit promise to return ⌫2aF credible?

I We treat “lender default” default in a symmetric way and show the lender no default constraint does not bind in equilibrium. Lender Default

Collateral re-use

I So far, repo = collateralized loan.

!Main di↵erence: collateral is sold in a repo: lender can re-use it.

!Proposition 1 (alow): Agent 1 wants to buy to pledge more!

I Agent 2 becomes owner of fraction ⌫22[0,1] of collateral pledged.

Legal Definition

I When pledgingaF, Agent 1 lends⌫2aF units of asset Agent 2.

!Is lender implicit promise to return ⌫2aF credible?

I We treat “lender default” default in a symmetric way and show the lender no default constraint does not bind in equilibrium. Lender Default

Re-use: Sequential process

I How much can you pledge with collateral re-use ?

!Illustration as a sequential process.

A1 a

A2 Collateral Segregated

0

Pledge aE[s]/(1 ✓)

(1 ⌫2)a

Sell⌫2a

⌫2aE[s]

Figure:Re-use and Pledgeability: Step 0

I At step n, agent 1 can pledge (in expected terms) an additional:

⌫₂^{n 1}aE[s] ✓

1 ✓

I In the model, simultaneous trades with a consolidated collateral constraint. ^Details

Re-use: Sequential process

I How much can you pledge with collateral re-use ?

!Illustration as a sequential process.

A1 A2

⌫2a

Collateral Segregated (1 ⌫2)a Pledgea

aE[s]/(1 ✓)

(1 ⌫2)a

Sell⌫2a

⌫2aE[s]

Figure:Re-use and Pledgeability: Step 1

I At step n, agent 1 can pledge (in expected terms) an additional:

⌫₂^{n 1}aE[s] ✓

1 ✓

I In the model, simultaneous trades with a consolidated collateral constraint. ^Details

Re-use: Sequential process

I How much can you pledge with collateral re-use ?

!Illustration as a sequential process.

A1 A2

⌫²2a

Collateral Segregated

⇥(1 ⌫2) +⌫2(1 ⌫2)⇤ a Pledge ⌫2a

⌫2aE[s]/(1 ✓)

⌫2(1 ⌫2)a

Sell⌫2a

⌫2aE[s]

Figure:Re-use and Pledgeability: Step 2

I At step n, agent 1 can pledge (in expected terms) an additional:

⌫₂^{n 1}aE[s] ✓

1 ✓

I In the model, simultaneous trades with a consolidated collateral constraint. ^Details

Re-use: Sequential process

I How much can you pledge with collateral re-use ?

!Illustration as a sequential process.

A1 A2 Collateral Segregated

⇥(1 ⌫2) +⌫2(1 ⌫2)⇤ a Pledge ⌫2a

⌫2aE[s]/(1 ✓)

⌫2(1 ⌫2)a

Sell⌫2a

⌫2aE[s]

Figure:Re-use and Pledgeability: Step 2

I At step n, agent 1 can pledge (in expected terms) an additional:

⌫₂^{n 1}aE[s] ✓

1 ✓

I In the model, simultaneous trades with a consolidated collateral constraint.

Equilibrium Repo: Re-use

Proposition

Defines^⇤(⌫) :=s^⇤(a,✓,⌫)as the solution to u⁰

✓

!+as^⇤(⌫)

1 ⌫

 1

1 ✓ ⌫

◆

= The equilibrium repo contract with re-use is

¯ p(s,⌫) =

( _s

1 ✓ ifs<s^⇤(⌫)

s^⇤(⌫)

1 ✓ +⌫(s s^⇤(⌫)) ifs s^⇤(⌫) Ifs^⇤(⌫)>s

a¹1= a¹F = 1

1 ⌫a, a¹2= ⌫

1 ⌫a, a²F = aF¹

Corollary:

s^⇤(⌫) =1 ⌫(1 ✓) 1 ⌫ s^⇤(0)

There exists ¯⌫ such that if⌫2 ⌫, equilibrium allocation is FB.¯

Equilibrium Repo: Re-use

Proposition

Defines^⇤(⌫) :=s^⇤(a,✓,⌫)as the solution to u⁰

✓

!+as^⇤(⌫)

1 ⌫

 1

1 ✓ ⌫

◆

= The equilibrium repo contract with re-use is

¯ p(s,⌫) =

( _s

1 ✓ ifs<s^⇤(⌫)

s^⇤(⌫)

1 ✓ +⌫(s s^⇤(⌫)) ifs s^⇤(⌫) Ifs^⇤(⌫)>s

a¹1= a¹F = 1

1 ⌫a, a¹2= ⌫

1 ⌫a, a²F = aF¹

Corollary:

s^⇤(⌫) =1 ⌫(1 ✓) 1 ⌫ s^⇤(0)

There exists ¯⌫ such that if⌫2 ⌫, equilibrium allocation is FB.¯

Re-use: Multiplier E↵ect

I From Proposition 2:

u⁰

✓

!+as^⇤(⌫)

1 ⌫

 1

1 ✓ ⌫

◆

=

I Ultimate quantity of collateral available is a⁰= 1 ⌫(1 ✓)

1 ⌫

| {z }

Collateral Multiplierk(✓,⌫)

a

!Observe that k(0,⌫) = 1 for all⌫

!No multiplier e↵ect without some commitment (Maurin, 2015).

I Period 2 allocation (c₂¹(s),c₂²(s)) with asseta and re-use⌫ is the same than with asseta⁰ and re-use 0

Re-use and Intermediation

I Re-use also helpful to intermediate:

Hedge Fund Dealer MMF

Asset Cash

Asset re-use Cash

Repo 1 Repo 2

I Dealers lend on bilateral repo market and borrow on the tri-party repo market. Why does the Hedge Fund not borrow directly from the MMF. Is is just regulation ?

I We provide an explanation with di↵erences in counterparty quality✓.

!Endogenous intermediation through better borrower.

Extending the model: 3 agent types

I Let us have 2 type 1 agents:

!Agent 1L: a^L₀=a,✓_L, _L

v^L(c₁,c₂,c₃) =c₁+ _L(c₂+c₃)

!Agent 1H;a^H₀ = 0 ,✓H ✓L, H H:

v^H(c1,c2,c3) =c1+ H(c2+c3)

I For this presentation, only agent 1Hcan re-use collateral:

⌫_L=⌫₂= 0

I 1H is still a “borrower” with respect to 2

L H <u⁰(!)

Extending the model: 3 agent types

I Let us have 2 type 1 agents:

!Agent 1L: a^L₀=a,✓_L, _L

v^L(c₁,c₂,c₃) =c₁+ _L(c₂+c₃)

!Agent 1H;a^H₀ = 0 ,✓H ✓L, H H:

v^H(c1,c2,c3) =c1+ H(c2+c3)

I For this presentation, only agent 1Hcan re-use collateral:

⌫L=⌫2= 0

I 1H is still a “borrower” with respect to 2

L H <u⁰(!)

Intermediation Equilibrium: Conjecture

I Intermediation + Asset circulation in background.

A1L Pledgea A1H A2

¯ pLH

Pledge↵⌫Ha

¯ pH2

Segregate (1 ⌫H)a

Sell (1 ↵)⌫Ha

I 1H must be indi↵erent betweenred andgreen:

1 1 ✓H

Z

s

¯ pH2(s)h

u⁰⇣ c2²(s)⌘

H

idF(s) = ( H L)✓L

(1 ⌫H)(1 ✓L)

I 1H lendsb_LH to 1Land borrowsb_H2from 2.

bLH(1 ⌫H) +bH2=a

Intermediation Equilibrium

I 1H more patient, better counterparty: ✓_L<✓_H, _L< _H.

Proposition

If✓_H ✓_L ✓¯andaa, the only contracts traded in equilibrium are :¯ 1. A repop¯LH where1Lborrows from1H

¯

pLH(s) = s 1 ✓L

2. A repop¯H2where1Hborrows from2

I Importantly, 1Land 2 do not trade directly but 1H intermediates.

Benchmark cases

Intermediation Equilibrium: Intuition

I Why does 1Lnot trade with 2?

!He has the asset and higher gains from trade with 2: u⁰(!) _L.

!But✓_L is low : cannot pledge much period 1 income.

I 1H intermediates for 1Lwith his higher borrowing capacity✓H >✓L.

I Condition for intermediation:

Let ₁^H be the shadow price of the collateral constraint for 1H (1 ⌫_H) ₁^H

| {z }

Intermediation Cost

E⇥

( ¯p_H2(s) p¯_LH(s)) u⁰(c₂²(s)) _H ⇤

| {z }

Intermediation Benefit

Intermediation Equilibrium: Interpretation

I Intermediation valuable for non-trustworthy borrowers:

Hedge Fund

✓L

Dealer

✓H MMF

Asset Cash

Asset re-use Cash

Bilateral Repo Tri-Party Repo

I With partial commitment, counterparty and asset quality mixed.

!Intermediation makes the collateral more acceptable to MMF..

Conclusion

I We presented a simple model of repurchase agreements :

!Equilibrium repo among contracts with limited commitment.

!Haircut increase with asset risk and counterparty risk.

I Repos are an efficient way of using asset for borrowing/lending:

!Equilibrium contract trades o↵borrowing/hedging motive.

!Selling collateral allows for asset circulation/intermediation.

I What’s next?

!Collateral Transformation.

!Central Bank Policy : E↵ect of an asset purchase on repos..

Trading Surplus

I Net trading surplusSⁱ =v_eqⁱ (c₁ⁱ,c₂ⁱ,c₃ⁱ) v_autⁱ .

I Agent 1 enjoys the liquidity premium on his asset holdings:

S¹=⌘¹₁a=E[ ¯p(s)(u⁰(c₂²(s) )]a An increase in the asset supply gives

@S¹

@a =⌘¹₁+a@⌘1¹

@a

= Z s^⇤

s

s

1 ✓

 u⁰

✓

!+ as

1 ✓

◆

+u⁰⁰

✓

!+ as 1 ✓

◆

as dG(s) Agent 2 gets hedging:

@S²

@a 0

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Lender Default

I Let now✓2be the reliability of agent 2.

I Lender default : lose payment ¯p(s)aF + penalty✓2⌫2aFs.

!No (lender) default if:

¯

p(s)aF ⌫2(1 ✓2)aFs

¯

p(s) ⌫₂(1 ✓₂)s (2)

I For a given{p(s)¯ }^s, (2) gives the maximal feasible⌫2.

I In equilibrium, agents trade{p(s)¯ }s such that (2) holds for ✓₂= 0 and⌫₂= 1.

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Collateral Constraint with Re-use

I RepoF: distinguish longaⁱ_F,+ 0 vs. shortaⁱ_F, 0 positions.

I Agent 1 (Borrower):

a¹₁ a¹_F,

!Collateral constraint unchanged.

I Agent 2 (Lender):

a2₁+⌫₂a²_F,+ 0

!Agent can re-use (sell)⌫2a²_F,+with... agent 1

I Agent 1 has more asset to borrow by market clearing a²₁+a²₂=a

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3 agents: Benchmark case 1

I Identical Agents : ✓L=✓H and _L= _H

I Equilibrium:

!1Lborrowsa with contract ¯pL2with agent 2

¯ p_L2(s) =

( _s

1 ✓ if ss^⇤

s^⇤

1 ✓ if s>s^⇤

!1H stays inactive

I 1H would like to borrow from 2 as well buta^H₁ = 0.

3 agents: Benchmark case 2

I Gains from trade: ✓L=✓H, L< H.

I Equilibrium:

!1Lborrowsb_L2with contract ¯p_L2from agent 2

¯ pL2(s) =

( _s

1 ✓ if ss^⇤(b_L2,a,✓_L)

s^⇤(bL2,a,✓L)

1 ✓ if s>s^⇤(b_L2,a,✓_L)

!1H borrowsb_LH from 1Hwith contract ¯p_LH(s) =s/(1 ✓_L)

I Equilibrium conditions

Agent 1Lsolves a portfolio allocation problem:

a= (1 ⌫_H)b_LH+b_L2

Must be indi↵erent between borrowing from 1H and 2.

I Importantly 1H and 2 do not trade ! Back to Presentation

Definitons : Source ICMA

I Repurchase agreement: In a repo, one party sells an asset (usually fixed-income securities) to another party at one price at the start of the transaction and commits to repurchase the fungible assets from the second party at a di↵erent price at a future date.

I Lender Rights: In Europe, repo transfers legal title to collateral from the seller to the buyer by means of an outright sale. [Under New York law],collateral is pledged but exempted from certain provisions of the US Bankruptcy Code that normally apply to pledges, in particular, the automatic stay on enforcement of

collateral in the event of insolvency. In addition, unlike in traditional pledges, the pledgee/buyer in a US repo is given a general right of use of collateral. Consequently, the resulting rights are deemed to be much the same as those achieved by an outright sale. Back to Presentation