Youth Employment, Camps and Activities Guide - NUPACE

Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Illiquidity in Financial Networks

Maryam Farboodi

May 17, 2013

Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Outline

Introduction

Model

Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Motivation

I Contagion and systemic risk

I A lot of focus on bank inter-connections after the crisis

I Too-interconnected-to-failI Interconnections:

I Propagate a shock from a bank to many banksI Exposes banks to counterparty risk

I Reasonable to study bank inter-connections in a netorksetting

I Focus on Counterparty risk: negative spillover betweenbanks

I Can induce run on banks in certain states

Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

This Paper!

I Focuses on network formation among banks

I Externalities that banks form the ”wrong” networkI Classic externality: Each bank does not fully internalize

the failure of others due to his failureI Equilibrium social surplus and on profit hurt

I What I want to address: Change in division of surplusI Each bank does not care to hit the social surplus as

long as his own share increases

Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Network Literature

I How does a negative shock propagate through thenetwork?

I Can the network structure amplify a shock?

I A lot of work on random networks

I Some recent work focusing on contagion given thenetwork structure

I Very little done on strategic network formation amongbanks

I Network on a ringI Even less when counter party risk is involved

Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

What is Difficult? :D

I What is a link between two banks (financialinstitutions)?

I Superposition of at least three networks:I OTC derivativesI Bilateral lendingI Common asset holding

I Complex interaction between the three, banks adjust ondifferent margins

Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Evidence

I Data: bilateral exposures not really knownI OTC network: approximately a core-periphery networkI Interconnected coreI Core banks (”dealers”) low net exposure, high grossI peripheries net lenders

Figure : OTC bank exposures as a Core-Periphery model

Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Financial Network

I Directed Graph G (N,E )I Nodes are banks {i , j}I Edges are lending eij : i has lent to j

Figure : Simple interbank lending network with 5 banks

Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Basic Idea

I i and j choose to enter a lending relationship (edge eijadded to the network) if

Φi (G + ij) > Φi (G )

Φj(G + ij) > Φj(G )

I Has nothing to do with∑k

Φk(G + ij) >∑k

Φk(G )

Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Equilibrium Concept: Stability

I Pairwise StabilityI No node prefer to unilaterally break a connectionI No pair of nodes prefer to add a connection

I Coalitional StabilityI No coalition of nodes want to deviate

Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Outline

Introduction

Model

Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Environment

I 4 dates t = 0, 1, 2, 3I 4 banks

I 2 with risky investment opportunity (R1,R2)I 2 without (S1,S2)

I No discounting

Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Bank Choice Set

I Bank with investment opportunityI From/to which banks borrow/lend (size fix)I How much liquidity to holdI Invest in long term h(.)

I Bank without investment opportunityI To which banks lendI Invest in h(.)

Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Timeline

Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Banks

I Each bank has charter value V i , i ∈ {R, S}I Each bank has raised one unit from uninformed passive

outside investors

I Banks can lend to each other

I All borrowing of the form of 1-period debt

I Universal risk neutrality

Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Technology

I Risky AssetI Investment I at date 0I Can be of three types U,M,BI Liquidity shock ρ ∈ {+αI , 0,−αI} at date 2

I iid across the two investments

I Can be liquidated at date 1 for LI Return realized at date 3 if not liquidated and potential

liquidity need metI Gk(R) ∼ [0, R̄], k ∈ {U,M,B}

I If debt not met: bankruptcy and return is destroyed

I Safe long term asset: h(.) concaveI Safe final returnI No intermediate liquidity need

Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Asset Random Type

Type Probability Liquidity Shock (ρ) Return Dist.B p −αI GB(.)/0M p1 0 GM(.)U 1− p − p1 αI GU(.)

Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Information

I Each bank knows own and counterparty liquidity needat date 1

I Can withdraw short term debt

Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Assumptions

I Each bank can borrow from at most two banks

I Each bank can not allocate more than half of it’sresources to any use (lend/risky investment/safe longterm investment/etc)

I Each bank can lend 0.5 to any other bank

I If invest I , can choose to hold θ ∈ {αI , 0} liquidity

Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Risky Bank R1 Balance Sheet

Liabilities Assets (= A)

1 IbS1R1 ∈ {0, 1

2} θ ∈ {αI , 0}bS2R1 ∈ {0, 1

2} h(A− I − θ)bR2R1 ∈ {0, 1

2} bR1R2 ∈ {0, 12}

Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Link Formation Process

I Each bank chooses a set of links to form(lend andborrow):

{{ei .}, {e.i}

}I Connection formed

I Borrower chooses the amount of liquidity to holdI Lender chooses the face value of debt

I The face value would be such that if accepted, in theinduced equilibrium it maximizes the surplus which goesto lender

I Can not offer to borrow from more than two banks

Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Possible Outcomes

Figure : Possible Outcome Networks

Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Equilibrium Concept: Stability

I Pairwise StabilityI No node prefer to unilaterally break a connectionI No pair of nodes prefer to add a connection

I Coalitional StabilityI No coalition of nodes want to deviate

I I will only consider symmetric equilibria for now

Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Intuition

I Risky bank can affect the realized distribution of returnthrough inducing a run in certain states

I Run can be induced through

I Run erodes some surplus, but also change thedistribution of surpus

Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Asset Random Type

Type Probability Liquidity Shock (ρ) Return Dist.B p −αI GB(.)/0M p1 0 GM(.)U 1− p − p1 αI GU(.)

Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Division of Surplus

I Resources in short supply

I lender must be payed maximum amount

D∗ = arg maxD

D(1− G (D))

S =

∫ R̄

D∗Rg(R)dR

L = D∗(1− G (D∗))

B =

∫ R̄

D∗(R − D∗)g(R)dR

Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Example. Division of Surplus

Figure : Division of Surplus among lender and borrower at theface value which maximizes lender share. Plot is made for returndistribution family is G n(R) = Rn

R̄n ∼ [0, R̄].

Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Excessive Exposure to Counterparty Risk

I Risky bank dislikes the eventual division of surplus in Mbut likes it in U

I Connect to the other risky and not holding any liquidity

I Chance of failure in M due to counterparty failure

I Preventive run by safe lender at date 1

I Some surplus destructed, but the division of the resttilted towards risky banks

Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Results

I I show that under some parameter values, risky banksover connect

I Equilibrium network is such thatI Connections between risky banks create counterparty

riskI Counterparty risk destroys social value (too much run)I Risky banks get a bigger share of the realized social

value at the expense of othersI So they have an incentive to form those connections in

the first place

I Adding even less informed outsiders amplifies the losses