Equilibrium collateral and firesales

Bruno Biais

TSE, FBF IDEI Chair on investment banking & financial markets

December 2014

Repos

Really interesting economic object (and very important in practice)

Thanks lots Eugene & Vivien for making it possible for us to learn about it !

For one year, work with Johan Hombert (HEC) and Pierre Olivier Weill (UCLA) on model specifically designed to analyze repo contracts

Mathematically challenging, analysis too preliminary for presentation (maybe in one year ;-)

My presentation today: less ambitious model, not specifically focused on repos, but collateralized loan markets (also preliminary)

Hopefully complementary to Eugene’s presentation

Collateralized funding

E.g. Asset Backed Commercial Paper: Institution issues commercial paper (borrows, e.g. from Money Market Mutual Funds) to purchase assets, and pledges these assets as collateral for the loan

Securitized loans, such as ABCP or Repos = important source of funding for financial institutions

But concerns about this funding mechanism raised by empirical studies:

Gorton Metrick 2012

Krishnamurthy et al 2014

Gorton & Metrick JFE 2012

“changes in … counterparty risk … correlated with changes in credit spreads and repo rates for securitized bonds…

Implied higher uncertainty about bank solvency and lower values for repo collateral…

Concerns about the liquidity of markets for the bonds used as collateral led to increases in repo “haircuts”: the amount of collateral required for any given transaction…

declining asset values and increasing haircuts… U.S. banking system … insolvent for the first time since the Great Depression.”

Krishnamurthy et al JF 2014

disagree with Gorton & Metrick that repo market was the problem

agree that something went wrong with another segment of securitized loan market: Asset Backed Commercial Paper

from 2007Q2 to 2009Q2, ABCP market contracted by $662 bn

«contraction in the short term debt market of shadow banks played an important role in the collapse of the shadow banking sector »

« data suggests that MMF … stop lending when collateral becomes too illiquid or risky and so we see quantities for these types of collateral going to 0 »

Issues

What is the economic mechanism underlying such events?

Can we rely on optimizing agents and market forces to prevent this ?

(invisible hand)

Or are there market failures implying policy intervention needed?

To address these issues you need a model in which i) market participants optimize and this leads them to use collateral, ii) market is in nequilibrium, iii) welfare is well defined (rules out noise trading, ad hoc exogenous contracts, etc.)

Brunnermeier and Pedersen RFS 2008

Vicious circle: price drop => more collateral needed => price drop ….

But collateral constraints are exogenous in their model

First best can be achieved in their setting …

by removing collateral constraints…

Begs question why collateral constraint there in the first place

Model in which collateral constraints only entails costs: difficult to study tradeoff, precludes policy implications

Results (1): optimal contracts

Even in frictionless economy, collateral useful:

relax participation constraint of lenders

when borrower cannot repay, lender seizes collateral

lender more willing to fund projects initially

Under asymmetric information, additional benefits: incentives

unobservable effort to increase probability of success

threaten to take collateral from agent in case of failure

more collateral => greater threat => more effort

Tradeoff with inefficiency cost of collateral: lender (or other market particiants to whom collateral can be sold) value it less than borrower

Results (2): equilibrium

Borrower and lender write privately optimal contract, taking resale price/liquidation value of collateral as given

Possibility of vicious circle (« spiral »):

anticipate low collateral liquidation price

demand large collateral

large liquidation more when failure

depress collateral resale price

Equilibrium multiplicity:

good equ: self-fulfilling expectation that collateral price high

bad equ: self-fulfilling expectation that collateral price low

good equ more efficient: less inefficient liquidation

Results (3): welfare

Pecuniary externality:

I request large collateral & sell if failure: I depress price

Cost for others, exacerbates info asymmetry cost for them

Equilibrium not information constrained Pareto optimum

Bad equ is inefficient (even if symmetric info)

Even good equ can be inefficient, if asymmetric info

when I request very high effort, I demand high collat

this depresses collateral price for others

negative externality

because private contracts don’t internalize externality

invisible hand does not work

Results (4): empirical implications

Higher information asymmetry or cost of effort

privately optimal contracts request high collateral

collateral price severely depressed at time of liquidation

When info asymmetry/cost of effort varies

volatility in collateral value

switch from buoyant collateralized loan market (when cost low)

to market contraction/breakdown (crisis?)

Results (5): policy implications

Central bank pledge to stabilize collateral price to get rid of bad equ

helps market coordinate on good equilibrium

costless in «easy case» where firesales out of equ

but can be costly if firesales can occur

ex-post cost of central bank intervention + « moral hazard »

Pareto dominated equ = too much collateral

cap collateral?

or impose capital requirements or risk-management regulation

so that less collateral needed

in the aggregate: all borrowers comply & need less collat

or: regulator only lets compliant firms borrow

Model

Simplest possible framework to make these points in model where

contracts optimal, markets in equilbrium, welfare well defined

policy implications can be derived

Maybe not ground-breaking innovation …. hopefully helps clarify point

1) With symmetric info:

Optimal contract involves collat (liquidation irrespective of fail)

Bad (inefficient) equilibrium can arise

But good equilibrium Pareto optimal (invisible hand)

2) Under moral hazard:

Liquidation after failure not success

Even good equilibrium not info constrained Pareto optimum

1) A simple model of collateral without incentive problems

p = ½

1 -p = ½

R I = 40

- LI = 0

invest I=100 to buy asset effort cost C I = 5

t=0 t=1

asset value for firm

I = 100

asset value for lender

P I = 80

cash self-financing A=60

loan D = 40

Improve returns thanks to careful investment

asset worth more to borrower (1/unit) than lender (P/unit)

For simplicity, first consider case where no losses, Relaxed later

Collateral relaxes creditor’s participation constraint

Repay 40 if success, 0 if failure: creditor not willing to lend (p R < 1)

To increase amount repaid to creditor, liquidate l (for simplicity irrespective of success/failure, when incentive pb: after failure)

Lender participation constraint (denote A = a I)

p R I + l P I > D = I - A l > [(1-a) - p R ]/P = 1/4

Liquidation = ex-post inefficient (if P < 1) but ex-ante privately optimal:

(1-l) I - C I = 70 > A = 60

Haircut: (I-D)/I = (100-40)/100 = 60%

Remarks

For simplicity, in numerical example I – A = RI, but wlog Liquidation inefficient => paying out RI to creditors dominates liquidating (liquidate as little as possible) [things will change when incentive problems] Value to borrower = if successful can keep I [with incentive problems also need to pay bonus if success] [model with incentive problems yields more realistic implications for optimal contract]

Vicious or vertuous circle

Lender participation constraint: must be promised l P in case of failure

l P > ((I – A) – p R I )/ I

Greater P (liquidation price) = more redeployable asset => better collateral = less inefficient liquidation => less firesales => greater P A contrario: lower P (liquidation price) => larger l (liquidate more) => more firesales => lower P

Equilibrium

Mass 1 pairs lender-borrower

Mass 1 arbitrageurs valuation v in [0,1], cdf F(v)

t = 0: contracting for funding => l. t = 1: market for collateral

Demand: mass arbitrageurs with v > P: 1 – F(P), decreasing in P

Supply: l(P) = [(1-a) - p R ]/P also decreasing in P !

Equilibrium: P s.t. l(P) = 1 – F(P) P = F-1(1-l) decreasing in l

Supply l(P)

Demand 1 – F(P)

P

Firesales

Because both supply & demand decreasing in P, possibly multiple equ: when they anticipate low price, creditors demand large liquidation, which pushes prices down, confirming the initial expectation

Supply l(P)

Demand

P

If F uniform: equilibria = roots of P2 – P + [(1-a) - p R ] = 0: 0.27 and 0.72

Policy

Bad equilibrium: self-fulfilling expectation of low collateral price Plow leading to firesales Less efficient than good equilibrium, with higher collateral price Phigh : more liquidation & purchase by arbitrageurs, who value asset at price P < 1 = borrower’s value To avoid inefficiency due to miscoordination: central bank announces it will « stabilize market» at Phigh anticipating this, lenders require low collateral leading to equlibrium price = Phigh in our simple model: CB does not have to actually intervene in reality firesales may be on equ path raises problems of cost of intervention & credibility

2) Collateral with moral hazard (// Tirole, 2006)

R I = 40

0

I=100

t=0 t=1

A=60

D=40

unobservable effort cost C I = 5

no effort

R I = 40

0

p - D

If no effort: proba of success reduced by D

Effort efficient: D > C/R

Effort unobservable + manager has limited liability => moral hazard

p = ½

1 - p + D

With moral hazard, threat of liquidation incentivizes agent

to strengthen incentives, privately optimal to liquidate only after failure (if this is enough) and to leave share a of profit to manager

incentive constraint of manager:

p (aR+1)I + (1- p) (1-l) I – C I > (p - D) (aR+1)I + (1- p + D) (1-l) I l > C/D – a R

participation constraint bank:

p (1-a) R I +(1- p) l P I > I-A = I(1 – a) l P > (1 – a - p (1-a) R)/(1-p)

Optimal contracts

Set l and a to minimize inefficient liquidation s.t IC and PC

IC : l = C/D – a R

PC: l = (1 – a - p (1-a) R)/[(1-p)P]

a

IC PC

a*

l*

Market breakdown

Now assume losses if failure: L > 0 Then if severe moral hazard (implying l high, P low) Positive NPV with effort in first best: p R > (1-p) L Negative NPV if no effort: (p-D) R > (1-p+D) L Negative NPV with moral hazard: p R < (1-p) (L + (1-l) P) Worsening of moral hazard can trigger « contraction » in market for collateralized loans (market breakdown)

Mixed strateggy equilibrium

When borrower and lender meet, contract with probability g Supply in collateral market = g l => P = F-1(1-gl) s.t. Lender earns 0 profit: p (aR+1)I + (1- p) (1-l) I – C I So does borrower: p R = (1-p) (L + (1-l) P(gl)) (indifferent between contracting or not)

Partial market breakdown with heterogeneous agents

Assume agents differ, e.g., in incentive problems: C (observable) (Biais, Rochet, Woolley, RFS 2014: unobservable C => financial sector too large) Firms with large incentive problem, but socially valuable investment opportunities are credit rationed

Macro incentive shocks

mild incentive problems

severe incentive problems

m

1 - m

Low cost of effort Cm < 0.05

High cost of effort Cs > 0.05

Low liquidation rate lm < 0.3

High collateral price Pm

High liquidation rate ls > 0.3

Low collateral price Ps

Adverse shocks to incentives generate volatility in collateral price

Over-colateralization

Extend to 3 levels of effort: no effort, medium effort, high effort

Taking price as given, borrower/lender prefer high effort, high-powered incentives reducing default rate

=> high collateral rate and low collateral price in equilibrium

By doing so exert negative externality on others: depress collateral price

=> equilibrium high collateral inducing high effort can be Pareto dominated by medium effort/medium collateral rate

=> regulatory response: cap collateralization ? Or reduce agency problems and therefore need for collateral (capital requirements, transparency)