Introduction
A Model of Haircuts
Results
Haircuts and Credit Risk Over the Cycle
Zongbo Huang
Econometric Society World Congress
August 21, 2015
Discussions
Introduction
A Model of Haircuts
Results
Rapid tightening of haircuts exacerbated deleveraging
pressures during the crisis.
To generate countercyclical haircuts, Brunnermeier-Pedesen
(2009), Geanakoplos (2010), Jurek-Staord (2010)
1. Haircuts such that loans are riskfree
2. Underlying risk is countercyclical
This paper: countercyclical haircuts with risky loans
Discussions
Introduction
A Model of Haircuts
Results
Discussions
This Paper
A dynamic GE model in countinuous-time
• Heterogeneous beliefs as motive to trade
• Collateral equilibrium á la Geanakoplos → endogenous
interest rates and haircuts
Preview of results:
• Endogenously determined haircuts are countercyclical
• Credit risk accumulates at the background before erupts
• Countercyclical equity premium, potentially negative
Introduction
A Model of Haircuts
Results
Discussions
A Model of Haircuts
• A tree (asset) produces apples
yt = a kt .
• A Poisson shock with intensity λ and size u ∼ G(·), on
[u, 1) with positive density
dkt = gkt− dt + (ukt− − kt− ) M(dt).
• Optimists and pessimists only disagree on the intensity
λo < λ < λp
Introduction
A Model of Haircuts
Results
Portfolio
Agents choose among
• Shares of the tree/asset x,
• Lending under contracts indexed by C
• Borrowing under contracts indexd by C
Holding the asset:
1. Exogenous risk: asset depreciates from k → uk
2. Endogenous risk: asset price q → v(u)q
3. Amplication of risk: qk → v(u)u ·qk
| {z }
z
Discussions
Introduction
A Model of Haircuts
Results
Discussions
Portfolio
Agents choose among
• Shares of the tree/asset x,
• Lending under contracts indexed by C
• Borrowing under contracts indexd by C
Short-term contracts indexed by C
1. Borrow 1 apple at t with interest rate R(C)
2. Use assets that worth C apples as collateral
3. If hit by Possion shock, value of collateral jumps C → Czt
4. Repay min{1, Czt } at t + dt
Introduction
A Model of Haircuts
Results
Discussions
Collateral Equilibrium
1. Agents of group i solve
V (Nt , t) = sup
x,c,µ+,−
s.t.
Eit
dNt
= xt drkt − ct dt +
Nt
∞
Z
Z h
C
t
2. All markets clear.
exp(−ρs) log(cs Ns ) ds
i
Rt (C)dt +((Czt ∧ 1)− 1)dMit dµ
* All collaterals ≤ α· Total Asset
* Budget constraint
Introduction
A Model of Haircuts
Results
Discussions
Proposition
Only a single contract is actively traded in nonzero quatities
given the current (single) state variable
ηt =
Nto
p.
Nto + Nt
Introduction
A Model of Haircuts
Results
Discussions
1. 0.5[C1 , R1 ] + 0.5[C2 , R2 ]
2. [0.5C1 + 0.5C2 ,
0.5R1 + 0.5R2 ]
min{Cz, 1}
1
C1
C2
1
C1 +C2
2
z
Introduction
A Model of Haircuts
Results
Discussions
1. 0.5[C1 , R1 ] + 0.5[C2 , R2 ]
2. [0.5C1 + 0.5C2 ,
0.5R1 + 0.5R2 ]
min{Cz, 1}
C1 +C2
2
1
C1
C2
1
z
Introduction
A Model of Haircuts
Results
Discussions
Proposition
There exists an implicit solution
I (C, η ) = 0
given the
parameters. Moreover,
∂C
<0
∂η
.
1. In recessions optimists take more risk by levering up (only risk-free
debt)
2. New channel: take more risk by increasing haircuts
Introduction
A Model of Haircuts
Results
Discussions
Haircuts and Default Prob.
0.2
0.2
0.18
0.16
Default rate
Margin
0.15
0.1
0.14
0.12
0.1
0.05
0.08
0
0
3.
0.5
η
1
0.06
0
0.5
η
1
Introduction
A Model of Haircuts
Results
Discussions
Wealth Share
0.03
1
η(t+dt) after default
0.025
µη η
0.02
0.015
0.01
0.6
0.4
0.2
0.005
0
0
0.8
0.5
η
1
0
0
0.5
η
1
Introduction
A Model of Haircuts
Results
Discussions
Equity premium
0.015
0.01
Rk−Rf
0.005
0
−0.005
−0.01
0
0.2
0.4
η
0.6
0.8
1
Introduction
A Model of Haircuts
Results
Discussions
Loss Spiral
Optimists are more patient than pessimists
1.8
1.5
1.7
1.4
Amplification
capiral price q
1.6
1.5
1.4
1.3
1.3
1.2
1.2
1.1
1.1
1
0
0.5
η
1
1
0
0.5
η
1
k
Introduction
A Model of Haircuts
Results
Discussions
Time-varying Belief
• Belief spiral: more pessimistic in bad times
• Endogenously underlying risk is higher in bad times
0.18
0.2
0.16
0.18
0.14
0.16
Default rate
Margin
0.12
0.1
0.08
0.14
0.12
0.06
0.1
0.04
0.08
0.02
0
0
0.5
η
1
0.06
0
0.5
η
1
Introduction
A Model of Haircuts
Results
Discussions
Conclusion
• A model with endogenous haircuts and defaults
• Counterclical haircut without countercyclical underlying
risk
• Credit risk accumulates at the background and sows the
seeds for the next crisis