Introduction
Theory
Applications
Conclusion
Margin-Based Asset Pricing and
Deviations from the Law of One Price
Nicolae Gârleanu
Berkeley, CEPR, and NBER
Lasse H. Pedersen
NYU, CEPR, and NBER
N. Gârleanu and L. H. Pedersen
Margin-Based Asset Pricing
Introduction
Theory
Applications
Conclusion
Motivation: Financial Frictions in the Macro Economy
Key friction: margin constraints
These constraints can become binding; e.g., 2007-2009
One remarkable consequence: Failure of Law of One Price
Corporate-bond basis: price gap between bond and CDS
Covered interest-rate parity
Research question:
How do margin requirements affect asset prices?
N. Gârleanu and L. H. Pedersen
Margin-Based Asset Pricing
Introduction
Theory
Applications
Conclusion
What We Do
Standard Lucas economy, extended in minimal way:
with 2 two agents
facing margin constraints
Derive equilibrium: Margin CAPM
Quantify effects of margin
Help explain:
CDS-bond basis
Failure of covered interest-rate parity (CIP)
The effects of the Fed’s lending facilities
The incentive for regulatory arbitrage
N. Gârleanu and L. H. Pedersen
Margin-Based Asset Pricing
Introduction
Theory
Applications
Conclusion
Results: Theory
Margin (C)CAPM
Et (r i ) − rtc = λt βti + ψt xt mti
Shadow cost of capital ψt can be captured by
interest-rate spreads (LIBOR minus GC repo).
Binding constraints, ψt > 0 (e.g., since August 2007):
occur following bad fundamental shocks
¯
¯ + f (xt ) SR
increase Sharpe market ratio: SR = SR
σ̄ −
1
m
+
Basis: can arise due to difference in margins
b
b
Et (r i ) − Et (r ik ) =
βtC ,i − βtC ,ik + ψt (mti − mtik )
High-margin assets have high sensitivity to funding risk
N. Gârleanu and L. H. Pedersen
Margin-Based Asset Pricing
Introduction
Theory
Applications
Conclusion
Results: Applications
Calibrate model using standard parameters: consumption
growth, discount rate, risk aversion, observed margins
Large pricing effect of binding constraints
– Collateralized interest rates drop
– Interest-rate spreads blow out
– Margin premium rises
High margin assets have high sensitivity to funding risk
– higher beta
– higher comovement with each other
Consistent with model, CDS-bond basis related to:
credit tightness (time series)
relative margin requirements (cross section)
Relate interest-rate spread to failure of covered interest parity
Transmission of unconventional monetary policy:
Compute effect of Fed’s lending facilities on asset values
Quantify banks’ incentives to loosen capital requirements
N. Gârleanu and L. H. Pedersen
Margin-Based Asset Pricing
Introduction
Theory
Applications
Conclusion
Related Literature
Heterogeneous risk-aversion economies: Dumas (1989); Basak and Cuoco
(1998), Chan and Kogan (2002)
Collateral value: Bernanke and Gertler (1989), Detemple and Murthy (1997),
Geanakoplos (1997), Kiyotaki and Moore (1997), Caballero and Krishnamurthy
(2001), Lustig and Van Nieuwerburgh (2005), Shleifer and Vishny (1992, 2009)
Equilibrium restrictions with portfolio constraints: Hindy (1995), Hindy and
Huang (1995), Cuoco (1997), Aiyagari and Gertler (1999)
Limits of arbitrage: Shleifer and Vishny (1997), and possible ‘arbitrage’ in
equilibrium: Basak and Croitoru (2000, 2006), Geanakoplos (2003)
Margin spiral, theory: Brunnermeier and Pedersen (2009); Evidence: Gorton and
Metrick (2009)
Direct evidence from Fed that prices depend significantly on haircuts: Ashcraft,
Garleanu, and Pedersen (2010)
Evidence on stocks, bonds, and credit markets: Frazzini and Pedersen (2010)
N. Gârleanu and L. H. Pedersen
Margin-Based Asset Pricing
Introduction
Theory
Applications
Conclusion
Model
Required Returns
Explicit Equilibrium
Calibration
Model: Assets
Continuous-time endowment economy
Multiple assets in positive supply, characterized by
– dividend stream: δti
– margin requirement: mti
⊤
– endogenous price: dPti = µit Pti − δti dt + Pti σti dBt
Multiple “derivatives”:
– derivative ik has the same payoffs δti as asset i
– smaller margin: mtik ≤ mti
Two types of risk-free lending/borrowing:
– collateralized (rate rtc )
– uncollateralized (rate rtu )
N. Gârleanu and L. H. Pedersen
Margin-Based Asset Pricing
Introduction
Theory
Applications
Conclusion
Model
Required Returns
Explicit Equilibrium
Calibration
Model: Agents
Two types of agents g = a, b:
Risk averse:
γa > 1
Risk tolerant (brave): γ b = 1 (i.e., log)
Utility: constant relative risk aversion
Z ∞
g 1−γ g
−ρs Cs
max E0
e
ds
1 − γg
C g ,θ i ,ηu
0
Constraints:
Solvency: Wt ≥ 0
P i i
u
Funding constraint:
i mt |θt | + ηt ≤ 1
Agent a
– Does not lend uncollateralized
– Faces derivative-trading restrictions
N. Gârleanu and L. H. Pedersen
Margin-Based Asset Pricing
Introduction
Theory
Applications
Conclusion
Model
Required Returns
Explicit Equilibrium
Calibration
Shadow Cost of Capital
Agent b solves
X
1X i j i j ⊤
c
u u
c
i
i
c
max rt + ηt (rt − rt ) +
θt (µt − rt ) −
θt θt σt (σt )
2
θti ,ηtu
i
subject to
P
i
i ,j
mti |θti | + ηtu ≤ 1.
Proposition: The shadow cost of the margin constraint is
ψt = rtu − rtc
Proposition: If agent b is long asset i , its excess return is
b
b
b
dC dP i
µit − rtc = βtC ,i + ψt mti where βtC ,i = covt
,
C b Pi
N. Gârleanu and L. H. Pedersen
Margin-Based Asset Pricing
Introduction
Theory
Applications
Conclusion
Model
Required Returns
Explicit Equilibrium
Calibration
CCAPM with Margins
Suppose that agent a is unconstrained w.r.t. asset i and let
1
γt
xt
βtC ,i
=
=
1 Cta
1 Ctb
+
γ a Ct
γ b Ct
Ctb
γb
Cta
γa
Cb
+ γtb
dC dP i
= covt
,
C Pi
Proposition:
µit − rtc = γt βtC ,i + xt ψt mti
N. Gârleanu and L. H. Pedersen
Margin-Based Asset Pricing
Introduction
Theory
Applications
Conclusion
Model
Required Returns
Explicit Equilibrium
Calibration
CAPM with Margins
Let q be the portfolio with highest correlation with aggregate
consumption and
i
dP q
covt dP
,
Pq
Pi
βti =
dP q
vart P q
Proposition:
µit − rtc = λt βti + xt ψt mti
N. Gârleanu and L. H. Pedersen
Margin-Based Asset Pricing
Introduction
Theory
Applications
Conclusion
Model
Required Returns
Explicit Equilibrium
Calibration
Basis Trades
Proposition:
If agent b is long asset i and derivative ik
b
b
µit − µitk = ψt mti − mtik + βtC ,i − βtC ,ik
If he is long i and short ik , then
b
b
µit − µitk = ψt mti + mtik + βtC ,i − βtC ,ik
The derivative price P ik decreases with mik .
N. Gârleanu and L. H. Pedersen
Margin-Based Asset Pricing
Introduction
Theory
Applications
Conclusion
Model
Required Returns
Explicit Equilibrium
Calibration
Explicit Equilibrium
Specializing the setup for tractability to consider explicit
equilibrium and calibration:
Aggregate consumption C is geometric Brownian motion
Continuum of underlying assets with dividend δi = Cs i , where
s i independent martingales
All underlying assets have the same margin mi = m
Derivatives with mik ≤ m traded only by b
N. Gârleanu and L. H. Pedersen
Margin-Based Asset Pricing
Introduction
Theory
Applications
Conclusion
Model
Required Returns
Explicit Equilibrium
Calibration
Solving Explicitly
It suffices to calculate equilibrium as if there were one
underlying paying C and derivatives on it
State variables: C and c b = C b /C
Pricing kernel for underlying assets: Agent a is marginal:
a
ξt = e −ρt (C a )−γ
dξt = ξt µξt dt + σtξ dwt
Collateralized interest rate:
a
D e −ρt (Cta )−γ
rtc = −µξt = −
a
e −ρt (Cta )−γ
Market price of aggregate wealth Pt = Ct ζ(ctb ):
Z ∞
Pt ξt = Et
Cs ξs ds
t
N. Gârleanu and L. H. Pedersen
Margin-Based Asset Pricing
Introduction
Theory
Applications
Conclusion
Model
Required Returns
Explicit Equilibrium
Calibration
Solution
Proposition:
Agent b’s margin constraint binds iff
1
µ − rc
SR
≥
=
2
σ
σ
m
The price-to-dividend ratio Pt /Ct = ζ(ctb ) is given as the
solution to an ODE and all other endogenous variables are
explicit functions of ζ.
Binding margin constraint increases the Sharpe Ratio:
+
¯
σ̄
SR
1
¯ + x
SR = SR
−
′
b
1−x
σ̄
m
ζ c
1−
mζ
¯ = γσ C and σ̄ are the Sharpe and return volatility
where SR
without constraints.
N. Gârleanu and L. H. Pedersen
Margin-Based Asset Pricing
Introduction
Theory
Applications
Conclusion
Model
Required Returns
Explicit Equilibrium
Calibration
Limit Basis
Proposition:
As c b → 0, the basis between asset i and derivative ik
becomes
µi − µik
= ψ(mi − mik )
where
2 σC
1 +
a
ψ =
γ −
m
m
In the cross section of asset-derivative pairs,
µi − µik
µj − µjk
=
i
i
m −mk
m j − m jk
N. Gârleanu and L. H. Pedersen
Margin-Based Asset Pricing
Introduction
Theory
Applications
Conclusion
Model
Required Returns
Explicit Equilibrium
Calibration
Calibration: Parameters
We use the following parameter values
µC
0.03
σC
0.08
γa
8
ρ
0.02
m
0.4
mmed
0.3
mlow
0.1
Constraint binds for c b ≤ 0.22
Since b is levered more than a, low c b is the result of bad
shocks to fundamentals
N. Gârleanu and L. H. Pedersen
Margin-Based Asset Pricing
Introduction
Theory
Applications
Conclusion
Model
Required Returns
Explicit Equilibrium
Calibration
Calibration: Interest Rates
0.12
Complete market
Collateralized rate
Uncollateralized rate
0.11
0.1
0.09
Interest rate
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0
0.05
0.1
0.15
0.2
0.25
c
0.3
0.35
0.4
0.45
0.5
b
Figure: Interest rates: complete markets, collateralized with constraints
(r c ), and uncollateralized with constraints (r u ).
N. Gârleanu and L. H. Pedersen
Margin-Based Asset Pricing
Introduction
Theory
Applications
Conclusion
Model
Required Returns
Explicit Equilibrium
Calibration
Calibration: Bases
0.035
Low margin spread
High margin spread
0.03
Return spread (basis)
0.025
0.02
0.015
0.01
0.005
0
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
b
c
Figure: Return spreads of high-margin underlying versus low-margin
derivative (i.e., large margin spread munderlying − mlow = 30%) and versus
intermediate-margin derivative (i.e., small margin spread
munderlying − mmedium = 10%).
N. Gârleanu and L. H. Pedersen
Margin-Based Asset Pricing
Introduction
Theory
Applications
Conclusion
Model
Required Returns
Explicit Equilibrium
Calibration
Calibration: Sharpe Ratios
0.8
Complete market
Underlying, high margin (m=40%)
Derivative, medium margin (m=30%)
Derivative, low margin (m=10%)
0.7
Market price of risk (SR)
0.6
0.5
0.4
0.3
0.2
0.1
0
0.05
0.1
0.15
0.2
0.25
c
0.3
0.35
0.4
0.45
0.5
b
Figure: Sharpe ratios: complete markets, underlying with constraints,
and two derivatives with constraints.
N. Gârleanu and L. H. Pedersen
Margin-Based Asset Pricing
Introduction
Theory
Applications
Conclusion
Model
Required Returns
Explicit Equilibrium
Calibration
Calibration: Price Premium
0.8
Low constant margin, m=10%
Time−varying margin, m∈[10%,30%]
High constant margin, m=30%
0.7
0.6
Excess price
0.5
0.4
0.3
0.2
0.1
0
0
0.05
0.1
0.15
0.2
0.25
c
0.3
0.35
0.4
0.45
0.5
b
Figure: Price Premium. The figure shows how the price premium,
P derivative /P underlying − 1 for three derivatives with identical cash flows
and different margins.
N. Gârleanu and L. H. Pedersen
Margin-Based Asset Pricing
Introduction
Theory
Applications
Conclusion
CDS-Bond Basis
Monetary Policy and Lending Facilities
Failure of the Covered Interest Rate Parity
Regulatory Arbitrage
CDS-Bond Basis: Time Series
200
4.5
4
3.5
150
3
2.5
percent
percent
100
2
1.5
50
1
0.5
0
0
-0.5
IG CDS-bond basis
LIBOR-GCrepo
1/3/2009
9/3/2008
11/3/2008
7/3/2008
5/3/2008
3/3/2008
1/3/2008
9/3/2007
11/3/2007
7/3/2007
5/3/2007
3/3/2007
1/3/2007
9/3/2006
11/3/2006
7/3/2006
5/3/2006
3/3/2006
1/3/2006
9/3/2005
11/3/2005
7/3/2005
5/3/2005
3/3/2005
-50
1/3/2005
-1
Tightening credit standards (right axis)
Figure: The CDS-Bond basis, the LIBOR-GCrepo Spread, and Credit
Standards.
N. Gârleanu and L. H. Pedersen
Margin-Based Asset Pricing
Introduction
Theory
Applications
Conclusion
CDS-Bond Basis
Monetary Policy and Lending Facilities
Failure of the Covered Interest Rate Parity
Regulatory Arbitrage
CDS-Bond Basis: Cross Section
16
14
12
10
percent
8
6
4
2
0
-2
IG basis, margin adjusted
1/3/2009
9/3/2008
11/3/2008
7/3/2008
5/3/2008
3/3/2008
1/3/2008
9/3/2007
11/3/2007
7/3/2007
5/3/2007
3/3/2007
1/3/2007
9/3/2006
11/3/2006
7/3/2006
5/3/2006
3/3/2006
1/3/2006
9/3/2005
11/3/2005
7/3/2005
5/3/2005
3/3/2005
1/3/2005
-4
HY basis, margin adjusted
Figure: Investment Grade (IG) and High Yield (HY) CDS-Bond Bases,
Adjusted for Their Margins.
N. Gârleanu and L. H. Pedersen
Margin-Based Asset Pricing
Introduction
Theory
Applications
Conclusion
CDS-Bond Basis
Monetary Policy and Lending Facilities
Failure of the Covered Interest Rate Parity
Regulatory Arbitrage
Monetary Policy and Lending Facilities
Term Auction Facility (TAF), Dec. 2007
Term Securities Lending Facility (TSLF), March 2008
Term Asset-Backed Securities Loan Facility (TALF), Nov 2008
Goal: Improve funding conditions and “help market
participants meet the credit needs of households and small
businesses by supporting the issuance of asset-backed
securities”
The model suggests that when the Fed offers lower margins,
liquidity risk and required returns go down:
E (r i ,Fed ) − E (r i ,no Fed ) ≈
λ(β Fed,i − β no Fed,i ) + ψx(mFed,i − mi ) + ∆ψ xmi < 0
I.e., ABS yield down, access to credit eases, helping the real
economy
N. Gârleanu and L. H. Pedersen
Margin-Based Asset Pricing
Introduction
Theory
Applications
Conclusion
CDS-Bond Basis
Monetary Policy and Lending Facilities
Failure of the Covered Interest Rate Parity
Regulatory Arbitrage
Two Monetary Tools: Interest Rates and Haircuts
(Ashcraft, Garleanu, and Pedersen (2009))
Super Senior Bonds
16%
12%
Yield
3-year
5-year
8%
Matched
4%
0%
Low TALF haircut
High TALF haircut
No TALF
Haircut regime
N. Gârleanu and L. H. Pedersen
Margin-Based Asset Pricing
Introduction
Theory
Applications
Conclusion
CDS-Bond Basis
Monetary Policy and Lending Facilities
Failure of the Covered Interest Rate Parity
Regulatory Arbitrage
Two Monetary Tools: Interest Rates and Haircuts
(Ashcraft, Garleanu, and Pedersen (2009))
Safest Super Senior Bonds
1.50
Price Relative to No-TALF Price
1.40
1.30
3-year
1.20
5-year
Matched
1.10
1.00
0.90
Low TALF haircut
High TALF haircut
No TALF
Haircut regime
N. Gârleanu and L. H. Pedersen
Margin-Based Asset Pricing
Introduction
Theory
Applications
Conclusion
CDS-Bond Basis
Monetary Policy and Lending Facilities
Failure of the Covered Interest Rate Parity
Regulatory Arbitrage
Evidence on Monetary Policy and Margins Affecting Prices
(Ashcraft, Garleanu, and Pedersen (2009)
Figure: Market reaction to TALF-related announcements.
N. Gârleanu and L. H. Pedersen
Margin-Based Asset Pricing
Introduction
Theory
Applications
Conclusion
CDS-Bond Basis
Monetary Policy and Lending Facilities
Failure of the Covered Interest Rate Parity
Regulatory Arbitrage
Failure of the Covered Interest Rate Parity
10
4/23/2008
10/23/2008
4/23/2007
10/23/2007
4/23/2006
10/23/2006
4/23/2005
10/23/2005
4/23/2004
10/23/2004
4/23/2003
10/23/2003
4/23/2002
CIP deviation
10/23/2002
0
4/23/2001
1
0
10/23/2001
2
0.2
4/23/2000
3
0.4
10/23/2000
4
0.6
4/23/1999
5
0.8
10/23/1999
6
1
4/23/1998
7
1.2
10/23/1998
8
1.4
10/23/1997
9
1.6
4/23/1997
percent
2
1.8
TED spread (right axis)
Figure: Average Deviation from Covered-Interest Parity and the TED
Spread.
N. Gârleanu and L. H. Pedersen
Margin-Based Asset Pricing
Introduction
Theory
Applications
Conclusion
CDS-Bond Basis
Monetary Policy and Lending Facilities
Failure of the Covered Interest Rate Parity
Regulatory Arbitrage
Regulatory Arbitrage
Pressure to free capital by moving assets off the balance sheet
or titling portfolios towards low capital-requirement assets
Basel requirement is similar to the margin constraint
X
mReg ,i |θ i | ≤ 1
i
Required return increased by mReg ,i ψ
N. Gârleanu and L. H. Pedersen
Margin-Based Asset Pricing
Introduction
Theory
Applications
Conclusion
Conclusion
Margin-based general-equilibrium model
Strong asset pricing predictions
Predicts that a decline in fundamentals leads to
Binding constraints
Drop in Treasury and GC repo rates
Spikes in interest-rate spreads, risk premium, margin premium
Basis between securities with identical cash flows, related to
margin differences
Calibrated model predicts large margin premium in crisis
Applications:
CDS-bond basis
Covered interest parity
Monetary policy, fed lending facilities
Banks’ incentives to use off-balance-sheet instruments
N. Gârleanu and L. H. Pedersen
Margin-Based Asset Pricing