Introduction
Model
Data
Estimation
Liquidity
Decomposition
Predictability
Extensions
An Equilibrium Model of
Institutional Demand and Asset Prices
Ralph S.J. Koijena
a London
Motohiro Yogob
Business School and CEPR
b Princeton
University and NBER
Conclusion
Introduction
Model
Data
Estimation
Liquidity
Decomposition
Predictability
Extensions
Conclusion
Motivating questions
Questions about the role of institutions in financial markets:
How did market liquidity change with the growing importance
of institutional investors?
Do institutional trades affect the volatility and predictability of
returns?
Do large institutions amplify volatility in bad times? Should
they be regulated as SIFI (OFR 2013)?
How do large-scale asset purchases affect asset prices through
institutional holdings?
To answer these questions, we need an equilibrium model of
demand curves of institutional investors.
Introduction
Model
Data
Estimation
Liquidity
Decomposition
Predictability
Extensions
Contributions
1
A new demand system for financial assets.
Model asset demand as a logit function of prices and
characteristics.
Matches institutional holdings.
Consistent with traditional asset pricing and portfolio choice
with heterogeneous beliefs or constraints.
2
Identification in the presence of price impact by coefficient
restriction or IV.
3
Asset pricing applications:
Estimate price impact as a liquidity measure.
Explain the role of institutions in volatility and predictability.
Conclusion
Introduction
Model
Data
Estimation
Liquidity
Decomposition
Predictability
Extensions
Conclusion
Asset pricing model
Investor i has wealth Ai , allocated between an outside asset
and inside assets: Ni ⊆ {1, . . . , N}.
Investor i’s demand for asset n ∈ Ni :
wi (n) =
where
exp{δi (n)}
P
1 + m∈Ni exp{δi (m)}
δi (n) = β0,i p(n) +
K
X
(1)
βk,i xk (n) + i (n)
k=1
p(n): Log price.
xk (n): Observed characteristics (e.g., dividends, earnings, book
equity, assets).
i (n): Unobserved characteristics.
Introduction
Model
Data
Estimation
Liquidity
Decomposition
Predictability
Extensions
Conclusion
Asset pricing model
Market clearing:
P(n)S(n) =
I
X
Ai wi (n)
i =1
Proposition: Equilibrium unique if demand is downward
sloping (i.e., β0,i ≤ 1).
(2)
Introduction
Model
Data
Estimation
Liquidity
Decomposition
Predictability
Extensions
Conclusion
Asset pricing model
Market clearing:
P(n)S(n) =
I
X
Ai wi (n)
i =1
Proposition: Equilibrium unique if demand is downward
sloping (i.e., β0,i ≤ 1).
Motivation for our model:
1
2
Differentiated product demand systems in IO.
Standard equilibrium model where investors have
Different opinions about future cash flows.
Cash flows have a factor structure.
Price impact.
(2)
Introduction
Model
Data
Estimation
Liquidity
Decomposition
Predictability
Extensions
Conclusion
Relation to traditional asset pricing and portfolio choice
Investors have CARA preferences with risk aversion γi .
Dividends are normally distributed, D ∼ N(μi , Σ).
No asymmetric information: Investors agree to disagree.
1
Euler equation
∂P
0
= 0,
Ei U (AiT ) D − P − Qi
∂Q0i
where ∂P/∂Q0i reflects investor i’s price impact.
2
Optimal portfolio choice
Qi =
1 −1
Σ (μi − P).
γi ci
Introduction
Model
Data
Estimation
Liquidity
Decomposition
Predictability
Extensions
Conclusion
Factor models and characteristics-based demand model
In empirical asset pricing, we commonly assume that
1
2
3
Returns or cash flows follow a factor model.
Factor exposures depend linearly on characteristics.
Expected returns or cash flows depend linearly on
characteristics.
Under this assumption, investor i’s demand schedule is
Qi = Pβ0,i + xβ1,i + i .
The equilibrium price is
P=
PI
i =1 (xβ1,i + i )
P
− Ii =1 β0,i
where S is the residual supply.
−S
,
Introduction
Model
Data
Estimation
Liquidity
Decomposition
Predictability
Extensions
Conclusion
Identifying the price elasticity of demand
Estimating β0,i from the cross-section of holdings using OLS
is biased
P


I
,
Cov
i
j
j=1
2c
−
1
i
OLS
.
→ β0,i 1 −
βb0,i
ci − 1 Var PI + Var(S)
j=1 j
An IV estimator using residual supply, S, as instrument is
consistent
IV
βb0,i
→ β0,i .
Empirical goal: Identify exogenous variation in residual supply.
Introduction
Model
Data
Estimation
Liquidity
Decomposition
Predictability
Extensions
Summary of 13F institutions
SEC Form 13F: Quarterly stock holdings of institutions
managing over $100m.
Merged with stock prices and characteristics in
CRSP-Compustat.
Big data: 44 million observations.
Percent
Period
1980–1984
1985–1989
1990–1994
1995–1999
2000–2004
2005–2009
2010–2014
Assets under
management
($ million)
Number of
stocks held
Number of
institutions
of market
held
Median
90th
percentile
Median
90th
percentile
539
769
965
1,298
1,776
2,414
2,802
35
41
46
51
57
65
63
339
405
409
473
376
337
328
2,678
3,636
4,643
6,759
6,146
5,491
5,554
121
122
111
108
92
76
69
395
464
534
597
547
477
454
Conclusion
Introduction
Model
Data
Estimation
Liquidity
Decomposition
Predictability
Extensions
Empirical specification
Rewrite investor i’s demand for asset n as
log
wi (n)
wi (0)
= β0,i p(n) +
K
X
βk,i xk (n) + i (n)
k=1
Characteristics:
1
2
3
4
5
6
Log dividends per share (interacted with paying dummy).
Log book equity.
Log book equity to assets.
Profitability.
Nasdaq dummy.
S&P 500 dummy.
Estimate coefficients for each 13F institution and the
household sector.
Conclusion
Introduction
Model
Data
Estimation
Liquidity
Decomposition
Predictability
Extensions
Identification by coefficient restriction
Traditional assumption in endowment economies:
E[i (n)|x(n), p(n)] = 0.
Price taking may not be appropriate for large institutions.
Conclusion
Introduction
Model
Data
Estimation
Liquidity
Decomposition
Predictability
Extensions
Conclusion
Identification by coefficient restriction
Traditional assumption in endowment economies:
E[i (n)|x(n), p(n)] = 0.
Price taking may not be appropriate for large institutions.
Assumption: Coefficients on log price and dividends per share
sum to zero.
Rewrite the estimation equation as
log
wi (n)
wi (0)
= β0,i (p(n) − x1 (n)) +
Moment condition: E[i (n)|x(n)] = 0.
K
X
k=2
βk,i xk (n) + i (n).
Introduction
Model
Data
Estimation
Liquidity
Decomposition
Predictability
Extensions
Conclusion
Identification by IV
Assumptions
1
2
Investors have an exogenous investment universe. For example,
index funds (Harris and Gurel 1986, Shleifer 1986).
My demand doesn’t depend on investment universe of investors
outside my group, defined by size and investment style.
We compute counterfactual prices as if
1
2
Prices are set by investors outside my group.
These investors follow a “1/N” rule for the stocks in their
universe.
The instrument exploits exogenous variation in investment
universes across dissimilar investors to isolate exogenous
variation in residual supply.
Introduction
Model
Data
Estimation
Liquidity
Decomposition
Predictability
Extensions
Conclusion
Identification by IV
Assumptions
1
2
1
2
Investors have an exogenous investment universe. For example,
index funds (Harris and Gurel 1986, Shleifer 1986).
My demand doesn’t depend on investment universe of investors
outside my group, defined by size and investment style.
Start with market clearing:
X X
X
1
1
+
.
Aj wj (n) +
Aj
Aj wj (n) −
P(n)S(n) =
|Nj |
|Nj |
j∈Gi
j ∈G
/ i
j ∈G
/ i
| {z }
exogenous
Isolate price variation from exogenous demand:


X
1 
b
pi (n) = log 
Aj
− s(n).
|Nj |
j ∈G
/ i
Moment condition: E[i (n)|x(n), b
pi (n)] = 0.
Introduction
Model
Data
Estimation
Liquidity
Decomposition
Predictability
Extensions
Conclusion
Comparison of estimated coefficients on price
1
1
Left: Least squares is upward biased.
Right: Coefficient restriction and IV lead to similar estimates.
.6
-1
-1.4
-1.4
-1
-.6
Least squares
-.2
.2
Coefficient restriction only
-.6
-.2
.2
.6
Linear fit
45-degree line
-1.4
-1
-.6
-.2
.2
Instrumental variables
.6
1
-1.4
-1
-.6
-.2
.2
Instrumental variables
.6
1
Introduction
Model
Data
Estimation
Liquidity
Decomposition
Predictability
Extensions
Estimated coefficients on price and characteristics
Log dividends per share
Mean coefficient
0
.2
-.2
AUM above 90th percentile
AUM below 90th percentile
Households
-.4
-.6
-.4
Mean coefficient
-.2
0
.4
.2
.6
.4
Log price
Log book equity
Log book equity to assets
Mean coefficient
-.1
0
-.2
-.3
.7
Mean coefficient
.5
.6
.4
.3
1980:1 1985:1 1990:1 1995:1 2000:1 2005:1 2010:1 2015:1
Year: Quarter
.1
1980:1 1985:1 1990:1 1995:1 2000:1 2005:1 2010:1 2015:1
Year: Quarter
.8
1980:1 1985:1 1990:1 1995:1 2000:1 2005:1 2010:1 2015:1
Year: Quarter
1980:1 1985:1 1990:1 1995:1 2000:1 2005:1 2010:1 2015:1
Year: Quarter
Conclusion
Introduction
Model
Data
Estimation
Liquidity
Decomposition
Predictability
Extensions
Liquidity measurement
Price impact as a liquidity measure (Kyle 1985).
Coliquidity matrix for investor i:
I
X
∂p
= (I −
Ai β0,j Z−1 Yj )−1 Ai Z−1 Yi
0
∂i
j=1
|
{z
}
demand elasticity
(n, m)th element: Elasticity of asset price n with respect to
demand for asset m.
Aggregate coliquidity matrix:
I
X
∂p
∂0i
i =1
Conclusion
Introduction
Model
Data
Estimation
Liquidity
Decomposition
Predictability
Extensions
Conclusion
.08
Variation in average price impact across stocks
0
.02
Price elasticity
.04
.06
90th percentile
Median
10th percentile
1980:1
1985:1
1990:1
1995:1
2000:1
Year: Quarter
2005:1
2010:1
2015:1
Introduction
Model
Data
Estimation
Liquidity
Decomposition
Predictability
Extensions
Conclusion
90th percentile
Median
10th percentile
1
1.4
Price elasticity
1.8
2.2
2.6
3
3.4
Variation in aggregate price impact across stocks
1980:1
1985:1
1990:1
1995:1
2000:1
Year: Quarter
2005:1
2010:1
2015:1
Introduction
Model
Data
Estimation
Liquidity
Decomposition
Predictability
Extensions
Variance decomposition of stock returns
Start with definition of log return:
Dt+1 (n)
rt+1 (n) = pt+1 (n) − pt (n) + log 1 +
Pt+1 (n)
Model implies that
pt = g (st , xt , At , βt , t )
1
2
3
4
5
st : Shares outstanding.
xt : Asset characteristics.
At : Assets under management.
βt : Coefficients on characteristics.
t : Latent demand.
Conclusion
Introduction
Model
Data
Estimation
Liquidity
Decomposition
Predictability
Variance decomposition of stock returns
Percent of
variance
Supply:
Shares outstanding
Stock characteristics
Dividend yield
Demand:
Assets under management
Coefficients on characteristics
Latent demand
Observations
1.9
(0.1)
6.2
(0.2)
0.4
(0.0)
14.4
(0.2)
2.7
(0.1)
74.5
(0.3)
142,783
Extensions
Conclusion
Introduction
Model
Data
Estimation
Liquidity
Decomposition
Predictability
Extensions
Variance decomposition of stock returns in 2008
Are large investment managers systemic (OFR 2013)?
AUM
ranking
Institution
AUM
($ billion)
Change
in AUM
(percent)
Supply: Shares outstanding, stock
characteristics & dividend yield
1
2
3
4
5
6
7
8
9
10
Barclays Bank
Fidelity Management & Research
State Street Corporation
Vanguard Group
AXA Financial
Capital World Investors
Wellington Management Company
Capital Research Global Investors
T. Rowe Price Associates
Goldman Sachs & Company
Subtotal: Largest 25 institutions
Smaller institutions
Households
Total
Percent of
variance
4.6
(0.7)
699
577
547
486
309
309
272
270
233
182
5,684
-41
-63
-37
-41
-70
-44
-51
-53
-44
-59
-47
1.0
0.8
0.5
0.8
0.3
0.1
0.4
0.2
0.2
0.3
7.0
(0.0)
(0.1)
(0.0)
(0.0)
(0.0)
(0.0)
(0.1)
(0.1)
(0.0)
(0.0)
6,483
6,322
18,489
-53
-47
-49
29.8
58.6
100.0
(1.8)
(2.0)
Conclusion
Introduction
Model
Data
Estimation
Liquidity
Decomposition
Predictability
Extensions
Conclusion
Predictability of stock returns
Recall that
pt+1 = g (st+1 , xt+1 , At+1 , βt+1 , t+1 )
First-order approximation of expected log returns:
Et [rt+1 ] ≈ g (Et [st+1 ], Et [xt+1 ], Et [At+1 ], Et [βt+1 ], Et [t+1 ]) − pt
Model t+1 as mean reverting and everything else as random
walk.
Intuition: Assets with high latent demand are expensive and
have low expected returns.
Introduction
Model
Data
Estimation
Liquidity
Decomposition
Predictability
Extensions
Conclusion
Characteristics of portfolios sorted by expected returns
Form 5 portfolios in December of each year, sorted by
estimated expected returns.
Model identifies small-value stocks as having high expected
returns.
Portfolios sorted by expected returns
Characteristic
Expected return
Log market equity
Book-to-market equity
Book equity to assets
Profitability
Number of stocks
Low
2
3
4
High
-0.15
6.07
0.26
0.51
0.28
909
-0.02
5.98
0.49
0.50
0.29
912
0.07
5.24
0.67
0.48
0.27
910
0.17
4.20
0.87
0.47
0.26
908
0.32
2.83
1.30
0.49
0.29
868
Introduction
Model
Data
Estimation
Liquidity
Decomposition
Predictability
Extensions
Equal-weighted portfolios sorted by expected returns
Portfolios sorted by expected returns
Low
2
3
Panel A: Average excess returns (percent)
1982–2014
3.87
9.13
10.64
(3.77) (3.28) (3.16)
1982–1997
0.03
8.39
10.76
(4.70) (4.13) (4.03)
1998–2014
7.49
9.82
10.53
(5.84) (5.05) (4.83)
Panel B: Fama-French three-factor betas and
Market beta
1.13
1.04
0.97
(0.03) (0.02) (0.02)
SMB beta
0.72
0.65
0.73
(0.06) (0.06) (0.06)
HML beta
-0.03
0.21
0.32
(0.05) (0.04) (0.04)
Alpha (percent)
-6.13
-0.99
0.57
(1.11) (0.89) (0.94)
High
4
High
−Low
11.90
(3.21)
12.56
(4.20)
11.28
(4.83)
alpha
0.90
(0.03)
0.84
(0.06)
0.36
(0.06)
2.14
(1.29)
18.57
(3.77)
19.60
(4.61)
17.59
(5.91)
14.70
(2.18)
19.58
(2.70)
10.10
(3.36)
0.86
(0.05)
1.02
(0.10)
0.40
(0.11)
8.75
(2.27)
-0.27
(0.04)
0.30
(0.07)
0.43
(0.09)
14.88
(1.93)
Conclusion
Introduction
Model
Data
Estimation
Liquidity
Decomposition
Predictability
Extensions
Extensions of the model
1
Endogenize supply (i.e., shares outstanding and asset
characteristics) through the firm’s problem.
2
Endogenize flows into institutions through the household’s
problem.
3
Model the extensive margin through a Tobit model:
wi (n) =
4
where δi (n) ≥ 0.
1+
α (exp{δi (n)} − 1)
P i
m∈Ni αi (exp{δi (m)} − 1)
Relax factor structure assumption through
wi
= Σ−1
i exp{Xβi + i }
wi (0)
Conclusion
Introduction
Model
Data
Estimation
Liquidity
Decomposition
Predictability
Extensions
Conclusion
Conclusion
Asset pricing model that matches institutional holdings.
1
2
Rich heterogeneity in asset demand.
Potential price impact.
Could answer questions that are difficult with reduced-form
regressions or event studies.
Future projects:
1
2
3
4
How does QE affect bond markets?
Koijen, Koulischer, Nguyen, Yogo (2016).
How would regulatory reform (banks and insurance companies)
affect asset prices and real investment?
Which institutions affect anomaly returns?
The impact of monetary policy on international bond and
equity markets.
Introduction
Model
Data
Estimation
Liquidity
Decomposition
Predictability
Extensions
Value-weighted portfolios sorted by expected returns
Portfolios sorted by expected returns
Low
2
3
Panel A: Average excess returns (percent)
1982–2014
7.66
8.88
9.23
(2.85) (2.59) (2.62)
1982–1997
9.64
11.25
12.13
(3.93) (3.58) (3.43)
1998–2014
5.79
6.65
6.51
(4.11) (3.73) (3.93)
Panel B: Fama-French three-factor betas and
Market beta
1.01
0.97
0.98
(0.01) (0.01) (0.01)
SMB beta
-0.12
-0.06
0.06
(0.02) (0.02) (0.02)
HML beta
-0.20
0.10
0.27
(0.02) (0.03) (0.03)
Alpha (percent)
0.32
0.71
0.17
(0.49) (0.56) (0.61)
High
4
High
−Low
11.27
(2.79)
14.01
(3.97)
8.68
(3.92)
alpha
0.97
(0.02)
0.31
(0.04)
0.49
(0.03)
1.15
(1.00)
13.68
(3.37)
15.66
(4.53)
11.82
(4.96)
6.02
(2.29)
6.02
(3.17)
6.03
(3.31)
1.00
(0.04)
0.67
(0.06)
0.45
(0.06)
2.98
(1.62)
-0.01
(0.05)
0.79
(0.06)
0.65
(0.07)
2.67
(1.79)
Conclusion
Introduction
Model
Data
Estimation
Liquidity
Decomposition
Predictability
Extensions
Conclusion
AUM above 90th percentile
AUM below 90th percentile
Households
.8
1
Standard deviation
1.2
1.4
1.6
1.8
2
Standard deviation of latent demand
1980:1
1985:1
1990:1
1995:1
2000:1
Year: Quarter
2005:1
2010:1
2015:1