Lectures on the Investment CAPM
3. Quantitative Investment Theories
Lu Zhang1
1 The
Ohio State University
and NBER
Shanghai University of Finance and Economics
December 2015
Prof. Lu Zhang (2015)
Quantitative Investment Theories
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Theme
Four lectures based on Zhang (2015, The Investment CAPM), with
additional details from the original articles referenced:
1
2
3
4
The q -factor model
The structural investment CAPM
Quantitative investment theories
The big picture: Past, present, and future
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The Investment CAPM
A two-period stochastic general equilibrium model
Three dening characteristics of neoclassical economics:
Rational expectations
Consumers maximize utility, and rms maximize market value
Markets clear
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The Investment CAPM
The consumption CAPM
A representative household maximizes:
U(Ct ) + ρEt [U(Ct+1 )]
subject to:
Ct +
X
Pit Sit+1 =
i
X
(Pit + Dit )Sit
i
Ct+1
X
=
(Pit+1 + Dit+1 )Sit+1
i
The rst principle of consumption:
S
Et [Mt+1 rit+
1] = 1
Prof. Lu Zhang (2015)
⇒
M
S
Et [rit+
1 ] − rft = βit λMt
Quantitative Investment Theories
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The Investment CAPM
Heterogeneous rms
An individual rm i maximizes:
"
Pit + Dit ≡ max Πit Kit − Iit −
{Iit }
a
2
Iit
Kit
2
#
Kit + Et [Mt+1 Πit+1 Kit+1 ]
The rst principle of investment:
1 = Et Mt+1
Πit+1
1 + a(Iit /Kit )
Pit+1 + Dit+1
Πit+1
S
I
≡ rit+
1 = rit+1 ≡
Pit
1 + a(Iit /Kit )
Capital budgeting implies cross-sectionally varying expected returns
Prof. Lu Zhang (2015)
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The Investment CAPM
Implications
The evidence that characteristics predicting returns is consistent with the
investment CAPM, does not necessarily mean mispricing
The consumption CAPM and the investment CAPM deliver identical
expected returns in general equilibrium:
S
rft + βitM λMt = Et [rit+
1] =
Et [Πit+1 ]
1 + a(Iit /Kit )
S ]
Consumption: Covariances are sucient statistics of Et [rit+
1
S
Investment: Characteristics are sucient statistics of Et [rit+1 ]
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Outline
1
Real Options
2
Neoclassical Investment Models
3
Controversies
Is Value Riskier Than Growth?
Does the Conditional CAPM Explain the Value Premium?
What Explains the Failure of the CAPM?
4
Notes
Momentum
Beyond Value and Momentum
Debt Dynamics
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Real Options
Outline
1
Real Options
2
Neoclassical Investment Models
3
Controversies
Is Value Riskier Than Growth?
Does the Conditional CAPM Explain the Value Premium?
What Explains the Failure of the CAPM?
4
Notes
Momentum
Beyond Value and Momentum
Debt Dynamics
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Real Options
Real Options
This applied theoretical literature is pioneered by Berk, Green, and Naik (1999)
Berk (1995)
Berk, Green, and Naik (1999)
Gomes, Kogan, and Zhang (2003)
Carlson, Fisher, and Giammarino (2004, 2006)
Cooper (2006)
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Neoclassical Investment Models
Outline
1
Real Options
2
Neoclassical Investment Models
3
Controversies
Is Value Riskier Than Growth?
Does the Conditional CAPM Explain the Value Premium?
What Explains the Failure of the CAPM?
4
Notes
Momentum
Beyond Value and Momentum
Debt Dynamics
Prof. Lu Zhang (2015)
Quantitative Investment Theories
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Neoclassical Investment Models
Neoclassical Investment Models
Zhang (2005): A quantitative neoclassical benchmark for cross-sectional returns
THE JOURNAL OF FINANCE • VOL. LX, NO. 1 • FEBRUARY 2005
The Value Premium
LU ZHANG∗
ABSTRACT
The value anomaly arises naturally in the neoclassical framework with rational expectations. Costly reversibility and countercyclical price of risk cause assets in place
to be harder to reduce, and hence are riskier than growth options especially in bad
times when the price of risk is high. By linking risk and expected returns to economic primitives, such as tastes and technology, my model generates many empirical
regularities in the cross-section of returns; it also yields an array of new refutable
hypotheses providing fresh directions for future empirical research.
WHY DO VALUE STOCKS EARN HIGHER EXPECTED RETURNS than growth stocks? This appears to be a troublesome anomaly for rational expectations, because according
to conventional wisdom, growth options hinge upon future economic conditions
and must be riskier than assets in place. In a widely used corporate finance
textbook,
Grinblatt
and Titman
(2001,
p. 392) Theories
contend that “Growth opportuniProf.
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(2015)
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Investment
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Neoclassical Investment Models
Neoclassical Investment Models
Mechanisms based on asymmetry and time-varying price of risk
Asymmetry causes the value-minus-growth risk to be countercyclical
Time-varying price of risk interacts with and propagates the eect
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Neoclassical Investment Models
Neoclassical Investment Models
Why would asymmetry lead to countercyclical value-minus-growth risk?
Higher adjustment costs lead to higher risk with production:
Capital adjustment helps rms smooth dividend stream
Adjustment costs are the osetting force of changing capital
Both in the data and in the model, high book-to-market signals sustained
low protability, and low book-to-market signals high protability
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Neoclassical Investment Models
Neoclassical Investment Models
Why would asymmetry lead to countercyclical value-minus-growth risk?
The link between book-to-market and risk across business cycles:
In bad times:
Value Firms ⇒II Burdened With More Unproductive Capital
⇒ Want to Cut More Capital ⇒ More Adjustment Cost ⇒I Higher Risk
In good times:
Growth Firms ⇒II More Productive Capital
⇒ Want to Expand More ⇒ More Adjustment Cost ⇒I Higher Risk
Time-varying price of risk implies a positive value premium on average
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Neoclassical Investment Models
Neoclassical Investment Models
The Zhang (2005) model a la the Lucas-Prescott (1971) industry equilibrium
The prot function:
πjt = e (xt +zjt +pt ) kjtα − f
in which
xt+1 = x̄(1 − ρx ) + ρx xt + σx xt+1
zjt+1 = ρz zjt + σz zjt+1
The stochastic discount factor:
log Mt,t+1 = log β + γt (xt − xt+1 )
γt
Prof. Lu Zhang (2015)
= γ0 + γ1 (xt − x̄);
Quantitative Investment Theories
γ1 < 0
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Neoclassical Investment Models
Neoclassical Investment Models
The value maximization of rms
Industry demand function: Pt = Yt−η ; η ∈ (0, 1)
The rms' optimal investment problem is:

Current Period Dividend

z
}|
{
v (kt , zt ; xt , pt ) = max e xt +zt +pt ktα − f − it − h(it , kt ) +
it 

Expected Continuation Value
zZZ


{


Mt,t+1 v (kt+1 , zt+1 ; xt+1 , pt+1 ) Qz (dzt+1 |zt ) Qx (dxt+1 |xt )




}|
subject to the capital accumulation rule: kt+1 = it + (1 − δ)kt
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Neoclassical Investment Models
Neoclassical Investment Models
Asymmetric adjustment costs:
h(it , kt ) =
θt
2
it
kt
2
kt
in which θt = θ+ χ{it ≥0} + θ− χ{it <0} and θ− > θ+
74
The Journal of Finance
Figure 1. Asymmetric adjustment cost. This figure illustrates the specification of capital adjustment cost, equations (10) and (11). The investment rate, i/k, is on the x-axis and the amount
of adjustment cost, h(i, k), is on the y-axis. The adjustment cost is assumed to be
Prof. Lu Zhang (2015)
2
it
θt
Quantitative
=
ktTheories
,
h(it , kt )Investment
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Neoclassical Investment Models
Neoclassical Investment Models
Risk and expected returns
The risk and expected return of rm j satisfy the linear relation:
Et [Rjt+1 ] = Rft + βjt λmt ,
in which Rft is the real interest rate, and the stock return is
Rjt+1 ≡ vjt+1 /(vjt − djt )
Dividends: djt ≡ πjt − ijt − h(ijt , kjt )
The quantity of risk: βjt ≡ −Covt [Rjt+1 , Mt+1 ]/Vart [Mt+1 ]
The price of risk: λmt ≡ Vart [Mt+1 ]/Et [Mt+1 ]
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Neoclassical Investment Models
Neoclassical Investment Models
Aggregation
The law of motion of the cross-sectional distribution of rms, µt :
µt+1 (Θ; xt+1 ) = T (Θ, (kt , zt ); xt )µt (kt , zt ; xt )
in which
T (Θ, (kt , zt ); xt ) ≡
ZZ
χ{(kt+1 ,zt+1 )∈Θ} Qz (dzt+1 |zt )Qx (dxt+1 |xt )
Industry output:
Yt ≡
Prof. Lu Zhang (2015)
ZZ
y (kt , zt ; xt ) µt (dk, dz; xt )
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Neoclassical Investment Models
Neoclassical Investment Models
Recursive competitive equilibrium
A recursive competitive equilibrium consists of (T ∗ , v ∗ , i ∗ , pt∗ ) such that
the following conditions hold: optimality; consistency; and market-clearing
Computation: in standard value functions, the laws of motion of state
variables are usually explicit and straightforward
But pt , depends upon the rm distribution:
Approximate aggregation: Krusell and Smith (1998), approximate the
distribution using a nite number of moments, e.g., k, σ(k).
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Neoclassical Investment Models
Neoclassical Investment Models
Approximate aggregation
1
2
3
4
5
6
Guess an explicit law of motion: pt+1 = a1 + a2 pt + a3 (xt − x) + a4 σk
Solve the rms' problem by the value function iteration method
Use the optimal investment and exit rules to simulate the industry
with 5,000 rms for 12,000 monthly periods
Use the data in the stationary region to update the coecients a1 , a2 ,
and a3
Check convergence; if yes, go to next step; otherwise go back to step 2
Check goodness-of-t; if yes, done; otherwise try a dierent
specication
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Neoclassical Investment Models
serves as the reference
point.
Table I summarizes the key parameter values in the model. All model parameters are calibrated at the monthly frequency to be consistent with the
empirical
literature.
Calibration
in Zhang
(2005)I break down all the parameters into three groups. The
first group includes parameters that can be restricted by prior empirical or
Neoclassical Investment Models
Table I
Benchmark Parameter Values
This table lists the benchmark parameter values used to solve and simulate the model. I break
all the parameters into three groups. Group I includes parameters whose values are restricted by
prior empirical or quantitative studies: capital share, α; depreciation, δ; persistence of aggregate
productivity, ρx ; conditional volatility of aggregate productivity, σx ; and inverse price elasticity of
demand, η. Group II includes parameters in the pricing kernel, β, γ0 , and γ1 , which are tied down
by matching the average Sharpe ratio and the mean and volatility of real interest rate. The final
group of parameters is calibrated with only limited guidance from prior empirical studies. I start
with a reasonable set of parameter values and conduct extensive sensitivity analysis in Tables III
and IV.
Group I
α
0.30
Group II
Group III
δ
ρx
σx
η
β
γ0
γ1
θ −/θ +
θ+
ρz
σz
f
0.01
0.951/3
0.007/3
0.50
0.994
50
−1000
10
15
0.97
0.10
0.0365
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Neoclassical Investment Models
Neoclassical Investment Models
80
The Journal of Finance
Aggregate
moments in Zhang (2005)
Table II
Key Moments under the Benchmark Parametrization
This table reports a set of key moments generated under the benchmark parameters reported
in Table I. The data source for the average Sharpe ratio is the postwar sample of Campbell and
Cochrane (1999). The moments for the real interest rate are from Campbell et al. (1997). The data
moments for the industry returns are computed using the 5-, 10-, 30-, and 48-industry portfolios in
Fama and French (1997), available from Kenneth French’s web site. The numbers of the average
volatility of individual stock return in the data are from Campbell et al. (2001) and Vuolteenaho
(2001). The data source for the moments of book-to-market is Pontiff and Schall (1999), and the
annual average rates of investment and disinvestment are from Abel and Eberly (2001).
Moments
Model
Data
Average annual Sharpe ratio
Average annual real interest rate
Annual volatility of real interest rate
Average annual value-weighted industry return
Annual volatility of value-weighted industry return
Average volatility of individual stock return
Average industry book-to-market ratio
Volatility of industry book-to-market ratio
Annual average rate of investment
Annual average rate of disinvestment
0.41
0.022
0.029
0.13
0.27
0.286
0.54
0.24
0.135
0.014
0.43
0.018
0.030
0.12–0.14
0.23–0.28
0.25–0.32
0.67
0.23
0.15
0.02
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Neoclassical Investment Models
Neoclassical Investment Models
The Value Premium
Properties of portfolios sorted on book-to-market
in Zhang (2005)
81
Table III
Properties of Portfolios Sorted on Book-to-Market
This table reports summary statistics for HML and 10 book-to-market portfolios, including mean,
m, volatility, σ , and market beta, β. Both the mean and the volatility are annualized. The average
HML return (the value premium) is in annualized percent. Panel A reports results from historical
data and benchmark model with asymmetry and countercyclical price of risk (θ −/θ + = 10 and γ1 =
−1000). Panel B reports results from two comparative static experiments. Model 1 has symmetric
adjustment cost and constant price of risk (θ −/θ + = 1 and γ1 = 0), and Model 2 has asymmetry
and constant price of risk (θ −/θ + = 10 and γ1 = 0). All the model moments are averaged across
100 artificial samples. All returns are simple returns.
Panel A: Data and Benchmark
Data
Panel B: Comparative Statics
Benchmark
Model 1
Model 2
m
β
σ
m
β
σ
m
β
σ
m
β
σ
HML
4.68
0.14
0.12
4.87
0.43
0.12
2.19
0.09
0.04
2.54
0.11
0.04
Low
2
3
4
5
6
7
8
9
High
0.11
0.12
0.12
0.11
0.13
0.13
0.14
0.15
0.17
0.17
1.01
0.98
0.95
1.06
0.98
1.07
1.13
1.14
1.31
1.42
0.20
0.19
0.19
0.21
0.20
0.22
0.24
0.24
0.29
0.33
0.09
0.10
0.10
0.11
0.11
0.12
0.12
0.12
0.13
0.15
0.85
0.92
0.95
0.98
1.01
1.04
1.08
1.12
1.18
1.36
0.23
0.24
0.25
0.26
0.27
0.28
0.28
0.30
0.31
0.36
0.08
0.09
0.09
0.09
0.10
0.10
0.10
0.10
0.11
0.11
0.95
0.97
0.99
1.00
1.00
1.01
1.02
1.03
1.04
1.07
0.30
0.31
0.31
0.32
0.32
0.32
0.32
0.33
0.33
0.34
0.08
0.09
0.09
0.10
0.10
0.10
0.10
0.11
0.11
0.12
0.94
0.97
0.98
0.99
1.00
1.01
1.02
1.04
1.05
1.08
0.30
0.31
0.31
0.31
0.32
0.32
0.32
0.33
0.33
0.34
To
the
Prof.
Luevaluate
Zhang (2015)
role of asymmetry
the countercyclical
price of risk,
I con- 24
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Theories
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Neoclassical Investment Models
Neoclassical Investment Models
84 factor in protability inThe
Journal
of Finance
The value
Zhang
(2005)
Panel A: Return on Equity (ROE)
Panel B: Time-Series of ROE
0.4
0.5
Growth
0.3
0.4
0.3
Profitability
Profitability
0.2
0.1
0.2
0
−0.1
−0.2
−6
Value
−4
Growth
0.1
0
Value
−0.1
−2
0
Formation Year
2
4
6
−0.2
0
10
20
30
40
50
Time Series
60
70
80
Figure 2. The value factor in profitability (ROE). Following Fama and French (1995), I measure profitability by return on equity, that is [kt + dt ]/kt−1 , where kt denotes the book value of
equity and dt is the dividend payout. Thus profitability equals the ratio of common equity income for
the fiscal year ending in calender year t and the book value of equity for year t − 1. The profitability
of a portfolio is defined as the sum of [kjt + djt ] for all firms j in the portfolio divided by the sum
of kjt−1 ; thus it is the return on book equity by merging all firms in the portfolio. For each portfolio
formation year t, the ratios of [kt+i + dt+i ]/kt+i−1 are calculated for year t + i, where i = −5, . . . , 5.
The ratio for year t + i is then averaged across portfolio formation years. Panel A shows the
11-year evolution of profitability for value and growth portfolios. Time 0 on the horizontal axis
is the portfolio formation year. Panel B shows the time series of profitability for value and growth
portfolios. Value portfolio contains firms in the top 30% of the book-to-market ratios and growth
portfolio contains firms in the bottom 30% of the book-to-market ratios. The figure is generated
under the benchmark model, and varying θ −/θ + and γ1 yields similar results.
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x, and bad times
are defined
as Models
times when xt is more than one standard deNeoclassical
Investment
viation below its unconditional mean. Within each simulated sample, I average the adjustment costs and the investment rates of value and growth firms
across all the good or bad times. I then repeat the simulation 100 times and
Neoclassical Investment Models
The value factor in corporate investment in Zhang (2005)
Panel A: Bad Times
−3
1.5
Panel B: Good Times
x 10
0.01
Value
0.009
Adjustment Cost
Adjustment Cost
0.008
1
Growth
0.5
0.007
0.006
Value
0.005
0.004
0.003
0.002
Growth
0.001
0
−6
−4
−2
0
2
i/k
4
6
8
10
−3
0
0.005
x 10
0.01
0.015
0.02
0.025
i/k
Figure 3. The value factor in corporate investment. This figure illustrates the value factor
in corporate investment under the benchmark model. Panel A plots the adjustment cost, h(it , kt ) =
θt it 2
2 ( kt ) kt , as a function of the investment rate, it /kt , in bad times for value firms (the “+”s) and
growth firms (the “o”s). Panel B presents the same plot in good times. Good times are defined
as times
when the aggregate productivity, xt , is more than one unconditional standard deviation,
σx / 1 − ρx2 , above its unconditional mean, x. Bad times are defined as times when xt is more than
one standard deviation below its long-run level. Within each simulated sample, the investment
rates and adjustment costs are averaged across all the good or the bad times for value and growth
firms. I then repeat the simulation 100 times and plot the cross-simulation average adjustment
costs against the cross-simulation average investment rates. The figure is generated within the
benchmark model, and varying θ −/θ + and γ1 yields similar results.
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Neoclassical Investment Models
Neoclassical Investment Models
Risk as inexibility
The Value Premium
Panel A: Expected Value Premium
Panel B: The Value Spread
18
0.08
16
0.07
Benchmark
14
Benchmark
0.06
Book−to−Market
Expected Excess Return
87
0.05
Model 2
0.04
0.03
12
10
6
0.02
4
0.01
2
0
−5.73
Model 1
−5.72
−5.71
x
−5.7
−5.69
−5.68
Model 2
8
0
−5.73
Model 1
−5.72
−5.71
x
−5.7
−5.69
−5.68
Figure 4. Time-varying spreads in expected excess return and in book-to-market between low-productivity (value) and high-productivity (growth) firms. This figure plots
the spread in expected excess returns (Panel A) and the spread in book-to-market (Panel B) between firms with low idiosyncratic productivity and firms with high idiosyncratic productivity as
functions of aggregate productivity, x. As is evident from Figure 2, sorting on firm-level productivity,
zt , in the model is equivalent to sorting on book-to-market. In effect, Panel A plots the time-varying
expected value premium, and Panel B plots the time-varying spread in book-to-market (which
Cohen et al. (2003) call the value spread) across business cycles. Three versions of the model are
considered. The solid lines are for the benchmark model with asymmetry and countercyclical price
of risk (θ −/θ + = 10 and γ1 = −1000). The broken lines are for Model 1 with symmetric adjustment
cost and a constant price of risk (θ −/θ + = 1 and γ1 = 0). Finally, the dotted lines are for Model 2
with asymmetry and constant price of risk (θ −/θ + = 10 and γ1 = 0). The figure is generated with
firm-level capital k and log output price p at their long-run average levels. Other values of k and p
yield similar results.
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Neoclassical Investment Models
Neoclassical Investment Models
Summary, Zhang (2005)
A quantitative neoclassical benchmark for cross-sectional returns
A careful quantitative evaluation with nonlinear solutions for asset pricing,
deviating from continuous time math and macro-style loglinearization
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Controversies
Outline
1
Real Options
2
Neoclassical Investment Models
3
Controversies
Is Value Riskier Than Growth?
Does the Conditional CAPM Explain the Value Premium?
What Explains the Failure of the CAPM?
4
Notes
Momentum
Beyond Value and Momentum
Debt Dynamics
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Controversies
Is Value Riskier Than Growth?
Controversies
Is value riskier than growth?
Lakonishok, Shleifer, and Vishny (1994)
Lettau and Ludvigson (2001)
Petkova and Zhang (2005)
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Figure 13.2 HML Beta in Different Economic
States
Controversies
Controversies
Is Value Riskier Than Growth?
Bodie, Kane, and Marcus (2010, p. 430 Figure 13.3) based on Petkova and Zhang (2005)
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Controversies
Does the Conditional CAPM Explain the Value Premium?
Controversies
Lewellen and Nagel (2006): The conditional CAPM is bad, 1/196312/2014
Low
2
3
4
5
6
7
8
9 High
H−L
Average conditional alphas
Quarterly
−0.17 −0.01 0.03
0.04
Semiannual 1 −0.14
0.00 0.03
0.02
Semiannual 2 −0.11
0.03 0.02 −0.00
Annual
−0.11
0.02 0.05
0.06
Average conditional
0.07 0.13 0.18 0.24
0.06 0.10 0.15 0.20
0.01 0.09 0.13 0.20
0.05 0.10 0.14 0.21
alphas, t -statistics
0.28
0.23
0.19
0.30
0.36
0.34
0.29
0.39
0.53
0.49
0.40
0.51
2.76
2.42
2.01
2.44
Quarterly
−1.97 −0.10
Semiannual 1 −1.57
0.06
Semiannual 2 −1.19
0.46
Annual
−1.17
0.42
0.62
0.60 0.94 1.89 2.34
0.59
0.20 0.69 1.44 1.75
0.26 −0.05 0.07 1.22 1.59
0.83
0.66 0.57 1.26 1.46
Average conditional betas
2.69
2.26
2.16
2.25
3.09
2.52
1.82
3.09
2.72
2.50
2.16
2.80
Quarterly
Semiannual 1
Semiannual 2
Annual
0.97
0.97
1.01
1.00
0.90
0.90
0.93
0.91
0.95
0.94
1.00
0.98
1.04 −0.03
1.04 −0.03
1.10
0.08
1.08
0.03
1.07
1.07
1.02
1.05
Prof. Lu Zhang (2015)
1.02
1.02
1.01
1.04
0.97
0.96
0.99
0.99
0.92
0.93
0.95
0.93
0.93
0.93
0.95
0.94
Quantitative Investment Theories
0.91
0.91
0.90
0.91
SUFE
32 / 68
Controversies
Does the Conditional CAPM Explain the Value Premium?
Controversies
The Lewellen-Nagel (2006) evidence disappears in the 7/192612/2014 sample
Low
2
3
4
5
6
7
8
9
High H−L
Average conditional alphas
Quarterly
−0.13
Semiannual 1 −0.10
Semiannual 2 −0.05
Annual
−0.07
0.03 0.04
0.04 0.08 0.10
0.04 0.17
0.03 0.05
0.01 0.07 0.07
0.02 0.14
0.07 0.05 −0.01 0.03 0.03 −0.02 0.13
0.08 0.07
0.04 0.04 0.05 −0.00 0.11
Average conditional alphas, t -statistics
0.21
0.09
0.16
0.07
0.14 −0.00
0.20
0.10
0.21
0.16
0.05
0.16
Quarterly
−2.23
Semiannual 1 −1.60
Semiannual 2 −0.85
Annual
−1.07
0.65
0.77
1.36
1.61
1.06
0.74 1.41 1.89
0.66
1.09
0.22 1.19 1.34
0.32
0.94 −0.19 0.50 0.50 −0.31
1.33
0.52 0.63 0.79 −0.03
Average conditional betas
2.55
1.99
1.65
1.39
2.55
0.75
1.87
0.56
1.43 −0.01
1.95
0.72
1.41
1.06
0.29
0.96
Quarterly
Semiannual 1
Semiannual 2
Annual
1.00
1.01
1.00
1.01
0.96
0.96
0.99
0.98
1.01
1.01
1.02
1.02
1.08
1.07
1.11
1.11
1.05
1.05
1.01
1.04
Prof. Lu Zhang (2015)
0.96
0.96
0.98
0.98
0.94
0.94
0.95
0.94
0.96
0.96
0.97
0.97
0.99
0.98
0.99
1.00
Quantitative Investment Theories
1.24
1.23
1.27
1.24
SUFE
0.18?
0.19?
0.26?
0.20?
33 / 68
Controversies
What Explains the Failure of the CAPM?
Controversies
The CAPM regressions across the book-to-market deciles, the short sample
Low
2
m
0.42 0.52
tm
2.07 2.77
α −0.12 0.01
tα −1.24 0.19
β
1.06 1.01
tβ 40.91 46.40
R2
0.86 0.92
Prof. Lu Zhang (2015)
3
4
5
6
7
8
9
High H−L
Panel A: July 1963December 2014
0.56 0.56 0.54 0.60 0.68 0.70 0.79 0.93
3.00 2.94 3.01 3.29 3.83 3.82 4.11 3.95
0.06 0.06 0.08 0.12 0.24 0.25 0.32 0.39
0.96 0.60 0.83 1.45 2.23 2.12 2.92 2.50
0.98 0.99 0.91 0.93 0.88 0.88 0.94 1.07
34.65 29.43 27.58 28.41 22.94 17.56 20.90 15.47
0.90 0.87 0.83 0.85 0.78 0.76 0.76 0.66
Quantitative Investment Theories
SUFE
0.50
2.72
0.50
2.23
0.01
0.06
0.00
34 / 68
Controversies
What Explains the Failure of the CAPM?
Controversies
The CAPM regressions across the book-to-market deciles, the long sample
Low
2
3
4
5
6
7
8
9
High H−L
Panel B: July 1926December 2014
m
0.58 0.68 0.68
0.68 0.73 0.76 0.76 0.92 1.03 1.09
tm
3.29 4.13 4.06
3.69 4.11 4.03 3.86 4.43 4.35 3.86
α −0.08 0.06 0.04 −0.01 0.07 0.07 0.05 0.18 0.20 0.15
tα −1.22 1.26 0.85 −0.16 0.96 0.85 0.54 1.88 1.76 0.98
β
1.01 0.95 0.97
1.05 1.00 1.05 1.09 1.13 1.27 1.44
tβ 52.11 27.19 57.09 22.29 26.81 15.88 16.92 15.48 13.69 13.63
R2
0.90 0.92 0.92
0.90 0.89 0.87 0.84 0.83 0.79 0.72
Prof. Lu Zhang (2015)
Quantitative Investment Theories
SUFE
0.51
2.58
0.23
1.19
0.43
3.52
0.13
35 / 68
Controversies
What Explains the Failure of the CAPM?
Controversies
Properties of the book-to-market deciles in the baseline quantitative investment model
(Lin and Zhang 2013, Table 4)
Mean
Std
α
tα
α, 2.5
α, 97.5
β
tβ
β , 2.5
β , 97.5
Low
2
3
0.62
5.9
−0.02
−0.8
−0.09
0.02
0.86
123.2
0.83
0.91
0.66
6.3
−0.01
−0.6
−0.08
0.02
0.91
164.4
0.87
0.94
0.69
6.5
−0.01
−0.5
−0.06
0.02
0.95
219.8
0.93
0.96
Prof. Lu Zhang (2015)
4
5
6
7
8
9 High H−L
0.70 0.77 0.76 0.81 0.86 0.92 1.12 0.50
6.6
7.1
7.0
7.4
7.8
8.2
9.5
3.9
−0.01 0.00 0.00 0.01 0.02 0.04 0.10 0.11
−0.4
0.0 −0.1
0.5
0.6
1.0
1.5
1.4
−0.06 −0.03 −0.03 −0.03 −0.03 −0.03 −0.04 −0.05
0.02 0.04 0.03 0.07 0.12 0.21 0.50 0.59
0.96 1.03 1.02 1.07 1.13 1.17 1.36 0.50
162.5 123.9 227.4 127.3 112.2 76.9 42.0 12.4
0.93 1.00 1.00 1.05 1.07 1.10 1.18 0.27
0.99 1.07 1.06 1.12 1.18 1.29 1.52 0.68
Quantitative Investment Theories
SUFE
36 / 68
Controversies
What Explains the Failure of the CAPM?
Controversies
Use two-shock models to explain the failure of the CAPM
Papanikolaou (2011)
Ai and Kiku (2013)
Kogan and Papanikolaou (2013)
Belo, Lin, and Bazdresh (2014)
Garlappi and Song (2015), Li (2015):
Positive risk premium estimates on investment shocks
Koh (2015)
Prof. Lu Zhang (2015)
Quantitative Investment Theories
SUFE
37 / 68
Controversies
What Explains the Failure of the CAPM?
Controversies
Bai, Hou, Kung, and Zhang (2015, The CAPM strikes back?...)
An investment model with disasters quantitatively replicates:
The failure of the CAPM in capturing the value premium in nite
samples in which disasters are not materialized;
The success of the CAPM in nite samples with disasters
Intuition: In a sample without disasters, estimated betas only reect risk in
normal times, but the value premium is driven by disaster risk
Prof. Lu Zhang (2015)
Quantitative Investment Theories
SUFE
38 / 68
Controversies
What Explains the Failure of the CAPM?
Controversies
The value premium versus the market factor, 7/19266/2014
80
80
32Aug
60
39Sep
33May
32Jul
40
34Jan
20
29Oct
98Aug
32May
87Oct32Apr31May
30Jun
31Sep
33Feb
80Mar
37Sep
08Oct
32Oct
40May 31Dec
38Mar
0
−20
75Jan
76Jan
31Jun 38Jun
33Jun
38Apr
33Aug
28Nov
87Jan
33Apr
74Oct
The value premium
The value premium
60
40
20
0
−20
−40
−40
−40
−20
0
20
The market excess return
Prof. Lu Zhang (2015)
40
−40
Quantitative Investment Theories
−20
0
20
The market excess return
SUFE
40
39 / 68
Controversies
What Explains the Failure of the CAPM?
Controversies
Large swings in the stock market and the value premium
MKT
November 1928
October 1929
June 1930
May 1931
June 1931
September 1931
December 1931
April 1932
May 1932
July 1932
August 1932
October 1932
February 1933
April 1933
May 1933
June 1933
Prof. Lu Zhang (2015)
H−L
11.79 −0.41
−20.07
7.57
−16.25 −3.54
−13.16 −3.09
13.75
14.80
−29.07 −5.03
−13.42 −16.73
−17.98 −2.85
−20.44
3.61
33.47
45.73
36.41
69.99
−13.09 −12.97
−15.06 −7.45
37.93
22.41
21.36
45.01
13.05
10.29
August 1933
January 1934
September 1937
March 1938
April 1938
June 1938
September 1939
May 1940
October 1974
January 1975
January 1976
March 1980
January 1987
October 1987
August 1998
October 2008
Quantitative Investment Theories
MKT
H −L
12.03
12.63
−13.57
−23.80
14.49
23.77
16.94
−21.93
16.10
13.66
12.16
−12.90
12.47
−23.24
−16.08
−17.23
4.92
34.10
−10.90
−22.67
8.76
15.22
56.61
−15.49
−13.58
19.70
15.04
−9.02
−2.98
−1.21
6.33
−11.93
SUFE
40 / 68
Controversies
What Explains the Failure of the CAPM?
Controversies
The CAPM's problem, the beta anomaly, 7/19636/2014, Fama and French (2006)
L
2
3
4
5
6
7
8
9
H H −L
m 0.51 0.52 0.52 0.56 0.66 0.54 0.68 0.53 0.62 0.63 0.12
tm 3.64 3.46 3.11 3.15 3.46 2.67 3.06 2.25 2.33 1.92 0.43
α
0.22 0.17 0.11 0.12 0.17 0.02 0.10 −0.08 −0.06 −0.18 −0.40
tα 2.03 1.75 1.32 1.39 1.89 0.22 1.17 −0.83 −0.47 −0.90 −1.48
β
0.57 0.68 0.81 0.87 0.98 1.03 1.14 1.22 1.35 1.61 1.04
tβ 12.29 16.79 19.13 20.74 27.23 30.22 46.72 41.42 34.60 30.04 11.41
R 2 0.54 0.68 0.77 0.79 0.86 0.86 0.88 0.86 0.84 0.78 0.43
Prof. Lu Zhang (2015)
Quantitative Investment Theories
SUFE
41 / 68
Controversies
What Explains the Failure of the CAPM?
Controversies
The CAPM's problem, the beta anomaly, 7/19286/2014, Fama and French (2006)
L
2
3
4
5
6
7
8
9
H H −L
m 0.57 0.63 0.64 0.73 0.82 0.71 0.80 0.72 0.82 0.81 0.24
tm 4.80 4.51 4.23 4.33 4.36 3.55 3.69 2.99 3.04 2.59 0.94
α
0.21 0.17 0.12 0.14 0.16 0.01 0.04 −0.13 −0.11 −0.26 −0.47
tα 2.68 2.18 2.04 2.37 2.29 0.11 0.54 −1.53 −1.09 −1.80 −2.40
β
0.57 0.74 0.82 0.93 1.05 1.12 1.22 1.36 1.49 1.70 1.12
tβ 22.94 29.62 35.56 40.62 41.07 40.12 46.51 36.08 26.55 40.59 18.46
R 2 0.67 0.81 0.85 0.88 0.90 0.90 0.91 0.90 0.88 0.85 0.58
Prof. Lu Zhang (2015)
Quantitative Investment Theories
SUFE
42 / 68
Controversies
What Explains the Failure of the CAPM?
Controversies
The Bai-Hou-Kung-Zhang (2015) model
Embedding disasters into a standard investment model:
Rare disasters in consumption (and productivity) growth
Asymmetric adjustment costs: Value rms are more exposed to
disaster risk than growth rms
Recursive preferences:
Mt+1 = ι
Prof. Lu Zhang (2015)
Ct+1
Ct
− 1
ψ

 1/ψ−γ
U 1−γ
 h t+1 i 
1−γ
Et Ut+
1
Quantitative Investment Theories
1−γ
SUFE
43 / 68
Controversies
What Explains the Failure of the CAPM?
Controversies
The Bai-Hou-Kung-Zhang (2015) model, consumption dynamics
Log consumption growth:
gct = ḡ + gt
Normal states follow a discretized autoregressive process:
Five states: {g1 , g2 , g3 , g4 , g5 }
Transition matrix: pij ≡ Prob(gt+1 = gi |gt = gj ):

p11 p12
 p21 p22

P=
..
..

.
.
p51 p52
Prof. Lu Zhang (2015)

. . . p15
. . . p25 

.. 
...
.
. . . p55
Quantitative Investment Theories
SUFE
44 / 68
Controversies
What Explains the Failure of the CAPM?
Controversies
The Bai-Hou-Kung-Zhang (2015) model, consumption dynamics
Insert the disaster state, g0 = λD (disaster size < 0), and the recovery
state, g6 = λR (recovery size > 0)
Modify transition matrix:

θ
η
η




P= .
 ..

 η
0
0
p11 − η
p21
p12
p22 − η
p51
p52
..
.
..
.
...
...
...
...
...
0
p15
p25
..
.
p55 − η
0 (1 − ν)/5 (1 − ν)/5 . . . (1 − ν)/5
1−θ
0
0
..
.
0









ν
η : disaster probability; θ: disaster persistence; ν : recovery persistence
Prof. Lu Zhang (2015)
Quantitative Investment Theories
SUFE
45 / 68
Controversies
What Explains the Failure of the CAPM?
Controversies
Firms, technology
Operating prots:
Πit = (Xt Zit )1−ξ Kitξ − fKit
Aggregate productivity growth:
gxt = g + φgt
Firm-specic productivity:
zit+1 = (1 − ρz )z̄ + ρz zit + σz eit+1
Prof. Lu Zhang (2015)
Quantitative Investment Theories
SUFE
46 / 68
Controversies
What Explains the Failure of the CAPM?
Controversies
Firms, asymmetric adjustment costs
Capital accumulation:
Kit+1 = Iit + (1 − δ)Kit
Asymmetric capital adjustment costs:
Φ(Iit , Kit ) =

+


 a Kit +
c+
Iit
Kit


 a− K +
it
c−
Iit
Kit
0
2
2
2
2
Kit
Kit
for Iit > 0
for Iit = 0
for Iit < 0
in which c − > c + > 0 and a− > a+ > 0 capture asymmetry
Prof. Lu Zhang (2015)
Quantitative Investment Theories
SUFE
47 / 68
Controversies
What Explains the Failure of the CAPM?
Controversies
Firms, value maximization
Source of funds constraint:
Dit = Πit − Iit − Φ(Iit , Kit )
Value maximization:
Vit = max
{χit }
max Dit + Et [Mt+1 V (Kit+1 , Xt+1 , Zit+1 )] , sKit ,
{Iit }
in which s ≥ 0 is the liquidation value parameter
Entry and exit, delisting return, reorganizational costs
Prof. Lu Zhang (2015)
Quantitative Investment Theories
SUFE
48 / 68
Controversies
What Explains the Failure of the CAPM?
Controversies
The Bai-Hou-Kung-Zhang (2015) model, calibration
Parameters
ι
γ
ψ
ḡ
ρg
σg
η
λD
θ
λR
ν
Value
0.99035
5
1.5
0.019/12
0.6
0.0025
0.028/12
−0.0275
0.9141/3
0.0325
0.95
Prof. Lu Zhang (2015)
Description
Time discount factor
The relative risk aversion
The elasticity of intertemporal substitution
The average consumption growth
The persistence of consumption growth
The conditional volatility of consumption growth
The disaster probability
The disaster size
The disaster persistence
The recovery size
The recovery persistence
Quantitative Investment Theories
SUFE
49 / 68
Controversies
What Explains the Failure of the CAPM?
Controversies
The impulse response of log consumption to a disaster shock in the model mimics that in
the data, Nakamura, Steinsson, Barro, and Ursua (2013)
0
−0.05
−0.1
−0.15
−0.2
−0.25
0
Prof. Lu Zhang (2015)
5
10
15
Quantitative Investment Theories
20
25
SUFE
50 / 68
Controversies
What Explains the Failure of the CAPM?
Controversies
Calibration, technology
Parameters
ξ
δ
f
φ
z
ρz
σz
a+
a−
c+
c−
s
κ
Re
Value
0.65
0.01
0.005
1
−9.75
0.985
0.5
0.035
0.05
75
150
0
0.25
−0.425
Prof. Lu Zhang (2015)
Description
The curvature parameter in the production function
The capital depreciation rate
Fixed costs of production
The leverage of productivity growth
The long-run mean of log rm-specic productivity
The persistence of log rm-specic productivity
The conditional volatility of log rm-specic productivity
Upward nonconvex adjustment costs
Downward nonconvex adjustment costs
Upward convex adjustment costs
Downward convex adjustment costs
The liquidation value parameter
The reorganizational cost parameter
The delisting return
Quantitative Investment Theories
SUFE
51 / 68
Controversies
What Explains the Failure of the CAPM?
Controversies
The CAPM regressions for the book-to-market deciles, no-disaster samples
m
tm
α
tα
β
tβ
R2
L
2
3
4
5
6
7
8
9
0.77
18.58
−0.01
−0.07
0.95
11.07
0.11
0.76
18.43
−0.02
−0.24
0.96
10.87
0.12
0.75
18.09
−0.06
−0.73
1.00
11.32
0.12
0.75
17.98
−0.11
−1.26
1.05
11.98
0.14
0.75
18.11
−0.10
−1.24
1.05
11.89
0.14
0.77
18.57
−0.08
−0.95
1.05
11.88
0.13
0.80
19.32
−0.02
−0.18
1.00
11.47
0.13
0.85
20.52
0.08
0.99
0.95
10.95
0.11
0.95
22.55
0.23
2.83
0.89
9.85
0.10
Prof. Lu Zhang (2015)
Quantitative Investment Theories
H H−L
1.21 0.45
24.99 7.10
0.46 0.47
5.02 3.71
0.92 −0.03
9.00 −0.24
0.08 0.00
SUFE
52 / 68
Controversies
What Explains the Failure of the CAPM?
Controversies
The CAPM regressions for the book-to-market deciles, disaster samples
L
2
4
5
6
7
8
9
m 0.74 0.74 0.73 0.74
tm 13.83 13.61 13.43 13.24
α
0.08 0.06 0.04 0.01
tα 1.38 1.09 0.76 0.32
β
0.82 0.85 0.87 0.90
tβ 18.82 23.74 28.64 33.03
R 2 0.45 0.47 0.49 0.50
0.75
13.15
−0.00
−0.08
0.94
33.72
0.52
0.77
13.07
−0.03
−0.53
1.00
30.60
0.55
0.81
13.10
−0.05
−0.82
1.08
26.47
0.57
0.86
13.07
−0.09
−1.15
1.19
20.63
0.60
0.96
13.17
−0.13
−1.40
1.37
16.00
0.64
Prof. Lu Zhang (2015)
3
Quantitative Investment Theories
H H −L
1.19 0.45
13.61 5.83
−0.13 −0.21
−1.38 −1.72
1.64 0.82
18.05 6.82
0.65 0.24
SUFE
53 / 68
Controversies
What Explains the Failure of the CAPM?
Controversies
Value is more exposed to disaster risk than growth
30
30
20
20
10
10
0
0
20
0
10
Capital
−10
0 −20
Prof. Lu Zhang (2015)
z
20
0
10
Capital
Quantitative Investment Theories
−10
0 −20
z
SUFE
54 / 68
Controversies
What Explains the Failure of the CAPM?
Controversies
Impulse responses of risk and risk premiums for value/growth deciles to a disaster shock
0.4
5
0.35
4
0.3
3
0.25
0.2
2
0.15
1
0.1
0
0.05
0
0
5
10
Prof. Lu Zhang (2015)
15
20
25
−1
0
5
Quantitative Investment Theories
10
15
20
SUFE
25
55 / 68
Controversies
What Explains the Failure of the CAPM?
Controversies
Nonlinearity in the CAPM regressions
60
The value premium
40
20
0
−20
−40
−20
Prof. Lu Zhang (2015)
Quantitative Investment Theories
0
20
40
The market excess return
SUFE
60
56 / 68
Controversies
What Explains the Failure of the CAPM?
Controversies
Nonlinearity in the pricing kernel
25
The pricing kernel
20
15
10
5
0
−20
Prof. Lu Zhang (2015)
Quantitative Investment Theories
0
20
40
The market excess return
SUFE
60
57 / 68
Controversies
What Explains the Failure of the CAPM?
Controversies
Comparative statics
λD
−0.025 −0.03
Disaster samples
θ
0.955
η
0.985 0.13% 0.33%
ν
0.935
λR
0.965 2.75% 3.75%
m
0.34
0.55
0.29
0.47
0.42
0.46
0.46
0.43
0.45
0.44
tm
4.78
6.75
4.49
5.62
5.72
5.78
5.94
5.61
5.83
5.70
α
−0.22 −0.20 −0.21 −0.16 −0.21 −0.21 −0.20 −0.22 −0.21 −0.21
tα −1.98 −1.51 −2.08 −1.33 −1.60 −1.89 −1.66 −1.80 −1.75 −1.78
β
0.77
0.86
0.74
0.77
0.79
0.86
0.85
0.78
0.85
0.81
tβ
6.65
7.11
6.56
7.39
6.01
7.80
6.74
6.75
6.74
7.04
No-disaster samples
m
tm
α
tα
β
tβ
0.33
0.54
5.63
8.08
0.24
0.71
2.14
4.96
0.12 −0.19
0.89 −1.35
Prof. Lu Zhang (2015)
0.28
0.55
0.42
0.46
0.45
0.43
0.44
0.45
5.24
7.89
6.74
7.29
7.09
6.90
6.99
7.06
0.07
0.86
0.43
0.50
0.49
0.45
0.47
0.47
0.67
5.66
3.38
3.97
3.88
3.52
3.72
3.77
0.32 −0.33 −0.02 −0.05 −0.05 −0.02 −0.04 −0.04
2.56 −2.32 −0.13 −0.35 −0.41 −0.19 −0.31 −0.34
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Controversies
What Explains the Failure of the CAPM?
Controversies
Comparative statics
a−
a+
0.025 0.045
Disaster samples
0.035
c−
c+
0.065
50
100
100
f
200
0
0.015
m
0.48
0.29
0.25
0.47
0.37
0.49
0.39
0.46
0.47
0.40
tm
6.57
3.75
3.73
5.97
4.64
6.59
5.25
5.90
6.30
4.86
α −0.25 −0.23 −0.21 −0.23 −0.24 −0.20 −0.21 −0.22 −0.21 −0.22
tα −1.91 −2.05 −1.66 −1.82 −2.04 −1.61 −1.82 −1.80 −1.71 −1.89
β
0.96
0.64
0.61
0.89
0.73
0.90
0.76
0.85
0.87
0.75
tβ
6.42
6.19
4.32
6.77
7.23
6.57
6.57
6.85
6.61
7.25
No-disaster samples
m
0.45
tm
8.48
α
0.63
tα
5.39
β −0.23
tβ −1.71
0.28
0.22
0.46
4.24
3.84
7.32
0.14
0.26
0.49
1.10
2.16
3.83
0.16 −0.04 −0.04
1.20 −0.32 −0.31
Prof. Lu Zhang (2015)
0.38
0.49
0.39
0.46
0.45
5.54
8.42
6.35
7.29
7.78
0.27
0.62
0.41
0.49
0.54
1.98
5.12
3.27
3.89
4.42
0.13 −0.17 −0.02 −0.04 −0.10
0.96 −1.25 −0.15 −0.36 −0.77
Quantitative Investment Theories
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0.40
5.81
0.31
2.31
0.11
0.76
59 / 68
Controversies
What Explains the Failure of the CAPM?
Controversies
Comparative statics
s
κ
0.15
0.3
Disaster samples
m
0.20
tm
2.95
α −0.27
tα −2.72
β
0.63
tβ
7.06
No-disaster
0
Re
0.5
−0.3 −0.55
γ
3.5
ψ
6.5
1
2
−0.03
0.45
0.45
0.47
0.44
0.18
0.57 −0.06
0.51
−0.28
5.79
5.87
6.08
5.64
2.61
7.19 −2.67
5.74
−0.35 −0.21 −0.21 −0.19 −0.23 −0.23 −0.11 −0.29 −0.18
−3.80 −1.72 −1.73 −1.58 −1.89 −2.48 −0.81 −10.00 −1.60
0.48
0.82
0.83
0.83
0.83
0.75
0.67
1.74
0.67
6.57
6.84
6.80
6.75
6.85
6.24
5.29
10.34
8.43
samples
m
0.27
0.10
0.44
0.45
0.46
0.44
0.15
0.60 −0.07
0.50
tm
4.37
1.68
7.07
7.11
7.27
7.03
3.18
8.47 −3.15
7.10
α
0.34
0.20
0.47
0.47
0.48
0.47 −0.12
0.96 −0.31
0.82
tα
2.78
1.74
3.68
3.69
3.76
3.65 −1.64
5.87 −11.70
5.23
β −0.09 −0.13 −0.03 −0.03 −0.03 −0.03
0.51 −0.34
1.98 −0.30
tβ −0.66 −1.01 −0.22 −0.23 −0.22 −0.25
4.35 −2.45
17.67 −2.27
Prof. Lu Zhang (2015)
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Controversies
What Explains the Failure of the CAPM?
Controversies
The beta anomaly, deciles formed on rolling market betas, disaster samples
L
2
7
8
9
m 0.76 0.78 0.81 0.83 0.85 0.86 0.86
tm 13.72 14.09 14.04 13.89 13.55 13.41 13.08
α
0.04 0.06 0.06 0.04 0.01 −0.01 −0.04
tα 0.69 1.29 1.17 0.82 0.29 −0.05 −0.49
β
0.90 0.90 0.95 0.99 1.04 1.08 1.12
tβ 19.75 25.57 33.62 34.40 31.60 25.92 21.23
R 2 0.53 0.53 0.54 0.55 0.56 0.57 0.58
0.85
12.65
−0.08
−0.89
1.16
18.56
0.59
0.83
11.79
−0.16
−1.45
1.23
15.11
0.60
Prof. Lu Zhang (2015)
3
4
5
6
Quantitative Investment Theories
H H −L
0.79 0.04
11.50 0.53
−0.17 −0.21
−2.10 −1.73
1.20 0.30
17.35 2.49
0.61 0.06
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61 / 68
Controversies
What Explains the Failure of the CAPM?
Controversies
The beta anomaly, deciles formed on rolling market betas, no-disaster samples
L
2
8
9
m 0.80 0.82 0.84 0.85 0.85 0.86 0.84 0.82
tm 20.12 20.36 20.48 20.45 19.82 20.00 19.58 18.98
α
0.01 0.12 0.17 0.19 0.15 0.16 0.11 0.03
tα 0.16 1.55 2.15 2.28 1.75 1.88 1.30 0.39
β
0.97 0.86 0.82 0.82 0.86 0.86 0.90 0.97
tβ 11.79 10.20 9.50 9.27 9.30 9.15 9.72 10.37
R 2 0.13 0.10 0.09 0.09 0.09 0.09 0.10 0.11
0.79
18.24
−0.09
−1.06
1.08
11.67
0.14
Prof. Lu Zhang (2015)
3
4
5
6
7
Quantitative Investment Theories
H H −L
0.74
16.65
−0.42
−4.98
1.43
15.74
0.23
−0.06
−0.93
−0.44
−3.49
SUFE
0.47
3.49
0.01
62 / 68
Controversies
What Explains the Failure of the CAPM?
Controversies
The beta anomaly, measurement errors in rolling market betas
Prof. Lu Zhang (2015)
Quantitative Investment Theories
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Controversies
What Explains the Failure of the CAPM?
Controversies
Summary, Bai, Hou, Kung, and Zhang (2015)
An investment model with disasters quantitatively replicates the failure of
the CAPM in capturing the value premium in no-disaster samples, and its
relative success in disaster samples
The beta anomaly largely due to measurement errors in betas
A rst step in integrating the investment CAPM literature with the
disasters literature
Prof. Lu Zhang (2015)
Quantitative Investment Theories
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Notes
Outline
1
Real Options
2
Neoclassical Investment Models
3
Controversies
Is Value Riskier Than Growth?
Does the Conditional CAPM Explain the Value Premium?
What Explains the Failure of the CAPM?
4
Notes
Momentum
Beyond Value and Momentum
Debt Dynamics
Prof. Lu Zhang (2015)
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Notes
Momentum
Notes
Momentum
Johnson (2002)
Sagi and Seasholes (2007)
Liu and Zhang (2008)
Li (2015): Explaining value and momentum simultaneously
Prof. Lu Zhang (2015)
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Notes
Beyond Value and Momentum
Notes
Beyond value and momentum
Equity issues:
Carlson, Fisher, and Giammarino (2006); Li, Livdan, and Zhang (2009)
Real estate:
Tuzel (2010)
Inventories:
Belo and Lin (2012); Jones and Tuzel (2013)
Intangibles:
Berk, Green, and Naik (2004); Li (2011); Lin (2012); Eisfeldt and
Papanikolaou (2013); Donangelo (2014)
Prof. Lu Zhang (2015)
Quantitative Investment Theories
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Notes
Debt Dynamics
Notes
Debt dynamics: Integrating the investment CAPM with dynamic corporate nance
(Hennessy and Whited 2005, 2007)
Livdan, Sapriza, and Zhang (2009)
Gomes and Schmid (2010)
Garlappi and Yan (2011)
Ozdagli (2012); Choi (2013); Obreja (2013)
Kuehn and Schmid (2014)
Prof. Lu Zhang (2015)
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