Lecture Notes
Belo, Xue, and Zhang (2013, Review of Financial
Studies): A Supply Approach to Valuation
Lu Zhang1
1 The
Ohio State University
and NBER
BUSFIN 8250: Advanced Asset Pricing
Autumn 2013, Ohio State
Theme
A supply approach to valuation
Motivation
Cochrane (2011, “Presidential address: Discount rate”)
“[W]e have to answer the central question, what is the
source of price variation? When did our field stop being
‘asset pricing’ and become ‘asset expected returning’ ?
Why are betas exogenous? A lot of price variation comes
from discount-factor news. What sense does it make to
‘explain’ expected returns by the covariation of expected
return shocks with market market return shocks?
Market-to-book ratios should be our left-hand variable,
the thing we are trying to explain, not a sorting
characteristic for expected returns (p. 1063, our
emphasis).”
Motivation
What determines equity valuation? Immensely important
The standard demand approach to valuation:
Pit = Et
∞
X
4t=1
∞
X
Dit+4t
Yit+4t − dBit+4t
⇔ Pit = Et
1 + Rit+4t
1 + Rit+4t
4t=1
Accounting-based valuation, standard b-school curriculum:
Ohlson (1995), Lundholm and Sloan (2007), Penman (2010)
We explore the supply approach to valuation:
Pit = Qit Kit+1 − Bit+1
in which
Qit = f
Iit
,θ
Kit
Motivation
The supply versus demand approach to valuation
Parsimony:
Investment-to-capital as the only input
No need to estimate the discount rate
No terminal valuation assumptions
Reliability:
“Structural” parameters are likely more stable than
nonstructural parameters
Weakness: Only portfolio-level estimation, firm-level analysis
upcoming
Motivation
Weaknesses with the demand approach
Penman (2010, p. 666):
“Compound the error in beta and the error in the risk
premium and you have a considerable problem. The
CAPM, even if true, is quite imprecise when applied. Let’s
be honest with ourselves: No one knows what the market
risk premium is. And adopting multifactor pricing models
adds more risk premiums and betas to estimate. These
models contain a strong element of smoke and mirrors.”
Outline
1 The Model
2 Econometric Methodology
3 Empirical Results
4 Summary, Interpretation, and Future Work
Outline
1 The Model
2 Econometric Methodology
3 Empirical Results
4 Summary, Interpretation, and Future Work
The Model
The neoclassical investment model
Operating profits, Π(Kit , Xit ), constant returns to scale
Convex adjustment costs:
Φ(Iit , Kit ) =
1
ν
η
Iit
Kit
ν
Kit
B
One-period debt, Bit+1 , with pretax corporate bond return rit+1
Ba = r B
B
and after-tax corporate bond return: rit+1
it+1 − (rit+1 − 1)τt+1
Mt+1 : the pricing kernel, correlated with Xit+1
Firms maximize the cum-dividend market value of the equity
The Model
The valuation equation
"
Pit + Bit+1 = 1 + (1 − τt )η
Pit : ex-dividend market equity
Bit+1 : market value of debt
Kit+1 : capital
ν
Iit
Kit
ν−1 #
Kit+1
The Model
The investment Euler equation
ν−1
Iit
1 + (1 − τt )η ν
=
Kit



h
i
Yit+1
Iit+1 ν
ν−1
(1 − τt+1 ) κ K
+
η
+
δ
τ
it+1 t+1
ν
Kit+1
it+1



ν−1 
Et Mt+1 

Iit+1
ν
+(1 − δit+1 ) 1 + (1 − τt+1 )η Kit+1
The Model
The investment return = the WACC:
I
Ba
S
rit+1
= wit rit+1
+ (1 − wit )rit+1
Marginal benefits of investment at time t+1
z









}|
Yit+1
ν−1
Iit+1 ν
(1 − τt+1 ) κ
+
η
Kit+1
ν
Kit+1
|
{z
}
Marginal product plus economy
of
scale
(net
of
taxes)
"
#
Iit+1 ν−1
ν
+τt+1 δit+1 + (1 − δit+1 ) 1 + (1 − τt+1 )η
Kit+1
|
{z
}
I
rit+1
≡
1 + (1
|
Expected continuation value
ν−1
Iit
− τt )η ν
Kit
{z
}
Marginal costs of investment at time t
{









Outline
1 The Model
2 Econometric Methodology
3 Empirical Results
4 Summary, Interpretation, and Future Work
Econometric Methodology
Valuation tests
Test if the average Tobin’s q observed in the data equals the
average q predicted in the model:
"
#
ν−1 !
Iit
Kit+1
ν
E qit − 1 + (1 − τt )η
=0
Kit
Ait
in which qit ≡ (Pit + Bit+1 )/Ait
Econometric Methodology
Comparison with investment regressions
Matching average Tobin’s q differs critically from investment
regressions:
Portfolio level estimation mitigates the impact of measurement
errors in q
Average q moments alleviate the impact of temporal
misalignment between investment and q
Flexible adjustment costs allow nonlinear marginal costs of
investment
Econometric Methodology
Joint estimation of valuation moments and expected return
moments
Test whether the average stock return equals the average levered
investment return:
h
i
S
Iw
− rit+1
=0
E rit+1
in which
Iw
rit+1
≡
I
Ba
rit+1
− wit rit+1
1 − wit
Econometric Methodology
Joint estimation of valuation moments and the investment Euler
equation moments





E









ν−1
1 + (1 − τt )η ν KIitit
−
h
ν i
Yit+1
I
(1 − τt+1 ) κ Kit+1 + ν−1
η Kit+1
+ δit+1 τt+1
ν
it+1
ν−1 Iit+1
ν
+(1 − δit+1 ) 1 + (1 − τt+1 )η Kit+1
Ba +(1−w )r S
wit rit+1
it it+1












 Kit+1 


 Ait  = 0.




Econometric Methodology
Tobin’s q deciles as testing assets
Ait : Total assets
Kit : Net property, plant, and equipment
Iit : Capital expenditure minus sales of property, plant, and
equipment
Yit : Sales
Bit : Long-term debt and short-term debt
Pit : Market value of common equity
δit : Depreciation divided by capital
B : Impute bond ratings, assign corporate bond returns of a
rit+1
given rating to all firms with the same rating
Outline
1 The Model
2 Econometric Methodology
3 Empirical Results
4 Summary, Interpretation, and Future Work
Empirical Results
Descriptive statistics
Mean Low
qit
Iit
Kit
Kit+1
Ait
2
3
4
5
6
7
8
9 High H−L
[t]
1.56 0.44 0.65 0.77 0.89 1.02 1.19 1.43 1.80 2.52 4.94 4.50 12.11
0.22 0.15 0.16 0.16 0.17 0.18 0.20 0.22 0.25 0.29 0.39 0.24 14.70
0.43 0.30 0.40 0.44 0.46 0.48 0.49 0.49 0.47 0.41 0.40 0.10 3.44
Empirical Results
Parameter estimates and overidentification tests
Panel A: Point estimates and the χ2 tests
η
[t]
4.15 18.64
[t]
pν=2
Φ/Y |eiq |
3.75 18.62
0.00
4.78 0.07
ν
χ2 d.f.
7.63
pχ2
8
0.47
9
High H−L
Panel B: Valuation errors for individual deciles
Low
eiq
[t]
2
3
4
5
6
7
8
−0.10 −0.11 −0.06 −0.03 −0.05 −0.03 0.01 −0.05 0.24 −0.05 0.05
−1.77 −2.18 −1.49 −0.90 −1.20 −0.93 0.23 −0.80 1.83 −1.88 1.21
Empirical Results
Predicted Tobin’s q versus realized Tobin’s q
5
10
Predicted
4
3
9
2
8
1
1
0
0
56
4
23
1
7
2
3
Realized
4
5
Empirical Results
9
9
8
8
7
7
6
6
Predicted
Predicted
Predicted q versus realized q, Tobin’s q deciles within the low
and the high terciles split by the Size-age index
5
4
10
5
3
2
2
4
6
Realized
8
9
4
3
9
8
7
1 23456
1
0
0
2
10
7
6
5
1
4
123
0
0
2
8
4
6
Realized
8
Empirical Results
9
9
8
8
7
7
6
6
Predicted
Predicted
Predicted q versus realized q, Tobin’s q deciles within the low
and the high terciles split by idiosyncratic volatility
5
4
10
3
0
0
5
4
9
3
2
1
10
7
3456
12
9
8
1
2
8
2
4
6
Realized
8
0
0
5
1234
67
2
4
6
Realized
8
Empirical Results
9
9
8
8
7
7
6
6
5
Predicted
Predicted
Predicted q versus realized q, Tobin’s q deciles within the low
and the high terciles split by cash flows
10
4
3
9
4
3
9
8
3 56 7
1 12 4
2
8
7
1 456
123
0
0
2
10
5
2
4
6
Realized
8
0
0
2
4
6
Realized
8
Empirical Results
9
9
8
8
7
7
6
6
Predicted
Predicted
Predicted q versus realized q, Tobin’s q deciles within the low
and the high terciles split by lagged investment
5
4
10
3
2
1
0
0
5
4
3
9
2
7
0
0
2
56
1 1234
678
345
2
1
2
10
4
6
Realized
8
8
9
4
6
Realized
8
Empirical Results
Predicted q versus realized q, Tobin’s q deciles, joint estimation
of valuation moments and expected return moments
35
5
30
25
Predicted
Predicted
4
3
9
2
1
0
0
1
10
6 4
20
7
32
15
8
56
34
12
1
7
8
10
5
10 9
5
2
3
4
5
0
0
5
10
15
20
25
30
35
Empirical Results
Predicted q versus realized q, Tobin’s q deciles, joint estimation
of valuation moments and investment Euler equation moments
10
4
Predicted
Marginal benefits of investment
5
3
9
2
1
0
0
56
34
2
1
1
7
8
2
3
Realized
4
5
5
4
10
3
9
2
7
1
6
45
3
2
1
0
0
1
8
2
3
4
Marginal costs of investment
5
Empirical Results
Predicted q versus realized q, 10 and 20 portfolios formed on
Tobin’s q, quadratic and nonquadratic adjustment costs
5
7
10
20
6
4
20
10
3
8
7
56
2
4 8
23 7
1 1 456
23
1
0
0
1
2
9
9
3
Realized
4
5
Predicted
Predicted
5
4
1617 18 19
131415
12
19
11
910
8
2 4567
1617 18
23 131415
12
11
1 1 5678910
324
1
3
0
0
2
4
Realized
6
Empirical Results
Predicted q versus realized q, 50 and 100 portfolios formed on
Tobin’s q, quadratic and nonquadratic adjustment costs
15
16
100
14
50
50
4748
4
6
40
45
43
39
3841
4244
35
37
36
31
30
29
34
32
33
24
47
28
27
26
22
23
21
25
18
20
19
15
170 4546 48
13
14
16
12
40
43
42356789111
3941
4244
38
37
35
36
31
32
29
34
30
33
28
24
27
26
123456789111
22
25
21
23
20
19
18
15
17
16
13
12
14
0
01
5
0
5
49
49
10
100
12
Predicted
Predicted
10
15
99
99
10
97
98
93949697
6
8991
929596 98
80
77
86
78
85
83
88
79
81
87
90
84
82
74
76
72
65
75
71
69
70
73
60
63
4 43
68
61
62
52
57
66
64
56
67
58
53
47
54
59
48
55
46
44
50
39
45
35
41
51
939495
42
49
36
29
37
38
40
32
30
33
25
34
27
26
24
31
23
28
17
18
16
19
14
22
15
20
91
21
92
89
9
1
0
80
7
11
4
12
13
86
8890
2 3568 65
83
79
85
81
78
77
84
87
82
71
75
74
76
73
69
72
62
63
60
70
61
68
56
57
66
52
64
12479111
67
58
59
55
54
53
47
50
43
48
45
39
44
46
41
42
35
51
49
32
37
38
40
29
36
30
33
34
25
27
26
24
14
31
17
16
15
23
19
18
28
20
22
21
0
12
13
8
5
6
0 123
8
0
5
10
15
Empirical Results
Tobin’s q quintiles, industry-specific estimation
Autos
Books
6
BusEq
6
4
4
2
0
0
2
4
6
2
34
12
0
0
2
Clths
0
4
6
4
0
0
0
2
4
6
0
2
4
6
0
0
1
4
2 3
4
6
2
6
4
123
0
0
2
123
0
4
6
0
Steel
6
4
4
1234
0
0
4
6
0
2
6
12
0
4
6
5
123
6
5
2
4
12
0
2
4
6
3 4
0
2
4
6
Whlsl
6
4
2
0
5
2
5
1234
0
6
4
4
Txtls
1234
4
2
Servs
5
0
4
2
0
6
0
6
6
0
3 4
Rtail
4
0
4
6
5
2
2
2
4
4
4
0
6
2
4
123
0
2
6
5
2
2
5
Trans
5
2
5
4
0
Mines
4
123
0
4
123
0
Telcm
6
2
6
6
4
0
4
4
6
2
4
2
2
6
2
4
5
2
0
4
4
2
6
34
12
Meals
6
4
5
2
0
4
5
2
0
Paper
6
4
6
5
3
12
Other
6
4
2
4
5
4
123
0
2
0
Food
6
2
4
6
4
6
0
0
Oil
4
6
2
4
2
2
Hshld
0
2
0
5
4
4
0
FabPr
34
12
Hlth
5
123
6
5
2
6
4
4
5
34
12
0
6
0
Games
6
2
2
2
5
ElcEq
5
4
123
1234
0
4
2
4
2
6
4
5
123 4
6
4
3 4
0
6
2
12
Cnstr
6
Chems
6
5
4
5
2
5
1234
Carry
6
1234
0
2
4
6
0
2
4
6
Outline
1 The Model
2 Econometric Methodology
3 Empirical Results
4 Summary, Interpretation, and Future Work
Conclusion
The market value of equity and investment data are well aligned on
average at the portfolio level
Interpretation: A supply approach to valuation
Future work: Firm level estimation, nonconvexity, financial frictions,
labor, intangible capital...