Investor Sentiment Risk Factor
and
Asset Pricing Anomalies
Chienwei Ho
Massey University
Chi-Hsiou Hung
Durham University
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Motivations
• Standard CAPM (Sharpe, 1964; Lintner, 1965)
– Expected return is associated with market risk
– Unable to explain pricing anomalies
• Size effect (Banz, 1981)
• Value effect (Chan, Hamao, and Lakonishok, 1991)
• Momentum effect (Jegadeesh and Titman, 1993)
• Investor sentiment affects stock returns (Black, 1986; De Long, Shleifer,
Summers and Waldmann, 1990; Baker and Wurgler, 2006; Yu and Yuan,
2011).
• Investor sentiment as a risk factor.
• Conditional/Dynamic models outperform unconditional/static models
(Harvey, 1989; Gibbons and Ferson, 1985; Ferson, Kandel, and Stambaugh,
1987).
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Research Questions
• Is investor sentiment a risk factor? (i.e., Is investor sentiment priced?)
• Does investor sentiment, as a risk factor, help to explain pricing anomalies:
size, value, liquidity, and momentum effects?
• Asset pricing models: CAPM, FF, FFP, FFW, FFPW
• Time-varying: default spread, (Size+B/M)
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Contributions
• Constructing a sentiment risk factor, SMN (sensitive minus non-sensitive).
• Showing SMN is a priced factor.
• Stocks with certain firm characteristics react differently to investor
sentiment.
• SMN alone can explain the size premium.
• Sentiment-augmented asset pricing models can capture the pricing
anomalies: size, value, momentum effects.
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Literature
• Sentiment and stock returns
• A negative relationship b/t the consumer confidence level in one
month and returns in the following month (Fisher and Statman,
2002).
• High levels of sentiment result in lower returns over the next 2 to 3
years (Brown and Cliff, 2005).
• Changes in consumer sentiment are positively related to excess stock
market returns (Charoenrook, 2005).
• Investor sentiment has larger effects on stocks whose valuations are
highly subjective and difficult to arbitrage (Baker and Wurgler, 2006).
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Literature (Cont’d)
• Sentiment and firm characteristics
• Closed-end fund discount and net mutual fund redemptions predict
the size premium (Neal and Wheatley, 1998).
• Individual investors who are more prone to sentiment than
institutional investors tend to have disproportionally large holdings on
small stocks (Lee, Shleifer, and Thaler, 1991; Nagel (2005).
• Difficult-to-arbitrage and hard-to-value stocks (small, young, nondividend-paying, etc.) are more responsive to investor sentiment
(Baker and Wurgler, 2006; Lee, Shleifer, and Thaler; Lemmon and
Portniaguina, 2006)
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Construction of Sentiment Factor – SMN
𝑅𝑗𝑡𝑒 ≡ 𝑅𝑗𝑡 − 𝑅𝐹𝑡 = 𝛼𝑗 + 𝛽𝑗𝑠 ∆𝑆𝐸𝑁𝑇𝑡 + 𝜀𝑗𝑡
• Using 25-month rolling windows to obtain sentiment beta for each
stock, , (Brown and Cliff, 2005 find high sentiment results in lower
market returns over the next 2 to 3 years).
• In each month, break stocks into 5 groups based on the absolute
value of .
• Monthly SMN = Sensitive Return – Non-sensitive Return
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Conditional Sentiment-augmented Models
• Conditioning variables
• Macro variables: default spread
• Firm-specific characteristics: B/M and size
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Empirical Framework
adjusted return (second-pass regression)
𝑅𝑗𝑡∗
′
≡ 𝑅𝑗𝑡 − 𝑅𝐹𝑡 + 𝛽 𝜃; 𝑧𝑡−1 , 𝑋𝑗𝑡 −1 𝐹𝑡 = 𝑐0𝑡 + 𝑐𝑡 𝑍𝑗𝑡 −1 + 𝑒𝑗𝑡
pricing anomalies
conditional asset pricing model
(first-pass regression)
Ho: Ct = 0 ?
• Indicator of explanatory power of model: adj-R2 (lower ==> better)
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Asset Pricing Models
𝑟𝑗𝑡 = 𝛼𝑗 + 𝛽𝑗𝑆𝑀𝑁 𝑆𝑀𝑁𝑡 +𝑢𝑗 𝑡
𝑟𝑗𝑡 = 𝛼𝑗 + 𝛽𝑗𝑆𝑀𝑁 𝑆𝑀𝑁𝑡 + 𝛽𝑗𝑚 𝑟𝑚𝑡 + 𝛽𝑗𝑆𝑀𝐵 𝑆𝑀𝐵𝑡 + 𝛽𝑗𝐻𝑀𝐿 𝐻𝑀𝐿𝑡 + 𝛽𝑗𝑃𝑆 𝑃𝑆𝑡 + 𝛽𝑗𝑊𝑀𝐿 𝑊𝑀𝐿𝑡
+𝑢𝑗 𝑡
traditional risk factors
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Time-Varying Beta
𝛽𝑗𝑡 −1 = 𝛽𝑗 1 + 𝛽𝑗 2 𝑧𝑡−1 + 𝛽𝑗 3 + 𝛽𝑗 4 𝑧𝑡−1 𝑆𝐼𝑍𝐸𝑗𝑡 −1 + (𝛽𝑗 5 + 𝛽𝑗 6 𝑧𝑡−1 )𝐵/𝑀𝑗𝑡 −1
CAPM: rjt  R jt -R Ft   j   jt-1 (R mt -R Ft )  u jt
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Beta Specifications
 jt 1   j1
Unconditional Model
Specification A: function of (SIZE + B/M)
(i.e., 𝜷𝒋𝟐 = 𝜷𝒋𝟒 = 𝜷𝒋𝟔 = 𝟎)
Specification B: function of def
(i.e., 𝜷𝒋𝟑 = 𝜷𝒋𝟒 = 𝜷𝒋𝟓 = 𝜷𝒋𝟔 = 𝟎)
Conditional Model
Specification C: function of (SIZE + B/M)def
(i.e., 𝐚𝐥𝐥 𝜷𝒔 ≠ 𝟎)
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Two-Pass Framework (using CAPM as an Example)
1st-pass (time-series): R jt -R Ft   j   jt-1 (R mt -R Ft )  u jt
Risk Factors (for CAPM here)
M
2nd-pass (cross-sectional):  j  u jt  c0t   cmt Z mjt 1  e jt
m 1
Adjusted
Return
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Investor Sentiment Indices
• Baker and Wurgler, 2006 (∆BW)
• ∆BW: A composite sentiment index based on the first principal component of six
raw sentiment proxies: NYSE turnover, closed-end fund discount, the number of
IPOs, the first-day return on IPOs, the equity share in new issues and the
dividend premium.
• ∆BWWort: a cleaner sentiment measure that removes business cycle variations
from ∆BW.
• Investors’ Intelligence Index (II)
• Opinions of 150 newsletters: bullish, bearish, neutral.
• Proportion of bullish advices.
• Directly reflects (professional) investors’ opinions on stock markets.
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Trading Data and Variables for Anomalies
• 8,526 NYSE/AMEX/NASDAQ common stocks (1968-2005) from
CRSP/COMPUSTAT meeting the specified criteria:
• The returns in the current month, t, and over the past 60 months must be
available.
• Stock prices and shares outstanding have to be available in order to calculate firm
size, and trading volume in month t – 2 must be available to calculate the
turnover.
• Sufficient data has to be available from the COMPUSTAT dataset to calculate the
book-to-market ratio as of December of the previous year.
• Only stocks with positive book-to-market ratios are included in our sample.
• Book-to-market ratio values greater than the 0.995 fractile or less than the 0.005
fractile are set equal to the 0.995 and 0.005 fractile values, respectively.
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Table 1: Summary Statistics and Cross-Sectional Regressions
(8,526 firms: 1968 - 2005)
EXCESS RETS (%)
SIZE ($ billions)
B/M
TURNOVER (%)
RET2-3 (%)
RET4-6 (%)
RET7-12 (%)
R 2 (%)
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Mean
Median
0.88
1.22
0.90
6.27
2.69
4.00
8.01
1.06
0.70
0.86
5.19
2.92
3.70
7.33
Std
5.67
1.09
0.28
3.82
8.67
10.98
15.71
Reg. Coefficient (%)
t -value
- 0.11
0.32
- 0.09
0.64
0.82
0.86
- 2.10
4.96
-1.40
2.31
3.50
6.15
(size effect)
(value effect)
(momentum effect)
5.05
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Figure 1: Stock Returns by Firm Characteristics and Sentiment Beta
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Is the Investor Sentiment Factor (SMN) Priced?
𝑅𝑗𝑡 − 𝑅𝐹𝑡 = 𝜆0 + 𝜆1 𝛽𝑗𝑡𝑆𝑀𝑁 + 𝜇𝑗𝑡
Ho:
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Table 2: Cross-Sectional Regressions of Excess Returns on SMN Beta
SMN based on ∆BW
Window
13
25
37
SMN based on ∆BWort
Adj. R
(%)
Intercept
0.003*
0.012*
[1.98]
[2.49]
(0.048)
2
Window
SMN based on ∆II
Adj. R
(%)
Intercept
0.004*
0.010*
[2.22]
[2.19]
(0.013)
(0.027)
0.005**
0.012*
[2.63]
[2.22]
(0.009)
2
Window
Adj. R2
(%)
Intercept
0.004*
0.011*
[2.21]
[2.58]
(0.029)
(0.028)
(0.010)
0.005**
0.011*
0.004*
0.011*
[2.81]
[2.07]
[2.50]
[2.40]
(0.027)
(0.005)
(0.039)
(0.013)
(0.017)
0.005**
0.011*
0.005**
0.011*
0.005**
0.012*
[2.87]
[2.07]
[2.85]
[2.05]
[2.63]
[2.29]
(0.004)
(0.039)
(0.005)
(0.041)
(0.009)
(0.022)
10.3
7.4
6.0
13
25
37
10.3
7.4
5.8
13
25
37
10.0
7.0
5.6
* indicates significant at the level of 5%; ** indicates significant at the level of 1%.
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Table 3: Fama-MacBeth Regression Estimate for Unconditional Models
Coefficients
Panel A: SMN based on ∆BW
Intercept
SIZE ($ billions)
B/M
TURNOVER (%)
RET2-3 (%)
RET4-6 (%)
RET7-12 (%)
Adj. R 2 (%)
Panel B: SMN based on ∆BWort
Intercept
SIZE ($ billions)
B/M
TURNOVER (%)
RET2-3 (%)
RET4-6 (%)
RET7-12 (%)
Adj. R 2 (%)
Panel C: SMN based on ∆II
Intercept
SIZE ($ billions)
B/M
TURNOVER (%)
RET2-3 (%)
RET4-6 (%)
RET7-12 (%)
Adj. R 2 (%)
SMN
CAPM
CAPM
CAPM+SMN
FF
FF
FF+SMN
FFP
FFP
FFP+SMN
FFU
FFU
FFU+SMN
FFPU
FFPU
FFPU+SMN
0.442
(2.48)
-0.025
(-0.63)
0.342
(6.13)
-0.170
(-3.97)
0.864
(3.88)
1.007
(5.59)
0.930
(7.85)
3.29
0.416
(3.15)
-0.093
(-1.88)
0.329
(5.48)
-0.159
(-3.33)
0.737
(2.95)
0.819
(4.02)
0.928
(7.40)
4.04
0.313
(3.00)
-0.040
(-1.09)
0.329
(5.98)
-0.181
(-5.02)
0.967
(4.20)
0.938
(5.19)
0.915
(7.78)
2.95
0.135
(2.06)
-0.069
(-2.00)
0.190
(4.42)
-0.120
(-3.21)
0.549
(2.38)
0.719
(3.90)
0.761
(6.49)
2.29
0.079
(1.36)
-0.032
(-1.03)
0.212
(4.90)
-0.162
(-4.77)
0.690
(3.23)
0.777
(4.37)
0.786
(6.91)
2.12
0.133
(2.06)
-0.065
(-1.93)
0.189
(4.46)
-0.123
(-3.31)
0.529
(2.28)
0.699
(3.76)
0.771
(6.60)
2.29
0.072
(1.27)
-0.028
(-0.90)
0.212
(4.92)
-0.161
(-4.75)
0.655
(3.06)
0.775
(4.33)
0.795
(7.01)
2.13
0.253
(4.23)
-0.072
(-2.12)
0.197
(4.61)
-0.083
(-2.24)
0.541
(2.47)
0.711
(4.10)
0.736
(6.60)
2.24
0.202
(3.69)
-0.020
(-0.67)
0.236
(5.58)
-0.134
(-3.96)
0.678
(3.22)
0.769
(4.51)
0.771
(6.99)
2.08
0.249
(4.23)
-0.068
(-2.03)
0.197
(4.65)
-0.086
(-2.35)
0.520
(2.36)
0.692
(3.95)
0.747
(6.72)
2.24
0.193
(3.57)
-0.014
(-0.47)
0.238
(5.64)
-0.133
(-3.97)
0.649
(3.08)
0.769
(4.48)
0.777
(7.06)
2.09
0.513
(2.64)
-0.026
(-0.68)
0.338
(5.96)
-0.159
(-3.43)
0.772
(3.37)
0.902
(4.86)
0.877
(6.99)
3.34
0.416
(3.15)
-0.093
(-1.88)
0.329
(5.48)
-0.159
(-3.33)
0.737
(2.95)
0.819
(4.02)
0.928
(7.40)
4.04
0.323
(3.02)
-0.043
(-1.18)
0.326
(5.88)
-0.178
(-4.76)
0.847
(3.87)
0.857
(4.71)
0.885
(7.37)
2.92
0.135
(2.06)
-0.069
(-2.00)
0.190
(4.42)
-0.120
(-3.21)
0.549
(2.38)
0.719
(3.90)
0.761
(6.49)
2.29
0.083
(1.43)
-0.029
(-0.94)
0.215
(4.93)
-0.153
(-4.41)
0.631
(2.91)
0.737
(4.15)
0.760
(6.72)
2.10
0.133
(2.06)
-0.065
(-1.93)
0.189
(4.46)
-0.123
(-3.31)
0.529
(2.28)
0.699
(3.76)
0.771
(6.60)
2.29
0.077
(1.37)
-0.026
(-0.86)
0.214
(4.93)
-0.153
(-4.46)
0.599
(2.75)
0.730
(4.09)
0.772
(6.83)
2.11
0.253
(4.23)
-0.072
(-2.12)
0.197
(4.61)
-0.083
(-2.24)
0.541
(2.47)
0.711
(4.10)
0.736
(6.60)
2.24
0.209
(3.84)
-0.022
(-0.74)
0.237
(5.57)
-0.121
(-3.52)
0.625
(2.95)
0.735
(4.35)
0..740
(6.75)
2.05
0.249
(4.23)
-0.068
(-2.03)
0.197
(4.65)
-0.086
(-2.35)
0.520
(2.36)
0.692
(3.95)
0.747
(6.72)
2.24
0.202
(3.75)
-0.017
(-0.57)
0.238
(5.62)
-0.123
(-3.60)
0.599
(2.82)
0.730
(4.27)
0.749
(6.84)
2.06
0.358
(1.91)
-0.028
(-0.64)
0.344
(5.82)
-0.179
(-3.71)
0.955
(4.10)
0.970
(5.20)
0.926
(7.36)
3.89
0.416
(3.15)
-0.093
(-1.88)
0.329
(5.48)
-0.159
(-3.33)
0.737
(2.95)
0.819
(4.02)
0.928
(7.40)
4.04
0.278
(2.50)
-0.040
(-0.93)
0.338
(5.85)
-0..187
(-4.68)
0.937
(4.19)
0.876
(4.75)
0.969
(7.97)
0.135
(2.06)
-0.069
(-2.00)
0.190
(4.42)
-0.120
(-3.21)
0.549
(2.38)
0.719
(3.90)
0.761
(6.49)
2.29
0.087
(1.52)
-0.048
(-1.53)
0.200
(4.65)
-0.136
(-3.87)
0.695
(3.24)
0.740
(4.25)
0.824
(7.21)
0.133
(2.06)
-0.065
(-1.93)
0.189
(4.46)
-0.123
(-3.31)
0.529
(2.28)
0.699
(3.76)
0.771
(6.60)
0.084
(1.50)
-0.045
(-1.43)
0.201
(4.73)
-0.138
(-3.97)
0.674
(3.12)
0.722
(4.10)
0.834
(7.34)
0.194
(3.53)
-0.034
(-1.10)
0.227
(5.40)
-0.109
(-3.11)
0.698
(3.35)
0.752
(4.51)
0.805
(7.35)
0.249
(4.23)
-0.068
(-2.03)
0.197
(4.65)
-0.086
(-2.35)
0.520
(2.36)
0.692
(3.95)
0.747
(6.72)
0.190
(3.52)
-0.030
(-0.98)
0.228
(5.49)
-0.111
(-3.20)
0.676
(3.22)
0.734
(4.35)
0.817
(7.50)
2.17
2.29
2.17
0.253
(4.23)
-0.072
(-2.12)
0.197
(4.61)
-0.083
(-2.24)
0.541
(2.47)
0.711
(4.10)
0.736
(6.60)
2.24
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Table 4: Fama-MacBeth Regression Estimate with SMN (conditional models)
Coefficients
Intercept
SIZE ($ billions)
B/M
TURNOVER (%)
RET2-3 (%)
RET4-6 (%)
RET7-12 (%)
2
Adj. R (%)
Size+B/M
0.393
(2.26)
-0.013
(-0.35)
0.317
(6.03)
-0.169
(-4.07)
1.042
(4.92)
SMN based on ∆BW
def
(Size+B/M) def
0.434
0.434
(2.46)
(2.56)
-0.032
-0.018
(-0.83)
(-0.48)
0.329
0.273
(6.02)
(5.31)
-0.166
-0.155
(-3.96)
(-3.86)
0.867
1.104
(3.95)
(5.17)
Size+B/M
0.459
(2.42)
-0.014
(-0.38)
0.309
(5.80)
-0.159
(-3.53)
0.952
(4.34)
SMN based on ∆BWort
def
(Size+B/M) def
0.477
0.495
(2.48)
(2.68)
-0.030
-0.020
(-0.80)
(-0.56)
0.326
0.267
(5.90)
(5.13)
-0.158
-0.146
(-3.45)
(-3.34)
0.808
1.074
(3.60)
(4.86)
1.147
1.040
1.199
1.020
0.943
1.096
(6.74)
0.958
(8.25)
3.24
(5.90)
0.917
(7.91)
3.23
(7.09)
0.961
(8.58)
3.23
(5.90)
0.901
(7.25)
3.28
(5.28)
0.862
(6.98)
3.29
(6.46)
0.902
(7.49)
3.27
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Size+B/M
0.330
(1.79)
-0.024
(-0.58)
0.323
(5.73)
-0.173
(-3.69)
1.228
(5.29)
1.042
(5.83)
0.970
(7.86)
3.83
SMN based on ∆II
def
(Size+B/M) def
0.363
0.369
(1.96)
(2.07)
-0.037
-0.030
(-0.88)
(-0.74)
0.326
0.286
(5.60)
(5.24)
-0.170
-0.169
(-3.62)
(-3.75)
0.993
1.394
(4.28)
(5.91)
0.974
1.094
(5.30)
(6.17)
0.901
0.985
(7.15)
(8.05)
3.83
3.83
21
Table 5: Fama-MacBeth Regression Estimate with CAPM + SMN (conditional)
Coefficients
Intercept
SIZE ($ billions)
B/M
TURNOVER (%)
RET2-3 (%)
RET4-6 (%)
RET7-12 (%)
2
Adj. R (%)
Size+B/M
0.261
(2.70)
-0.023
(-0.66)
0.285
(5.66)
-0.178
(-5.28)
1.069
(5.23)
1.017
(5.80)
0.946
(8.33)
2.86
Creating leaders Transforming business
SMN based on ∆BW
def
(Size+B/M) def
0.342
0.291
(3.34)
(3.13)
-0.051
-0.029
(-1.45)
(-0.90)
0.315
0.235
(5.88)
(4.90)
-0.175
-0.160
(-5.00)
(-5.10)
0.873
1.146
(4.03)
(5.44)
0.924
1.045
(5.22)
(6.07)
0.902
0.930
(7.85)
(8.64)
2.90
2.88
Size+B/M
0.261
(2.64)
-0.023
(-0.66)
0.280
(5.55)
-0.179
(-5.16)
1.073
(5.22)
0.960
(5.54)
0.926
(7.91)
2.81
SMN based on ∆BWort
def
(Size+B/M) def
0.334
0.284
(3.19)
(2.99)
-0.049
-0.028
(-1.38)
(-0.84)
0.316
0.229
(5.90)
(4.79)
-0.173
-0.165
(-4.74)
(-5.09)
0.869
1.219
(4.01)
(5.79)
0.859
0.997
(4.87)
(5.89)
0.870
0.901
(7.43)
(8.10)
2.87
2.80
Te Kunenga
ki Pūrehuroa
Size+B/M
0.244
(2.30)
-0.029
(-0.71)
0.286
(5.38)
-0.178
(-4.72)
1.148
(5.20)
0.933
(5.23)
1.025
(8.67)
3.38
SMN based on ∆II
def
(Size+B/M) def
0.282
0.258
(2.57)
(2.54)
-0.045
-0.028
(-1.09)
(-0.73)
0.322
0.240
(5.74)
(4.79)
-0.183
-0.175
(-4.72)
(-4.98)
0.903
1.246
(4.05)
(5.54)
0.899
1.022
(4.95)
(5.87)
0.961
1.030
(7.81)
(8.90)
3.47
3.41
22
Table 6: Fama-MacBeth Regression Estimate with FF + SMN (conditional)
Coefficients
Intercept
SIZE ($ billions)
B/M
TURNOVER (%)
RET2-3 (%)
RET4-6 (%)
RET7-12 (%)
2
Adj. R (%)
Size+B/M
0.111
(2.29)
-0.024
(-0.83)
0.066
(1.87)
-0.143
(-4.71)
0.887
(4.20)
0.936
(5.53)
0.897
(8.48)
1.99
Creating leaders Transforming business
SMN based on ∆BW
def
(Size+B/M) def
0.068
0.099
(1.28)
(2.15)
-0.025
-0.012
(-0.84)
(-0.45)
0.164
0.001
(4.14)
(0.02)
-0.151
-0.117
(-4.59)
(-4.36)
0.457
0.787
(2.12)
(3.63)
0.723
0.956
(4.20)
(5.90)
0.715
0.893
(6.47)
(9.06)
2.10
2.06
Size+B/M
0.103
(2.16)
-0.025
(-0.89)
0.078
(2.21)
-0.136
(-4.40)
0.918
(4.24)
0.932
(5.58)
0.859
(8.09)
1.96
SMN based on ∆BWort
def
(Size+B/M) def
0.064
0.099
(1.21)
(2.11)
-0.022
-0.016
(-0.74)
(-0.61)
0.175
0.013
(4.37)
(0.43)
-0.143
-0.107
(-4.25)
(-3.92)
0.468
0.905
(2.14)
(4.05)
0.719
0.977
(4.21)
(6.13)
0.695
0.822
(6.39)
(8.40)
2.08
2.04
Te Kunenga
ki Pūrehuroa
Size+B/M
0.117
(2.55)
-0.038
(-1.30)
0.074
(2.08)
-0.116
(-3.67)
1.010
(4.73)
0.928
(5.71)
0.904
(8.49)
2.01
SMN based on ∆II
def
(Size+B/M) def
0.082
0.117
(1.60)
(2.52)
-0.043
-0.032
(-1.44)
(-1.20)
0.164
0.010
(4.11)
(0.31)
-0.134
-0.107
(-3.96)
(-3.80)
0.518
0.946
(2.43)
(4.38)
0.740
0.979
(4.40)
(6.11)
0.774
0.864
(6.93)
(8.64)
2.13
2.08
23
Table 7: Fama-MacBeth Regression Estimate with FF + PS + SMN (conditional)
Coefficients
Intercept
SIZE ($ billions)
B/M
TURNOVER (%)
RET2-3 (%)
RET4-6 (%)
RET7-12 (%)
2
Adj. R (%)
Size+B/M
0.091
(1.97)
-0.013
(-0.47)
0.061
(1.77)
-0.137
(-4.60)
0.880
(4.22)
0.964
(5.60)
0.913
(8.78)
2.01
Creating leaders Transforming business
SMN based on ∆BW
(Size+B/M) def
def
0.062
0.054
(1.45)
(1.05)
0.009
-0.015
(0.34)
(-0.52)
-0.012
0.165
(-0.41)
(4.17)
-0.099
-0.149
(-3.77)
(-4.60)
0.811
0.447
(3.84)
(2.06)
0.975
0.702
(6.09)
(4.11)
0.868
0.713
(8.97)
(6.46)
2.08
2.11
SMN based on ∆BWort
(Size+B/M) def
def
Size+B/M
0.073
0.052
0.082
(1.65)
(1.01)
(1.82)
-0.001
-0.013
-0.014
(-0.05)
(-0.46)
(-0.51)
-0.002
0.173
0.069
(-0.08)
(4.34)
(2.00)
-0.102
-0.145
-0.130
(-3.88)
(-4.38)
(-4.28)
0.897
0.456
0.896
(4.08)
(2.07)
(4.18)
0.982
0.705
0.948
(6.20)
(4.15)
(5.59)
0.797
0.685
0.878
(8.38)
(6.30)
(8.34)
2.04
2.09
1.98
Te Kunenga
ki Pūrehuroa
Size+B/M
0.103
(2.32)
-0.028
(-0.96)
0.068
(1.97)
-0.110
(-3.55)
0.961
(4.53)
0.905
(5.40)
0.922
(8.78)
2.02
SMN based on ∆II
(Size+B/M) def
def
0.106
0.082
(2.46)
(1.61)
-0.025
-0.039
(-0.98)
(-1.30)
-0.013
0.158
(-0.44)
(4.00)
-0.095
-0.135
(-3.53)
(-4.09)
0.884
0.516
(4.17)
(2.38)
0.94
0.706
(5.79)
(4.19)
0.840
0.760
(8.62)
(6.85)
2.09
2.14
24
Table 8: Fama-MacBeth Regression Estimate with FF + momentum + SMN
(conditional)
Coefficients
Intercept
SIZE ($ billions)
B/M
TURNOVER (%)
RET2-3 (%)
RET4-6 (%)
RET7-12 (%)
2
Adj. R (%)
Size+B/M
0.195
(4.00)
-0.004
(-0.13)
0.105
(3.11)
-0.122
(-4.16)
0.908
(4.37)
0.921
(5.77)
0.882
(8.82)
1.91
Creating leaders Transforming business
SMN based on ∆BW
def
(Size+B/M) def
0.187
0.160
(3.71)
(3.71)
-0.011
0.020
(-0.36)
(0.74)
0.195
0.036
(5.03)
(1.27)
-0.117
-0.100
(-3.64)
(-3.93)
0.399
0.758
(1.90)
(3.68)
0.679
0.882
(4.12)
(5.84)
0.677
0.856
(6.41)
(9.55)
2.04
1.95
SMN based on ∆BWort
Size+B/M
def
(Size+B/M) def
0.198
0.185
0.163
(4.15)
(3.67)
(3.78)
-0.013
-0.010
0.017
(-0.44)
(-0.34)
(0.68)
0.113
0.204
0.055
(3.32)
(5.26)
(1.91)
-0.110
-0.107
-0.089
(-3.68)
(-3.24)
(-3.44)
0.939
0.415
0.857
(4.49)
(1.95)
(4.06)
0.921
0.692
0.925
(5.87)
(4.26)
(6.21)
0.839
0.651
0.790
(8.41)
(6.23)
(8.79)
1.87
2.01
1.92
Te Kunenga
ki Pūrehuroa
Size+B/M
0.201
(4.46)
-0.018
(-0.63)
0.107
(3.15)
-0.091
(-2.96)
1.021
(4.94)
0.922
(6.02)
0.879
(8.85)
1.92
SMN based on ∆II
def
(Size+B/M) def
0.187
0.175
(3.76)
(4.15)
-0.026
-0.001
(-0.87)
(-0.02)
0.196
0.050
(5.10)
(1.70)
-0.105
-0.083
(-3.14)
(-3.09)
0.492
0.910
(2.41)
(4.46)
0.707
0.904
(4.39)
(5.95)
0.734
0.818
(6.97)
(9.04)
2.06
1.97
25
Table 9: Fama-MacBeth Regression Estimate with FF + PS + momentum + SMN
(conditional)
Coefficients
Intercept
SIZE ($ billions)
B/M
TURNOVER (%)
RET2-3 (%)
RET4-6 (%)
RET7-12 (%)
2
Adj. R (%)
Size+B/M
0.177
(3.87)
0.006
(0.21)
0.094
(2.86)
-0.117
(-4.06)
0.880
(4.33)
0.940
(5.78)
0.891
(9.06)
1.93
Creating leaders Transforming business
SMN based on ∆BW
def
(Size+B/M) def
0.170
0.177
(3.44)
(4.28)
0.001
0.026
(0.05)
(0.97)
0.195
(0.028)
(5.06)
(0.96)
-0.116
-0.144
(-3.64)
(-5.53)
0.398
0.789
(1.89)
(3.86)
0.653
0.902
(3.97)
(5.71)
0.680
0.792
(6.45)
(8.60)
2.06
1.68
SMN based on ∆BWort
Size+B/M
def
(Size+B/M) def
0.179
0.169
0.089
(4.05)
(3.42)
(2.12)
-0.001
0.001
0.069
(-0.05)
(0.02)
(2.60)
0.103
0.205
0.034
(3.11)
(5.30)
(1.04)
-0.105
-0.110
-0.073
(-3.60)
(-3.38)
(-2.74)
0.902
0.412
0.729
(4.39)
(1.92)
(2.40)
0.922
0.670
0.970
(5.78)
(4.11)
(5.15)
0.853
0.647
0.910
(8.61)
(6.19)
(8.00)
1.89
2.03
1.84
Te Kunenga
ki Pūrehuroa
Size+B/M
0.187
(4.31)
-0.009
(-0.30)
0.100
(3.02)
-0.085
(-2.81)
0.969
(4.75)
0.895
(5.66)
0.897
(9.15)
1.93
SMN based on ∆II
def
(Size+B/M) def
0.184
0.146
(3.73)
(3.52)
-0.021
0.017
(-0.71)
(0.65)
0.192
0.021
(5.02)
(0.73)
-0.106
-0.097
(-3.24)
(-3.70)
0.490
0.981
(2.36)
(4.53)
0.669
0.901
(4.12)
(5.36)
0.726
0.821
(6.93)
(8.44)
2.08
1.79
26
Summary of Findings
• Stocks with certain firm characteristics are more vulnerable to investor
sentiment.
• Returns on small firms are more sensitive to changes in investor sentiment
than large firms.
• Value stocks (high B/M) have larger sentiment beta than growth stocks.
• A positive relationship between turnover and sentiment beta.
• Past winners tend to be more responsive to changes in investor sentiment
than past losers.
• Stocks with higher sentiment beta earn higher returns.
Creating leaders Transforming business
Te Kunenga
ki Pūrehuroa
27
Summary of Findings
• Investor sentiment helps to explain the cross-section of stock returns and
pricing anomalies.
• SMN is a risk factor, i.e., investor sentiment factor is priced.
• SMN can always explain the size effect without requiring conditional
pricing model.
• Conditional versions of the sentiment-augmented FF-based models often
capture the size and value effects.
• Momentum effect sharply reduces when the factor loadings are
conditional on the default spread in the sentiment-augmented models
that contain the momentum factor. Hence, investor sentiment is also
associated with the momentum profits.
Creating leaders Transforming business
Te Kunenga
ki Pūrehuroa
28
Q&A
Creating leaders Transforming business
Te Kunenga
ki Pūrehuroa
29