investor sentiment risk factor and asset pricing anomalies

Te Kunengaki PūrehuroaCreating leaders Transforming business

Investor Sentiment Risk Factor and

Asset Pricing Anomalies

Chienwei Ho Massey University

Chi-Hsiou Hung Durham University


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).

2


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)

3


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.

4


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, non-dividend-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

• 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

7

𝑅𝑗𝑡𝑒 ≡ 𝑅𝑗𝑡 − 𝑅𝐹𝑡 = 𝛼𝑗 + 𝛽𝑗𝑠∆𝑆𝐸𝑁𝑇𝑡 + 𝜀𝑗𝑡


Conditional Sentiment-augmented Models

• Conditioning variables• Macro variables: default spread• Firm-specific characteristics: B/M and size

8


Empirical Framework

• Indicator of explanatory power of model: adj-R2 (lower ==> better)

9

Ho: Ct = 0 ?

𝑅𝑗𝑡∗ ≡ 𝑅𝑗𝑡 −ቂ𝑅𝐹𝑡 + 𝛽൫𝜃;𝑧𝑡−1,𝑋𝑗𝑡−1൯′𝐹𝑡ቃ = 𝑐0𝑡 + 𝑐𝑡𝑍𝑗𝑡−1 + 𝑒𝑗𝑡

adjusted return (second-pass regression)

conditional asset pricing model (first-pass regression)

pricing anomalies


Asset Pricing Models

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𝑟𝑗𝑡 = 𝛼𝑗 + 𝛽𝑗𝑆𝑀𝑁𝑆𝑀𝑁𝑡 +𝑢𝑗𝑡

𝑟𝑗𝑡 = 𝛼𝑗 + 𝛽𝑗𝑆𝑀𝑁𝑆𝑀𝑁𝑡 + 𝛽𝑗𝑚𝑟𝑚𝑡 + 𝛽𝑗𝑆𝑀𝐵𝑆𝑀𝐵𝑡 + 𝛽𝑗𝐻𝑀𝐿𝐻𝑀𝐿𝑡 + 𝛽𝑗𝑃𝑆𝑃𝑆𝑡 + 𝛽𝑗𝑊𝑀𝐿𝑊𝑀𝐿𝑡

+𝑢𝑗𝑡

traditional risk factors


Time-Varying Beta

11

jt jt Ft jt-1 mt FtCAPM: r R -R (R -R )j jtu

𝛽𝑗𝑡−1 = 𝛽𝑗1 + 𝛽𝑗2𝑧𝑡−1 +൫𝛽𝑗3 + 𝛽𝑗4𝑧𝑡−1൯𝑆𝐼𝑍𝐸𝑗𝑡−1 + (𝛽𝑗5 + 𝛽𝑗6𝑧𝑡−1)𝐵/𝑀𝑗𝑡−1


Beta Specifications

1 1jt j

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Unconditional Model

Conditional 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)

Specification C: function of (SIZE + B/M)def

(i.e., 𝐚𝐥𝐥 𝜷𝒔≠ 𝟎)


Two-Pass Framework (using CAPM as an Example)

jt Ft jt-1 mt Ft1st-pass (time-series): R -R (R -R )j jtu

0 11

2nd-pass (cross-sectional): M

j jt t mt mjt jtm

u c c Z e

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Risk Factors (for CAPM here)

AnomaliesAdjusted Return


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)

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(size effect)

(value effect)

Mean Median Std Reg. Coefficient (%) t -value EXCESS RETS (%) 0.88 1.06 5.67 SIZE ($ billions) 1.22 0.70 1.09 - 0.11 - 2.10 B/M 0.90 0.86 0.28 0.32 4.96 TURNOVER (%) 6.27 5.19 3.82 - 0.09 -1.40 RET2-3 (%) 2.69 2.92 8.67 0.64 2.31 RET4-6 (%) 4.00 3.70 10.98 0.82 3.50 RET7-12 (%) 8.01 7.33 15.71 0.86 6.15

R 2 (%) 5.05

(momentum effect)


Figure 1: Stock Returns by Firm Characteristics and Sentiment Beta


Is the Investor Sentiment Factor (SMN) Priced?

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Ho: = 0

𝑅𝑗𝑡 − 𝑅𝐹𝑡 = 𝜆0 + 𝜆1𝛽𝑗𝑡𝑆𝑀𝑁+ 𝜇𝑗𝑡


Table 2: Cross-Sectional Regressions of Excess Returns on SMN Beta

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SMN based on ∆BW SMN based on ∆BWort SMN based on ∆II

Window Intercept

Adj. R2 (%) Window Intercept

Adj. R2 (%) Window Intercept

Adj. R2 (%)

13

0.003* 0.012*

10.3

13

0.004* 0.010*

10.3

13

0.004* 0.011*

10.0 [1.98] [2.49] [2.22] [2.19] [2.21] [2.58]

(0.048) (0.013) (0.027) (0.029) (0.028) (0.010)

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0.005** 0.012*

7.4

25

0.005** 0.011*

7.4

25

0.004* 0.011*

7.0 [2.63] [2.22] [2.81] [2.07] [2.50] [2.40]

(0.009) (0.027) (0.005) (0.039) (0.013) (0.017)

37

0.005** 0.011*

6.0

37

0.005** 0.011*

5.8

37

0.005** 0.012*

5.6 [2.87] [2.07] [2.85] [2.05] [2.63] [2.29]

(0.004) (0.039) (0.005) (0.041) (0.009) (0.022)

* indicates significant at the level of 5%; ** indicates significant at the level of 1%.


Table 3: Fama-MacBeth Regression Estimate for Unconditional Models

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SMNCAPM CAPM+SMN FF FF+SMN FFP FFP+SMN FFU FFU+SMN FFPU FFPU+SMN

Panel A: SMN based on ∆BWIntercept 0.442 0.416 0.313 0.135 0.079 0.133 0.072 0.253 0.202 0.249 0.193

(2.48) (3.15) (3.00) (2.06) (1.36) (2.06) (1.27) (4.23) (3.69) (4.23) (3.57)SIZE ($ billions) -0.025 -0.093 -0.040 -0.069 -0.032 -0.065 -0.028 -0.072 -0.020 -0.068 -0.014

(-0.63) (-1.88) (-1.09) (-2.00) (-1.03) (-1.93) (-0.90) (-2.12) (-0.67) (-2.03) (-0.47)B/M 0.342 0.329 0.329 0.190 0.212 0.189 0.212 0.197 0.236 0.197 0.238

(6.13) (5.48) (5.98) (4.42) (4.90) (4.46) (4.92) (4.61) (5.58) (4.65) (5.64)TURNOVER (%) -0.170 -0.159 -0.181 -0.120 -0.162 -0.123 -0.161 -0.083 -0.134 -0.086 -0.133

(-3.97) (-3.33) (-5.02) (-3.21) (-4.77) (-3.31) (-4.75) (-2.24) (-3.96) (-2.35) (-3.97)RET2-3 (%) 0.864 0.737 0.967 0.549 0.690 0.529 0.655 0.541 0.678 0.520 0.649

(3.88) (2.95) (4.20) (2.38) (3.23) (2.28) (3.06) (2.47) (3.22) (2.36) (3.08)RET4-6 (%) 1.007 0.819 0.938 0.719 0.777 0.699 0.775 0.711 0.769 0.692 0.769

(5.59) (4.02) (5.19) (3.90) (4.37) (3.76) (4.33) (4.10) (4.51) (3.95) (4.48)RET7-12 (%) 0.930 0.928 0.915 0.761 0.786 0.771 0.795 0.736 0.771 0.747 0.777

(7.85) (7.40) (7.78) (6.49) (6.91) (6.60) (7.01) (6.60) (6.99) (6.72) (7.06)Adj. R 2 (%) 3.29 4.04 2.95 2.29 2.12 2.29 2.13 2.24 2.08 2.24 2.09

Panel B: SMN based on ∆BWortIntercept 0.513 0.416 0.323 0.135 0.083 0.133 0.077 0.253 0.209 0.249 0.202

(2.64) (3.15) (3.02) (2.06) (1.43) (2.06) (1.37) (4.23) (3.84) (4.23) (3.75)SIZE ($ billions) -0.026 -0.093 -0.043 -0.069 -0.029 -0.065 -0.026 -0.072 -0.022 -0.068 -0.017

(-0.68) (-1.88) (-1.18) (-2.00) (-0.94) (-1.93) (-0.86) (-2.12) (-0.74) (-2.03) (-0.57)B/M 0.338 0.329 0.326 0.190 0.215 0.189 0.214 0.197 0.237 0.197 0.238

(5.96) (5.48) (5.88) (4.42) (4.93) (4.46) (4.93) (4.61) (5.57) (4.65) (5.62)TURNOVER (%) -0.159 -0.159 -0.178 -0.120 -0.153 -0.123 -0.153 -0.083 -0.121 -0.086 -0.123

(-3.43) (-3.33) (-4.76) (-3.21) (-4.41) (-3.31) (-4.46) (-2.24) (-3.52) (-2.35) (-3.60)RET2-3 (%) 0.772 0.737 0.847 0.549 0.631 0.529 0.599 0.541 0.625 0.520 0.599

(3.37) (2.95) (3.87) (2.38) (2.91) (2.28) (2.75) (2.47) (2.95) (2.36) (2.82)RET4-6 (%) 0.902 0.819 0.857 0.719 0.737 0.699 0.730 0.711 0.735 0.692 0.730

(4.86) (4.02) (4.71) (3.90) (4.15) (3.76) (4.09) (4.10) (4.35) (3.95) (4.27)RET7-12 (%) 0.877 0.928 0.885 0.761 0.760 0.771 0.772 0.736 0..740 0.747 0.749

(6.99) (7.40) (7.37) (6.49) (6.72) (6.60) (6.83) (6.60) (6.75) (6.72) (6.84)Adj. R 2 (%) 3.34 4.04 2.92 2.29 2.10 2.29 2.11 2.24 2.05 2.24 2.06

Panel C: SMN based on ∆IIIntercept 0.358 0.416 0.278 0.135 0.087 0.133 0.084 0.253 0.194 0.249 0.190

(1.91) (3.15) (2.50) (2.06) (1.52) (2.06) (1.50) (4.23) (3.53) (4.23) (3.52)SIZE ($ billions) -0.028 -0.093 -0.040 -0.069 -0.048 -0.065 -0.045 -0.072 -0.034 -0.068 -0.030

(-0.64) (-1.88) (-0.93) (-2.00) (-1.53) (-1.93) (-1.43) (-2.12) (-1.10) (-2.03) (-0.98)B/M 0.344 0.329 0.338 0.190 0.200 0.189 0.201 0.197 0.227 0.197 0.228

(5.82) (5.48) (5.85) (4.42) (4.65) (4.46) (4.73) (4.61) (5.40) (4.65) (5.49)TURNOVER (%) -0.179 -0.159 -0..187 -0.120 -0.136 -0.123 -0.138 -0.083 -0.109 -0.086 -0.111

(-3.71) (-3.33) (-4.68) (-3.21) (-3.87) (-3.31) (-3.97) (-2.24) (-3.11) (-2.35) (-3.20)RET2-3 (%) 0.955 0.737 0.937 0.549 0.695 0.529 0.674 0.541 0.698 0.520 0.676

(4.10) (2.95) (4.19) (2.38) (3.24) (2.28) (3.12) (2.47) (3.35) (2.36) (3.22)RET4-6 (%) 0.970 0.819 0.876 0.719 0.740 0.699 0.722 0.711 0.752 0.692 0.734

(5.20) (4.02) (4.75) (3.90) (4.25) (3.76) (4.10) (4.10) (4.51) (3.95) (4.35)RET7-12 (%) 0.926 0.928 0.969 0.761 0.824 0.771 0.834 0.736 0.805 0.747 0.817

(7.36) (7.40) (7.97) (6.49) (7.21) (6.60) (7.34) (6.60) (7.35) (6.72) (7.50)Adj. R 2 (%) 3.89 4.04 3.49 2.29 2.17 2.29 2.17 2.24 2.12 2.24 2.11

CoefficientsFFPUCAPM FF FFP FFU


Table 4: Fama-MacBeth Regression Estimate with SMN (conditional models)

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CoefficientsSize+B/M def (Size+B/M) def Size+B/M def (Size+B/M) def Size+B/M def (Size+B/M) def

Intercept 0.393 0.434 0.434 0.459 0.477 0.495 0.330 0.363 0.369(2.26) (2.46) (2.56) (2.42) (2.48) (2.68) (1.79) (1.96) (2.07)

SIZE ($ billions) -0.013 -0.032 -0.018 -0.014 -0.030 -0.020 -0.024 -0.037 -0.030(-0.35) (-0.83) (-0.48) (-0.38) (-0.80) (-0.56) (-0.58) (-0.88) (-0.74)

B/M 0.317 0.329 0.273 0.309 0.326 0.267 0.323 0.326 0.286(6.03) (6.02) (5.31) (5.80) (5.90) (5.13) (5.73) (5.60) (5.24)

TURNOVER (%) -0.169 -0.166 -0.155 -0.159 -0.158 -0.146 -0.173 -0.170 -0.169(-4.07) (-3.96) (-3.86) (-3.53) (-3.45) (-3.34) (-3.69) (-3.62) (-3.75)

RET2-3 (%) 1.042 0.867 1.104 0.952 0.808 1.074 1.228 0.993 1.394(4.92) (3.95) (5.17) (4.34) (3.60) (4.86) (5.29) (4.28) (5.91)

RET4-6 (%) 1.147 1.040 1.199 1.020 0.943 1.096 1.042 0.974 1.094(6.74) (5.90) (7.09) (5.90) (5.28) (6.46) (5.83) (5.30) (6.17)

RET7-12 (%) 0.958 0.917 0.961 0.901 0.862 0.902 0.970 0.901 0.985(8.25) (7.91) (8.58) (7.25) (6.98) (7.49) (7.86) (7.15) (8.05)

Adj. R 2 (%) 3.24 3.23 3.23 3.28 3.29 3.27 3.83 3.83 3.83



Table 5: Fama-MacBeth Regression Estimate with CAPM + SMN (conditional)

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Intercept 0.261 0.342 0.291 0.261 0.334 0.284 0.244 0.282 0.258(2.70) (3.34) (3.13) (2.64) (3.19) (2.99) (2.30) (2.57) (2.54)

SIZE ($ billions) -0.023 -0.051 -0.029 -0.023 -0.049 -0.028 -0.029 -0.045 -0.028(-0.66) (-1.45) (-0.90) (-0.66) (-1.38) (-0.84) (-0.71) (-1.09) (-0.73)

B/M 0.285 0.315 0.235 0.280 0.316 0.229 0.286 0.322 0.240(5.66) (5.88) (4.90) (5.55) (5.90) (4.79) (5.38) (5.74) (4.79)

TURNOVER (%) -0.178 -0.175 -0.160 -0.179 -0.173 -0.165 -0.178 -0.183 -0.175(-5.28) (-5.00) (-5.10) (-5.16) (-4.74) (-5.09) (-4.72) (-4.72) (-4.98)

RET2-3 (%) 1.069 0.873 1.146 1.073 0.869 1.219 1.148 0.903 1.246(5.23) (4.03) (5.44) (5.22) (4.01) (5.79) (5.20) (4.05) (5.54)

RET4-6 (%) 1.017 0.924 1.045 0.960 0.859 0.997 0.933 0.899 1.022(5.80) (5.22) (6.07) (5.54) (4.87) (5.89) (5.23) (4.95) (5.87)

RET7-12 (%) 0.946 0.902 0.930 0.926 0.870 0.901 1.025 0.961 1.030(8.33) (7.85) (8.64) (7.91) (7.43) (8.10) (8.67) (7.81) (8.90)

Adj. R 2 (%) 2.86 2.90 2.88 2.81 2.87 2.80 3.38 3.47 3.41



Table 6: Fama-MacBeth Regression Estimate with FF + SMN (conditional)

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Intercept 0.111 0.068 0.099 0.103 0.064 0.099 0.117 0.082 0.117(2.29) (1.28) (2.15) (2.16) (1.21) (2.11) (2.55) (1.60) (2.52)

SIZE ($ billions) -0.024 -0.025 -0.012 -0.025 -0.022 -0.016 -0.038 -0.043 -0.032(-0.83) (-0.84) (-0.45) (-0.89) (-0.74) (-0.61) (-1.30) (-1.44) (-1.20)

B/M 0.066 0.164 0.001 0.078 0.175 0.013 0.074 0.164 0.010(1.87) (4.14) (0.02) (2.21) (4.37) (0.43) (2.08) (4.11) (0.31)

TURNOVER (%) -0.143 -0.151 -0.117 -0.136 -0.143 -0.107 -0.116 -0.134 -0.107(-4.71) (-4.59) (-4.36) (-4.40) (-4.25) (-3.92) (-3.67) (-3.96) (-3.80)

RET2-3 (%) 0.887 0.457 0.787 0.918 0.468 0.905 1.010 0.518 0.946(4.20) (2.12) (3.63) (4.24) (2.14) (4.05) (4.73) (2.43) (4.38)

RET4-6 (%) 0.936 0.723 0.956 0.932 0.719 0.977 0.928 0.740 0.979(5.53) (4.20) (5.90) (5.58) (4.21) (6.13) (5.71) (4.40) (6.11)

RET7-12 (%) 0.897 0.715 0.893 0.859 0.695 0.822 0.904 0.774 0.864(8.48) (6.47) (9.06) (8.09) (6.39) (8.40) (8.49) (6.93) (8.64)

Adj. R 2 (%) 1.99 2.10 2.06 1.96 2.08 2.04 2.01 2.13 2.08



Table 7: Fama-MacBeth Regression Estimate with FF + PS + SMN (conditional)

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Intercept 0.091 0.054 0.062 0.082 0.052 0.073 0.103 0.082 0.106(1.97) (1.05) (1.45) (1.82) (1.01) (1.65) (2.32) (1.61) (2.46)

SIZE ($ billions) -0.013 -0.015 0.009 -0.014 -0.013 -0.001 -0.028 -0.039 -0.025(-0.47) (-0.52) (0.34) (-0.51) (-0.46) (-0.05) (-0.96) (-1.30) (-0.98)

B/M 0.061 0.165 -0.012 0.069 0.173 -0.002 0.068 0.158 -0.013(1.77) (4.17) (-0.41) (2.00) (4.34) (-0.08) (1.97) (4.00) (-0.44)

TURNOVER (%) -0.137 -0.149 -0.099 -0.130 -0.145 -0.102 -0.110 -0.135 -0.095(-4.60) (-4.60) (-3.77) (-4.28) (-4.38) (-3.88) (-3.55) (-4.09) (-3.53)

RET2-3 (%) 0.880 0.447 0.811 0.896 0.456 0.897 0.961 0.516 0.884(4.22) (2.06) (3.84) (4.18) (2.07) (4.08) (4.53) (2.38) (4.17)

RET4-6 (%) 0.964 0.702 0.975 0.948 0.705 0.982 0.905 0.706 0.94(5.60) (4.11) (6.09) (5.59) (4.15) (6.20) (5.40) (4.19) (5.79)

RET7-12 (%) 0.913 0.713 0.868 0.878 0.685 0.797 0.922 0.760 0.840(8.78) (6.46) (8.97) (8.34) (6.30) (8.38) (8.78) (6.85) (8.62)

Adj. R 2 (%) 2.01 2.11 2.08 1.98 2.09 2.04 2.02 2.14 2.09



Table 8: Fama-MacBeth Regression Estimate with FF + momentum + SMN (conditional)

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Intercept 0.195 0.187 0.160 0.198 0.185 0.163 0.201 0.187 0.175(4.00) (3.71) (3.71) (4.15) (3.67) (3.78) (4.46) (3.76) (4.15)

SIZE ($ billions) -0.004 -0.011 0.020 -0.013 -0.010 0.017 -0.018 -0.026 -0.001(-0.13) (-0.36) (0.74) (-0.44) (-0.34) (0.68) (-0.63) (-0.87) (-0.02)

B/M 0.105 0.195 0.036 0.113 0.204 0.055 0.107 0.196 0.050(3.11) (5.03) (1.27) (3.32) (5.26) (1.91) (3.15) (5.10) (1.70)

TURNOVER (%) -0.122 -0.117 -0.100 -0.110 -0.107 -0.089 -0.091 -0.105 -0.083(-4.16) (-3.64) (-3.93) (-3.68) (-3.24) (-3.44) (-2.96) (-3.14) (-3.09)

RET2-3 (%) 0.908 0.399 0.758 0.939 0.415 0.857 1.021 0.492 0.910(4.37) (1.90) (3.68) (4.49) (1.95) (4.06) (4.94) (2.41) (4.46)

RET4-6 (%) 0.921 0.679 0.882 0.921 0.692 0.925 0.922 0.707 0.904(5.77) (4.12) (5.84) (5.87) (4.26) (6.21) (6.02) (4.39) (5.95)

RET7-12 (%) 0.882 0.677 0.856 0.839 0.651 0.790 0.879 0.734 0.818(8.82) (6.41) (9.55) (8.41) (6.23) (8.79) (8.85) (6.97) (9.04)

Adj. R 2 (%) 1.91 2.04 1.95 1.87 2.01 1.92 1.92 2.06 1.97



Table 9: Fama-MacBeth Regression Estimate with FF + PS + momentum + SMN (conditional)

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Intercept 0.177 0.170 0.177 0.179 0.169 0.089 0.187 0.184 0.146(3.87) (3.44) (4.28) (4.05) (3.42) (2.12) (4.31) (3.73) (3.52)

SIZE ($ billions) 0.006 0.001 0.026 -0.001 0.001 0.069 -0.009 -0.021 0.017(0.21) (0.05) (0.97) (-0.05) (0.02) (2.60) (-0.30) (-0.71) (0.65)

B/M 0.094 0.195 (0.028) 0.103 0.205 0.034 0.100 0.192 0.021(2.86) (5.06) (0.96) (3.11) (5.30) (1.04) (3.02) (5.02) (0.73)

TURNOVER (%) -0.117 -0.116 -0.144 -0.105 -0.110 -0.073 -0.085 -0.106 -0.097(-4.06) (-3.64) (-5.53) (-3.60) (-3.38) (-2.74) (-2.81) (-3.24) (-3.70)

RET2-3 (%) 0.880 0.398 0.789 0.902 0.412 0.729 0.969 0.490 0.981(4.33) (1.89) (3.86) (4.39) (1.92) (2.40) (4.75) (2.36) (4.53)

RET4-6 (%) 0.940 0.653 0.902 0.922 0.670 0.970 0.895 0.669 0.901(5.78) (3.97) (5.71) (5.78) (4.11) (5.15) (5.66) (4.12) (5.36)

RET7-12 (%) 0.891 0.680 0.792 0.853 0.647 0.910 0.897 0.726 0.821(9.06) (6.45) (8.60) (8.61) (6.19) (8.00) (9.15) (6.93) (8.44)

Adj. R 2 (%) 1.93 2.06 1.68 1.89 2.03 1.84 1.93 2.08 1.79



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.

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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.

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Q & A

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investor sentiment risk factor and asset pricing anomalies

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