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Chapter Five Conclusion
I propose a further test to examine the predictive power of prospect theory on stock returns following different sentiment periods. Some investors allocate money to stocks according to prospect theory, and this process involves two steps: representation and valuation. I use the distribution of the stock’s past returns as mental representation and derive the value of stocks using prospect theory elements. My explanations cover two elements. The first is probability weighting, which incorporates lottery-type and insurance-type demand, causing stocks to be overvalued. As a result, following high-sentiment periods, expected return is negatively associated with probability weighting. The second is loss aversion, which indicates investors are more sensitive to losses than to gains of the same magnitude, negatively predicting stock returns following low-sentiment periods because of investors’ biased beliefs about expected returns and underinvestment in high loss aversion stocks.
I also empirically examine how overpricing caused by probability weighting or under-pricing caused by loss aversion is affected by investor sentiment. I find the short leg of the probability weighting strategy more profitable following high sentiment, but the sentiment exhibits no significant effect on the profit of the long leg of loss aversion strategy. Using predictive regressions, I find the overpricing of probability weighting sensitive to the change in sentiment, and underpricing of loss aversion concentrated mainly in extreme sentiment periods because of short-sale impediments and disposition effect.
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Stocks calculated by probability weighting and loss aversion also exhibit separate char-acteristics. Stocks with low loss aversion value have by nature low past average return, low minimum return, and high volatility; stocks with high probability weighting value are those with high past average return, high maximum return, and high skewness.
Overall, my empirical results reveal in depth the mechanism behind prospect theory in the framework of investor sentiment. These findings not only indicate which element plays a role in which sentiment period but also reveal the factors that cause this phenomenon and the dynamic change of the valuation process of investors. This study further develops empirical research on prospect theory, which is helpful for a better grasp of the psychological changes in investors and a better understanding of the investor behavior.
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APPENDIX
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This table presents average monthly excess returns, four-factor alphas, and five-factor alphas on the equal-weighted basis of portfolios of stocks sorted on PT, PW, LA, and CC in the sample period and following different sentiment periods in Panel A, Panel B, Panel C, and Panel D, respectively. Each month, all stocks in the CRSP sample are sorted in the portfolios based on the corresponding prospect theory value. Then I sort the sample period into low and high levels of investor sentiment, classified based on the median level of Baker and Wurgler’s (2006) sentiment index. I report the average excess return for each of the 10 decile portfolios and long the first decile portfolio and short the 10th decile portfolio as well as Carhart’s (1997) four-factor alpha and alpha of the four-factor model augmented by the Pastor and Stambaugh (2003) liquidity factor following different sentiment periods. The sample period runs from September 1965 to December 2016, except in the case of five-factor alpha, which starts in January 1968 because of the availability constraint of the liquidity factor. t-statistics appear in parentheses.
1 2 3 4 5 6 7 8 9 10 1-10
Panel A: Returns of portfolios of stocks sorted on PT Whole periods
Excess return 1.694 1.075 0.917 0.890 0.822 0.830 0.783 0.708 0.726 0.617 1.077 (4.50) (3.71) (3.56) (3.76) (3.72) (3.95) (3.97) (3.67) (3.80) (2.64) (2.43) Four-factor alpha 1.064 0.442 0.256 0.256 0.191 0.211 0.151 0.055 0.074 -0.027 1.091 (5.36) (4.21) (3.33) (4.08) (3.47) (4.26) (3.15) (1.05) (1.42) (-0.38) (5.39) Five-factor alpha 1.095 0.424 0.251 0.277 0.209 0.229 0.163 0.060 0.104 0.010 1.085 (5.28) (3.91) (3.23) (4.42) (3.88) (4.73) (3.46) (1.14) (1.95) (0.14) (5.16)
Low sentiment
Excess return 2.487 1.578 1.188 1.102 1.033 1.044 0.890 0.886 0.929 0.970 1.517 (4.34) (3.52) (2.96) (3.04) (3.02) (3.23) (3.00) (3.05) (3.37) (3.18) (2.34) Four-factor alpha 1.372 0.572 0.175 0.187 0.151 0.192 0.051 0.027 0.073 0.022 1.351 (5.03) (3.62) (1.56) (2.15) (2.00) (2.67) (0.78) (0.37) (1.01) (0.24) (4.73) Five-factor alpha 1.451 0.564 0.173 0.224 0.200 0.230 0.062 0.034 0.131 0.075 1.376 (4.93) (3.40) (1.55) (2.72) (2.87) (3.52) (1.01) (0.46) (1.74) (0.81) (4.53)
High sentiment
Excess return 0.905 0.575 0.648 0.680 0.614 0.617 0.677 0.532 0.524 0.265 0.640 (1.87) (1.57) (2.00) (2.24) (2.18) (2.30) (2.60) (2.09) (1.98) (0.75) (1.07) Four-factor alpha 0.741 0.297 0.331 0.308 0.224 0.207 0.245 0.079 0.080 0.001 0.740 (2.55) (2.14) (3.15) (3.38) (2.80) (3.06) (3.49) (1.05) (1.06) (0.01) (2.61) Five-factor alpha 0.761 0.291 0.325 0.316 0.214 0.212 0.256 0.082 0.083 -0.001 0.762 (2.60) (2.07) (3.08) (3.43) (2.65) (3.10) (3.62) (1.08) (1.09) (-0.01) (2.67) Panel B: Returns of portfolios of stocks sorted on PW
Whole periods
Excess return 1.272 0.914 0.848 0.863 0.852 0.934 0.923 0.988 0.812 0.659 0.613 (4.57) (4.33) (4.25) (4.39) (4.22) (4.34) (3.99) (3.92) (2.87) (1.94) (1.40) Four-factor alpha 0.791 0.391 0.266 0.249 0.198 0.235 0.216 0.304 0.070 -0.047 0.838 (6.20) (5.53) (4.31) (4.38) (3.56) (4.00) (3.45) (4.34) (0.78) (-0.35) (5.16) Five-factor alpha 0.817 0.400 0.278 0.273 0.224 0.256 0.215 0.310 0.079 -0.030 0.847 (6.17) (5.58) (4.57) (4.87) (3.96) (4.29) (3.37) (4.33) (0.85) (-0.22) (5.06)
Low sentiment
Excess return 1.638 1.036 0.931 0.986 0.996 1.212 1.200 1.377 1.337 1.401 0.237 (3.59) (3.03) (2.94) (3.20) (3.22) (3.70) (3.52) (3.81) (3.35) (3.06) (0.37) Four-factor alpha 0.992 0.354 0.176 0.182 0.115 0.261 0.172 0.320 0.146 0.106 0.886 (5.21) (3.46) (1.95) (2.23) (1.51) (3.18) (2.01) (3.59) (1.18) (0.63) (3.91)
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Table A.1 – Continued from previous page
1 2 3 4 5 6 7 8 9 10 1-10
Five-factor alpha 1.066 0.381 0.205 0.218 0.174 0.315 0.173 0.338 0.151 0.124 0.942 (5.25) (3.68) (2.40) (2.88) (2.30) (3.87) (2.00) (3.75) (1.16) (0.69) (3.94)
High sentiment
Excess return 0.908 0.792 0.765 0.742 0.708 0.657 0.648 0.602 0.291 -0.079 0.987 (2.85) (3.18) (3.14) (3.03) (2.72) (2.35) (2.07) (1.71) (0.73) (-0.16) (1.67) Four-factor alpha 0.543 0.386 0.337 0.295 0.266 0.201 0.269 0.297 0.045 -0.126 0.669 (3.30) (4.16) (4.05) (3.79) (3.30) (2.40) (2.99) (2.83) (0.35) (-0.62) (3.20) Five-factor alpha 0.550 0.389 0.335 0.311 0.265 0.199 0.265 0.292 0.047 -0.117 0.667 (3.32) (4.16) (4.00) (3.98) (3.25) (2.36) (2.92) (2.77) (0.36) (-0.58) (3.16) Panel C: Returns of portfolios of stocks sorted on LA
Whole periods
Excess return 1.763 1.017 0.904 0.863 0.850 0.809 0.786 0.736 0.697 0.638 1.126 (4.41) (3.32) (3.39) (3.58) (3.79) (3.93) (3.98) (3.95) (3.74) (3.00) (2.48) Four-factor alpha 1.115 0.363 0.263 0.227 0.216 0.199 0.157 0.108 0.041 -0.015 1.131 (4.95) (3.04) (3.28) (3.67) (3.97) (3.88) (3.31) (2.13) (0.75) (-0.26) (4.71) Five-factor alpha 1.144 0.356 0.244 0.252 0.231 0.228 0.170 0.127 0.056 0.015 1.129 (4.85) (2.88) (3.00) (4.10) (4.46) (4.56) (3.68) (2.47) (1.00) (0.24) (4.52)
Low sentiment
Excess return 2.680 1.598 1.305 1.089 1.038 0.961 0.934 0.817 0.834 0.850 1.830 (4.48) (3.41) (3.18) (2.95) (3.00) (3.06) (3.11) (2.94) (3.08) (2.91) (2.75) Four-factor alpha 1.453 0.509 0.324 0.151 0.147 0.133 0.102 0.030 0.014 -0.042 1.494 (4.64) (3.07) (2.72) (1.67) (1.88) (1.83) (1.48) (0.45) (0.18) (-0.49) (4.42) Five-factor alpha 1.525 0.512 0.299 0.201 0.184 0.192 0.125 0.066 0.032 0.009 1.515 (4.49) (2.95) (2.49) (2.26) (2.69) (2.92) (1.94) (0.98) (0.42) (0.10) (4.16)
High sentiment
Excess return 0.852 0.439 0.505 0.638 0.663 0.657 0.638 0.655 0.561 0.427 0.425 (1.61) (1.12) (1.48) (2.05) (2.32) (2.47) (2.48) (2.64) (2.19) (1.38) (0.69) Four-factor alpha 0.782 0.215 0.210 0.301 0.276 0.243 0.208 0.180 0.067 0.031 0.751 (2.41) (1.25) (1.92) (3.55) (3.64) (3.38) (3.19) (2.38) (0.82) (0.39) (2.20) Five-factor alpha 0.803 0.220 0.202 0.300 0.270 0.247 0.212 0.177 0.073 0.032 0.770 (2.45) (1.27) (1.83) (3.51) (3.53) (3.41) (3.23) (2.32) (0.90) (0.40) (2.24) Panel D: Returns of portfolios of stocks sorted on CC
Whole periods
Excess return 1.674 0.970 0.945 0.853 0.836 0.850 0.781 0.832 0.762 0.558 1.116 (4.85) (3.88) (4.18) (4.02) (4.04) (4.10) (3.68) (3.71) (3.10) (1.91) (2.47) Four-factor alpha 1.099 0.392 0.372 0.235 0.194 0.174 0.104 0.147 0.065 -0.109 1.208 (5.79) (4.23) (4.98) (3.78) (3.45) (3.15) (1.93) (2.50) (1.05) (-1.26) (5.92) Five-factor alpha 1.146 0.406 0.371 0.252 0.222 0.178 0.128 0.137 0.063 -0.081 1.226 (5.79) (4.28) (4.99) (4.13) (4.00) (3.20) (2.35) (2.32) (0.99) (-0.91) (5.78)
Low sentiment
Excess return 2.328 1.266 1.122 1.043 0.978 1.048 1.019 1.100 1.145 1.059 1.269 (4.32) (3.11) (3.10) (3.14) (2.99) (3.32) (3.26) (3.37) (3.32) (2.77) (1.92) Four-factor alpha 1.405 0.430 0.317 0.173 0.105 0.133 0.091 0.111 0.105 -0.049 1.454 (5.13) (3.17) (2.93) (1.96) (1.29) (1.71) (1.24) (1.39) (1.27) (-0.41) (4.87) Five-factor alpha 1.518 0.467 0.314 0.207 0.160 0.151 0.136 0.087 0.108 -0.003 1.521 (5.16) (3.36) (3.02) (2.55) (2.08) (1.98) (1.83) (1.12) (1.25) (-0.02) (4.78)
High sentiment
Excess return 1.024 0.675 0.768 0.664 0.695 0.653 0.544 0.567 0.382 0.061 0.964 (2.39) (2.32) (2.82) (2.51) (2.73) (2.42) (1.90) (1.84) (1.09) (0.14) (1.57) Four-factor alpha 0.780 0.325 0.405 0.279 0.267 0.198 0.124 0.193 0.047 -0.107 0.887 (2.94) (2.63) (3.96) (3.22) (3.51) (2.57) (1.59) (2.26) (0.53) (-0.92) (3.22) Five-factor alpha 0.795 0.334 0.413 0.286 0.274 0.195 0.124 0.192 0.036 -0.113 0.908 (2.97) (2.68) (4.01) (3.28) (3.58) (2.52) (1.57) (2.22) (0.40) (-0.96) (3.27)
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Figure A.1 Performance of deciles in different sentiment periods: Equal-weighted
I sort stocks into ten portfolios from bottom to top by PT, PW, and LA in each month and calculate each decile’s return over the following month on an equal-weighted basis. Then I sort the sample period into low and high levels of investor sentiment and compute Carhart’s (1997) four-factor alpha for these ten deciles, using the average of time-series returns following different periods. I plot the results in Figure A.1. Figure A.1a is for PT; Figure A.1b is for PW; and Figure A.1c is for LA. The vertical axis is the percentage monthly alpha; the horizontal axis represents
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This table presents Fama-French three-factor alphas, Fama-French five-factor alphas and six-factor alphas (Fama-French five-factor+momentum factor) on the value-weighted basis of portfolios of stocks sorted on PT, PW, and LA following different sentiment periods in Panel A, Panel B, and Panel C, respectively. Each month, all stocks in the CRSP sample are sorted on the portfolios based on the corresponding prospect theory value. Then I sort the whole period into low and high levels of investor sentiment, classified based on the median level of Baker and Wurgler’s (2006) sentiment index. I report the Fama-French three-factor alpha for each of the 10 decile portfolios and long the decile 1 portfolio and short the decile 10 portfolio. I also report the Fama-French five-factor alpha and alpha of the five-factor model augmented by the momentum factor following different sentiment periods. The sample period runs from September 1965 to December 2016. t-statistics appear in parentheses.
1 2 3 4 5 6 7 8 9 10 1-10
Panel A: Returns of portfolios of stocks sorted on PT Low sentiment
Three-factor alpha 0.131 -0.458 -0.089 -0.109 -0.128 -0.069 -0.107 -0.111 0.172 0.153 -0.022 (0.41) (-2.09) (-0.52) (-0.77) (-0.97) (-0.63) (-1.14) (-1.35) (2.01) (1.45) (-0.06) Five-factor alpha 0.189 -0.380 -0.081 -0.105 -0.091 -0.043 -0.151 -0.150 0.129 0.137 0.053
(0.59) (-1.71) (-0.47) (-0.73) (-0.67) (-0.38) (-1.58) (-1.82) (1.50) (1.27) (0.14) Six-factor alpha 0.694 0.019 0.251 0.176 0.128 0.120 -0.068 -0.116 0.062 -0.063 0.757 (2.44) (0.10) (1.79) (1.53) (1.09) (1.16) (-0.72) (-1.40) (0.72) (-0.71) (2.54)
High sentiment
Three-factor alpha 0.050 -0.190 0.052 0.205 -0.022 0.067 0.231 0.116 0.063 -0.006 0.057 (0.16) (-0.90) (0.34) (1.41) (-0.18) (0.63) (2.66) (1.29) (0.72) (-0.06) (0.16) Five-factor alpha 0.231 -0.133 0.033 0.204 -0.005 -0.055 0.097 -0.034 -0.092 0.008 0.223 (0.72) (-0.61) (0.21) (1.35) (-0.04) (-0.52) (1.13) (-0.38) (-1.10) (0.07) (0.61) Six-factor alpha 0.674 0.177 0.215 0.369 0.094 0.002 0.142 -0.056 -0.109 -0.099 0.773 (2.47) (0.95) (1.50) (2.65) (0.77) (0.02) (1.66) (-0.64) (-1.30) (-0.99) (2.57) Panel B: Returns of portfolios of stocks sorted on PW
Low sentiment
Three-factor alpha -0.276 -0.209 -0.024 0.121 0.125 0.044 0.006 0.170 0.424 0.392 -0.668 (-1.16) (-1.63) (-0.24) (1.17) (1.27) (0.43) (0.05) (1.29) (2.47) (1.54) (-1.66) Five-factor alpha -0.237 -0.227 -0.112 0.046 0.045 -0.026 -0.041 0.165 0.531 0.639 -0.876 (-0.98) (-1.73) (-1.12) (0.44) (0.47) (-0.26) (-0.35) (1.24) (3.11) (2.75) (-2.23) Six-factor alpha 0.305 0.022 -0.021 0.086 0.017 -0.119 -0.175 0.013 0.384 0.340 -0.035 (1.74) (0.21) (-0.21) (0.83) (0.18) (-1.21) (-1.59) (0.10) (2.30) (1.57) (-0.12)
High sentiment
Three-factor alpha 0.074 0.196 0.229 -0.021 0.052 -0.054 -0.058 0.062 -0.104 -0.605 0.679 (0.41) (1.90) (2.26) (-0.23) (0.53) (-0.51) (-0.48) (0.43) (-0.59) (-2.99) (2.41) Five-factor alpha -0.059 0.019 -0.024 -0.230 -0.144 -0.189 -0.080 0.196 0.231 -0.277 0.218 (-0.32) (0.19) (-0.26) (-2.77) (-1.56) (-1.92) (-0.66) (1.34) (1.37) (-1.39) (0.79) Six-factor alpha 0.209 0.135 0.043 -0.219 -0.147 -0.217 -0.087 0.162 0.191 -0.291 0.500 (1.35) (1.48) (0.49) (-2.61) (-1.58) (-2.18) (-0.71) (1.09) (1.12) (-1.44) (1.95) Panel C: Returns of portfolios of stocks sorted on LA
Low sentiment
Three-factor alpha 0.391 -0.247 -0.204 -0.219 -0.027 -0.135 -0.107 0.024 0.125 0.132 0.260 (1.10) (-0.98) (-1.04) (-1.39) (-0.19) (-1.18) (-1.07) (0.26) (1.40) (1.36) (0.66) Five-factor alpha 0.446 -0.241 -0.121 -0.205 0.000 -0.141 -0.122 -0.024 0.073 0.120 0.326
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Table B.1 – Continued from previous page
1 2 3 4 5 6 7 8 9 10 1-10
(1.24) (-0.97) (-0.62) (-1.29) (0.00) (-1.21) (-1.20) (-0.26) (0.82) (1.22) (0.83) Six-factor alpha 0.876 0.217 0.268 0.075 0.248 0.055 0.030 -0.009 0.014 -0.044 0.921 (2.59) (1.06) (1.74) (0.56) (2.12) (0.54) (0.33) (-0.10) (0.16) (-0.52) (2.64)
High sentiment
Three-factor alpha -0.220 -0.320 -0.109 0.077 0.032 0.127 0.115 0.095 0.030 0.129 -0.349 (-0.68) (-1.42) (-0.57) (0.50) (0.23) (1.17) (1.27) (1.08) (0.30) (1.36) (-0.99) Five-factor alpha 0.100 -0.155 -0.021 0.136 0.078 0.096 -0.024 -0.038 -0.183 0.059 0.041
(0.30) (-0.67) (-0.11) (0.85) (0.54) (0.85) (-0.26) (-0.43) (-2.02) (0.62) (0.11) Six-factor alpha 0.508 0.149 0.225 0.301 0.235 0.183 0.021 -0.043 -0.211 -0.024 0.532 (1.74) (0.74) (1.29) (2.01) (1.76) (1.68) (0.24) (-0.49) (-2.31) (-0.27) (1.75)
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Appendix C
Table C.1 Portfolio analysis: Exclude the January effect
This table presents four-factor alphas on value-weighted basis of portfolios of stocks sorted on PT, PW, and LA following different sentiment periods in Panel A and Panel B, respectively. Each month, all stocks in the CRSP sample are sorted on the portfolios based on the corresponding prospect theory value. Then I sort the whole period into low and high levels of investor sentiment, classified based on the median level of Baker and Wurgler’s (2006) sentiment index. I report the four-factor alpha for each of the 10 decile portfolios and long the decile 1 portfolio and short the decile 10 portfolio. The sample period runs from September 1965 to December 2016 but excludes Januarys to control the January Effect. t-statistics appear in parentheses.
1 2 3 4 5 6 7 8 9 10 1-10
Panel A: Low sentiment
PT 0.478 -0.057 0.204 0.180 0.135 0.115 -0.019 -0.072 0.100 -0.072 0.549 (1.69) (-0.32) (1.44) (1.60) (1.15) (1.21) (-0.20) (-0.84) (1.13) (-0.80) (1.87) PW 0.246 0.082 0.029 0.158 0.089 -0.087 -0.097 0.063 0.275 0.104 0.142 (1.41) (0.74) (0.29) (1.56) (0.88) (-0.86) (-0.87) (0.50) (1.63) (0.42) (0.44) LA 0.566 0.076 0.210 0.071 0.268 0.083 0.054 0.067 0.056 -0.052 0.618 (1.69) (0.37) (1.34) (0.54) (2.36) (0.85) (0.64) (0.69) (0.61) (-0.59) (1.79) Panel B: High sentiment
PT 0.112 -0.058 0.262 0.365 0.092 0.201 0.317 0.114 0.029 -0.114 0.227 (0.48) (-0.31) (1.75) (2.61) (0.74) (1.83) (3.47) (1.19) (0.32) (-1.08) (0.84) PW 0.201 0.400 0.359 -0.015 0.081 -0.066 0.036 0.029 -0.019 -0.570 0.771 (1.21) (3.88) (3.30) (-0.16) (0.77) (-0.59) (0.28) (0.19) (-0.10) (-2.58) (2.66) LA -0.378 -0.196 0.118 0.183 0.199 0.235 0.238 0.121 0.027 0.013 -0.390 (-1.50) (-0.99) (0.65) (1.17) (1.49) (2.08) (2.53) (1.29) (0.27) (0.13) (-1.40)
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Table D.1 Fama-MacBeth regressions using different return distribution
This table presents the results of Fama-MacBeth (1973) regression analyses of the relation between the percentage return and prospect theory value that contains various components. I use monthly returns over the previous three or four years as a stock’s past return distribution in Panel A and Panel B. PT is the prospect theory value of a stock’s historical return distribution, containing the following components: diminishing sensitivity, loss aversion, and probability weighting. PW and LA is the prospect theory value of a stock’s historical return distribution, consisting of probability weighting and loss aversion, respectively. I report the results in the low- sentiment periods and the high-sentiment periods, the classification point of which is the median of Baker and Wurgler’s (2006) sentiment index. I standardize the independent variables to have a mean of zero and a standard deviation of one for easy comparison across different specifications. The sample period runs from September 1965 to December 2016.
t-statistics are Newey-West adjusted with six lags and appear in parentheses. The row labelled "Adj. R2" reports the average adjusted r-square of each regression. The row labelled "n" reports the average number of stocks in each regression.
Panel A: 3 years
Variable PT PW LA PT PW LA
Low sentiment High sentiment
Component -0.229 -0.100 -0.264 -0.048 -0.177 0.043 (-2.19) (-1.06) (-1.95) (-0.61) (-3.13) (0.42) Rev -0.908 -0.939 -0.901 -0.790 -0.772 -0.808 (-8.49) (-8.60) (-8.47) (-9.84) (-9.75) (-9.95)
Mom 0.491 0.418 0.483 0.422 0.482 0.374
(4.43) (3.51) (4.26) (5.28) (6.60) (4.39) Ltrev -0.243 -0.304 -0.215 -0.070 -0.047 -0.097 (-3.73) (-4.19) (-3.14) (-1.75) (-1.07) (-2.44) Size -0.387 -0.442 -0.362 -0.172 -0.216 -0.175 (-4.04) (-4.60) (-3.81) (-2.18) (-2.71) (-2.28)
BM 0.105 0.106 0.109 0.158 0.136 0.164
(1.41) (1.46) (1.47) (2.74) (2.45) (2.83) Beta 0.260 0.311 0.222 -0.036 -0.006 -0.030 (2.03) (2.22) (1.85) (-0.37) (-0.05) (-0.31)
Ilq 0.506 0.543 0.501 0.476 0.477 0.478
(2.22) (2.35) (2.21) (2.86) (2.92) (2.94)
Max 0.160 0.161 0.162 -0.092 -0.079 -0.101
(1.53) (1.56) (1.55) (-0.90) (-0.77) (-1.00) Min -0.426 -0.375 -0.427 -0.468 -0.452 -0.464 (-4.74) (-4.21) (-4.70) (-6.35) (-6.20) (-6.34)
Svar 0.843 0.720 0.845 0.082 0.075 0.067
(2.71) (2.32) (2.71) (0.74) (0.69) (0.61) Resd -0.381 -0.328 -0.413 -0.095 -0.078 -0.057 (-2.22) (-1.93) (-2.48) (-0.60) (-0.46) (-0.38) Adj. R2 0.079 0.078 0.080 0.066 0.066 0.068
n 2182 2182 2182 2577 2577 2577
Panel B: 4 years
Variable PT PW LA PT PW LA
Low sentiment High sentiment
Component -0.301 -0.102 -0.377 -0.058 -0.179 0.037 (-2.73) (-0.98) (-2.48) (-0.69) (-2.94) (0.32)
Continued on next page
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Table D.1 – Continued from previous page
Variable PT PW LA PT PW LA
Low sentiment High sentiment
Rev -0.902 -0.941 -0.894 -0.784 -0.774 -0.802 (-8.46) (-8.69) (-8.44) (-9.89) (-9.79) (-10.04)
Mom 0.500 0.411 0.493 0.431 0.477 0.389
(4.51) (3.44) (4.36) (5.65) (6.82) (4.71) Ltrev -0.185 -0.289 -0.140 -0.069 -0.037 -0.110 (-2.54) (-3.73) (-1.63) (-1.77) (-0.83) (-2.57) Size -0.382 -0.454 -0.342 -0.172 -0.221 -0.176 (-3.97) (-4.72) (-3.60) (-2.21) (-2.74) (-2.38)
BM 0.112 0.107 0.119 0.162 0.142 0.168
(1.51) (1.48) (1.60) (2.81) (2.55) (2.93)
Beta 0.274 0.322 0.239 -0.035 0.001 -0.026
(2.08) (2.28) (1.94) (-0.35) (0.01) (-0.27)
Ilq 0.521 0.551 0.509 0.473 0.474 0.474
(2.27) (2.37) (2.26) (2.85) (2.93) (2.93)
Max 0.156 0.162 0.159 -0.098 -0.080 -0.107
(1.49) (1.56) (1.53) (-0.95) (-0.77) (-1.05) Min -0.426 -0.378 -0.427 -0.466 -0.449 -0.464 (-4.73) (-4.21) (-4.71) (-6.30) (-6.11) (-6.35)
Svar 0.841 0.728 0.832 0.077 0.069 0.063
(2.67) (2.36) (2.64) (0.69) (0.63) (0.57) Resd -0.393 -0.325 -0.433 -0.088 -0.082 -0.046 (-2.29) (-1.92) (-2.63) (-0.55) (-0.48) (-0.31) Adj. R2 0.079 0.078 0.081 0.066 0.066 0.068
n 2182 2182 2182 2577 2577 2577
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Table E.1 Fama-MacBeth regressions using different sentiment indexes
This table presents the results of Fama-MacBeth (1973) regression analyses of the relation between the percentage return and prospect theory value that contains various components. PT is the prospect theory value of a stock’s historical return distribution that contains the following components: diminishing sensitivity, loss aversion, and probability weighting. PW and LA is the prospect theory value of a stock’s historical return distribution, consisting of probability weighting and loss aversion, respectively. I report the results in the low sentiment periods and the high sentiment periods. In Panel A, the classification point is the median of the average for the past three months’
Baker and Wurgler’s (2006) sentiment index. In Panel B, the classification point is the median of the investor sentiment index aigned with Huang, Jiang, Tu, and Zhou (2015). In Panel C, the classification point is the median of economic policy uncertainty index. I standardize the independent variables to have a mean of zero and a standard deviation of one for easy comparison across different specifications. The sample period runs from September 1965 to December 2016 in Panel A and Panel B and from January 1985 to December 2016 in Panel C. t-statistics are Newey-West adjusted with six lags and appear in parentheses. The row labelled "Adj. R2" reports the average adjusted r-square of each regression. The row labelled "n" reports the average number of stocks in each regression.
Panel A: Average for the past three months’ sentiment index
Variable PT PW LA PT PW LA
Low sentiment High sentiment
Component -0.369 -0.147 -0.499 -0.129 -0.252 -0.004 (-3.03) (-1.36) (-2.96) (-1.44) (-3.36) (-0.03) Rev -0.904 -0.938 -0.892 -0.789 -0.792 -0.803
(-8.47) (-8.62) (-8.37) (-9.99) (-9.94) (-10.17)
Mom 0.474 0.387 0.478 0.480 0.510 0.434
(4.30) (3.35) (4.14) (6.35) (7.03) (5.40) Ltrev -0.109 -0.261 -0.032 -0.014 0.006 -0.075 (-1.29) (-3.48) (-0.30) (-0.33) (0.13) (-1.43) Size -0.332 -0.429 -0.273 -0.179 -0.259 -0.186
(-3.54) (-4.45) (-2.98) (-2.26) (-3.19) (-2.47)
BM 0.129 0.106 0.141 0.166 0.138 0.172
(1.78) (1.47) (1.93) (2.88) (2.49) (3.01)
Beta 0.227 0.287 0.179 -0.013 0.047 -0.002
(1.76) (2.04) (1.52) (-0.13) (0.46) (-0.02)
Ilq 0.670 0.668 0.665 0.382 0.384 0.380
(2.80) (2.80) (2.85) (4.11) (4.24) (4.17)
Max 0.189 0.198 0.200 -0.092 -0.080 -0.101
(1.87) (1.95) (1.96) (-0.83) (-0.72) (-0.92) Min -0.391 -0.344 -0.385 -0.485 -0.461 -0.481
(-4.45) (-3.86) (-4.38) (-6.38) (-6.06) (-6.39)
Svar 0.613 0.559 0.577 0.149 0.112 0.155
(1.99) (1.80) (1.88) (1.19) (0.90) (1.31) Resd -0.448 -0.376 -0.508 -0.102 -0.053 -0.064 (-2.55) (-2.17) (-3.05) (-0.60) (-0.30) (-0.40)
Adj. R2 0.079 0.078 0.081 0.066 0.066 0.068
n 2179 2179 2179 2587 2587 2587
Panel B: Aligned investor sentiment index
Variable PT PW LA PT PW LA
Low sentiment High sentiment
Component -0.308 -0.073 -0.421 -0.199 -0.323 -0.096 (-2.84) (-0.75) (-2.76) (-1.83) (-3.74) (-0.61) Rev -0.778 -0.809 -0.771 -0.897 -0.904 -0.906
(-7.45) (-7.66) (-7.43) (-11.26) (-11.16) (-11.24) Continued on next page
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Table E.1 – Continued from previous page
Variable PT PW LA PT PW LA
Low sentiment High sentiment
Mom 0.496 0.413 0.507 0.471 0.493 0.419
(5.19) (4.43) (5.10) (5.23) (5.81) (4.29) Ltrev -0.068 -0.210 -0.001 -0.058 -0.056 -0.105 (-0.90) (-3.00) (-0.01) (-1.06) (-0.90) (-1.64) Size -0.312 -0.381 -0.265 -0.197 -0.305 -0.191
(-3.41) (-4.13) (-2.97) (-2.18) (-3.32) (-2.23)
BM 0.173 0.159 0.187 0.128 0.091 0.133
(2.93) (2.73) (3.19) (1.79) (1.31) (1.86)
Beta 0.281 0.324 0.249 -0.056 0.022 -0.062
(2.58) (2.76) (2.51) (-0.50) (0.18) (-0.60)
Ilq 0.688 0.683 0.685 0.307 0.312 0.307
(2.69) (2.66) (2.76) (3.29) (3.44) (3.36)
Max 0.196 0.202 0.200 -0.137 -0.125 -0.138
(1.99) (2.05) (2.04) (-1.37) (-1.25) (-1.39) Min -0.401 -0.364 -0.394 -0.499 -0.469 -0.495
(-4.56) (-4.05) (-4.45) (-6.69) (-6.40) (-6.75)
Svar 0.556 0.498 0.500 0.336 0.303 0.351
(1.90) (1.69) (1.74) (2.17) (1.95) (2.35) Resd -0.378 -0.308 -0.416 -0.133 -0.072 -0.120 (-2.18) (-1.77) (-2.53) (-0.79) (-0.41) (-0.76)
Adj. R2 0.066 0.065 0.068 0.080 0.079 0.081
n 2562 2562 2562 2199 2199 2199
Panel C: Policy uncertainty index
Variable PT PW LA PT PW LA
Low uncertainty High uncertainty Component -0.053 -0.159 0.024 -0.443 -0.271 -0.500
(-0.75) (-2.63) (0.18) (-2.75) (-3.10) (-2.17) Rev -0.464 -0.465 -0.476 -0.755 -0.776 -0.744
(-5.01) (-4.92) (-5.13) (-7.30) (-7.38) (-7.28)
Mom 0.520 0.554 0.493 0.322 0.246 0.298
(6.12) (6.98) (5.40) (2.63) (1.64) (2.38)
Ltrev -0.002 0.023 -0.035 0.056 -0.089 0.092
(-0.03) (0.42) (-0.53) (0.84) (-1.23) (1.01) Size -0.155 -0.209 -0.162 -0.150 -0.286 -0.084 (-1.65) (-2.33) (-2.02) (-1.76) (-3.10) (-0.90)
BM 0.118 0.095 0.122 0.186 0.165 0.211
(1.45) (1.25) (1.52) (2.90) (2.67) (3.13)
Beta -0.099 -0.066 -0.088 0.419 0.504 0.374
(-0.75) (-0.51) (-0.73) (2.76) (2.89) (2.73)
Ilq 0.655 0.658 0.660 0.240 0.235 0.229
(4.01) (4.03) (4.04) (2.90) (2.82) (2.75)
Max -0.015 -0.003 -0.024 0.129 0.139 0.127
(-0.12) (-0.02) (-0.19) (0.94) (0.99) (0.93) Min -0.540 -0.529 -0.535 -0.440 -0.376 -0.436 (-6.01) (-5.90) (-5.90) (-3.98) (-3.42) (-3.94)
Svar 0.349 0.333 0.333 0.464 0.420 0.479
(2.55) (2.47) (2.47) (4.02) (3.69) (4.08) Resd -0.220 -0.197 -0.178 -0.327 -0.234 -0.375 (-1.01) (-0.90) (-0.87) (-1.47) (-1.01) (-1.78)
Adj. R2 0.051 0.050 0.052 0.062 0.060 0.063
n 3203 3203 3203 2928 2928 2928
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Table F.1 Fama-MacBeth regressions that vary the value of probability weighting
This table presents the results of Fama- MacBeth (1973) regression analyses of the percentage return on PT and PW that varies with the degree of probability weighting. I change the values of the parameters γ and δ used to construct the PT or PW. Other control variables are defined in Tabel 3. I sort the sample period into low and high levels
This table presents the results of Fama- MacBeth (1973) regression analyses of the percentage return on PT and PW that varies with the degree of probability weighting. I change the values of the parameters γ and δ used to construct the PT or PW. Other control variables are defined in Tabel 3. I sort the sample period into low and high levels