投資者情緒與展望理論效應 - 政大學術集成

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(1)國立政治大學財務管理學系研究所博士論文. 政治大. 立 and Prospect Theory Effect Investor Sentiment ‧. ‧ 國. 學 er. io. sit. y. Nat. n. 指導教授：岳夢蘭博士 a. iv l C n U h e n陳鴻毅 g c h i 博士. 研究生：韓. 靖撰. 中華民國一百零九年六月. DOI:10.6814/NCCU202001429.

(2) INVESTOR SENTIMENT AND PROSPECT THEORY EFFECT. By. 政治大. HAN, JING. 立. ‧. ‧ 國. 學. ADVISOR: YUEH, MENG-LAN ; CHEN, HONG-YI. n. er. io. sit. y. Nat. al. Ch. engchi. i n U. v. A dissertation submitted in partial fulfillment of the requirements for the degree of DOCTOR OF FINANCE. NATIONAL CHENGCHI UNIVERSITY Department of Finance JUNE 2020 c Copyright by HAN, JING, 2020. All Rights Reserved. DOI:10.6814/NCCU202001429.

(3) ACKNOWLEDGMENT. I would like to express my deep appreciation to my PhD supervisors, Dr. Meng-Lan Yueh and Hong-Yi Chen. Dr. Yueh’s attainments in financial engineering make me grasp the quintessence of financial economic models and lay a solid academic foundation for me, a former “layman” in the financial field. Dr. Chen imparts his research skills and experience in the field of mutual funds to me unreservedly. I also have to thank the members of my PhD. 政治大. committee, Dr. Robin K. Chou, Yao-Min Chiang, Kuan-Cheng Ko for their helpful advice. 立. and suggestions on my PhD dissertation.. ‧ 國. 學. Furthermore, I am grateful for my parents and other family members who have supported me along the way and helped me financially and emotionally. I also would like to express. ‧. my deep gratitude to those friends who live by my side every day and give me professional. y. Nat. sit. support: Li-Xin Huang, Ding-Yuan Chen, Yi-Kang Ho, and Kivi Zhang.. a. er. io. Also I thank my beloved, Wang Ting, your presence is the best of luck in my life. You. n. i v you can I become complete. seem to be a part of me that never wakes l up before, and only with. n U i e h n c to Kwang-Hua Scholarship jointly esMore importantly, a very special gratitudeggoes. Ch. tablished by the Kwang-Hua Education Foundation and National Chengchi University for helping and providing the funding throughout my PhD career. Last but not least, I deliver my heartfelt thanks to National Chengchi University, along with its pleasant natural scenery. I have spent six years of my life in this charming university for both my master and doctoral degrees. The theoretical framework of this dissertation popped out of my mind in the way of Wind and Rain Corridor to the Art and Culture Center.. ii DOI:10.6814/NCCU202001429.

(4) INVESTOR SENTIMENT AND PROSPECT THEORY EFFECT. Abstract. by Han, Jing National Chengchi University June 2020. 政治大 Advisor: Yueh, Meng-Lan ; Chen, Hong-Yi 立. ‧ 國. 學. In prospect theory the value function of a stock, which consists of probability weighting,. ‧. loss aversion, and concavity/convexity, is negatively related to its expected return. In this. sit. y. Nat. paper, I find the effect of probability weighting or loss aversion on stock returns varies with. er. io. investor sentiment levels. Specifically, probability weighting plays the most important role. n. in predicting stock returns following a high-sentiment periods, but v investors tend to overvalue. i l C n U stocks with high probability weighting.hLoss aversion stock returns following low eng c h i predicts sentiment periods, but stocks with low loss aversion are undervalued. After examining the characteristics of stocks, I suggest that stocks with high probability weighting are those with high past average returns, high maximum, and high skewness, resembling lottery-type stocks attractive to investors during high-sentiment periods; stocks with low loss aversion have low past average returns, low minimum, and high volatility, which are unappealing to investors during low-sentiment periods.. iii DOI:10.6814/NCCU202001429.

(5) TABLE OF CONTENTS Page ACKNOWLEDGMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. ii. ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. iii. 政治大. LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 立. LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 學. ‧ 國. vi viii. 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1. 2 Prospect Theory and Investor Sentiment . . . . . . . . . . . . . . . . . .. 8. ‧. 8. 2.2 Prospect theory value based on a stock’s historical return . . . . . . . . .. 9. 2.3 Investor sentiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12. er. io. sit. y. Nat. 2.1 Prospect theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3 Data and Variable Definitions . . . . . . . . . . . . . . . . . . . . . . . . .. 15. C hResults . . . . U. n. . . . . . . . . . . . . . . . 4 Methodology and Empirical. 18. 4.1 Summary statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 18. 4.2 Portfolio analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 20. 4.3 Fama-MacBeth tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 27. 4.4 Limits to arbitrage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 34. 4.5 Double sorts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 36. 4.6 Construction of long-short portfolio returns . . . . . . . . . . . . . . . . .. 40. 4.7 Time-varying prospect theory effect . . . . . . . . . . . . . . . . . . . . .. 41. 4.8 Characteristics of prospect theory portfolios . . . . . . . . . . . . . . . .. 47. 5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 53. REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 55. n. al. engchi. iv. APPENDIX iv DOI:10.6814/NCCU202001429.

(6) A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 61. B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 64. C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 66. D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 67. E. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 69. F. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 71. G . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 75. H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 77. I J. 政治大 . . . . . . . . . . . . . .立 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 80 81. ‧. ‧ 國. 學. K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 79. n. er. io. sit. y. Nat. al. Ch. engchi. i n U. v. v DOI:10.6814/NCCU202001429.

(7) LIST OF TABLES 4.1. Data Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 19. 4.2. Portfolio analysis: Value-weighted . . . . . . . . . . . . . . . . . . . . . . . .. 21. 4.3. Fama-MacBeth regression analysis: PT . . . . . . . . . . . . . . . . . . . . .. 4.4. Fama-MacBeth regression analysis: PW. 4.5. Fama-MacBeth regression analysis: LA . . . . . . . . . . . . . . . . . . . . .. 31. 4.6. Fama-MacBeth regressions using different elements of prospect theory . . . .. 33. 4.7. Fama-MacBeth analysis of limits to arbitrage. 35. 4.8. Double sorts: Value-weighted . . . . . . . . . . . . . . . . . . . . . . . . . .. 4.9. The constitution of long-short l portfolio returns. 立. 政治大. . . . . . . . . . . . . . . . . . . . .. ‧. ‧ 國. 學. n. a. Ch. engchi. 30. 37. er. io. sit. y. Nat. . . . . . . . . . . . . . . . . .. 28. . .i n U. v.. . . . . . . . . . . . . .. 40. 4.10 Prospect theory portfolios during periods of low and high investor sentiment: Excess returns and benchmark-adjusted returns on long-short portfolios . . .. 42. 4.11 Prospect theory value and investor sentiment (level): Predictive regressions for excess returns and benchmark-adjusted returns on long-short portfolios .. 45. 4.12 Characteristics of different prospect theory value portfolios . . . . . . . . . .. 49. A.1 Portfolio analysis: Equal-weighted . . . . . . . . . . . . . . . . . . . . . . . .. 61. B.1 Portfolio analysis: Fama-French . . . . . . . . . . . . . . . . . . . . . . . . .. 64. C.1 Portfolio analysis: Exclude the January effect . . . . . . . . . . . . . . . . .. 66. vi DOI:10.6814/NCCU202001429.

(8) D.1 Fama-MacBeth regressions using different return distribution . . . . . . . . .. 67. E.1 Fama-MacBeth regressions using different sentiment indexes . . . . . . . . .. 69. F.1 Fama-MacBeth regressions that vary the value of probability weighting . . .. 71. G.1 Fama-MacBeth analysis of limits to arbitrage. . . . . . . . . . . . . . . . . .. 75. H.1 Double sorts: Equal-weighted . . . . . . . . . . . . . . . . . . . . . . . . . .. 77. I.1. Prospect theory value and investor sentiment (indicator): predictive regressions for excess returns and benchmark-adjusted returns on long-short portfolios 79. J.1 Portfolio analysis: Average subsequent three months’ excess returns . . . . .. 立. 政治大. 80. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. i n U. v. vii DOI:10.6814/NCCU202001429.

(9) LIST OF FIGURES 4.1. Performance of deciles in different sentiment periods: Value-weighted . . . .. 25. 4.2. Return distribution over the past 60 months of long- and short- portfolio . .. 51. 政治大. A.1 Performance of deciles in different sentiment periods: Equal-weighted . . . .. 立. K.1 Return distribution over the past 60 months of long- and short- portfolio . .. 63 81. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. i n U. v. viii DOI:10.6814/NCCU202001429.

(10) Chapter One Introduction Behavior has been frequently considered in the model of asset prices. Although most previous. 政治大. models assume that investors evaluate risk using the expected utility hypothesis, prospect. 立. theory, proposed by Kaheman and Tversky in 1979 and modified into the cumulative prospect. ‧ 國. 學. theory in 1992, has been widely considered the most successful descriptive theory for investors’ attitudes toward risk in recent years. Despite its initial development in laboratory. ‧. settings, prospect theory has been successfully proven to explain some financial phenomena,. y. Nat. sit. including the pricing of skewed securities (N. Barberis and Huang, 2008), cross-section of. er. io. average stock returns (Conrad, Dittmar, and Ghysels, 2013; N. Barberis, Mukherjee, and. n. B. Wang, 2016), corporate bondareturns (Zhong and J. Wang, i v 2018), portfolio choice (He l. n U i e h n and Zhou, 2011), and IPO returns (Z. Wang etgal., c 2018) among others.. Ch. According to Barberis et al. (2016), prospect theory investors use a two-step procedure: representation and valuation. In representation they form a mental representation of the risk they are considering. Once they form the mental presentation of the gains and losses while taking the risk, they evaluate the representation based on the distribution of gains and losses. People regard past return distribution as a good and easily accessible proxy for the distribution of the stock’s future returns. In this case, investors’ mental representation of a stock is the distribution of the stock’s past returns (N. Barberis, Mukherjee, and B. Wang, 2016).. 1 DOI:10.6814/NCCU202001429.

(11) Barberis et al. (2016) use the distribution of five years of monthly returns as their stock market mental representation and calculate the prospect theory value, which consists of three elements: probability weighting, loss aversion, and concavity or convexity. They show that a high prospect theory value predicts a low subsequent return and that probability weighting is the decisive factor. Zhong and Wang (2018) apply this principle to the bond market, determining the PT value of a bond based on the historical distribution of its returns. In contrast with Barberis et al., their results suggest that loss aversion is the most important element and that probability weighting predicts only junk bonds, not investmentgrade bonds. Concavity or convexity play no important role in the stock or the bond market. 政治大 Actually, these three elements 立capture features of the investors’ prospect theory value,. (N. Barberis, Mukherjee, and B. Wang, 2016; Z. Wang et al., 2018).. ‧ 國. 學. but I cannot guarantee they always work together among all assets or under any market condition. Investors experience difficulty incorporating all these elements into a dynamic. ‧. framework and making investment decisions (N. Barberis and R. Thaler, 2003), and for. sit. y. Nat. various research objects, some features are important and some can be ignored. The two studies noted above differ from most others—Barberis and Huang (2008), for example—that. er. io. point out that probability weighting a explains mainly the pricing of a security’s skewness.. n. iv l C n (2018) provide a prospect perspective on Chinese IPOs and use the h etheory ngchi U. . Wang et al.. skewness-related measure to depict the motives for IPO investment and how they affect initial and long-run returns . Barberis and Huang (2001) suggest that a typical individual stock has a high average return and is excessively volatile in the economy and that investors are loss averse over the fluctuations of individual stocks . Moreover, according to Li and Yang (2013), diminishing sensitivity capturing concavity and convexity predicts a disposition effect, and loss aversion predicts the opposite, meaning that some features predict opposing results . Two characteristics distinguish behavioral asset pricing from traditional asset pricing. The first is the psychologically based prospect theory noted above, which is inconsistent with the assumption of expected utility in the traditional approach; and the other is sentiment. In 2 DOI:10.6814/NCCU202001429.

(12) traditional finance literature investor sentiment is considered negligible, but its proponents argue that investors are largely unbiased in their use of available information. However, since Baker and Wurgler’s (2006) use of a number of proxies to form a composite sentiment index showed that investor sentiment plays an important role in the cross-section of stock expected returns, many follow-up studies have also focused on the important role of market sentiment—not only investor sentiment but also manager sentiment, media sentiment, and more (Baker and Wurgler, 2006; Stambaugh, Yu, and Yuan, 2012; Antoniou, Doukas, and Subrahmanyam, 2016; Zhu et al., 2017; Jiang et al., 2019). For instance, Baker and Wurgler (2006) find that following a low sentiment period, the stocks that are difficult to value or. 政治大 each long-short strategy on 11 anomalies 立 or the short leg of each strategy is more profitable. arbitrage tend to earn relatively high subsequent returns. Stambaugh et al. (2012) show that. ‧ 國. 學. following high levels of sentiment. Evidence suggests that in the presence of market-wide sentiment, overpricing is more prevalent than underpricing and causes this phenomenon.. ‧. Antoniou et al. (2016) find that during optimistic periods unsophisticated, overconfident. sit. y. Nat. traders who prefer high beta stocks invest frequently, and during pessimistic periods such noise trading is reduced. Investors and investor behavior will change according to sentiment.. er. io. Previous literature has documented the close relationship between prospect theory and a. n. iv l C n Barberis and h Huang (2008) point e n g c h i U out that “cumulative prospect. skewness. For example,. theory investors exhibit a preference for (positive) skewness.” Barberis et al. (2016) also. find that the stock’s past skewness increases with its prospect theory value, attributing this phenomenon to probability weighting. Similar to the prospect theory value calculated by Barberis et al. (2016), positively skewed assets of the lottery type often subsequently underperform (Kumar, 2009; Kumar, Page, and Spalt, 2011; Green and Hwang, 2012; Boyer and Vorkink, 2014). Moreover, Fong and Toh (2014) state that when sentiment is high, investors are likely to increase their preferences for lottery-like stocks .1 Because the role of 1. According to Blau (2017) negative return premia for stocks with the highest skewness are driven primarily by high investor sentiment when investors assign higher probabilities to lottery-like stock returns . Lin (2019) also finds that lottery-like stocks, which have high skewness, are associated with sentiment-. 3 DOI:10.6814/NCCU202001429.

(13) skewness in investor psychology is affected by sentiment, whether or not the role of prospect theory value will change as a result of the volatility of market sentiment is of interest. As contended in psychology literature, individuals overweight the probability of observing favorable (unfavorable) outcomes during positive (negative) sentiment periods (Johnson and Tversky, 1983; Mayer et al., 1992; Lerner and Keltner, 2000; Lerner and Keltner, 2001)2 , When probability weighting is more strongly correlated with lottery-like demand and the loss aversion element is more associated with negative outcomes 3 , do the elements of prospect theory value play a role in different sentiment periods? Meanwhile, is mispricing the result of overreaction or underreaction?. 政治大 timent periods. I first calculate the 立complete prospect theory value using all three elements In this paper, I examine the predictive power of prospect theory following different sen-. ‧ 國. 學. (PT) and then decompose the prospect theory into two elements: probability weighting and loss aversion. I ignore diminishing sensitivity (concavity and convexity) because it has. ‧. been proven insignificant in both stock and bond markets. That is to say, for probability. sit. y. Nat. weighting-related prospect theory value (PW), I turn off loss aversion and concavity and. io. er. convexity; and for loss aversion-related prospect theory value (LA), I turn off probability weighting and concavity and convexity. a. n. iv l C n or LAheffect operates U e n g c h i in pessimistic 4. The results suggest the PT. optimistic periods, and the PW effect. periods rather than. shows the opposite pattern. Regarding the PW. effect, previous literature usually associates the probability weighting feature of prospect theory with skewness, which represents the investor’s preference for lottery-type stocks, and shows that demand for lottery-like stocks drives these stocks to overvalue and thus they exhibit preference-induced underperformance more intensely during high investor sentiment 2. 3. 4. driven overpricing . For example, Lerner and Keltner (2000) point out that people who are fearful are prone to make pessimistic judgments of future events, consistent with the appraisal–tendency hypothesis. These fearful people are also likely to make risk-averse choices (Lerner and Keltner, 2001). Berkelaar and Kouwenberg (2009) find that in negative situations, investors who are loss averse are forced to sell stocks in order to avoid bankruptcy and eventually lead to market bust. PT, PW, or LA effect involves how the corresponding values affects the stock returns.. 4 DOI:10.6814/NCCU202001429.

(14) periods. Actually, probability weighting represents two aspects of investors’ demand: lotterytype and insurance-type demand. The former (latter) is represented by the high probability weight given by investors to extreme positive (negative) returns. To some extent, this result is consistent with previous literature. Regarding the PT or LA effect, PT and LA are highly correlated with each other (correlation coefficient: 0.89). Both of them are captured by the loss aversion element, and I find a significant and negative relation between the PT or LA and future stock returns following low sentiment periods. Guiso et al. (2018) find that both qualitative and quantitative measures of risk aversion exhibit large increases following crises because of perceived proba-. 政治大 stocks. They suggest that fear is立 a potential mechanism underlying financial decisions and. bilities and emotion-based changes in the utility function; as a result investors divest more. ‧ 國. 學. that it increases the salience of negative outcomes. During recessions, a “flight to quality” also occurs in equities; in other words investors will sell riskier stocks and prefer safer secu-. ‧. rities (Næs, Skjeltorp, and Ødegaard, 2011). I consider the following: during low sentiment. averse to this stock, thus leading to undervaluation.. er. io. sit. y. Nat. periods, the negative past returns of a stock would reduce its valuation and make investors. My finding is also related to the a forces of arbitrage; however, PT or LA and PW present. n. iv l C n The predictive power former for subsequent returns is stronger h eofnthe gchi U. different patterns.. among stocks that are difficult to arbitrage, which is consistent with Barberis et al. (2016); but the latter is not affected by the limits of arbitrage, and the effect of PW is even stronger on high-cap stocks. This evidence suggests how the transformation of sentiment changes the moderating effect of the limits of arbitrage on features of prospect theory value.. Because the PT or LA effect originates from investors’ fear of future negative return and the PW effect is mainly driven by the lottery-like demand, I expect investors to sell (buy) stocks with low PT or LA (high PW) during periods of low (high) investor sentiment, causing them to be undervalued (overvalued). Using portfolio analysis, I show that the average returns of a long (short) portfolio based on PT or LA (PW) mainly account for its 5 DOI:10.6814/NCCU202001429.

(15) average returns on a long-short portfolio following low (high) sentiment. Following Stambaugh et al. (2012), I also explore sentiment-related mispricing as a partial explanation for these prospect theory effects. The result reveals that the returns on the short leg of PW are significantly lower when sentiment is high, and the returns on the long leg of PT or LA are higher when sentiment is low but less significant. The time-series regressions also confirm a significant negative relation between the level of investor sentiment and the returns on the short leg or the long-short difference of PW. The relation between sentiment and the returns on the long leg or long-short difference of LA is negative but not significant. That is to say, the PW effect is sensitive to the change in sentiment but. 政治大 that short-sale is not so popular,立 and the disposition effect, indicating that with decreasing the LA effect is not. I attribute this phenomenon to the short-sale constraints, indicating. ‧ 國. 學. sentiment, loss aversion investors tend to keep the stocks until the sentiment drops to a low enough level. I refer to one extreme example: after the stock market crash, prices bounced. ‧. back strongly in the following few weeks, but loss aversion investors overreacted to panic. and Vishny, 1998; Berkelaar and Kouwenberg, 2009).. er. io. sit. y. Nat. selling by other investors in the extremely depressed market sentiment (Barberies, Shleifer,. Finally, I try to further understand why high PW stocks appeal to investors following a. n. iv l C n high sentiment and low PT or LA stocks following low sentiment. By depicting h are e naversive gchi U. the characteristics of stocks with different prospect theory features, I find that high PT stocks. 5. accompany high average past returns, high maximum, and high skewness. These. characteristics strongly resemble lottery stocks, which have been proven easily overvalued in high sentiment periods (N. Barberis and Huang, 2008; Kumar, 2009; Bali, Cakici, and Whitelaw, 2011; Fong and Toh, 2014; Hung and J. J. Yang, 2018). Low LA or PT stocks are those with low average past returns, low minimum, and high volatility. I use the idiosyncratic volatility to represent long-term volatility. The relation between idiosyncratic volatility and 5. A PT stock is one with the prospect theory value calculated by probability weighting, loss aversion, and concavity/convexity. Similarly, a PW (LA) stock is a stock with the prospect theory value calculated by probability weighting (loss aversion).. 6 DOI:10.6814/NCCU202001429.

(16) expected returns is mixed, documented in previous literature. My result is consistent with Yuan et al. (2015), who find that the idiosyncratic volatility–return relation is positive among underpriced stocks (Ang et al., 2006; Ang et al., 2009; Fu, 2009; Stambaugh, Yu, and Yuan, 2015). To some extent investors may be averse to this volatility risk, and their aversion leads to the undervaluation and high subsequent returns. Semivariance measures short-term volatility and downside risk. As Barberis et al. (2001) point out, investors are more loss averse after being burned by previous loss. I organize the reminder of the paper as follows: Section II introduces the prospect theory and stock market-wide investor sentiment. Section III describes the data and provides the. 政治大 of the role of market sentiment, 立 stock characteristics, and further examination.. definition of variables. Section IV presents the empirical results along with a discussion. ‧. ‧ 國. 學. io. sit. y. Nat. n. al. er. concludes the paper.. Section V. Ch. engchi. i n U. v. 7 DOI:10.6814/NCCU202001429.

(17) Chapter Two Prospect Theory and Investor Sentiment 2.1. Prospect theory. 立. 政治大. The portfolio choice model in an expected utility maximization framework assumes that. ‧ 國. 學. people are rational, uniformly risk averse, and capable of evaluating probabilities objectively; however, empirical and experimental evidence on attitudes toward risk have shown. ‧. that choices made by investors often deviate from those predicted by the expected utility. y. Nat. sit. paradigm. Consequently, scholars have developed alternative nonexpected utility models to. er. io. explain decision-making under uncertainty. Among them, the prospect theory of Kahne-. n. a l and Kahneman (1992),i v consistent with experimental man and Tversky (1979) and Tversky n U i e h n evidence, is the leading theory describing how g people c evaluate risk.. Ch. Prospect theory describes how people choose from among proposed options and how they determine the probability of those options. Under this descriptive theory of decisionmaking, people evaluate risk using a value function in place of a utility function and employ a probability weighting function to obtain transformed probabilities. The value function is concave (risk averse) over gains, convex (risk loving) over losses relative to some neutral reference point, and kinked at the origin. The S-shaped value function incorporates loss aversion, referring to the behavioral phenomenon that losing something feels worse than gaining the same thing feels good, that is, losses matter more than gains. Empirical estimates. 8 DOI:10.6814/NCCU202001429.

(18) of loss aversion are typically around 2, meaning that the pain of losing is psychologically about twice as powerful as the pleasure of gaining (Tversky and Kahneman, 1992). The probability weighting function nonlinearly transforms investors’ objective probability into subjective probability by assigning larger (lower) weight to low (high) probability events.. 2.2. Prospect theory value based on a stock’s historical return. I employ the model of Barberis et al. (2016) to construct a stock’s prospect theory value. 政治大. based on its past 60-month return. Specifically, given a certain stock, I calculate the stock’s. 立. return in excess of the market and then sort these sixty excess returns in increasing order.. ‧ 國. 學. I assume m of these returns are negative, and the remaining are non-negative. I denote the most negative return r−m and the second most negative return r−m+1 , and so on, through. ‧. the most positive return rn . Finally this process leads to a series of ri , where r is a monthly. Nat. er. io. sit. y. return in excess of the market and i is the subscript of it:. n. (r−m , π−m ; r−m+1 a , π−m+1; ...; r0, π0; ...; rn−1, πn−1; rn, πn),. iv l C n hengchi U. (2.1). which should be read as “ gain or lose r−m with probability π−m , r−m+1 with probability π−m+1 , and so on”, where r−m through r−1 are losses, r0 = 0, and r1 through rn are gains. The probability πi is calculated by the probability weighting function rather than the objective probability pi . The prospect theory value based on a stock’s historical return can be calculated as follows:. PT =. n X. v(ri )πi. (2.2). i=−m. 9 DOI:10.6814/NCCU202001429.

(19) where:. πi =.    w− ( i+m+1 ) − w− ( i+m ) −m ≤ i ≤ −1 60 60   w+ ( n−i+1 ) − w+ ( n−i ) 60 60. (2.3). 0≤i≤n. and where v(·) is known as the value function and w+ (·) and w− (·) as the probability weighting functions. The value function calculated for each return is follows:. v(r) =.    rα. r≥0. (2.4).   −λ(−r)α r < 0. 政治大. and the probability weighting functions are:. 立. pγ pδ − , w (p) = (pγ + (1 − p)γ )1/γ (pδ + (1 − p)δ )1/δ. (2.5). ‧. ‧ 國. 學. w+ (p) =. where α, γ, δ ∈ (0, 1) and λ > 1. In my assumption, p = 1/60 because each stock has 60. sit. y. Nat. months data.. er. io. The formulation of the prospect value in equations (2)-(5) contains five parameters, r,. n. α, λ, γ and δ,corresponding to afour vital elements: reference v dependence r, diminishing. i l C n sensitivity α, loss aversion λ and probability weighting heng c h i Uγ and δ (N. C. Barberis, 2013; N. Barberis, Mukherjee, and B. Wang, 2016). First, investors derive the value of the stock from gains and losses rather than final wealth levels. Gains and losses are measured relative to some reference point, this assumption is known as “ reference dependence”, developed by Kahneman and Tversky (Kahneman and Tversky, 1979; Tversky and Kahneman, 1992). As a result, the argument of v(·) in (2) is ri , not w(1 + ri ). The second element is diminishing sensitivity, which is represented by the parameter α and decides the value function’s concavity and convexity. In equation (4) I can see that the value function is concave over gains and convex over losses. Diminishing sensitivity implies that with the increasing of gains (losses), the positive (negative) marginal utility 10 DOI:10.6814/NCCU202001429.

(20) is decreasing (increasing). α is between 0 and 1. Smaller α is equivalent to larger concavity/convexity. While α = 1, the value function will be a linear function. According to Tversky and Kahneman (1992), estimated by experimental data, α = 0.88. Third, the loss aversion element, λ, implies that the investor is more sensitive to losses than to gains of the same magnitude. In Kahneman and Tversky’s inference, most people would turn down a gamble (-$100, 21 ; $110, 12 ) because the pain of losing $100 outweighs the pleasure of winning $110. The higher the value of λ, the more sensitive the investor is to losses. I use λ = 2.25 in my analysis estimated, by Tversky and Kahneman (1992). The forth and final element, probability weighting, is reflected in equation (3), w+ and. 政治大 First, investors weigh outcomes 立 by transformed probabilities or decision weights π , which. w− , for gains and losses, respectively. Three properties of this element require attention. i. ‧ 國. 學. is calculated as the difference between two cumulative probabilities instead of the objective probability p, which is equal to 1/60 for each outcome in my data. Compared to objective. ‧. probability, investors who use transformed probability tend to overweight unlikely extreme. sit. y. Nat. outcomes. Smaller γ and δ represent more overweighting of extreme outcomes. Second, investors overweights of the tails of any distribution they face implies both lottery and. er. io. insurance demand. For example, a investors typically prefer a gamble ($1000, 0.001) to a. n. iv l C n certain gain $1, which is a lottery-typehdemand, but also e n g c h i U prefer a certain loss of $1 to a gamble (-$1000, 0.001), which is a insurance-type demand. Third, equation (5) implies that for gains and losses, two different probability weighting parameters are γ and δ, respectively. Generally, δ is greater than γ because investors tend to weight losses relatively more than. gains in the case of loss aversion (Gonzalez and Wu, 1999; Tversky and Kahneman, 1992). Tversky and Kahneman (1992) estimate γ = 0.61 for gains and δ = 0.69 for losses. According to previous studies, parameters λ, γ, and δ play the most important role in explaining subsequent equity returns. Barberis et al. (2016) find that a stock whose past return distribution has a high (low) prospect theory value earns a low (high) subsequent returns on average. They adjust the values of the four parameters corresponding to con11 DOI:10.6814/NCCU202001429.

(21) cavity/convexity, loss aversion, and probability weighting, respectively, and find that while removing probability weighting from the variable representing prospect theory value and retaining the other features of prospect theory, the predictive power of the prospect theory variable drops markedly (N. Barberis, Mukherjee, and B. Wang, 2016). Zhong and Wang (2018) examine the predictive power of prospect theory in the corporate bond market, including junk bonds and investment-grade bonds, and obtain different conclusions: loss aversion plays the most important role in predicting the corporate bond returns despite the predictive power of probability weighting for only junk bonds. I can see that which element plays the largest the role depends on the specific asset type. 政治大 theory during different investor sentiment 立 periods. Thus, in this paper, the prospect theory. or the specific situation. I want to test the predictive power and mechanism of the prospect. ‧ 國. 學. value is divided into three categories: intact prospect theory value (PT), prospect theory value contains only probability weighting (PW), and prospect theory value contains only loss. ‧. aversion (LA). Specifically, PT contains all five parameters, r, α, λ, γ and δ; PW contains. sit. n. al Investor sentiment. er. io. 2.3. y. Nat. r, γ and δ; and LA contains r and λ.. Ch. engchi. i n U. v. Whether investor sentiment has impact on stock prices has been a question of longstanding interest to economists. Many empirical researchers in behavioral finance have suggested that investor sentiment can affect asset prices, especially for stocks that are hard to arbitrage and difficult to value (Baker and Wurgler, 2006; Baker and Wurgler, 2007). Some researchers also find that asset prices exhibit different patterns in high sentiment and low sentiment periods. For example, Yuan and Yu (2011) find that the stock market’s expected excess return is positively related to the market’s conditional variance in low sentiment periods but unrelated to variance in high sentiment periods. Stambaugh et al. (2012) consider overpricing more prevalent than underpricing as a result of short-sale impediments.. 12 DOI:10.6814/NCCU202001429.

(22) They find the anomalies are stronger or their long-short strategy is more profitable following high levels of sentiment. Shen et al. (2017) find that investors undermine the traditional risk–return trade-off, especially during high-sentiment periods. The phenomenon happens because of three channels through investor sentiment. First, investor sentiment drives the relative demand for speculative investments. This influence will cause cross-section effects. Second, investor sentiment appears as optimism or pessimism about stocks in general, which means it contains a time-varying market-wide element that could affect securities’ prices in the same direction. Of course, these two channels have overlapping effects even though I outline them separately. Together, they account for the main. 政治大 periods. Third, more sentiment 立 traders will appear in high-sentiment periods and because. reason for the pricing patterns of stock types in high-sentiment periods and low-sentiment. ‧ 國. 學. of short-sale impediments the relationship between return and other anomalies or variables will vary with sentiment level.. ‧. Many researchers also study how to measure investor sentiment. The sentiment index has. sit. y. Nat. been constructed by market liquidity (Baker and Stein, 2004), mutual fund flows (Brown et al., 2003; Ben-Rephael, Kandel, and Wohl, 2012), the Internet search behavior of households. er. io. (Da, Engelberg, and Gao, 2014), overnight returns (Aboody et al., 2018) among other factors. a. n. iv l C n In this paper, my sentiment index was created and Wurgler (BW; 2006). h e n gbycBaker hi U. The BW sentiment index is the monthly market-based sentiment series, spanning over 50. years from July 1965 to September 2015. It is constructed based on five proxies: the closedend fund discount, the number of initial public offerings, the average first day’s return of initial public offerings, the equity share in new issues, and the value-weighted dividend premium. In order to remove macroeconomic conditions from their composite index, prior to using the principal element analysis to isolate the common element from these six proxies, each of the proxies has first been orthogonalized with respect to a set of six macroeconomic indicators: industrial production index, nominal durables consumption, nominal nondurables consumption, nominal services consumption, NBER recession indicator, and employment. 13 DOI:10.6814/NCCU202001429.

(23) Thus, I will obtain cleaner proxies for investor sentiment, or orthogonalized proxies. Finally, the BW sentiment index is constructed based on the first principal element of the five (standardized) orthogonalized proxies. I use the BW sentiment index for three reasons. First, it synthesizes many indicator studies by numerous previous researchers (Lee, Shleifer, and R. H. Thaler, 1991; Ibbotson, Sindelar, and Ritter, 1994; Baker and Wurgler, 2000; Baker and Wurgler, 2004). The principal element analysis and orthogonalizing process of the proxy variables filter out idiosyncratic noise in the six measures and capture the common element that excludes a common business cycle element. Second, this index has been widely used in extensive studies (McLean and. 政治大 2011) and roughly aligns with anecdotal 立 accounts of fluctuations in sentiment.. M. Zhao, 2014; Shen, Yu, and S. Zhao, 2017; Stambaugh, Yu, and Yuan, 2012; Yu and Yuan, Third, the. ‧ 國. 學. BW sentiment index has a strong negative relationship with realizations in investors’ relative risk aversion, which is related to an important element of the prospect theory value (Y. Lin,. ‧. Lehnert, and Wolff, 2019).. n. er. io. sit. y. Nat. al. Ch. engchi. i n U. v. 14 DOI:10.6814/NCCU202001429.

(24) Chapter Three Data and Variable Definitions My key variables are the prospect theory value proposed by Tversky and Kahneman (1992). 政治大. and the sentiment index developed by Baker and Wurgler (2006). Specifically, my analysis. 立. includes all stocks in the CRSP universe from 1926 to 2017 for which the variable PT can. ‧ 國. 學. be calculated; that requires at least five years of monthly return data. I measure sentiment using the monthly index provided by Baker and Wurgler (2006). This index is available from. ‧. 1965 to 2016, so my sample covers the period from 1965 to 2016.. y. Nat. sit. I also consider two categories of control variables. One is related to firm characteristics,. er. io. including market capitalization (size), book-to-market ratio (BM ), momentum (Mom), pre-. n. a l reverse effect (LtRev ), and vious month return (Rev ), long-term i v stock illiquidity (Illiq). The. n U i e h n other is related to risk, including market betag(Beta), c idiosyncratic volatility (Ivol ), Max,. Ch. Min, skewness (Skew ), and semivariance (Svar ). Most of the variables measured on a return scale (PT, Mom, Rev, Ivol, Max, Min, Svar ) are recorded as percentages, which are scaled up by 100. Specifically, these control variables’ time t values are defined as follows. Size of a stock is the log of the month-end stock price times the number of shares outstanding in month t-1. BM is the log of the book value of equity of the stock divided by the market capitalization of the stock; following Bali, Engle, and Murray (2016), the book value of equity is defined as the book value of the stockholder’s equity plus deferred taxes and investment tax credit. 15 DOI:10.6814/NCCU202001429.

(25) minus the book value of preferred stock. The BM for the months t from June of year y through May of year y+1 is taken to be the book value of equity measured at the end of the fiscal year ending in calendar year y-1 divided by the market value of equity at the end of December of the calendar year y-1. Mom is defined as the stock’s cumulative return during the period from month t − 12 to t − 2 in order to control for the medium-term momentum effect (Jegadeesh and Titman, 1993). In order to take control of short-term reversal effect and long-term reversal effect, I define the Rev as the stock’s return in month t − 1 and define the Lt Rev as the stock’s cumulative return from month t − 60 to month t − 13, respectively. I calculate the Illiq for a stock as the average of the absolute return (decimal) divided by. 政治大 (Amihud, 2002). For each stock 立 i in month t − 1: D. Illiqi,t =. 1 X | Rd | D d=1 V OLDd. 學. ‧ 國. the dollar volume traded in the stock (in millions of dollars) using daily data in month t − 1. (3.1). ‧. where D is the number of trading days of stock i in month t − 1; Rd is stock i’s daily return;. y. Nat. io. sit. and V OLDd is the daily dollar volume on the associated day, calculated as the closing price. er. times the number of shares traded.. n. a. v. l C Beta is estimated byn ithe approach of running a oneFollowing Fama and French (1992),. hen. hi U. g c observations over the past five years. I factor model regression using monthly excess return calculate IVOL following Ang et al.(2006) as the standard deviation of the residuals from a Fama-French three factor regression using daily return data from month t−1. The regression specification is as follows:. ri,d = αi + βM KT,i M KTd + βSM B,i SM Bd + βHM L,i HM Ld + i,d. (3.2). where ri,d is the excess return of stock i on day d, and M KTd , SM Bd , and HM Ld are the returns of the market, size, and book-to-market factors, respectively, on day d.. 16 DOI:10.6814/NCCU202001429.

(26) Max and Min are computed as a stock’s maximum and minimum one-day return in month t − 1, as in Bali, Cakici, and Whitelaw (2011), respectively. I calculate Skew using previous five years worth of monthly return data. The semi-variance of a stock is calculated as follows: D. 1 X 1R <R (Rd − Rf,d )2 Semivar = D d=1 d f,d. (3.3). where D is the number of trading days in the month t − 1; Rd and Rf,d are the stock return and the risk-free rate on day d in the month t − 1, respectively; and 1Rd <Rf,d is an indicator. 治政 I measure sentiment using the monthly index provided大 by Baker and Wurgler (2006) from 立 Jeffrey Wurgler’s website. For calculating PT value, Size, Mom, Rev, Lt Rev, Illiq, Beta, function equal to one if Rd < Rf,d and zero otherwise.. ‧ 國. 學. Ivol, Max, Min, Skew, and Svar, I collect daily and monthly stock data from the CRSP. All. ‧. stocks should be with at least five years of monthly return data. Balance sheet data come from Compustat for which the variable BM can be calculated. Daily and monthly market. y. Nat. n. al. er. io. Kenneth French’s data library.. sit. excess returns, size factor, value factor, and the U.S. 1-month treasury-bill rates are from. Ch. engchi. i n U. v. 17 DOI:10.6814/NCCU202001429.

(27) Chapter Four Methodology and Empirical Results PT is calculated by three elements: probability weighting, represented by γ and δ; loss. 政治大. aversion, represented by λ; concavity/convexity, represented by α. When I calculate the. 立. initial PT, I use (γ, δ, λ, α)=(0.61, 0.69, 2.25, 0.88). To extract elements that combine the. ‧ 國. 學. PT for examining their roles during various sentiment periods, I turn off one or more features of prospect theory. Specifically, first, I retain probability weighting and turn off loss aversion. ‧. and concavity/convexity. In other words, I use (λ, α)=(1, 1) in place of (λ, α)=(2.25, 0.88);. y. Nat. sit. I call this prospect theory variable feature probability weighting PW. Similarly, I retain loss. n. using (γ, δ, λ)=(1, 1, 1) and callaitl CC.. er. io. aversion by using (γ, δ, α)=(1, 1, 1) and call it LA; and I retain diminishing sensitivity by. Ch. 4.1. engchi. i n U. v. Summary statistics. In Table 4.1, I present summary statistics for the variables used in this paper, during the period from September 1965 through December 2016. Panel A reports the mean (Mean), standard deviation (SD), minimum (Min), 25th percentile (25%), median (Median), 75th percentile (75%), and maximum (Max); Panel B reports the time-series averages of monthly cross-section correlations between these variables. I examine the correlations between the prospect theory value calculated using different. 18 DOI:10.6814/NCCU202001429.

(28) Table 4.1 Data Summary This table reports summary statistics for the variables used in my analysis. I calculate the mean (Mean), standard deviation (SD), minimum (Min), 25th percentile (25%), median (Median), 75th percentile (75%), and maximum (Max ) values of the cross-sectional distribution of each variable and the correlations among them in each month. Panel A presents the time-series averages for each cross-sectional value and Panel B presents the time-series averages of the monthly cross-sectional correlations between pairs of variables. PT is the prospect theory value of a stock’s historical return distribution that contains the following elements: diminishing sensitivity, loss aversion, and probability weighting. PW and LA is the prospect theory value of a stock’s historical return distribution, that consisting of probability weighting and loss aversion, respectively. Retp is the return in month t − 1. Mom is the 11-month cumulative return during months t − 12 through t − 2. LtRev is the 48-month cumulative return during months t − 60 through t − 13. Size is the natural log of market capitalization at the end of previous month. BM is the natural log of book-to-market ratio. Beta is the stock’s beta using five years of monthly return data. Ilq is Amihud’s (2002) measure of liquidity. Max and Min are the maximum and the negative of the minimum daily return in month t − 1, as in Bali, Cakici, and Whitelaw (2011). Svar is the semivariance of a stock in month t − 1. Ivol is the volatility of the stock’s daily idiosyncratic returns over month t − 1, as in Ang et al. (2006). Skew is the skewness of monthly returns over the previous five years. The sample period runs from September 1965 to December 2016.. 1.00 0.42 1.00 0.89 0.18 1.00 0.12 0.05 0.13 1.00 0.36 0.23 0.37 0.02 1.00 0.73 0.39 0.79 0.01 0.01 0.40 -0.21 0.55 0.08 0.19 -0.35 -0.32 -0.37 -0.10 -0.31 -0.14 0.31 -0.20 -0.02 -0.06 -0.38 0.15 -0.51 -0.07 -0.21 -0.31 0.27 -0.41 0.23 -0.15 -0.36 0.23 -0.45 -0.26 -0.14 -0.40 0.24 -0.50 -0.32 -0.16 -0.40 0.28 -0.51 0.01 -0.18 0.06 0.59 -0.26 -0.03 -0.01. 0.06 0.05 0.01 0.03 0.05 0.08 0.43. Svar Ivol Skew. 0.05 5.47 0.04 8.74 0.01 0.08 0.03 1.24 0.04 2.64 0.07 5.90 0.28 81.19. 0.02 0.55 0.02 0.77 0.00 -1.21 0.01 0.06 0.02 0.42 0.03 0.88 0.13 4.28. sit. LA Retp Mom LtRev. al. n. PW. io. PT. -0.45 1.15 3.00 1.01 0.61 10.36 -4.46 -0.34 0.00 -0.98 0.72 0.03 -0.40 1.08 0.19 0.08 1.50 1.22 3.95 3.47 108.28. ‧. 0.76 5.17 1.48 1.94 -0.91 0.15 -0.12 3.74 0.41 5.08 1.13 6.53 10.98 10.84. Ilq Max Min. 學. -0.06 0.02 -0.05 0.01 0.14 0.03 0.03 0.03 0.12 0.44 -0.22 -0.05 -0.19 -0.37 -0.76 -0.08 0.00 -0.06 -0.05 -0.13 -0.06 0.01 -0.04 0.00 0.07 -0.04 0.03 -0.03 0.07 0.31 0.18 0.39 0.04 0.62 2.90. Panel B: Correlations. PT PW LA Retp Mom LtRev Size BM Beta Ilq Max Min Svar Ivol Skew. LA Retp. y. PW. Nat. Mean SD Min 25% Median 75% Max. PT. ‧ 國. Statistic. 政治大 Mom 立 LtRev Size BM Beta. Ch. 1.00 0.32 -0.34 -0.04 -0.31 -0.21 -0.21 -0.23 -0.26 -0.12. Size. BM Beta. er. Panel A: Summary Statistics. n engchi U. 1.00 -0.35 1.00 -0.07 -0.11 1.00 -0.94 0.35 -0.01 -0.43 0.02 0.30 -0.46 0.07 0.30 -0.52 0.10 0.32 -0.58 0.09 0.30 -0.42 0.03 0.14. iv. Ilq Max Min. 1.00 0.39 0.42 0.48 0.54 0.39. 1.00 0.62 0.65 0.86 0.28. 1.00 0.95 0.81 0.27. Svar Ivol Skew. 1.00 0.86 1.00 0.31 0.34. 1.00. 19 DOI:10.6814/NCCU202001429.

(29) elements. Panel B indicates that PT and LA are highly positively correlated in the cross section, whereas the correlations between PW and LA are relatively low. This indicates that PT is similar to LA, and PW and LA represent two different aspects of mental representation: probability weighting and loss aversion. The correlations between the measure of prospect theory value and other stock-level characteristics show that PT, PW, and LA display different patterns. Specifically, PT and LA have a strong positive relation with measures of past returns (Mom, LtRev ) and a strong negative relation with a measure of past volatility (Ivol ), whereas PW is less positively related to LtRev and positively related to past volatility. High-PW stocks tend to have higher. 政治大 negative stock return (Min); but立 high-LA stocks represent an inverse pattern.. past skewness (Skew ), higher maximum positive stock return (Max ), and lower minimum PT or LA. ‧ 國. 學. stocks also tend to have higher market capitalizations. The correlation analyses also show a negative relation between PT or LA and book-to-market ratio (BM ), beta (Beta), and. ‧. illiquidity (Ilq); however, PW exhibits a converse relation with these variables. Preliminary. sit. y. Nat. evidence suggests that loss aversion captures mainly the effect of PT; PT, PW, and LA stocks have different return distributions; and different market cap categories probably explain the. er. io. various relations between PT, PW, a or LA and other stock-level characteristics. For example,. n. iv l C n small-cap stocks have less liquidity andhare more volatile. engchi U 4.2. Portfolio analysis. At the beginning of each month, I sort stocks into deciles based on PT, PW, LA, and CC. I then calculate the average value-weighted and equal-weighted return of each decile portfolio over the subsequent month. The excess return is the return in excess of the risk-free rate; the four-factor alpha is the return adjusted by the three factors from Fama and French 1993 and by a momentum factor; the five-factor alpha is the return adjusted by the three FamaFrench factors, the momentum factor, and the Pastor and Stambaugh (2003) liquidity factor. 20 DOI:10.6814/NCCU202001429.

(30) (Carhart, 1997; Fama and French, 1993; Pástor and Stambaugh, 2003). I perform univariate sort portfolio analyses based on PT, PW, LA, and CC to start my investigation of the cross-sectional relation between prospect theory values and expected stock returns. Each month, beginning in September 1965 and ending in December 2016, I sort all stocks in the sample into deciles based on an ascending sort of PT, PW, LA, and CC. I then calculate the average value-weighted return of each decile portfolio over the subsequent month and obtain time-series monthly returns of each decile. First, I compute the average return of each decile in the entire sample period, which I then I sort into low and high levels of investor sentiment 1 , classified based on the median level of Baker and. 政治大 two investor sentiment periods. I立 report the average value-weighted excess return for each of Wurgler’s (2006) sentiment index—and compute the average return in each decile over these. ‧ 國. 學. the ten decile portfolios as well as Carhart’s (1997) four-factor alpha and alpha of the fourfactor model augmented by the Pastor and Stambaugh (2003) liquidity factor in the sample. ‧. period and in the various sentiment periods in Table 4.2. I long the first decile portfolio and 2. sit. y. Nat. short the 10th decile portfolio, reporting the difference in the farthest right column.. n. al. er. io. Table 4.2 Portfolio analysis: Value-weighted. Ch. i n U. v. This table presents average monthly excess returns, four-factor alphas and five-factor alphas on the value-weighted basis of portfolios of stocks sorted on PT, PW, LA and CC in the sample period and the following sentiment periods in Panel A, Panel B, Panel C, and Panel D, 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 as 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 decile 10 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, where it 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 1.185 0.621 0.783 0.799 0.583 0.630 0.621 0.522 0.525 0.439 0.746 (3.20) (2.08) (3.16) (3.43) (2.80) (3.09) (3.38) (2.87) (2.98) (2.12) (1.76) Four-factor alpha 0.642 0.088 0.295 0.312 0.128 0.133 0.139 0.010 0.068 -0.117 0.759 (3.33) (0.68) (2.97) (3.54) (1.54) (1.78) (2.15) (0.17) (1.10) (-1.73) (3.64) Five-factor alpha 0.633 0.050 0.267 0.290 0.112 0.129 0.154 0.024 0.081 -0.124 0.757 Continued on next page 1. 2. engchi. I define low- (high-) sentiment period in time t as the sentiment index less (greater) than the median in time t − 1. I present the equal-weighted return and alpha in Table A.1 in Appendix A.. 21 DOI:10.6814/NCCU202001429.

(31) Four-factor alpha Five-factor alpha Panel B: Returns Excess return Four-factor alpha Five-factor alpha. Five factor alpha. Panel C: Returns Excess return Four-factor alpha Five-factor alpha. Excess return Four factor alpha Five factor alpha. Excess return. al. n. Five factor alpha. io. Four factor alpha. Nat. Excess return. 政治大. 0.603 0.447 0.238 (2.11) (1.30) (0.56) 0.061 -0.255 0.609 (0.49) (-1.55) (2.73) 0.044 -0.222 0.538 (0.34) (-1.30) (2.32) 1.227 (3.27) 0.285 (1.67) 0.299 (1.68). 1.362 -0.667 (2.92) (-1.08) 0.124 0.163 (0.50) (0.50) 0.199 0.053 (0.75) (0.15). -0.017 (-0.04) -0.091 (-0.50) -0.146 (-0.81). -0.463 1.138 (-0.92) (1.96) -0.576 0.955 (-2.79) (3.45) -0.568 0.912 (-2.73) (3.28). ‧. Four factor alpha. 0.353 0.164 0.576 (1.43) (0.53) (1.03) 0.033 -0.130 0.771 (0.37) (-1.31) (2.61) 0.042 -0.155 0.755 (0.46) (-1.56) (2.54). 學. Excess return. 立. 0.698 0.715 0.917 (2.78) (2.60) (1.44) 0.096 -0.060 0.740 (1.14) (-0.69) (2.49) 0.124 -0.048 0.742 (1.44) (-0.55) (2.37). y. Excess return. 9 10 1-10 (1.29) (-1.82) (3.52). sit. Five-factor alpha. er. Four-factor alpha. ‧ 國. Excess return. Table 4.2 – Continued from previous page 1 2 3 4 5 6 7 8 (3.16) (0.37) (2.60) (3.20) (1.32) (1.70) (2.34) (0.36) Low sentiment 1.632 0.786 0.938 0.845 0.692 0.710 0.566 0.514 (2.84) (1.72) (2.44) (2.40) (2.18) (2.31) (2.06) (1.90) 0.680 -0.030 0.266 0.189 0.103 0.102 -0.020 -0.082 (2.41) (-0.16) (1.92) (1.68) (0.89) (1.01) (-0.22) (-0.99) 0.694 -0.034 0.239 0.169 0.105 0.082 -0.008 -0.051 (2.31) (-0.17) (1.63) (1.44) (0.88) (0.81) (-0.08) (-0.60) High sentiment 0.740 0.456 0.630 0.752 0.474 0.551 0.675 0.529 (1.58) (1.19) (2.00) (2.46) (1.75) (2.04) (2.76) (2.17) 0.641 0.203 0.277 0.413 0.109 0.118 0.271 0.068 (2.41) (1.10) (1.97) (3.04) (0.92) (1.11) (3.07) (0.74) 0.600 0.130 0.260 0.389 0.092 0.139 0.285 0.063 (2.25) (0.71) (1.84) (2.85) (0.77) (1.31) (3.21) (0.69) of portfolios of stocks sorted on PW Whole periods 0.685 0.618 0.667 0.564 0.614 0.480 0.468 0.573 (2.76) (3.27) (3.68) (3.14) (3.28) (2.49) (2.16) (2.29) 0.353 0.206 0.190 0.088 0.074 -0.074 -0.105 0.014 (2.90) (2.74) (2.60) (1.24) (1.03) (-1.03) (-1.26) (0.14) 0.315 0.219 0.210 0.122 0.057 -0.057 -0.158 -0.008 (2.50) (2.88) (2.83) (1.69) (0.78) (-0.77) (-1.85) (-0.07) Low sentiment 0.695 0.514 0.640 0.710 0.777 0.654 0.695 0.885 (1.72) (1.74) (2.33) (2.65) (2.86) (2.39) (2.29) (2.74) 0.286 0.048 0.061 0.160 0.086 -0.060 -0.133 0.018 (1.65) (0.46) (0.61) (1.53) (0.86) (-0.61) (-1.21) (0.14) 0.252 0.057 0.086 0.223 0.080 0.000 -0.210 0.001 (1.37) (0.53) (0.84) (2.07) (0.78) (0.00) (-1.86) (0.00) High sentiment 0.674 0.720 0.694 0.419 0.453 0.307 0.243 0.262 (2.33) (3.06) (2.92) (1.75) (1.75) (1.13) (0.78) (0.69) 0.379 0.318 0.279 -0.033 0.035 -0.084 -0.048 0.046 (2.33) (3.20) (2.72) (-0.35) (0.35) (-0.79) (-0.39) (0.32) 0.344 0.335 0.301 -0.009 0.025 -0.108 -0.079 0.021 (2.11) (3.36) (2.92) (-0.10) (0.25) (-1.01) (-0.64) (0.14) of portfolios of stocks sorted on LA Whole periods 1.179 0.726 0.729 0.721 0.709 0.637 0.621 0.597 (3.00) (2.26) (2.56) (2.92) (3.21) (3.16) (3.22) (3.31) 0.554 0.172 0.203 0.191 0.262 0.173 0.126 0.060 (2.50) (1.20) (1.75) (1.93) (3.02) (2.34) (1.90) (0.93) 0.541 0.154 0.183 0.193 0.242 0.177 0.144 0.060 (2.34) (1.04) (1.53) (1.91) (2.75) (2.37) (2.11) (0.90) Low sentiment 1.981 1.089 0.979 0.817 0.855 0.664 0.643 0.655 (3.28) (2.19) (2.26) (2.16) (2.58) (2.16) (2.18) (2.44) 0.866 0.254 0.221 0.082 0.239 0.072 0.052 0.036 (2.58) (1.22) (1.42) (0.61) (2.07) (0.73) (0.57) (0.38) 0.900 0.240 0.234 0.119 0.237 0.083 0.078 0.047 (2.49) (1.09) (1.42) (0.86) (2.03) (0.85) (0.85) (0.48) High sentiment 0.382 0.365 0.481 0.627 0.565 0.609 0.600 0.539 Continued on next page. Ch. engchi. i n U. v. 0.539 0.477 0.702 (3.00) (2.39) (1.59) 0.022 -0.022 0.576 (0.34) (-0.35) (2.48) 0.021 -0.019 0.560 (0.31) (-0.30) (2.33) 0.683 0.671 1.310 (2.63) (2.51) (1.98) 0.058 -0.045 0.911 (0.66) (-0.54) (2.62) 0.058 -0.021 0.920 (0.64) (-0.25) (2.49) 0.396. 0.284. 0.097. 22 DOI:10.6814/NCCU202001429.

(32) Five factor alpha Panel D: Returns Excess return Four-factor alpha Five-factor alpha. Excess return Four-factor alpha Five-factor alpha. Excess return. Five-factor alpha. 學. Four-factor alpha. 立. 政治大. 9 10 (1.59) (0.96) -0.028 0.028 (-0.29) (0.31) -0.023 0.009 (-0.23) (0.10). 1-10 (0.17) 0.295 (0.96) 0.266 (0.86). 0.468 0.616 (2.18) (2.22) -0.079 0.087 (-0.98) (0.79) -0.128 0.075 (-1.58) (0.67). 0.199 (0.46) 0.216 (0.99) 0.175 (0.77). 0.710 1.034 (2.42) (2.92) -0.080 0.118 (-0.75) (0.82) -0.143 0.150 (-1.34) (1.01). 0.093 (0.15) 0.290 (0.97) 0.248 (0.78). 0.227 0.201 (0.73) (0.47) -0.067 0.116 (-0.57) (0.71) -0.095 0.056 (-0.80) (0.35). 0.304 (0.51) 0.108 (0.34) 0.072 (0.23). ‧. ‧ 國. Four factor alpha. Table 4.2 – Continued from previous page 1 2 3 4 5 6 7 8 (0.76) (0.89) (1.30) (1.96) (1.93) (2.33) (2.40) (2.23) 0.323 0.079 0.197 0.285 0.244 0.232 0.157 0.067 (1.11) (0.40) (1.13) (1.94) (1.89) (2.18) (1.70) (0.75) 0.276 0.055 0.143 0.252 0.223 0.232 0.175 0.060 (0.94) (0.28) (0.83) (1.71) (1.71) (2.16) (1.90) (0.66) of portfolios of stocks sorted on CC Whole periods 0.815 0.712 0.760 0.672 0.631 0.618 0.540 0.507 (2.42) (2.83) (3.69) (3.51) (3.39) (3.33) (2.86) (2.60) 0.303 0.269 0.270 0.184 0.128 0.064 -0.032 -0.033 (1.61) (2.26) (2.94) (2.15) (1.61) (0.81) (-0.43) (-0.43) 0.250 0.264 0.272 0.190 0.161 0.048 -0.044 -0.047 (1.27) (2.17) (2.92) (2.19) (1.98) (0.59) (-0.56) (-0.60) Low sentiment 1.127 0.766 0.683 0.701 0.637 0.773 0.743 0.732 (2.14) (1.83) (2.08) (2.33) (2.21) (2.76) (2.71) (2.66) 0.408 0.198 0.119 0.119 0.038 0.086 0.023 0.033 (1.56) (1.11) (0.91) (0.95) (0.32) (0.74) (0.23) (0.32) 0.398 0.214 0.116 0.129 0.096 0.072 0.008 0.024 (1.41) (1.16) (0.86) (1.00) (0.76) (0.62) (0.07) (0.23) High sentiment 0.505 0.658 0.836 0.643 0.625 0.463 0.338 0.284 (1.20) (2.34) (3.34) (2.71) (2.66) (1.91) (1.30) (1.03) 0.223 0.303 0.373 0.182 0.170 -0.002 -0.090 -0.121 (0.82) (2.03) (3.11) (1.66) (1.73) (-0.02) (-0.82) (-1.07) 0.128 0.293 0.388 0.202 0.190 -0.001 -0.081 -0.126 (0.47) (1.95) (3.22) (1.84) (1.92) (-0.01) (-0.73) (-1.10). io. sit. y. Nat. er. For portfolios formed by sorting on PT (PT portfolio), the average monthly excess returns. n. a. v. l Cof 0.917% in low sentiment of the value-weighted 1-10 portfolios n i periods or 0.576% in high. i U. he. gch sentiment periods per month are economicallynlarge but not statistically significant. However, the abnormal returns of the 1-10 portfolios relative to four- and five-factor models are positive and statistically significant. Changing from the four-factor model to the five-factor model does not much alter the alpha. I focus my discussion on the four-factor adjusted returns (FF4 alpha), the return adjusted by the three Fama-French factors and by a momentum factor. A strategy of buying low-PT stocks and shorting high-PT ones earns a very significant FF4 alpha of 0.740% (t-statistic=2.49) in low sentiment periods and 0.771% (t-statistic=2.61) in high sentiment periods, which is nearly 8.88% or 9.25% per annum. For portfolios formed by sorting on PW (PW portfolio), the excess return, the FF4. 23 DOI:10.6814/NCCU202001429.

(33) alpha, and the FF5 alpha (alphas relative to the four-factor model augmented with the liquidity factor) of the difference portfolio are not all statistically significant in low-sentiment periods. In contrast, in high-sentiment periods, they are all statistically significant and of economically important magnitude. The stocks in the lowest PW-decile, have a significantly positive FF4 alpha of 0.379% per month, and those in the highest PW-decile, have a negative alpha of −0.576%. The PW 1-10 portfolio produces an FF4 alpha of 0.955% per month (tstatistic=3.44), which is nearly 11.46% annually. The results of the portfolio analysis using LA as the sort variable run counter to the results generated by the PW-sorted portfolios. The relation between LA and expected stock. 政治大 the LA-sorted decile portfolios decreases, even though so not monotonically, from 0.866% 立. returns appears stronger in low investor sentiment periods. For example, the FF4 alpha of. ‧ 國. 學. per month for the first decile portfolio to −0.045% per month for the 10th decile portfolio. The difference in returns of 0.911% per month with a t-statistic of 2.62 is highly statistically. ‧. significant, which is over 10.93% per annum. Similar to the situation of PW portfolios in. sit. y. Nat. low sentiment periods, the excess return, the FF4 alpha, and the FF5 alpha of the LA 10-1 portfolio are all indistinguishable from zero in high sentiment periods.. er. io. In the sample period, the FF4 a alpha and the FF5 alpha on the PT/PW/LA long-short. n. iv l C n portfolio remain significant, and in terms they are approximately the average h eof nmagnitude, gchi U. of its corresponding value in two different sentiment periods. This result suggests the effect of prospect theory in the sample period is caused by its effect in different periods. For value-weighted portfolios formed by sorting on CC, no matter in the sample period, in lowsentiment periods, or in high-sentiment periods, the relation between CC and expected stock returns is insignificant, which is consistent with previous literature stating that diminishing sensitivity is not an important element in investors’ decisions on the stock market. Figure 4.1 reports a graphic view of the results in Table 4.2. It plots the value-weighted FF4 alphas on the ten PT-decile portfolios, ten PW-decile portfolios, and ten LA-decile portfolios in low- and high-sentiment periods in Figure 4.1a, Figure 4.1b, and Figure 4.1c, 24 DOI:10.6814/NCCU202001429.

(34) 立. 政治大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. i n U. v. Figure 4.1 Performance of deciles in different sentiment periods: Value-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 a value-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 by using the average of time-series returns following different periods. I plot the results in Figure 4.1. The Figure 4.1a is for PT; the Figure 4.1b is for PW; the Figure 4.1c is for LA. The vertical axis is the percentage monthly alpha; the horizontal axis represents the ten portfolios from low corresponding prospect theory value on the left to high on the right (decile 1 to decile 10).. 25 DOI:10.6814/NCCU202001429.

(35) respectively. Figure 4.1a shows that FF4 alphas decrease in both low- and high-sentiment periods but not monotonically. Meanwhile, the FF4 alphas of the PT 1-10 portfolio are driven mainly by the significant positive abnormal returns of the low-PT stocks. Figure 4.1b and Figure 4.1c show that the decreasing pattern of PW portfolios or LA portfolios exists only in high- sentiment periods or low-sentiment periods, respectively. These two figures make another clear point that the FF4 alphas of the PW 1-10 portfolio are driven mainly by the significant negative abnormal returns of the high-PT stocks, and the LA 110 portfolio entirely driven by the substantial positive returns of the low-LA stocks. The decreasing patterns of PT portfolios and LA portfolios are similar in low-sentiment periods,. 政治大 look in greater detail at the origin 立of the FF4 alphas of the long-short portfolio and examine. which may be attributed to the fact that PT and LA are highly correlated. Later, I will. ‧ 國. 學. whether overvaluation or undervaluation contributes mainly to the FF4 alphas. To sum up, Table 4.2 shows that probability weighting works mainly in high-sentiment. ‧. periods, reflecting negative abnormal returns of high-PW stocks; loss aversion works pri-. sit. y. Nat. marily in low-sentiment periods, indicating positive abnormal returns of low-LA stocks; and no matter in low- or high-sentiment periods, the PT 1-10 portfolio produces a positive FF4. er. io. alpha. However, applying a dynamic a strategy that holding the PW 1-10 portfolio in high-. n. iv l C n sentiment periods and the LA 1-10 portfolio periods generates the FF4 h e n ginclow-sentiment hi U alpha of 11.20% per annum. The magnitude is over 2% higher than 9.07%, the FF4 alpha of holding the PT 1-10 portfolio statically. 3. 3. I examine Fama-French three-factor alphas, Fama-French five-factor alphas, and six-factor alphas (+momentum factor) on the value-weighted basis of portfolios of stocks sorted on PT, PW, and LA following different sentiment periods in Table B.1 in Appendix B. If I consider only the Fama-French three-factor model or five-factor model, the results suggest that no matter PT, PW, or LA little effect on the return of long-short portfolio occurs. After adding the momentum factor, the six-factor alphas remain similar to the previous results, proving that the momentum factor is first, too pervasive and important to ignore and second, plays a vital role in the prospect theory effect.. 26 DOI:10.6814/NCCU202001429.

(36) 4.3. Fama-MacBeth tests. In this section, I employ the Fama-MacBeth methodology to test my main hypothesis. Each month in high-sentiment periods or low-sentiment periods, I run a cross-sectional regression of stock returns on PT-related variables measured at the beginning of that month and on control variables already known to predict stock returns, yielding the time-series average of the coefficient estimates on the independent variables. I then continue my investigation using the Fama-MacBeth regressions. This methodology allows control for all of the other predictors simultaneously while examining the predictive power of PT, PW, or LA.. 政治大. I begin my Fama-MacBeth technique using cross-section regression specifications that. 立. include prospect theory value (PT, PW, or LA) as the single independent variable. Then I. ‧ 國. 學. use prospect theory value along with considerable predictors of stock returns as independent variables, such as various measures of past performances (Rev, Mom, LtRev ), market capi-. ‧. talization (Size), book-to-market ratio (BM ), illiquidity (Illiq), and idiosyncratic volatility. y. Nat. sit. (Ivol ). Finally, I also add the skewness-related variables, such as maximum (Max ), minimum. a. er. io. (Min), and skewness (Skew ) as control variables. All of the independent variables are win-. n. sorized at the 0.5% level in the full lsample. I conduct the Fama-MacBeth regression analyses iv. n U i e h n g c 4.3, Table 4.4, and Table 4.5 report the in low and high sentiment periods separately. Table. Ch. time-series averages of the coefficients along with t-statistics, Newey-West adjusted with six lags. Table 4.3 presents the results of Fama-MacBeth regression analyses of the relation between PT and excess stock returns. In low sentiment periods, using the univariate specification, the analysis detects a robust negative relation between PT and one-month-lag stock excess return because the average coefficient of −0.134 is statistically significant with a tstatistic of −3.28. In column (2), I include some control variables, but this inclusion does not affect the predictive power of PT very much. The average coefficient of −0.104 is little. 27 DOI:10.6814/NCCU202001429.

(37) Table 4.3 Fama-MacBeth regression analysis: PT Table 4.3 to Table 4.5 present the results of Fama-MacBeth (1973) regression analyses of the relation between the percentage return and prospect theory value that includes different elements. PT is the prospect theory value of a stock’s historical return distribution that contains the following elements: diminishing sensitivity, loss aversion, and probability weighting. PW and LA constitute the prospect theory value of a stock’s historical return distribution, consisting of probability weighting and loss aversion, respectively. Rev is the return in month t − 1. Mom is the 11-month cumulative return during months t − 12 through t − 2. LtRev is the 48-month cumulative return during months t − 60 through t − 13. Size is the natural log of market capitalization at the end of the previous month. BM is the natural log of book-to-market ratio. Beta is the stock’s beta using five years of monthly return data. Ilq is Amihud’s (2002) measure of liquidity. Svar is the semivariance of a stock in month t − 1. Ivol is the volatility of the stock’s daily idiosyncratic returns over month t − 1, as in Ang et al. (2006). Max and Min are the maximum and the negative of the minimum daily return in month t − 1, as in Bali, Cakici, and Whitelaw (2011). Skew is the skewness of monthly returns over the previous five years. I sort the whole periods into low and high levels of investor sentiment, classified based on the median level of Baker and Wurgler’s (2006) sentiment index. PT, Rev, Mom, Ivol, Max, Min are scaled up by 100. Svar is scaled up by 10000. 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.. 政治大. 立. -0.104 (-3.23) -0.061 (-7.79) 0.010 (4.40) -0.056 (-1.14) -0.154 (-3.52) 0.122 (1.88) 0.379 (1.98) 0.048 (2.56) 0.022 (0.96) -0.164 (-2.46). -0.106 (-3.33) -0.065 (-8.32) 0.010 (4.57) -0.051 (-1.05) -0.164 (-3.73) 0.117 (1.80) 0.399 (2.09) 0.043 (2.25) 0.072 (2.69) -0.195 (-2.43) 0.024 (1.45) -0.096 (-4.90). -0.113 (-3.09) -0.065 (-8.29) 0.010 (4.49) -0.046 (-0.88) -0.153 (-3.53) 0.122 (1.89) 0.388 (2.11) 0.045 (2.34) 0.069 (2.59) -0.202 (-2.66) 0.024 (1.44) -0.096 (-4.95) 0.066 (0.97). -0.050 (-1.63). 0.081 2182. 0.011 2576. Nat. Mom. 5. LtRev. io. Size. al. n. BM Beta Ilq Svar Ivol Max Min. Ch. Skew Adj. R2 n. 0.016 2182. 0.077 2182. 0.079 2182. Skewness controls. 6. 7. 8. -0.022 (-0.96) -0.053 (-9.03) 0.008 (5.84) -0.035 (-1.33) -0.065 (-1.79) 0.157 (3.11) -0.103 (-0.71) 0.044 (3.28) -0.016 (-1.77) -0.190 (-4.26). -0.027 (-1.17) -0.056 (-9.83) 0.008 (6.10) -0.024 (-0.93) -0.072 (-1.98) 0.147 (2.94) -0.073 (-0.50) 0.039 (2.86) 0.007 (0.67) -0.050 (-0.65) -0.015 (-0.89) -0.105 (-6.30). -0.005 (-0.18) -0.057 (-9.87) 0.008 (5.97) -0.044 (-1.63) -0.098 (-2.83) 0.137 (2.78) -0.045 (-0.32) 0.040 (2.92) 0.007 (0.67) -0.028 (-0.37) -0.015 (-0.93) -0.106 (-6.39) -0.158 (-2.60). 0.064 2576. 0.067 2576. 0.068 2576. y. Rev. 4. sit. -0.134 (-3.28). Controls. 3. er. PT. Skewness controls. 2. ‧. ‧ 國. Controls 1. High sentiment. 學. Low sentiment. engchi. i n U. v. 28 DOI:10.6814/NCCU202001429.

(38) smaller than −0.134 and statistically significant, with a t-statistic of −3.23. The specification that includes skewness-related variables in column (3) and column (4) also shows a highly significant average coefficient of −0.106 (t-statistic −3.33) and −0.113 (t-statistic −3.09) on PT. Interestingly, in high sentiment periods, when PT is included as the only independent variable, the average coefficient of −0.050 is negative but insignificant (t-statistic −1.63), and it is less than half as large as this in the corresponding univariate specification. This result is in contradiction with the univariate portfolio analysis reported in Panel A of Table 4.2. The difference may be attributed to the existence of the January effect in the portfolio analysis.. 4. After including other control variables in column (6) through column (8), the. 政治大. coefficient on PT decreases and is more statistically insignificant, especially when adding. 立. skewness (Skew).. ‧ 國. 學. Columns 1–4 of Table 4.4 show that the probability weighting (PW) element has no predictive power in low-sentiment periods, whether only PW is included as an independent. ‧. variable or the other control variables are added to the regression model. Consistent with. sit. y. Nat. the results of portfolio analysis in Table 4.2, the Fama-MacBeth regression analyses provide evidence of a negative relation between PW and future stock returns in high-sentiment. er. io. periods regardless of the specification. Compared to PW, the loss aversion (LA) element a. n. iv l C n works in reverse. In Table 4.5, I find significantly coefficients on LA in low-sentiment h e n g negative chi U periods, but they become insignificant in high-sentiment periods.. In order to comparing compare different specifications using these three various prospect theory- related variables, I standardize all independent variables to have a mean of zero and a standard deviation of one. The results in Table 4.6 suggest that in the whole sample period, the average coefficients on either PT, PW, or LA is negative and statistically significant. This result is consistent with Barberis et .al. (2016), as theywho point out, the coefficients 4. I report the four-factor alphas on the value-weighted basis of stock portfolios sorted on PT, PW, and LA following different sentiment periods in Table C.1 in Appendix C, and this time I exclude the sample in January to take control of the January effect. The results suggest that after considering the January effect, the four-factor alpha on 1-10 portfolio sorted on PT is insignificant in high-sentiment periods.. 29 DOI:10.6814/NCCU202001429.