Can investor sentiment predict the size premium?

Accepted Manuscript Can investor sentiment predict the size premium?

Mahmoud Qadan, David Y. Aharon PII: DOI: Reference:

S1057-5219(18)30631-8 https://doi.org/10.1016/j.irfa.2019.02.005 FINANA 1322

To appear in:

International Review of Financial Analysis

Received date: Revised date: Accepted date:

22 August 2018 19 January 2019 13 February 2019

Please cite this article as: M. Qadan and D.Y. Aharon, Can investor sentiment predict the size premium?, International Review of Financial Analysis, https://doi.org/10.1016/ j.irfa.2019.02.005

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Can Investor Sentiment Predict the Size Premium?

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Mahmoud Qadan, Ph.D Department of Business Administration, Faculty of Management University of Haifa, Haifa, Israel E-mail: [email protected] Phone: +972-4-8249584

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David Y. Aharon, Ph.D Department of Business Administration, Ono Academic College, Kiriat Ono, Israel. Tel: +972-9-8607421 E-mail address: [email protected]

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Can Investor Sentiment Predict the Size Premium?

Abstract

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This study uses theoretical arguments from the psychology and financial decision-making literature to assess the extent to which investor sentiment contributes to explaining the size premium. We use daily, weekly and monthly data for 1965–2017, and several investor sentiment measures often used in the recent literature, including stock market-based, survey-based and pressbased proxies. We provide empirical evidence that small stock premiums correlate with and are predictable through the use of a set of lagged investor sentiment measures. Our findings hold true for different sample periods and various modeling specifications.

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JEL: G10, G12, G14 Keywords: Investor sentiment, Market anomalies, Size effect, Size premium

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ACCEPTED MANUSCRIPT 1. Introduction The size effect anomaly, widely debated in the financial literature since documented by Banz (1981), asserts that small firms, on average, outperform the largest ones in terms of both returns and risk-adjusted returns. Research dealing with the question of what factors determine the size effect usually points to the macro-economic and financial fundamentals, and link them to theories suggesting that the size premium is paid to compensate for systematic risk, idiosyncratic risk,

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distress or default risk, liquidity, transaction costs and information asymmetry.1 Despite the

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prevalence of research examining the size premium and its reaction to economic and financial

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fundamentals, irrational factors such as sentiment or any other behavioral factors seem to be overlooked in explaining this premium. Given this gap in the literature, this paper builds upon the

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recent evidence that the size effect is alive and well, and attempts to assess the extent to which investor sentiment affects the size premium using different data frequencies.

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To accomplish this task, we use market-based, press-based and survey-based measures to proxy for investor sentiment for 1965-2017. We demonstrate that, even after controlling for

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macroeconomic and financial information, investor sentiment not only correlates with the size premium, but also serves as a tool for predicting this premium. Such a relationship can be exploited

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using a long-short trading rule, and generate significant excess returns. Our findings hold true for most of the proxies reflecting investor sentiment.

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In this study, we employ the following sentiment measures: Baker and Wurgler’s (2006) sentiment measures (BW1 and BW2), the aligned investor sentiment of BW proposed by Huang,

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Jiang, Tu and Zhou’s (2015) index, (HJTZ1 and HJTZ2), the Sentiment Survey conducted by the American Association of Individual Investors (AAII), the University of Michigan Consumer

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Sentiment Index (CSI), the Consumer Confidence Index (CCI), the Economic Policy Uncertainty (EPU) Index, the Federal Bank of St. Louis’ Financial Stress Index (STLFSI), and the CBOE Volatility Index (the VIX). The evidence explored here is consistent with the idea that market participants appear to overvalue small stocks relative to large stocks during periods when risk appetite, reflected by

Risk-based explanations of the size premium include systematic risk (Fama and French, 1992, 1995); liquidity and transaction costs (James and Edmister, 1983; Krueger and Johnson, 1991), information asymmetry (Nathan, 1997; Elfakhani and Zaher, 1998), macro-economic risk (e.g., Reinganum, 1981 and Chan et al., 1985), default risk, distress or default risk (Chan et al., 1985; Vassalou and Xing, 2004, Hur et al., 2014) and idiosyncratic risk (Fu, 2009). 1

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ACCEPTED MANUSCRIPT investor sentiment, is high, and vice versa. The underlying mechanism capable of explaining these findings accords with the psychological contention that an uptick in investor sentiment reduces risk aversion, making people willing to tolerate more risk (e.g., Forgas, 1995). As a result, when investors feel confident about the economy, they are more willing to expose their portfolios to riskier assets in the form of small stocks. In addition, the literature has established that individual investors are more likely to be affected by sentiment (e.g., Lee, Shleifer, and Thaler, 1991), and

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that small firms are disproportionately held by individuals as opposed to institutions (e.g., Nagel,

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2005; Lemmon and Portniaguina, 2006). As a result of these two factors, the difference in returns

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between small and large firms is more pronounced and related to investor sentiment. Despite the doubts about the robustness of the size effect in the US raised in the early 2000s (e.g., among

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others, Knez and Ready, 1997; Dimson and Marsh, 1999; Horowitz et al., 2000; Hirshleifer, 2001; Amihud, 2002), subsequent works argue that consensus about the demise of the small-firm effect

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is unfounded (Van Dijk, 2011; De Moor and Sercu, 2013; Aharon and Qadan, 2018). Identifying the existence or non-existence of the size effect is beyond the scope of this paper.

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However, many studies bridge on the contradicting findings and claim that the size effect varies considerably over time. Chan et al. (1985) published what might be the first empirical paper

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suggesting that the size premium varies over time, and report that the default spread provides a significant explanation for the size effect. Perez‐ Quiros and Timmermann (2000) and Hur et al.

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(2014) demonstrate that the size premium is higher during economic recessions because small firms become riskier during such economic conditions. Recent works extend the examination of

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the size effect and link it to the use of a set of lagged macro-financial variables (De Moor and Sercu, 2013: Zakamulin, 2013). The latter two studies relate the size premium to variables such as

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stock market returns, dividend yields, high-minus-low Fama–French factors (HML), the momentum factors of Jegadeesh and Titman (1993), default spreads, T-bill rates, term premiums and the inflation rate.

Our analysis extends the studies of De Moor and Sercu (2013) and Zakamulin (2013) and examines both the rational and behavioral channels through which investor sentiment might be manifested in the size premium. We contribute to the existing empirical evidence in several ways. First, we utilize a longer time span and extend the periods that have been examined in previous works. Second, we conduct parametric and non-parametric predictability tests and show that investor sentiment can predict the size premium including in- and out-of-sample predictions. 4

ACCEPTED MANUSCRIPT Third, the examination of this issue may enhance our understanding of the nature of the size effect anomaly by suggesting a new dimension previously ignored in the literature. To the best of our knowledge, this paper is a first attempt to link the size premium with market sentiment proxied by a rich variety of factors widely accepted in the literature that reflect individual, as well as, marketwide sentiment.

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The size effect addressed in this study appears to have played a significant role in the

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development of the small cap mutual fund and exchange traded fund (ETF) industries that specialize in investing in smaller companies, which has direct consequences for asset allocation.

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When retail or institutional investors decide on their optimal allocation across all asset classes, they are likely to pick small cap funds in order to gain exposure to a diversified portfolio of small

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stocks that completes their overall asset allocation. Based on standard portfolio theory, if small cap returns do not perfectly correlate with large cap returns, in terms of reacting differently to

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sentiment shocks, investors gain from "size" diversification. Overall, the development of small cap funds occurred despite the claim of the efficient market hypothesis that anomalies cannot exist for

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a long time, because investors will exploit them, and ultimately they will disappear. Keim (1999) provides evidence that investing in a mutual fund that tracks small cap stocks (the smallest 20%

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of publicly traded companies) yields abnormal returns and even outperforms its underlying index. Gorman (2003) reports that small cap funds earn a positive abnormal return of about 2.0% per

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year. Shynkevich (2012) argues that technical trading rules deliver superior performance for small cap portfolios. Finally, Cao et al. (2017) find that small cap funds investing in mid and large cap

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stocks do not outperform small cap funds that do not invest in large cap stocks. Hence, this study may have direct implications for a wide range of market participants such as retail and institutional

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investors, financial advisors or senior executives in the fund management industry. The remainder of this study proceeds as follows. Section 2 presents the scientific background and the core hypothesis followed by a summary of the relevant literature. Section 3 describes the data. Section 4 explains our research methodology. Section 5 provides the empirical findings as well as robustness tests and sensitivity analyses, while Section 6 provides a summary and discusses the

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2. Scientific Background

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findings.

ACCEPTED MANUSCRIPT Our core hypothesis postulates that return differentials between small and large cap stocks (the size premium) are dependent not only on rational economic factors but also on irrational factors such as sentiment. Indeed, studies have established that sentiment affects the pricing of assets (e.g., Brown and Cliff, 2004: Verma and Soydemir, 2006; Baker and Wurgler, 2007; Yang and Li, 2013; Gao and Süss, 2015; Kim et al., 2017; Xu and Zhou, 2018). Given these findings, positive sentiment might make investors more optimistic and willing to buy riskier assets. Consequently,

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we posit that high levels of optimism (or the tendency to speculate) will be associated with an

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increased demand for riskier assets. Small firms, certainly, can be good targets for such increased

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risk appetite. When a large number of people buy small stocks, they become overvalued relative to large stocks. We expect to see this situation during periods of elevated risk appetite as proxied

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by more positive investor sentiment and vice versa.

The financial research literature has established that high-risk assets are, in general, illiquid,

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non-paying dividends, and most importantly, usually include firms located in the smaller quintiles or deciles when constructing size-ranked portfolios. Furthermore, research has demonstrated that

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small firms are generally associated with higher betas. Many studies find a negative relationship between size-based portfolios and beta, implying that small firms are associated with more

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systematic risk (e.g., Binder, 1992; Chan and Chen, 1991;2 Fama and French,3 1992 and 2001). Others have established that small stocks may be costly to trade due to their illiquidity (Amihud

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and Mendelsohn, 1986), and tend not to pay dividends.4 Using the Consumption CAPM, Jagannathan and Wang (2007) report that smaller firms are associated with higher consumption

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betas. Underlying the majority of these findings is the common contention that size premiums represent a compensation for bearing greater systematic risk.

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This study attempts to verify whether investor sentiment accounts for the size premium, even partially. If the suggested proxies for investor sentiment actually hold and mirror the states of emotions that define the tendency to take a risk (for example, picking small firms), the size premium should be more pronounced during periods when investor sentiment is high. On the other hand, when investor sentiment is negative, the size premium should be less evident, because Chan and Chen (1991) find that small firm portfolios contain a large proportion of firms with high levels of financial leverage. As the literature notes, high levels of financial leverage imply that such companies may be riskier, a situation evident in their higher betas (e.g., Hamada, 1972; Bowman, 1979; Yagil, 1982). 3 See, e.g., page 436, Table 2. 4 Earlier works have also shown empirically that the beta estimates of the firms in the smallest size portfolios are higher than those in the largest size portfolios. See, for example, Reinganum (1981); Keim, (1983); Lamoureux and Sanger (1989). 2

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ACCEPTED MANUSCRIPT investors shift their capital from small firms, leading to a smaller size premium. Consequently, the results may suggest an explanation in line with empirical studies that report the inconsistency of the size effect across time (see, e.g., Lo and Mackinlay, 1990a; Black, 1993; Hur et al., 2014; Alhenawi, 2015).

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2.2 Investor Sentiment and Risk Taking

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The literature in psychology and economics has emphasized the major role of emotions in the formation of individuals’ attitudes toward risk and their possible impact on financial decision-

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making. Emotional states are capable of affecting people’s tolerance for, perceptions of and expectations about risk that, in turn, influence their choices.

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Nofsinger (2005), for example, contends that high levels of optimism drive people to overestimate their probability of success. However, at the same time they underestimate the

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riskiness of their decisions. Kuhnen and Knutson (2011) establish that positive emotional states prompt people to take risks and to be confident in their ability to evaluate investment options.

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Utilizing the weather conditions in a lab setting, Bassi et al. (2013) demonstrate that people are more willing to accept risks when they are in a good mood.

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The literature offers a number of definitions for the term "sentiment." While some scholars relate it to individuals' tendency for noise trading in individual stocks (e.g., De Long et al., 1990),

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Baker and Wurgler (2006) define it as the tendency to take a risk and speculate or the overall sense of optimism or pessimism about stocks. Brown and Cliff (2004, p. 2) argue that sentiment reflects

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the expectations of market participants relative to a norm. A bearish (bullish) investor expects returns to be below (above) average, whatever “average” may be. Regardless of the definition

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used, these perceived beliefs about either risk or future cash flows are not justified by the facts available at hand (Baker and Wurgler, 2007). Two competing strands of psychological literature have linked individuals’ emotions and their risk appetite. One stream, the affect infusion model (AIM; Forgas, 1995), maintains that a positive mood reduces risk aversion. According to the AIM, optimistic people are more likely to evaluate risky situations more positively, and thus be more willing to accept risks. Simply put, positive sentiments reduce risk aversion, because people in such situations focus disproportionately on positive environmental cues and change their subjective assessments about the likelihood of various outcomes occurring. As a result, their tendency to take more risks increases. Additional 7

ACCEPTED MANUSCRIPT support for the AIM comes from two complementary streams of research. The mood-asinformation model (Schwarz and Clore, 1983) assumes that the way people make judgments is partially affected by how they feel. More specifically, individuals are prone to make assessments based on their mood. Therefore, those in a positive mood are likely to evaluate the environment more positively (Bower, 1981), which, in turn, encourages proactive behavior. One explanation may be that a positive emotional state promotes the recall of positive material in memory, leading

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to judgments in line with positive memories (Isen et al., 1978; Forgas and Bower, 1987). A second

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line of research on heuristic processing contends that individuals experiencing a positive mood are

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expected to use a “processing strategy that relies heavily on the use of simple heuristics, and that is characterized by a lack of logical consistency and little attention to detail” (Schwarz and Bless,

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1991, p.56). People in a positive mood are therefore less likely to be aware of the potential negative consequences of their decisions. In addition, a lack of careful and rational thought may intensify

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their risk-prone responses (Mackie and Worth, 1991; Forgas, 1998). The other strand of thought, the mood maintenance hypothesis (MMH; Isen and Patrick, 1983; Isen, Nygren, and Ashby, 1988), maintains that a positive mood increases risk aversion when

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placing high-risk bets. Consequently, individuals are unwilling to make risky investments that

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might potentially result in losses that would worsen their mood. People in a positive mood are likely to behave cautiously and avoid taking risks (Isen and Geva, 1987; Arkes et al., 1988), or

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will take risks only when the risk is small or unlikely to materialize (e.g., Isen and Labroo, 2003). Empirical findings from the finance literature seem to support the AIM theory. Evidence

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includes studies that examine sentiment following non-financial events such as holidays (Bergsma and Jaing, 2016; Qadan and Kliger, 2016), sunshine and cloudy weather (Bassi et al., 2013, and

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the references therein), air pollution (Levy and Yagil, 2011; Lepori, 2016), temperature (Cao and Wei, 2005; Jacobsen and Marquering, 2008), popular TV series finales (e.g., Lepori, 2015) and other non-financial events.

3. The Data and Measurement of the Variables 3.1 Macro-Financial Variables Table 1 provides a detailed list of the macro-financial variables used in this study. The table lists the source, the sample period and the frequency for each data series.

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ACCEPTED MANUSCRIPT [Insert Table 1 here] The macro-financial variables consist of the excess returns on a market portfolio (MKT-Rf) measured as the difference between the value-weighted returns of all CRSP firms and the risk free return, the performance of small stocks relative to big stocks (Small Minus Big, commonly known as SMB),5 and the performance of value stocks relative to growth stocks (High Minus Low, henceforth, HML).6 We extracted the returns of MKT-Rf, SMB and HML from the data on the

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website of Kenneth French.

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Data for dividend yields (DVYLD) come from Robert Shiller’s data library and are calculated

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as the difference between the total return and the capital appreciation return on MKT. Data for the momentum factor return (MOM) come from six value-weighted portfolios constructed on the basis

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of firm size and prior (2–12 month) returns.7 The default spread (DEF) is computed as the simple difference between the yields of Moody’s Baa- and Aaa-rated corporate bonds. The monthly,

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weekly and daily default spreads are constructed using data obtained from the Federal Reserve Bank of St. Louis. From this data source, we also downloaded data about Treasuries (TBILL), and

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calculated the term premium (TERM), the difference between the yields on long-term (30-year) government bonds and Treasuries. Finally, we also use data about the rate of change in the

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consumer price index (CPI) to capture the monthly inflation rate.

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3.2 Investor Sentiment Measures

The lower part of Table 1 reports the measures of investor sentiment. We collected historical data

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on several existing sentiment measures that have been widely used in the literature. The sentiment measures consist of the following: Baker and Wurgler’s (2006) investor sentiment (henceforth, BW1 and BW2), commonly

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used in the literature to capture market sentiment. The construction of this index involves five stock market-based sentiment proxies: the closed-end fund discount, NYSE share turnover, the number and mean value of the first-day returns on IPOs, the equity share in new issues, and finally, the dividend premium. 5

SMB is defined as the average return on three small-stock portfolios minus the average return on three big-stock portfolios. HML is defined as the average return on two value portfolios minus the average return on two growth portfolios. 7 MOM is defined as the average return on two high prior return portfolios minus the average return on two low prior return portfolios, Mom =1/2 (Small High + Big High) - 1/2(Small Low + Big Low). In other words, the index is the average return on two portfolios with high prior returns minus the average return on two portfolios with low prior returns. 6

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Aligned Investor Sentiment suggested by Huang, Jiang, Tu, and Zhou (2015) as a

modified version of Baker and Wurgler’s index. Their indexes (HJTZ1 and HJTZ2), corresponding to BW1 and BW2, are measured using the partial least squares method. The authors personally provided us with the data. 

Consumer Sentiment Index (CSI) published by the University of Michigan, and

constructed using a nationally representative sample of households via telephone surveys. Consumer Confidence Index (CCI). This index provides information on consumer

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sentiment based on the response of a large number of households to questions about their personal

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financial situation, their likelihood of purchasing major household items in the near future, and their overall expectations regarding the economy.

Economic Policy Uncertainty (EPU) Index, developed by Baker et al. (2016). The index

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has three basic components. The first is based on a normalized measure of the volume of news

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articles discussing economic policy uncertainty from 10 newspapers in the U.S.8 The second component relies on reports by The Congressional Budget Office (CBO), which publishes a list of temporary federal tax code provisions. The third component uses the disagreement among

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economic forecasters as an indicator of uncertainty. The data are published monthly and daily 

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starting from 1985.

The CBOE Volatility Index (VIX). This is a key measure of market expectations of near-

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term volatility conveyed by S&P 500 stock index option prices. The literature regards the VIX as an indicator of market risk, uncertainty and macro-economic risk (Bloom, 2009), perceived risk

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(Qadan and Kliger, 2016), panic and fear (Whaley, 2000) as well as sentiment (Baker and Wurgler, 2007). The VIX and the EPU index differ conceptually in many aspects, so they do not always

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accord with one another. For example, as Table 3 illustrates, their correlation is 0.42. While the VIX reflects the volatility and uncertainty regarding capital markets, the EPU mirrors uncertainty about major policies. In addition, geopolitical events such as the election of a new president, political disputes over taxes and government spending, and security tensions in strategic areas can affect the EPU but not the VIX. 

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St. Louis Federal Reserve’s Financial Stress Index (STLFSI). This index measures the

The newspapers considered are USA Today, the Miami Herald, the Chicago Tribune, the Washington Post, the Los Angeles Times, the Boston Globe, the San Francisco Chronicle, the Dallas Morning News, the New York Times and the Wall Street Journal. 10

ACCEPTED MANUSCRIPT degree of financial stress in the US financial markets, and has measured stress weekly and monthly since 1994. The index is calculated based on weekly data series consisting of six yield spreads, seven interest rate series, and five other financial series (Kliesen and Smith, 2010). On this index, zero represents normal financial conditions. Hence, values above zero indicate above-average financial market stress, while values below zero suggest below-average financial market stress. 

American Association of Individual Investors’ (AAII) Sentiment Index. Data on

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individual investor sentiment from the American Association of Individual Investors’ Survey is

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published on a weekly basis and reported from July 1987 to the present. The index is calculated as

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the spread between the percentage of bullish investors and that of bearish investors. Many studies have utilized this index and argue in favor of its predictive ability relative to future equity price

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movements (e.g., Brown, 1999; Brown and Cliff, 2004). The weekly survey divides its members into one of the following three categories: "Bullish," "Bearish," or "Neutral" on the stock market

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over the next six months.

4. Method

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Our goal is to test the hypothesis that differences in the returns of small and large cap stocks,

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represented by the SMB returns, are a result not only of rational economic factors but also of sentiment, represented by investors’ beliefs about future cash flows. Underlying this research question, there are two competing perceptions. The first stems from the classical finance paradigm

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which maintains that markets are efficient, individuals are rational, and security prices are

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unaffected by any irrational factors such as sentiment. The second asserts that an exogenous increase in investor sentiment generates a corresponding wave of positive mood, which, in turn, is translated into intensified risk taking. Since small companies can be a good fit for such increased

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risk appetite, this rise in positive sentiment can ultimately affect the demand for them and the price equilibrium.

The research about the factors that explain the dynamics of the small stock premium has suggested a number of arbitrary possibilities but not arrived at a definitive explanation. The model we present here attempts to resolve some of the issues. To avoid specification errors originating from omitting variables, we suggest first regressing SMB against potential sentiment, and then adding the potential rational predictor variables suggested in prior works. The resulting model reads as follows.

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′ 𝑆𝑀𝐵𝑡 = 𝛽0 + 𝛽1 𝐽𝑎𝑛𝑢𝑎𝑟𝑦𝑡 + ∑ 𝛾𝑖 𝑆𝑗𝑡−𝑖 + 𝐶𝑋𝑡−1 + ∑ 𝛼𝑘 𝑆𝑀𝐵𝑡−𝑘 + 𝑢𝑡 . 𝑖=1

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𝑘=1

SMB is the Fama–French factor used to reflect the size premium and 𝛽0 is the intercept. The massive concentration of the size effect in January has been documented in the literature (Keim,

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1983; Van Dijk, 2011; Hur et al., 2014). Hence, we include a dummy variable that accounts for the

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January effect. Sjt denotes a proxy for jth investor’s sentiment (j=1, 2,…,10), X is a matrix of

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potential economic predictors for SMB, and to account for autocorrelations in error, we added lagged values of SMB.

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The rational predictors used in the X matrix accord with those used, for example, in De Moor and Sercu (2013) and Zakamulin (2013). We list these variables and demonstrate the rationale behind their inclusion in the models. In our analysis, we include the excess returns on the CRSP

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market portfolio (MKT-Rf). In fact, the value-weighted market return used is heavily influenced by big firms, so the weight of small firms in this index is negligible. Prior works have indicated

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that large cap firms positively influence the returns of small cap firms over short time horizons

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ranging from one week to four weeks. For example, Lo and MacKinlay (1990b) and McQueen et al. (1996), among others, point out that the returns on a portfolio of small stocks are correlated

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with the lagged returns on a portfolio of large stocks. Hence, we suggest that controlling for market returns might improve the capturing of the size premium. The model also includes the performance

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of value stocks relative to growth stocks (HML). We do so because the latter is related to future growth in the real economy (Liew and Vassalou, 2000), and contains information related to defaults

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(Avramov et al., 2007).

Another rational predictor we include is dividend yields (DVYLD). This factor is used extensively in the financial literature to reflect time variations in unobservable risk premiums. Specifically, the dividend yield is supposed to vary with expected returns. Indeed, many works document its ability to predict future stock and bond returns (e.g., Campbell and Shiller, 1988). We also include the momentum factor of Jegadeesh and Titman (1993, MOM) because prior works have established that the returns on this factor is related to macroeconomic conditions (Chordia and Shivakumar, 2002; Cooper et al., 2004). In line with the literature (e.g., Chan et al., 1985; Vassalou and Xing, 2004; Hur et al., 2014), the default spread (DEF) is also included in the model 12

ACCEPTED MANUSCRIPT because it is a significant factor in explaining the size premium. Finally, we utilize the term premium (TERM) - also known as the slope of the yield curve - defined as the difference between the yields on long-term (30-year) government bonds and Treasuries, and use data about the rate of change in the consumer price index (CPI) to capture the monthly inflation rate. In the literature, these variables are assumed to contain information about the conditions of the economy and future

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growth in the GDP (e.g., Fama, 1981; Liew and Vassalou, 2000).

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5. Empirical Findings

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5.1 Descriptive Statistics

Table 2 presents the descriptive statistics of the key variables in this study. The table includes

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three panels covering the statistics of the data for the various frequencies proposed: monthly, weekly and daily. The reported descriptive statistics for each table include the mean, median,

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maximum, minimum, standard deviation skewness, kurtosis and total sample for the variables we used. We conducted the analysis across the sample years with the earliest data that we could obtain.

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[Insert Table 2 here]

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When we compare the panels, we can see that most of the market sentiments fluctuate more on a monthly basis (Panel A) than a weekly (Panel B) or daily (Panel C) basis. Finally, Table 3 provides the correlation matrix for the key variables. Panel A of the table reports the pairwise

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correlation between the monthly sentiment variables, and Panel B presents the pairwise correlation between the monthly macro-financial variables utilized in the study. As the panels illustrate, most

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of the correlations are significant at the 1% level. To save space, we did not include a correlation

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matrix for the weekly and daily sentiment indicators, but they are available upon request. [Insert Table 3 here]

5.2 Estimation Results We start our analysis with a simple version of the model proposed above. The simple version links SMB only to January as well as to changes in sentiment. This version is given by: 𝑆𝑀𝐵𝑡 = 𝛽0 + 𝛽1 𝐽𝑎𝑛𝑡 + 𝛽2 𝑆𝑡−1 + 𝛽3 𝑆𝑀𝐵𝑡−1 + 𝑢𝑡 . The estimation results for this model, with respect to monthly data, are listed in Table 4. The results are presented for three different, but related periods. In Panel A, we report the results for the entire sample; in Panel B, we present the results for the 13

ACCEPTED MANUSCRIPT period ending in December 2002, and in Panel C we consider the consecutive years 2003-2017.9 The results are robust, and support our core hypothesis that the lagged values of investor sentiment have an influence on the current SMB. [Insert Table 4 here] The role of January in explaining the SMB is most evident in the period between 1965 and

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2002. As Panel B of Table 4 illustrates, the January effect is present and statistically significant in most cases. The coefficients are significant and positive, and range from 2.017% to 2.334%. For

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the most recent period, depicted in Panel C of Table 4 (2003-2017), the January effect does not exist at all, as evident in the insignificant values of the "Jan" coefficient. This finding is in line

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with a battery of studies documenting the fading away of many calendar anomalies after articles about these anomalies were published in the literature (e.g., Gu, 2003; Marquering et al., 2006;

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Moller and Zilca, 2008).

The Baker and Wurgler (2006) sentiment measures (BW1 and BW2) have a negative effect on

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the future SMB. Technically speaking, Baker and Wurgler (2006) constructed this index based on other variables commonly used as indicators of sentiment in prior works: the equity share in new

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public issues (equity and debt), the value-weighted closed-end funds discount (CEFD), the number of IPOs, average first-day IPO returns, the value-weighted dividend premium, and NYSE turnover.

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They calculated the first principal component of these sentiment measures and regressed it on several macro-economic variables, including personal consumption expenditures, the industrial

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production index, and a recession indicator as defined by the NBER data. Technically speaking, the first principal component is the best combination of the six indicators that maximally represents

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the total variations of the six proxies. The residual obtained from this regression is their primary measure of investor sentiment unwarranted by economic fundamentals. The key premise of these sentiment estimators is that they are contrarian predictors mainly for unprofitable, high volatility, non-dividend-paying, distressed, extreme growth and young stocks. Thus, high levels of these estimators predict future lower equity prices. We find that BW1 and BW2 negatively influence the next month’s SMB returns. As Table 4

For the sentiment estimators AAII, EPU and VIX, the period ending in December 2002, and the period between 2003 and 2017 we separate the sample into two relatively equal parts. In addition, as discussed in the introduction section, during the early 2000s many scholars raised doubts about the existence of the size premium. 9

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ACCEPTED MANUSCRIPT illustrates, the signs of the coefficients associated with BW1 and BW2 are consistently negative. In other words, an increase in BW1 and BW2 by one unit leads to a decrease in the next month’s SMB return by 0.365% for the entire sample, 0.36% in 1965-2002 and 1.396% in 2003-2017. Given that these proposed indicators can potentially have approximation errors with respect to the true but unobservable investor sentiment, and because these errors are part of their variations, Huang et al. (2015) utilize the partial least squares procedure to separate information in the indicators that is

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relevant to the expected stock returns from the errors or noise. The result is an aligned index.

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According to the table, Huang et al.’s (2015) aligned investor sentiment index provides similar

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signs, but with weak statistical significance.

While the tendency in BW1, BW2, HJTZ1 and HJTZ2 is to negatively affect the future size

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premium, we find that changes in the CCI and CSI have a positive effect on the premium. The different signs obtained when regressing SMB against either the CCI or CSI may stem from the

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fact that, in contrast to the BW (and HJTZ), which are measures that rely primarily on the use of past market variables to measure sentiment, the CCI and CSI focus on a direct measure of sentiment compiled from survey data. In other words, both of these indices are measures of pro-

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cyclical investor sentiment. The positive sign is evident in the different samples illustrated in the

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table.

Consumer attitudes with respect to the state of the economy, as captured by both indices,

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contain some information about future growth in aggregate consumer expenditures (Ludvigson, 2004). Moreover, consumer confidence is a component of the Index of Leading Economic

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Indicators in the US.10 Indeed, many economists claim that consumer spending depends not only on household income and wealth but also on their optimism regarding the future. With this

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evidence in hand, we can understand the underlying mechanism driving the investigated phenomenon. Consistent with the predictions of models based on noise trader models, Lemmon and Portniaguina (2006) report that shocks to consumer confidence have a significant influence on value but not for growth stocks. Fisher and Statman (2003) study the relationships between some components of consumer confidence and subsequent NASDAQ and small cap stock returns, and find statistically significant results. However, the relationship between consumer confidence and subsequent S&P 500 returns is not statistically significant. Finally, Schmeling (2006) provides corroborating evidence about the role of individual sentiment in affecting aggregate market returns 10

https://www.conference-board.org/data/bci/index.cfm?id=2160 15

ACCEPTED MANUSCRIPT in Germany. Similar results are obtained from the American Association of Individual Investors’ weekly sentiment survey. Since AAII is a weekly variable, the results are illustrated in Table 11. As previously stated, the AAII sentiment index for individual investors is computed as the spread between the percentage of bullish investors and the percentage of bearish investors (Bull–Bear spread). Since this survey deals with individual investors, we use it primarily as a measure of

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individual investor sentiment. The results, illustrated in Tables 11.5 and 11.6, indicate a positive

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and statistically significant effect of the AAII on the size premium. In other words, individual

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investors’ expectations regarding the direction of the stock market during the next six months not only strongly correlate with, but also are capable of driving, the size premium upward.

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One possible explanation underlying this strong relationship between individual investors’ sentiment and the size premium may be the dynamics of the participation of households in the

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equity markets in recent years. Many studies and reports indicate the increasing involvement of households and individuals in trading in the market place.11 The finding regarding the AAII’s impact on SMB is consistent with the predictions of noise trading (individuals) models (e.g., De

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Long et al., 1990). According to these models, changes in investor sentiment prompt price

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deviations from their fundamental values, and introduce a systematic risk that is priced into the market.

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Overall, the sentiment coefficient measures support our main hypothesis and are in line with the affect infusion model (AIM; Forgas, 1995). They imply that the demand for small stocks rises

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when sentiment is positive. In other words, the results support the contention that a better mood reduces risk aversion, thus leading to the willingness to pay a premium for small stocks.

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In the case of the VIX and the St. Louis Financial Stress Index (STLFSI), the signs are negative, indicating that heightened values of both predict a decrease in SMB, similar to BW1 and BW2. Recall that changes in both the VIX and STLFSI provide a contrarian indicator. The higher they are, the more bearish the market, and the lower they are, the more bullish the market will be. Hence, it seems that investors update their portfolios and tend to hold fewer risky assets when both indicators are higher, leading to smaller SMB returns in the next month. Qadan et al. (2018) maintain that an increase in the VIX may reflect an increase in investors’ risk aversion, prompting them to balance their portfolios by increasing the diversity and reduce the volatility of their 11

See, e.g., Chapter 7 Pages 140-157 in the 2018 Investment Company Fact Book. 16

ACCEPTED MANUSCRIPT portfolios. In addition to the monthly data, we also used daily and weekly data, and the results appear in Table 10 and Table 11, respectively. The weekly investor sentiment measures include the VIX, the EPU, AAII, and STLFSI, whereas the daily proxies are only the VIX and EPU. While the weekly and daily EPU provide the expected sign, meaning a negative sign, the results are statistically

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insignificant for both frequencies.12

5.3 Prediction Tests

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In order to assess the performance of our out-of-sample and in-sample forecasts, we use the sign-prediction test proposed by Pesaran and Timmerman (1992). Their test reads as follows. 𝑇

𝑡=𝑇1

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1 % 𝐶𝑜𝑟𝑟𝑒𝑐𝑡 S𝑖𝑔𝑛 P𝑟𝑒𝑑𝑖𝑡𝑖𝑜𝑛𝑠 = ∑ 𝑍𝑡+𝑠 , (2) 𝑇 − (𝑇1 − 1)

where T is the total number of observations that constitute the sample (in-sample observations +

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out-of-sample observations); T1 is the first out-of-sample forecast observation; 𝑍𝑡+𝑠 =

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1 , 𝑖𝑓 (𝑦𝑡+𝑠 ∙ 𝑓𝑡,𝑠 ) > 0, and equals 0, otherwise. 𝑦𝑡+𝑠 is the actual dependent variable in the forecasting window, and 𝑓𝑡,𝑠 is the forecasted variable.

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Table 5 reports the results about the predictive ability of the investor sentiment variables. For the period from 1965 to December 2002 (the in-sample), Panel A of the table demonstrates that

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BW1, BW2, HJTZ1, HJTZ2, ∆CCI, ∆CSI successfully predict the anticipated sign in more than 50% of the cases (56.1%, 55.2%, 53.7%, 54.3%, 59.7% and 57%, respectively). Using January

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1965 to December 2002 as the estimation period, and January 2003 to November 2017 as the forecasting window, Panel B indicates that they also successfully predict the direction of the next month’s SMB returns (57.8% for BW1, 56.2% for BW2; 55.9% for HJTZ1, 55.6% for HJTZ2, 57.5% for VIX, 55.3% for STLFSI, 55.3% for CCI and 55.9% for CSI). The only exception is the EPU, which, as Panel B of Table 5 indicates, fails to provide any significant sign prediction (46.4% with Z-stat.=0.972). The Kenneth French database provides data about "global" SMB portfolio for 1990 to the present. We regressed the latter against the "global" Economic Policy Uncertainty Index (available at http://www.policyuncertainty.com/), and got supportive results; EPU is negatively related to the global SMB. Although the picture obtained is partial, it implies that the US is not a distinct case. The results are available upon request. 12

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[Insert Table 5 here] 5.4 Non-Parametric Tests The results above indicate that lagged sentiment measures contribute significantly to the prediction of the size premium. We take these results one step further ahead and look for

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conditional SMB returns in a simple and non-parametric way. Specifically, we track the cumulative

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SMB returns according to the level of sentiment of Baker and Wurgler (2006) at the end of the

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previous calendar year. To test whether our results are robust, we also apply the same procedure to the aligned investor sentiment indexes proposed by Huang, Jiang, Tu and Zhou (2015) – HJTZ1

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and HJTZ2. First, we calculate the average cumulative SMB returns in the months in which the BW and HJTZ sentiments from the previous year-end are negative, and report them in Table 6. We

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then follow the same procedure and calculate the average SMB returns over the months in which the BW1, BW2, HJTZ1 and HJTZ2 sentiments from the previous year-end are positive, and report the results in Table 7. In both tables, we report the SMBi, which refers to the Small-Minus-Big

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portfolio’s cumulative returns until month i. For example, SMB3 refers to the cumulative returns

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on the SMB portfolio during consecutive three months: January, February and March. Each table of the two also reports the average, the t-statistic value with respect to the null hypothesis

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postulating that SMBi equals 0, that is, HO: SMBi=0 and H1: SMBi ≠0, and the significance level. In Table 8, we build a long-short trading rule, according to which, we short the SMB if the

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previous year-end sentiment is positive, and long it if the previous year-end sentiment is negative. In general, there is a unique relationship between these sentiments and the expected mean value of

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SMB in the following months. In particular, the results imply that SMB returns tend to be lower (higher) following higher (lower) values of these contrarian sentiments.

[Insert Table 6 here] [Insert Table 7 here] [Insert Table 8 here]

Comparing the results of Table 6 and Table 7 with respect to, for example BW1, reveals that if 18

ACCEPTED MANUSCRIPT the investor holds the SMB6 portfolio following negative sentiments from the previous year-end, the cumulative returns total 3.48%, while the corresponding return during higher values of BW1 sentiment is a negative value of -1.07%. This result is essentially similar when considering the BW2 sentiment measure with the corresponding cumulative returns of 2.88%, and -0.58%, respectively. When utilizing the HJTZ1 and HJTZ2 measures, similar results are also obtained. The SMB6 returns equal 3.21%, and -0.39% following lower and higher HJTZ1 measures, while for

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HJTZ2 the corresponding returns are 2.03% and -1.20%.

The trading strategy described in Table 8 suggests longing SMB following low year-end BW

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or HJTZ sentiment measures, and shorting SMB following high year-end BW or HJTZ sentiment measures. This strategy yields significant net profits that can total up to 9.15% and 7.14% for the

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next 12 months. The transactions costs that one would need to take into account are dwarfed by the significant high returns in most cases.

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Another interesting result relates to the “December barometer.” Looking at the SMB12 of each sentiment measure reveals that the cumulative returns for the next 12 months are conditional

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on the sentiment measure revealed in the previous December. For example, following a low sentiment in Decembert-1, the subsequent SMB12 cumulative returns are 7.48% and 6.20%, for the

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BW1 and BW2, respectively. These returns are substantially higher than the corresponding values of -1.77% and -0.94%, following the high sentiment values in the previous December. This

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interesting result also holds when HJTZ1 and HJTZ2 are used. Following a low sentiment value (in Decembert-1), the SMB12 cumulative returns are equal to 6.58% and 3.17%, compared with lower

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corresponding values of only 1.95% and 1.37%, when the sentiment value for Decembert-1 is high. The implication is that investors may not have to wait and look ahead to the January

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barometer, but instead can look back to the sentiment measure in December and act accordingly. 5.5 Robustness Checks Previous works show that the size premium reacts to common macroeconomic information. After controlling for these factors, we show that the size premium is still significantly correlated with and even driven by measures of investor sentiment. Specifically, we regressed the model in Eq. (1) gradually in order to develop a clear-cut understanding about the role of investor sentiment in affecting the size premium. The results are reported in Table 9. The results remain qualitatively unchanged, and indicate the significant role of sentiment in affecting the future returns of SMB for 19

ACCEPTED MANUSCRIPT the vast majority of measures used in this study. The signs of the coefficients of the macro-financial variables are consistent with previous works (McQueen et al., 1996; De Moor and Sercu, 2013; Zakamulin, 2013; Hur et al., 2014). The results indicate that while the momentum risk factor, inflation (the rate of change in the monthly consumer price index) and TBILL coefficients are negatively related to SMB, the factors HML and TERM are not statistically different from zero. Not surprisingly, many works have established that stock returns are negatively correlated with

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inflation (e.g., Fama, 1981), and that short-term interest rates act as predictors of inflation.

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MKT, capturing the market portfolio, has a positive effect on the size premium, supporting

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the idea that stock market returns (particularly those of large cap stocks) lead small cap returns (e.g., Lo and MacKinlay, 1990b; Hou and Moskowitz, 2005). In fact, the literature indicates that

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the spillover exists not only for returns but also for volatility (e.g., Ewing and Malik, 2005). In line with the literature (e.g., Zakamulin, 2013), Table 9 indicates that in most cases the

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dividend yield factor (DVYLD) also makes a positive and significant contribution to the size premium. As Chan et al. (1985) and Vassalou and Xing (2004) argue, the default spread is a significant factor explaining the size premium. The results in Tables 9.1-9.9 and 10.1-10.9 weakly

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support this contention. The coefficients of the default spread (DEF) are positive in most cases but

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not statistically significant. One reason for this weak relationship may originate in the significant correlation between DEF and the rest macro-financial variables. In addition, note that including

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all of the eight macro-financial variables in the model reveals an insignificant effect of sentiment on SMB. One explanation for this result may be the strong correlation detected between many of

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the control variables, as illustrated in Panel B of Table 3. Econometrically, the presence of multicollinearity between explanatory variables may lead to a distortion in the estimate of the

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variables’ impact on the explained variable. Furthermore, the standard errors of the affected coefficients tend to be large, resulting in the failure to reject a false null hypothesis of no effect of the explanatory variable. We also ran the model using two other types of data: weekly and daily. The estimation results appear in Table 10 and Table 11, and they were estimated gradually. For the sake of robustness, we present the estimation results once when the sentiment variable is contemporaneous, and again when it is lagged. The results remain the same. These findings indicate that the size effect is associated with changes in investor sentiment, and the size premium is affected by past changes in that sentiment. 20

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[Insert Tables 9, 10 and 11 here] Our results have a number of implications. First, the macro-financial variables we suggest appear to be predictive variables for this premium. Second, an increase in the values of the sentiment factors accessible to the public in the form of the VIX and EPU signals a deterioration

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in economic conditions, and has a negative effect on the size premium. This outcome suggests that

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the size premium tends to decrease during adverse economic conditions. On the other hand, an

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uptick in consumer confidence or consumer sentiment index signals the expansion of the economy. Optimistic people are more likely to evaluate risky situations more positively, and thus be more

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willing to accept risks in the form of investing in small companies. The results are consistent with the hypothesis that the size premium compensates investors for bearing greater systematic risk.

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Furthermore, note that proxies for investor sentiment are still capable of forecasting the size premium after controlling for the overall macro-economic conditions. Our results do not contradict the risk-based explanation for the size effect. They simply complete the picture by demonstrating

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the influence of another dimension often overlooked in prior works that focus on rational factors.

6. Conclusions

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As evident in prior works, the literature generally links the size premium to common macroeconomic information. However, it ignores behavioral factors that might explain the size

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premium anomaly. In this study, we document that market participants appear to overvalue small stocks relative to large stocks during periods when their risk appetite, reflected by investor

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sentiment, is strong, and vice versa. Our results reveal that the size premium correlates with investor sentiment, and is likely to be most noticeable in periods associated with very optimistic investor moods. We establish that this sentiment contains information about future size premium returns, is negatively related to proxies for contrarian investor sentiment, and demonstrates a positive relationship with pro-cyclical investor sentiment. Our findings are consistent with theories from the decision-making and psychology literature documenting that positive sentiment tends to reduce the perception of risk, and as such, contributes

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ACCEPTED MANUSCRIPT to the increase in the size premium. In other words, optimistic people are more likely to evaluate risky situations more positively, and thus, be more willing to accept risks. In addition, our results accord with the predictions of models in which correlated trading by noise traders (individuals) and limits to arbitrage can drive the prices of the securities primarily held by such investors to deviate from their economic fundamentals. Our results challenge the classical view of the factors affecting stock prices. In doing so, they

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have several possible useful inferences for financial managers, advisors, and other market

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participants. These inferences can potentially help such individuals create better investment

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policies in terms of managing their investment risks and asset allocations. Given our documented evidence that irrational factors play a major role in predicting the performance of portfolios based

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on the size of the companies in them, we recommend that managers pay attention to measures of market sentiment and those of individual investors. As we demonstrated here, investors can use

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market sentiment in various forms as a tool for possibly predicting the ex-ante returns of size ranked portfolios.

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Our study has a number of limitations that also offer suggested avenues for future research. First, it deals with only one market, that of the United States. We focused on the US capital market

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because it is the largest in the world in terms of market value, volume and global interest. Another limitation relates to the scarcity of and limited access to information about variables related to

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investor sentiment in other countries. We hope that future research can obtain such information and test our hypothesis in other developed as well as emerging economies.

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Nevertheless, despite these limitations, and given the evidence that large cap returns do not perfectly correlate with small cap returns, in terms of reacting differently to sentiment shocks,

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investors can benefit from "size" diversification. That is, market participants can utilize our findings about the relationship between investor sentiment and the size premium to develop an investment strategy that will yield abnormal returns by simply tracking the level of market sentiment, recognizing whether the sentiment is pro-cyclical or contrarian, and then rebalancing their portfolios accordingly.

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27

ACCEPTED MANUSCRIPT Table 1 – The Key Variables: Source, Sample Period and Frequency Source

Time Period

Frequency

Kenneth R. French's website

1965:07 – 2017:11

D/W/M

SMB

Kenneth R. French's website

1965:07 – 2017:11

D/W/M

HML

Kenneth R. French's website

1965:07 – 2017:11

D/W/M

DVYLD TERM

http://www.econ.yale.edu/~shiller/data.htm https://fred.stlouisfed.org/

1965:07 – 2018:12 1965:07 – 2017:11

M D/W/M

CPI

https://fred.stlouisfed.org/

1965:07 – 2017:09

M

MOM

Kenneth R. French's website

1965:07 – 2017:12

D/W/M

DEF

https://fred.stlouisfed.org/

1965:07 – 2017:10

D/W/M

TBILL

https://fred.stlouisfed.org/

1965:07 – 2017:11

D/W/M

EPU

http://www.policyuncertainty.com/index.html

1985:01 – 2017:12

D/W/M

BW1& BW2

http://people.stern.nyu.edu/jwurgler/

1965:07 – 2015:11

M

HJTZ1& HJTZ2

Directly from the authors

1965:07 – 2014:12

M

STLFSI

https://fred.stlouisfed.org/series/STLFSI

1994:01 – 2017:12

W/M

CCI

https://fred.stlouisfed.org/series/

1960:01 – 2017:10

M

CSI

https://fred.stlouisfed.org/series/UMCSENT

1978:01 -2017:11

M

VIX

Chicago Board of Exchange’s website

1990:01 – 2017:12

D/W/M

AAII

http://www.aaii.com/sentimentsurvey

1987:07 – 2017:12

W/M

ED

M

AN

US

IP

T

MKT

CR

Variable

AC

CE

PT

Notes: The upper part of the table lists the macro-financial variables, and the lower part lists the investor sentiment measures. For each variable, we report the website where the data are available, the period covered, and the frequency of the data. D, W and M in the last column stand for daily, weekly and monthly frequency, respectively. Complete definitions and descriptions of the variables are provided in Section 3. (MKT-RF) is the market risk premium. SMB is the Fama-French (1993) benchmark factor (Small Minus Big); HML is the average return on two value portfolios minus the average return on two growth portfolios (High Minus Low). EPU is the Economic Policy Uncertainty Index developed by Baker et al. (2016). BW1 and BW2 are the Baker and Wurgler (2006) sentiment indices. HJTZ1 and HJTZ2 are the aligned Investor Sentiment Index according to Huang, Jiang, Tu and Zhou (2015). STLFSI is the St. Louis Federal Bank’s Financial Stress Index. CCI is the US Consumer Confidence Index. CSI is the University of Michigan’s Consumer Sentiment Index. VIX is the CBOE volatility index, and AAII is the sentiment measure computed by the American Association of Individual Investors.

28

ACCEPTED MANUSCRIPT Table 2 – Descriptive Statistics Panel A – Monthly Data S.D 4.461 3.115 2.851 1.181 2.714 0.363 4.267 0.390 0.269

0.000 -0.005 0.000 0.000 107.924 -0.008 99.874 85.747 19.343

0.050 -0.080 -0.309 -0.390 101.214 -0.100 100.280 89.300 17.400

3.076 2.990 3.251 3.403 245.12 4.659 102.76 112.00 59.890

-2.325 -2.270 -1.738 -1.190 57.203 -1.671 96.218 51.700 9.220

1.000 0.988 0.989 0.999 31.651 1.005 1.409 12.699 7.525

M

Panel B: Weekly Data

Skew -0.523 0.488 0.081 0.562 0.482 -0.107 -1.324 3.060 0.543

Kurt 4.878 8.251 4.991 2.491 2.507 6.295 13.242 16.978 3.572

n 629 629 629 631 443 626 630 382 629

0.127 0.404 1.428 1.434 0.965 0.806 -0.379 -0.404 1.705

3.616 3.528 4.445 4.352 3.811 5.030 2.462 2.470 7.483

603 618 594 618 396 288 628 479 337

T

Min -23.240 -16.880 -11.100 1.109 2.210 -1.934 -34.385 0.530 0.000

IP

Max 16.10 21.71 12.90 6.237 13.440 1.790 18.35 3.430 1.350

CR

Med 0.860 0.130 0.270 2.904 6.390 0.297 0.778 0.900 0.400

US

BW1 BW2 HJTZ1 HJTZ2 EPU STLFSI CCI CSI VIX

Mean 0.508 0.222 0.340 2.946 6.549 0.327 0.667 0.978 0.391

AN

Variable (MKT-RF) SMB HML DVYLD TERM ∆CPI MOM DEF TBILL

Mean 0.158 0.008 0.057

Med 0.310 0.030 0.020

Max 12.610 6.960 9.860

Min -18.000 -10.660 -8.610

S.D 2.281 1.319 1.306

Skew -0.694 -0.359 0.619

Kurt 9.159 9.329 11.322

n 1683 1683 1683

VIX EPU AAII STLFSI

19.413 91.629 0.083 0.007

17.470 74.650 0.089 0.003

79.130 560.120 0.629 5.392

9.480 3.320 -0.540 -1.634

7.893 63.366 0.182 0.998

2.218 1.798 -0.084 0.996

11.714 7.916 2.986 5.996

1422 1683 1494 1214

CE

PT

ED

Variable (MKT-RF) SMB HML

Panel C: Daily Data

VIX EPU

Mean 0.034 0.001 0.012

Med 0.070 0.010 0.000

Max 11.350 6.200 4.800

Min -17.440 -11.600 -4.220

S.D 1.105 0.594 0.568

Skew -0.654 -1.013 0.436

Kurt 18.886 25.922 12.847

n 8130 8130 8130

19.604 96.934

17.735 79.625

80.860 719.070

9.310 3.320

7.849 67.430

2.110 2.026

10.733 10.382

6866 8130

AC

Variable (MKT-RF) SMB HML

Notes: The table reports the descriptive statistics of the rational and irrational variables used in the study.

29

ACCEPTED MANUSCRIPT Table 3 – Correlation Panel A- Correlation between the Monthly Sentiment Variables HJTZ 1

HJTZ 2

BW1

BW2

HJTZ 1

1

HJTZ 2

0.89***

1

BW1

0.57***

0.64***

1

BW2

0.65***

0.73***

0.97***

1

EPU

STLFSI

VIX

CEFD

CCI

0.06

-0.25***

-0.26***

1

0.56***

0.51***

0.20**

0.30***

-0.06

1

VIX

0.40***

0.41***

-0.07

0.02

0.42***

0.64***

0.04

-0.05

-0.30***

-0.24***

0.21***

0.17***

0.16***

1

CCI

0.22***

0.15***

0.38***

0.41***

-0.70***

0.09

-0.25***

-0.06

1

CSI

0.21***

0.15***

0.37***

0.40***

-0.69***

0.08

-0.25***

-0.05

0.99***

IP

CR

1

US

CEFD

T

0.00

STLFSI

EPU

AN

Notes: The table reports the pairwise correlation between the monthly sentiment variables in level. The notations are as described in Table 1. "***," "**," and "*" denote statistical significance at the 1%, 5% and 10% levels, respectively.

DEF

DEF

-0.25***

1

DVYLD

0.09*

0.32***

HML

0.05

-0.09*

MKT

0.02

-0.19***

MOM

-0.03

-0.13**

TBILL

0.24***

-0.23***

TERM

0.27***

-0.16***

DVYLD

CE

HML

MKT

MOM

TBILL

TERM

1

-0.04

1

0.01

-0.22***

1

-0.07

-0.25***

-0.12**

1

0.33***

0.03

0.02

0.10*

1

0.62***

0.05

0.04

0.06

0.81***

PT

1

ED

∆CPI ∆CPI

M

Panel B- Correlation between the Monthly Macro-Financial Variables

1

AC

Notes: Panel B reports the pairwise correlation between the monthly macro-financial variables. The notations are as described in Table 1. "***," "**," and "*" denote statistical significance at the 1%, 5% and 10% levels, respectively.

30

ACCEPTED MANUSCRIPT

HJTZ 2

ΔVIX

ΔEPU

ΔSTLFSI

ΔCCI

ΔCSI

0.078 1.803a -0.189 0.036 6.394a 0.027 594

0.087 1.660a -0.164 0.027 5.423a 0.021 618

0.136 0.737 -2.318b -0.075 3.536b 0.022 333

0.003 0.614 0.350 -0.069 1.039 0.000 392

0.125 0.149 -2.065a -0.105c 3.358b 0.024 285

0.118 1.398a 323.26a -0.017 15.30a 0.064 627

0.129 0.350 11.594a -0.058 6.661a 0.034 477

0.074 2.285a -0.232c 0.054 6.952a 0.038 449

0.077 2.315a -0.215 0.053 6.862a 0.038 449

0.004 1.499 -2.399 -0.057 1.332 0.006 155

-0.198 1.147 2.492 -0.023 1.460 0.006 214

0.023 0.084 -6.514b -0.086 1.929 0.026 107

0.086 2.017a 368.73a 0.006 13.97a 0.080 449

0.080 0.617 12.733a -0.034 3.718b 0.027 299

0.406 0.461 0.316 -0.106 0.818 -0.004 145

0.513 0.045 0.453 -0.146c 1.479 0.008 169

0.263 0.101 -2.082b -0.139c 4.021a 0.049 178

0.233 -0.041 -1.327a -0.153b 3.174b 0.036 178

0.238 -0.142 231.26a -0.182b 4.840a 0.061 178

0.234 -0.123 9.717a -0.160b 4.909a 0.062 178

CR

US

AN

T

HJTZ 1

M

Variable BW1 BW2 Panel A: Full Sample Intercept 0.070 0.086 Jan 1.847a 1.672a St-1 -0.365a -0.360a SMBt-1 0.022 0.018 F-stat 8.554a 7.625a R2 0.036 0.031 n 603 618 Panel B: 1965:06-2002:12 Intercept 0.038 0.058 Jan 2.334a 2.334a St-1 -0.332a -0.343a SMBt-1 0.046 0.046 F-stat 8.122a 8.252a R2 0.046 0.046 n 449 449 Panel C: 2003:01-2017:12 Intercept 0.136 -0.020 Jan 0.458 -0.015 St-1 -1.396a -1.327b SMBt-1 -0.162 -0.167b F-stat 3.528b 2.808b 2 R 0.047 0.031 n 154 169

IP

Table 4 - Regression Results of Monthly Data

0.263 0.048 -1.322 -0.161b 2.288c 0.021 178

AC

CE

PT

ED

Notes: The table presents the OLS regression results with the consideration of Newey-West (1987) for heteroscedasticity. The regression model is: 𝑆𝑀𝐵𝑡 = 𝑏0 + 𝑏1 𝐽𝑎𝑛t + 𝑏2 𝑆𝑡−1 + 𝑏3 𝑆𝑀𝐵𝑡−1 + 𝑢𝑡 , where St is the sentiment used. Note that for BW as well as for the HJTZ1 and HJTZ2 measures, we used the level data for the regression estimation, because they are stationary in level. For the other measures, we used the first difference, noted by the Greek letter Δ. The regression coefficients are reported in percentage terms. Jan is a dummy variable that receives the value of 1 for January months, and 0 otherwise. "n" is the observation number. “a,” “b” and “c” denote statistical significance at the 1%, 5% and 10% levels, respectively.

31

ACCEPTED MANUSCRIPT Table 5 – Prediction Performance Panel A: In-Sample Predictions (July 1965 – December 2002) BW2

HJTZ1

HJTZ2

∆VIX

∆EPU

∆STFSI

∆CCI

∆CSI

252 197 449 56.1% 2.596 0.005

248 201 449 55.2% 2.218 0.013

241 208 449 53.7% 1.557 0.060

244 205 449 54.3% 1.841 0.033

76 79 155 49.0% 0.241 0.405

105 109 214 49.1% 0.273 0.392

54 54 108 50.0% 0.000 0.500

268 181 449 59.7% 4.106 0.000

171 129 300 57.0% 2.425 0.008

IP

T

BW1

CR

Sentiment (S) Correct Wrong N %Correct Z-stat. Prob.

Panel B: Out-of-Sample Predictions (January 2003 – November 2017) HJTZ1

HJTZ2

89 65 154 57.8% 1.934 0.027

95 74 169 56.2% 1.615 0.053

81 64 145 55.9% 1.412 0.079

94 75 169 55.6% 1.462 0.072

∆VIX

∆EPU

∆STFSI

∆CCI

∆CSI

83 96 179 46.4% 0.972 0.166

99 80 179 55.3% 1.420 0.078

99 80 179 55.3% 1.420 0.078

100 79 179 55.9% 1.570 0.058

US

BW2

103 76 179 57.5% 2.018 0.022

AN

BW1

M

Sentiment (S) Correct Wrong N %Correct Z-stat. Prob.

AC

CE

PT

ED

Notes: The table reports the sign test results that assess the performance of the in-sample (Panel A) and out-of-sample (Panel B) forecasts. The predictive model used is: 𝑆𝑀𝐵𝑡 = 𝛼 + 𝛽1 𝑆𝑡−1 + 𝛽2 𝑆𝑀𝐵𝑡−1 + 𝑢𝑡 . We use the Newey–West (1987) procedure to account for possible heteroscedasticity. The in-sample period spans July 1965 to December 2002, and the out-of-sample period is January 2003 to November 2017. "Correct" refers to the number of cases in which the predicted value sign corresponds to that of the actual value sign, and "wrong" refers to the number of cases in which the expected value sign does not correspond to the actual value sign. "N" is the number of observations (correct + wrong); "%Correct" denotes the ratio of the correct sign prediction, computed as "correct" divided by "N." In determining the significance of the sign prediction, we use the sign test to ensure that the distribution is different from that of a coin toss. "Prob." denotes the statistical significance.

32

ACCEPTED MANUSCRIPT Table 6 - Cumulative Returns Following Negative Sentiment Indexes Sentiment BW1

BW2

HJTZ1

HJTZ2

SMB1

SMB2

Average T-Statistic Prob.

0.57% 0.95 0.351

1.05% 1.07 0.296

SMB3 SMB4 SMB5 SMB6 SMB7 SMB8 SMB9 Negative Sentiments Cumulative Returns on SMB portfolio 1.59% 1.93% 2.90% 3.48% 3.36% 4.23% 2.84% 1.43 1.46 2.01 2.25 1.86 2.14 1.43 0.167 0.158 0.057c 0.035b 0.077c 0.044b 0.168

Average T-Statistic Prob.

0.55% 0.999 0.328

1.19% 1.318 0.200

1.62% 1.578 0.128

1.70% 1.387 0.178

2.63% 1.968 0.061c

2.88% 1.937 0.065c

2.67% 1.539 0.137

3.27% 1.693 0.103

1.86% 0.943 0.355

Average T-Statistic Prob.

0.90% 1.494 0.151

1.96% 2.254 0.036b

2.27% 2.435 0.024b

2.62% 2.413 0.026b

3.59% 3.175 0.005a

3.21% 2.047 0.054c

2.80% 1.511 0.146

3.24% 1.511 0.146

Average T-Statistic Prob.

0.83% 1.967 0.058c

1.71% 2.648 0.012b

1.73% 2.353 0.025b

1.82% 2.181 0.036b

2.46% 2.780 0.009a

2.03% 1.757 0.088c

1.89% 1.347 0.187

2.00% 1.307 0.200

D E

SMB11

SMB12

n

3.66% 1.61 0.121

4.56% 1.74 0.095c

7.38% 2.71 0.013b

23

2.66% 1.199 0.242

3.47% 1.372 0.183

6.20% 2.354 0.027b

25

1.84% 0.826 0.418

3.28% 1.359 0.189

3.95% 1.477 0.155

6.58% 2.249 0.036b

21

0.03% 0.018 0.986

0.48% 0.280 0.782

1.39% 0.733 0.469

3.17% 1.482 0.148

34

T P

I R

C S U

N A

M

SMB10

Notes: The table reports the cumulative monthly returns of SMB over the months in which BW1, BW2, HJTZ1 and HJTZ2 sentiments from the previous year-end are negative. SMBi refers to the cumulative returns of an SMB portfolio until month i, following the publication of the sentiment index in December. By SMB 3 we indicate the cumulative returns on an SMB portfolio in the three consecutive months (January, February and March) following the publication of a negative sentiment index in the previous December. The table also reports the average and statistic T-tests to reject the null hypothesis where HO: SMBi=0 and H1: SMBi ≠0. "Prob." denotes the significance of the T-tests conducted. BW and HJTZ denote the sentiment measures developed by Baker and Wurgler (2006) and Huang et al. (2016), respectively.

T P E

C C

A

33

ACCEPTED MANUSCRIPT

Table 7 : Cumulative Returns Following Positive Sentiment Indexes Sentiment BW1

BW2

HJTZ1

HJTZ2

SMB1

SMB2

SMB3 SMB4 SMB5 SMB6 SMB7 SMB8 SMB9 Positive Sentiments Cumulative Returns on SMB portfolio 0.08% -0.13% 0.45% -1.07% -1.34% -1.40% -2.76% 0.074 -0.112 0.348 -0.800 -0.982 -1.131 -2.093 0.942 0.912 0.730 0.431 0.335 0.268 0.046

SMB10

SMB11

SMB12

n

-3.18% -2.298 0.030

-2.66% -1.782 0.086

-1.77% -1.202 0.240

27

T P

Average T-Statistic Significance

0.92% 1.023 0.316

0.89% 1.430 0.165

Average T-Statistic Significance

0.96% 1.031 0.312

0.77% 1.208 0.238

0.03% 0.024 0.981

0.02% 0.013 0.990

0.61% 0.451 0.656

-0.58% -0.414 0.682

-0.72% -0.503 0.619

-0.52% -0.402 0.691

-1.99% -1.516 0.142

-2.24% -1.538 0.137

-1.68% -1.080 0.290

-0.94% -0.608 0.549

26

Average T-Statistic Significance

0.54% 0.312 0.760

-0.90% -0.824 0.425

-1.16% -0.617 0.548

-1.27% -0.545 0.595

0.14% 0.054 0.958

-0.39% -0.161 0.875

-0.40% -0.171 0.867

0.49% 0.242 0.812

0.01% 0.006 0.995

-1.11% -0.433 0.672

-0.46% -0.153 0.881

1.95% 0.754 0.464

14

Average T-Statistic Significance

0.61% 0.379 0.710

-0.91% -0.915 0.376

-1.38% -0.752 0.465

-1.49% -0.672 0.513

-0.59% -0.237 0.816

-1.20% -0.518 0.612

-1.57% -0.753 0.464

-0.42% -0.223 0.827

-0.41% -0.215 0.833

-1.16% -0.479 0.639

-0.71% -0.257 0.801

1.37% 0.608 0.553

15

D E

T P E

SC

U N

A M

I R

Notes: The table presents the cumulative monthly returns of SMB over the months in which BW 1, BW2, HJTZ1 and HJTZ2 sentiments from the previous year-end are positive. By SMB3, for example, we indicate the cumulative returns of an SMB portfolio in the three consecutive months (January, February and March) following the publication of a positive sentiment index in the previous December. The table also reports the average and statistic T-tests to reject the null hypothesis where H0: SMBi=0 and H1: SMBi ≠0. "Prob." denotes the significance of the T-tests conducted. The rest of the notations appear in Table 6.

C C

A

34

ACCEPTED MANUSCRIPT Table 8 - Long-Short Position Strategy Following Sentiment Indexes Sentiment

SMB1

SMB2

SMB3

SMB4

SMB5

SMB6

SMB7

SMB8 -1.40% 4.23% 5.63%

SMB9

SMB10

SMB11

SMB12

-2.76% 2.84% 5.60%

T P

-3.18% 3.66% 6.84%

-2.66% 4.56% 7.22%

-1.77% 7.38% 9.15%

-1.99% 1.86% 3.84%

-2.24% 2.66% 4.90%

-1.68% 3.47% 5.15%

-0.94% 6.20% 7.14%

BW1

Positive (Short) Negative (Long) Net Return

0.92% 0.57% -0.35%

0.89% 1.05% 0.16%

0.08% 1.59% 1.52%

-0.13% 1.93% 2.06%

0.45% 2.90% 2.45%

-1.07% 3.48% 4.55%

-1.34% 3.36% 4.70%

BW2

Positive (Short) Negative (Long) Net Return

0.96% 0.55% -0.41%

0.77% 1.19% 0.43%

0.03% 1.62% 1.59%

0.02% 1.70% 1.68%

0.61% 2.63% 2.03%

-0.58% 2.88% 3.45%

-0.72% 2.67% 3.38%

HJTZ1

Positive (Short) Negative (Long) Net Return

0.54% 0.90% 0.36%

-0.90% 1.96% 2.86%

-1.16% 2.27% 3.44%

-1.27% 2.62% 3.90%

0.14% 3.59% 3.45%

-0.39% 3.21% 3.61%

-0.40% 2.80% 3.19%

0.49% 3.24% 2.75%

0.01% 1.84% 1.83%

-1.11% 3.28% 4.38%

-0.46% 3.95% 4.41%

1.95% 6.58% 4.62%

HJTZ2

Positive (Short) Negative (Long) Net Return

0.61% 0.83% 0.22%

-0.91% 1.71% 2.62%

-1.38% 1.73% 3.11%

-1.49% 1.82% 3.31%

-1.20% 2.03% 3.23%

-1.57% 1.89% 3.45%

-0.42% 2.00% 2.42%

-0.41% 0.03% 0.44%

-1.16% 0.48% 1.64%

-0.71% 1.39% 2.10%

1.37% 3.17% 1.81%

D E

C S U

N A

M

-0.59% 2.46% 3.05%

I R -0.52% 3.27% 3.79%

Notes: This table incorporates the results from the previous two tables, and reports the average SMB returns over the months in which the BW 1, BW2, HJTZ1 and HJTZ2 sentiments from the previous year-end are positive, months in which they are negative, and the difference between these two averages (in bold). By SMB3, for example, we indicate the average cumulative SMB returns for the three months following the year-end sentiment indices (i.e., returns for January to March).

T P E

C C

A

35

ACCEPTED MANUSCRIPT Table 9 - Predicting SMB using Investor Sentiment Proxies 9.1: Baker & Wurgler (1) Model (4) -0.233 1.777a -0.335a -0.064 -0.067c 0.197c -0.609c

Model (5) -0.337 1.646a -0.314b -0.007 -0.044 0.176c -0.51 0.123a

12.691a 0.037 603

8.884a 0.038 603

6.074a 0.050 603

7.922a 0.074 603

7.183a 0.076 603

2.457a 0.030 418

Model (4) -0.301 1.589a -0.35a -0.054 -0.068c 0.229b -0.652b

Model (5) -0.406 1.469a -0.326a 0.002 -0.043 0.206c -0.546c 0.125a

Model (6) -0.446 0.481 -0.061 -0.021 -0.059 0.499 -0.34 0.084b -0.51 -0.096

7.397a 0.040 618

5.762a 0.044 618

7.760a 0.071 618

2.410b 0.029 433

ED 7.839a 0.032 618

PT

11.348a 0.032 618

Model (1) 0.085 1.821a -0.195

Model (2) 0.104 1.818a -0.178 -0.050

Model (3) 0.150 1.917a -0.160 -0.069 -0.069c

Model (4) -0.556 1.746a -0.229 -0.062 -0.065c 0.301b -0.56c

Model (5) -0.618 1.634a -0.174 -0.009 -0.044 0.266b -0.455 0.119a

Model (6) -0.055 0.708 0.338c -0.040 -0.061 0.604a -0.236 0.083b -0.933 -0.180

9.204a 0.027 594

6.556a 0.027 594

6.265a 0.034 594

5.294a 0.042 594

6.956a 0.066 594

2.684a 0.036 409

AC

CE

9.3: HJTZ (1)

C JANt HJTZ1t-1 HML t-1 MOM t-1 DVYLD t-1 DCPI t-1 MKT t-1 TBILL t-1 TERM t-1 DEF t-1 F Stat. Adj- R2 n

Model (3) 0.152 1.776a -0.351a -0.059 -0.071b

M

C JANt BW2t-1 HML t-1 MOM t-1 DVYLD t-1 DCPI t-1 MKT t-1 TBILL t-1 TERM t-1 DEF t-1 F Stat. Adj- R2 n

Model (2) 0.105 1.676a -0.356a -0.04

AN

Model (1) 0.09 1.68a -0.366a

US

9.2: Baker & Wurgler (2)

Model (6) -0.419 0.669 -0.114 -0.029 -0.061 0.462 -0.355 0.081b -0.514 -0.082

T

Model (3) 0.141 1.953a -0.357a -0.069 -0.071c

IP

Model (2) 0.092 1.855a -0.362a -0.049

CR

C JANt BW1t-1 HML t-1 MOM t-1 DVYLD t-1 DCPI t-1 MKT t-1 TBILL t-1 TERM t-1 DEF t-1 F Stat. Adj- R2 n

Model (1) 0.074 1.859a -0.373a

36

Model (7) -0.285 0.446 0.097 -0.035 -0.066 -0.327 -0.833 0.073 -2.452b 0.31 0.097 1.305b 0.010 311

Model (7) -0.079 0.215 0.102 -0.021 -0.063 -0.218 -0.785 0.077 -2.26b 0.237 0.011 1.265b 0.008 326

Model (7) 0.021 0.470 0.330 -0.038 -0.068 -0.015 -0.804 0.068 -2.397b 0.205 -0.250 1.309b 0.010 302

ACCEPTED MANUSCRIPT 9.4: HJTZ1 (2) Model (4) -0.555 1.614a -0.211 -0.058 -0.067b 0.301b -0.528c

Model (5) -0.609 1.493a -0.151 -0.003 -0.043 0.262b -0.433 0.124a

7.906a 0.022 618

5.609a 0.022 618

5.676a 0.029 618

4.899a 0.037 618

6.930a 0.063 618

Model (1) 0.129 0.683 -2.357b

Model (2) 0.135 0.698 -2.373b -0.031

Model (3) 0.160 0.850 -2.203b -0.052 -0.070

Model (4) 0.643 0.617 -2.209a -0.049 -0.070 -0.164 -0.578

8.598a 0.019 333

2.979a 0.017 333

Model (6) -0.088 0.240 -2.456a -0.021 -0.034 -0.254 -0.718 0.090 -2.005 0.257

AN

M 3.134b 0.025 333

2.304b 0.023 333

3.324a 0.040 333

1.68b 0.021 285

Model (2) 0.006 0.580 0.556 -0.030

Model (3) 0.046 0.758 0.777 -0.060 -0.092c

Model (4) 0.667 0.490 0.792 -0.056 -0.091b -0.190 -0.741

Model (5) 0.580 0.296 1.345 -0.018 -0.070 -0.194 -0.81c 0.103b

Model (6) -0.075 0.223 1.578 -0.028 -0.064 -0.284 -0.871 0.092b -2.362b 0.271

0.536 0.019 391

2.120c 0.019 391

1.939c 0.025 391

2.719a 0.028 391

1.803c 0.019 344

ED

C JANt ∆VIXt-1 HML t-1 MOM t-1 DVYLD t-1 DCPI t-1 MKT t-1 TBILL t-1 TERM t-1 DEF t-1 F Stat. Adj- R2 n

2.833a 0.037 433

Model (5) 0.492 0.348 -2.569a -0.012 -0.038 -0.131 -0.632 0.111c

US

9.5: Volatility Index – The VIX

Model (6) -0.090 0.50 0.357b -0.036 -0.058 0.571b -0.194 0.091b -0.869 -0.170

T

Model (3) 0.155 1.769a -0.136 -0.065 -0.071b

IP

Model (2) 0.109 1.669a -0.153 -0.044

CR

C JANt HJTZ2t-1 HML t-1 MOM t-1 DVYLD t-1 DCPI t-1 MKT t-1 TBILL t-1 TERM t-1 DEF t-1 F Stat. Adj- R2 n

Model (1) 0.092 1.672a -0.168

Model (7) 0.122 0.221 0.338 -0.031 -0.064 0.076 -0.709 0.079 -2.073c 0.138 -0.294 1.371a 0.011 326

Model (7) -0.394 0.226 -2.505a -0.015 -0.030 -0.371 -0.647 0.098c -2.077 0.305 0.327 1.54 0.018 285

CE

Model (1) 0.000 0.574 0.512

AC

C JANt ∆EPUt-1 HML t-1 MOM t-1 DVYLDt-1 DCPI t-1 MKT t-1 TBILL t-1 TERM t-1 DEF t-1 F Stat. Adj- R2 n

PT

9.6: Economic Policy Uncertainty Index

0.652 0.022 391

37

Model (7) -0.100 0.224 1.514 -0.029 -0.065 -0.280 -0.874 0.089c -2.361b 0.275 0.000 1.525 0.014 334

ACCEPTED MANUSCRIPT 9.7: Consumer Sentiment Index (CSI) Model (3) 0.174 0.460 10.265a -0.077 -0.068

Model (4) -0.155 0.380 10.109a -0.074 -0.068 0.147 -0.236

Model (5) -0.211 0.334 8.771a -0.039 -0.058 0.139 -0.254 0.073b

9.149a 0.033 476

6.542a 0.034 476

6.077a 0.041 476

4.343a 0.041 476

4.445a 0.048 476

Model (1) 0.114 1.394a 318.127a

Model (2) 0.127 1.395a 314.796a -0.039

Model (3) 0.152 1.466a 298.189a -0.051 -0.039

Model (4) -0.331 1.407a 292.091a -0.050 -0.040 0.189c -0.20

22.882a 0.065 626

15.543a 0.065 626

IP

Model (6) -0.208 0.289 246.372a -0.026 -0.039 0.503b -0.146 0.048 0.270 -0.188c

AN

M 12.116a 0.066 626

8.633a 0.068 626

8.997a 0.082 626

3.776a 0.054 441

ED

PT

C JANt ∆CCIt-1 HML t-1 MOM t-1 DVYLD t-1 DCPI t-1 MKT t-1 TBILL t-1 TERM t-1 DEF t-1 F Stat. Adj- R2 n

3.061a 0.042 429

Model (5) -0.418 1.350a 236.846a -0.010 -0.026 0.182 -0.194 0.096a

US

9.8: Consumer Confidence Index

Model (6) -0.311 0.222 8.591a -0.034 -0.047 0.437c -0.258 0.067c -0.155 -0.118

T

Model (2) 0.135 0.330 11.272a -0.054

CR

C JANt ∆CSIt-1 HML t-1 MOM t-1 DVYLD t-1 DCPI t-1 MKT t-1 TBILL t-1 TERM t-1 DEF t-1 F Stat. Adj- R2 n

Model (1) 0.121 0.328 11.281a

Model (7) 0.053 0.060 7.867b -0.027 -0.055 -0.266 -0.724 0.056 -1.92c 0.224 -0.011 1.695c 0.020 334

Model (7) 0.093 0.016 213.537b -0.019 -0.046 -0.257 -0.64 0.046 -1.481 0.184 0.019 1.866b 0.025 334

9.9: St. Louis Financial Stress Index (STLFSI) Model (3) 0.131 0.168 -1.966a 0.01 -0.058

Model (4) 1.319 -0.085 -2.087a 0.007 -0.065 -0.547 -0.607

Model (5) 1.202 -0.177 -2.052a 0.022 -0.051 -0.503 -0.646 0.046

Model (6) 0.677 -0.373 -1.929a 0.024 -0.042 -0.723 -0.683 0.02 -2.808c 0.33

3.408b 0.017 284

2.348c 0.014 284

2.277c 0.018 284

1.882c 0.018 284

1.740c 0.018 284

1.020 0.001 237

CE

Model (2) 0.112 0.034 -2.149a 0.032

AC

C JANt ∆STLFSIt-1 HML t-1 MOM t-1 DVYLD t-1 DCPI t-1 MKT t-1 TBILL t-1 TERM t-1 DEF t-1 F Stat. Adj- R2 n

Model (1) 0.117 0.063 -2.1a

Model (7) 0.524 -0.38 -1.937a 0.027 -0.04 -0.791 -0.642 0.025 -2.823c 0.352 0.185 0.922 -0.003 237

Notes: Tables 9.1-9.9 report the estimation results of the prediction model 𝑆𝑀𝐵𝑡 = 𝛽0 + 𝛽1 𝐽𝑎𝑛𝑢𝑎𝑟𝑦𝑡 + 𝛽2 𝑆𝑡−1 + ′ 𝐶𝑋𝑡−1 + 𝑢𝑡 . The model is regressed with the gradual inclusion of macro-financial variables to show the robustness of the prediction. “a,” “b” and “c” denote statistical significance at the 1%, 5% and 10% levels, respectively.

38

AC

CE

PT

ED

M

AN

US

CR

IP

T

ACCEPTED MANUSCRIPT

39

ACCEPTED MANUSCRIPT Table 10 - Estimation Results of Eq. (1): Contemporaneous and Lagged Daily Sentiments

Model (3) 0.003 0.035 -0.188 -0.122a 0.033

Model (4) 0.018 0.034 -0.209 -0.123a 0.033 -0.005

Model (5) -0.04 0.023 -0.155 -0.143a 0.003 0.002 0.016c

Model (6) -0.049 0.022 -0.155 -0.143a 0.003 0.003 0.016c 0.008

3.337 0.001 7,012

49.509 0.020 7,012

40.862 0.022 7,012

34.078 0.023 6,952

26.027 0.025 5,958

22.326 0.024 5,957

8.699 0.002 7,011

21.902 0.009 7,011

18.584 0.010 7,011

10.3 Contemporaneous ∆EPUt

F Stat. Adj- R2 n

1.385 0.000 8,277

36.476 0.013 8,277

Model (5) -0.019 0.028 -0.482a -0.096a 0.008 0.000 0.011

Model (6) -0.030 0.028 -0.482a -0.095a 0.009 0.000 0.011 0.010

16.691 0.011 6,951

16.188 0.015 5,957

13.911 0.015 5,956

Model (3) 0.000 0.029 -0.005 -0.107a 0.022

Model (4) 0.017c 0.031 -0.004 -0.110a 0.021 -0.005b

Model (5) -0.031 0.019 -0.006 -0.128a -0.008 0.001 0.014c

Model (6) -0.032 0.015 -0.006 -0.133a -0.010 0.001 0.014 0.000

Model (7) -0.026 0.014 -0.006 -0.150a -0.025 0.001 0.014 -0.003 -0.055b

29.004 0.013 8,277

24.769 0.014 8,202

19.851 0.015 7,208

17.285 0.016 6,960

24.057 0.026 6,960

PT

Model (2) 0.001 0.027 -0.005 -0.118a

CE

AC

C JANt ∆EPUt HML MOM TBILL TERM DEF MKT

Model (1) 0.000 0.030 -0.006

Model (4) 0.021c 0.038 -0.413a -0.073a 0.024b -0.005c

US

Model (3) 0.003 0.036 -0.398a -0.069a 0.025b

M

F-Stat. Adj- R2 n

Model (2) 0.004 0.033 -0.381a -0.080a

ED

C JANt ∆VIXt-1 HML-1 MOM-1 TBILL-1 TERM-1 DEF-1

Model (1) 0.003 0.034 -0.419a

AN

10.2 Lagged VIX

IP

F Stat. Adj- R2 n

Model (2) 0.004 0.032 -0.167 -0.137a

CR

C JANt ∆VIXt HMLt-1 MOM t-1 TBILL t-1 TERM t-1 DEF t-1

Model (1) 0.002 0.035 -0.232

T

10.1: Contemporaneous ∆VIX

40

ACCEPTED MANUSCRIPT 10.4 Lagged ∆EPU Model (3) 0.000 0.031 -0.008 -0.089a 0.029c

Model (4) 0.022b 0.03 -0.007 -0.094a 0.028c -0.005b

Model (5) -0.008 0.021 -0.004 -0.116a 0.013 -0.002 0.008

Model (6) -0.015 0.018 -0.004 -0.114a 0.014 -0.002 0.008 0.008

1.996 0.000 8,276

28.288 0.010 8,276

24.111 0.011 8,276

21.389 0.012 8,201

19.311 0.015 7,207

15.877 0.015 6,959

Model (7) -0.023 0.022 -0.002 -0.089a 0.037c -0.003 0.007 0.013 0.081a

T

F Stat. Adj- R2 n

Model (2) 0.002 0.028 -0.008 -0.102a

33.091 0.036 6,959

IP

C JANt ∆EPUt-1 HML-1 MOM-1 TBILL-1 TERM-1 DEF-1 MKT-1

Model (1) 0.000 0.029 -0.009

US

CR

Notes: The daily measures of investor sentiment are used to explain the size premium in two different forms. In the first, the measure is used in contemporaneous terms, while in the second, the sentiment measures are used with one lag. “a,” “b” and “c” denote statistical significance at the 1%, 5% and 10% levels, respectively.

11.1: Contemporaneous ∆VIX

C JANt ∆VIXt-1 HML-1 MOM-1 TBILL-1 TERM-1 DEF-1 F-Stat. Adj- R2 n

25.713 0.049 1,451

Model (4) 0.08 0.178 -0.662c -0.208a -0.007 -0.018

Model (5) -0.217 0.167 -0.553 -0.233a -0.057 0.017 0.081c

Model (6) -0.173 0.169 -0.556 -0.234a -0.061 0.015 0.081c -0.038

16.340 0.050 1,447

15.398 0.065 1,241

13.213 0.064 1,241

M

Model (3) 0.028 0.178 -0.754b -0.202a -0.01

ED

6.237 0.007 1,451

AC

11.2: Lagged ∆VIX

Model (2) 0.028 0.178 -0.755b -0.202a

PT

F-Stat. Adj- R2 n

CE

C JANt ∆VIXt HML MOM TBILL TERM DEF

Model (1) 0.016 0.199 -0.84b

AN

Table 11 - Estimation Results for the Weekly Data

19.285 0.048 1,451

Model (1) 0.015 0.213c -0.859a

Model (2) 0.019 0.205 -0.832a -0.063c

Model (3) 0.020 0.200 -0.825a -0.067c -0.06

Model (4) 0.089c 0.198 -0.816b -0.067c -0.054 -0.022

Model (5) -0.102 0.189 -0.847b -0.088b -0.071 0.000 0.050

Model (6) -0.096 0.190 -0.848b -0.088b -0.071 0.000 0.050 -0.006

6.420 0.007 1,450

6.318 0.011 1,450

5.139 0.011 1,450

4.553 0.012 1,446

4.490 0.017 1,240

3.846 0.016 1,240

41

ACCEPTED MANUSCRIPT 11.3: Contemporaneous ∆EPU Model (2)

Model (3)

Model (4)

Model (5)

Model (6)

Model (7)

C JANt ∆EPUt HML MOM TBILL TERM DEF MKT

-0.004 0.185 -0.015

0.006 0.164 -0.009 -0.19a

0.006 0.162 -0.008 -0.193a -0.041

0.077 0.164 -0.005 -0.198a -0.037 -0.020c

-0.167 0.151 -0.007 -0.221a -0.086 0.005 0.067c

-0.122 0.160 -0.009 -0.226a -0.094 0.008 0.076c -0.071

-0.134 0.163 -0.006 -0.220a -0.086 0.007 0.076c -0.065 0.034

F-Stat. Adj- R2 n

1.488 0.001 1,712

22.323 0.036 1,712

16.945 0.036 1,712

15.147 0.040 1,707

14.864 0.053 1,501

12.701 0.054 1,450

Model (1) -0.013 0.189c 0.013

Model (2) -0.008 0.179 0.016 -0.088b

Model (3) -0.008 0.176 0.017 -0.091b -0.036

Model (4) 0.084c 0.175 0.021 -0.091b -0.03 -0.025b

Model (5) -0.087 0.168 0.022 -0.111a -0.042 -0.007 0.046

Model (6) -0.086 0.158 0.020 -0.109a -0.041 -0.007 0.045 0.002

Model (7) -0.126 0.175 0.029 -0.09a -0.015 -0.009 0.043 0.022 0.114a

1.487 0.001 1,711

5.459 0.008 1,711

4.363 0.010 1,706

4.451 0.014 1,500

3.537 0.012 1,449

10.421 0.049 1,449

11.5: Contemporaneous ∆AAII

F-Stat. Adj- R2 n

12.278 0.014 1,580

CR

IP

11.820 0.056 1,450

Model (2) -0.065c 0.129 1.031a -0.209a

Model (3) -0.065c 0.127 1.041a -0.212a -0.046

Model (4) 0.008 0.126 1.063a -0.217a -0.042 -0.022c

Model (5) -0.288b 0.103 1.078a -0.239a -0.094 0.010 0.089b

Model (6) -0.393b 0.093 1.141a -0.238a -0.085 0.013 0.087b 0.099

Model (7) -0.404b 0.103 1.099a -0.232a -0.074 0.013 0.086b 0.104 0.043

32.352 0.056 1,580

24.516 0.056 1,580

21.449 0.061 1,575

18.938 0.073 1,369

16.383 0.073 1,369

15.428 0.078 1,369

PT

CE

AC

C JANt ∆AAIIt HML MOM TBILL TERM DEF MKT

Model (1) -0.067c 0.146 0.889a

4.246 0.008 1,711

ED

F-Stat. Adj- R2 n

M

AN

C JANt ∆EPUt-1 HML-1 MOM-1 TBILL-1 TERM-1 DEF-1 MKT-1

US

11.4: Lagged ∆EPU

T

Model (1)

42

ACCEPTED MANUSCRIPT 11.6: Lagged ∆AAII Model (4) 0.061 0.139 0.462b -0.097b -0.040 -0.025b

Model (5) -0.129 0.133 0.425 -0.116a -0.053 -0.004 0.054

Model (6) -0.212 0.123 0.476c -0.115a -0.047 -0.001 0.052 0.078

2.986 0.003 1,579

6.554 0.010 1,579

5.145 0.010 1,579

4.951 0.012 1,574

4.588 0.016 1,368

4.018 0.015 1,368

Model (1) 0.018 0.079 -0.954

Model (2) 0.032 0.036 -0.951 -0.205a

Model (3) 0.032 0.036 -0.951 -0.205a 0.003

Model (4) 0.061 0.039 -0.907 -0.211a 0.005 -0.012

Model (5) -0.337b -0.001 -0.767 -0.237a -0.046 0.044c 0.113b

Model (6) -0.323 -0.001 -0.77 -0.237a -0.047 0.043 0.113b -0.011

Model (7) -0.361c 0.032 -0.204 -0.235a -0.022 0.041 0.107b 0.024 0.082b

3.452 0.004 1,243

21.523 0.047 1,243

16.131 0.046 1,243

13.859 0.049 1,239

13.093 0.066 1,033

11.213 0.065 1,033

12.529 0.082 1,033

11.8: Lagged ∆AAII

F-Stat. Adj- R2 n

AN

Model (3) 0.024 0.050 -0.840b -0.066 -0.050

Model (4) 0.074 0.051 -0.816b -0.066 -0.046 -0.019

Model (5) -0.162 0.024 -0.667c -0.088b -0.062 0.014 0.064

Model (6) -0.174 0.024 -0.664c -0.087b -0.061 0.015 0.065 0.009

Model (7) -0.210 0.069 -0.137 -0.085b -0.037 0.013 0.060 0.041 0.075a

3.499 0.006 1,242

2.875 0.006 1,242

2.557 0.006 1,238

2.460 0.008 1,032

2.107 0.007 1,032

3.837 0.022 1,032

PT

2.689 0.003 1,242

9.969 0.050 1,368

Model (2) 0.023 0.054 -0.837b -0.063

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C JANt ∆STLFSIt-1 HML-1 MOM-1 TBILL-1 TERM-1 DEF-1 MKT-1

Model (1) 0.019 0.068 -0.836b

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F-Stat. Adj- R2 n

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C JANt ∆STLFSIt HML MOM TBILL TERM DEF MKT

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11.7: Contemporaneous ∆AAII

Model (7) -0.240 0.153 0.367 -0.098a -0.019 -0.001 0.050 0.092 0.110a

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Model (3) -0.026 0.143 0.445c -0.096b -0.045

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F-Stat. Adj- R2 n

Model (2) -0.026 0.146 0.435c -0.093b

CR

C JANt ∆IIAAt-1 HML-1 MOM-1 TBILL-1 TERM-1 DEF-1 MKT-1

Model (1) -0.027 0.159 0.370

Notes: The weekly measures of investor sentiment are used to explain the size premium in two different forms. In the first, the measures are used in contemporaneous terms, while in the second, the measures are used with one lag. Except for the EPU, the lagged values of the sentiment measure have a significant effect on SMB. “a,” “b” and “c” denote statistical significance at

the 1%, 5% and 10% levels, respectively.

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ACCEPTED MANUSCRIPT

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Highlights  Investor sentiment is captured using a set of different measures, and they include  stock market-based, survey-based and press-based proxies  Size premium correlates with and is predictable using investor sentiment  Investors overvalue small stocks during times associated with very optimistic moods  investors can benefit from “size” diversification using a long-short trading rule

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