Investor sentiment and aggregate volatility pricing

Accepted Manuscript Title: Investor Sentiment and Aggregate Volatility Pricing Author: Chiraz Labidi Soumaya Yaakoubi PII: DOI: Reference:

S1062-9769(15)00113-1 http://dx.doi.org/doi:10.1016/j.qref.2015.11.005 QUAECO 891

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Received date: Revised date: Accepted date:

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Please cite this article as: Labidi, C., and Yaakoubi, S.,Investor Sentiment and Aggregate Volatility Pricing, Quarterly Review of Economics and Finance (2015), http://dx.doi.org/10.1016/j.qref.2015.11.005 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Highlights  Aggregate volatility is a priced risk factor only during low sentiment periods.

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 In high sentiment periods, the relation between aggregate volatility risk and expected returns is undermined.

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 The role of investor sentiment in the pricing of aggregate volatility risk is robust to

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various controls.

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Investor Sentiment and Aggregate Volatility Pricing by

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Chiraz Labidi and Soumaya Yaakoubi1

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Abstract

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October 2015

This paper aims at providing new insights on the pricing of aggregate volatility

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risk by incorporating investor sentiment in the relation between sensitivity to innovations in implied market volatility and expected stock returns. Using both

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cross-sectional and time series analysis, we investigate the effect of the exposure to aggregate volatility risk on stock returns in both high-sentiment and lowsentiment regimes. We find that exposure to aggregate volatility risk is negatively

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related to returns when sentiment is low. However, this relation loses its

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significance when sentiment is high. The documented negative relation is robust to controls for other variables and to the use of various sentiment proxies,

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suggesting that aggregate volatility risk is an independent risk factor only during low sentiment periods.

JEL Classification: G11, G12, G14, G17 Keywords: Investor sentiment; asset pricing; implied market volatility; aggregate volatility; VIX

1

Labidi: Corresponding author. Department of Economics and Finance, College of Business and Economics, United Arab Emirates University, P.O. Box 15551, Al Ain, UAE. Email: [email protected]: LEFA, IHEC, Carthage University, Carthage, 2016, Tunisia. Email: [email protected].

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1. Introduction Studies by Ang, Hodrick, Xing and Zhang (2006), Delisle, Doran and Peterson (2011), Chang, Christoffersen and Jacobs (2013), and more recently Cremers, Halling and Weinbaum

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(2015) reveal that aggregate volatility is a priced risk factor in the cross-section of stock returns. This finding can be explained theoretically within the Intertemporal Capital Asset

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Pricing Model (ICAPM) framework of Merton (1973) based on the hypothesis that an increase in market volatility represents a deterioration in the future investment opportunity

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set.2 Using ICAPM intuition, risk averse investors should find assets whose payoffs are

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positively (or less negatively) related to volatility risk desirable as they enhance their hedging ability against unfavorable shifts in the investment opportunity set (Campbell, 1993; 1996;

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Chen, 2003; Campbell et al., 2012). The high demand for such assets by risk averse investors drives their prices up, resulting in lower expected returns. Consequently, market-wide

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volatility risk should be negatively priced in the cross-section of stock returns.

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In traditional asset pricing models, such as the ICAPM, investor sentiment does not

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influence asset prices.3 Yet, behavioral finance theories emphasize the relevance of investor sentiment in asset pricing (e.g. Delong et al., 1990 and Shleifer and Vishny, 1997) and recent empirical studies provide overwhelming evidence that investor sentiment affects significantly stock returns.4 Given these findings, an investigation of the impact of investor sentiment on the validity of “rational” asset pricing and more precisely on the pricing of aggregate volatility in the cross section of stock returns seems worthwhile.

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French, Schwert and Stambaugh (1987) and Campbell and Hentshel (1992) document that periods of high volatility coincide with downward market moves or recessions (periods of low consumption). 3

Investor sentiment can be broadly defined as an excessive optimism or pessimism about the market’s prospects which is caused by investors’ errors of judgment and not justified by fundamentals. 4

e.g. Brown and Cliff (2004, 2005); Baker and Wurgler (2006, 2007); Baker, Wurgler and Yuan (2012).

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Using three different proxies of investor sentiment, the goal of this paper is to explore the persistence of aggregate volatility as a priced risk factor in the cross-section of stock returns across different sentiment states. We argue in favor of a strong negative relation

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between innovations in market-wide volatility and expected returns during low sentiment periods, but this relation weakens during high sentiment periods. This idea rests on two

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common assumptions in the literature.

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First, in accordance with previous behavioral studies (e.g. Baker and Wurgler, 2006, 2007), we assume that there are two types of investors: rational traders (i.e. arbitrageurs) and

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sentiment traders, who could be either optimistic or pessimistic about the market’s prospects. Unlike arbitrageurs who form correct expectations regarding the future value of an asset,

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sentiment traders make systematically errors in judgment leading them to over or underestimate asset prices depending on their sentiment.

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Second, sentiment traders will only be active in the market when their valuations are

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higher than those of rational traders – i.e. when the aggregate sentiment is high and when the

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market, as a result, is overvalued. However, when the sentiment of irrational traders is low, their reluctance to short keeps them out of the market. This assumption is consistent with the intuition of Miller (1977) who argues that, in the presence of short sale constraints, prices tend to reflect the most optimistic valuation of market participants. Baker and Stein (2004) also show that sentiment traders are more likely to trade when their sentiment is positive. Prompted by these assumptions, we expect that on one hand, in high sentiment

periods, the market is dominated by sentiment traders who are overly optimistic which tends to weaken the relation between aggregate volatility risk and expected returns. Indeed, when sentiment traders are overoptimistic, they require a smaller compensation for risk (Yu and Yuan, 2011). As a result, their demand for stocks that hedge against unfavorable changes in 3

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market volatility is lower and the effect of the sensitivity to market volatility risk on stocks expected returns is less important. On the other hand, during low sentiment periods, prices should reflect rational

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traders’ opinions since sentiment traders stay out of the market. In this setting, rational investors hedge against changes in future volatility by acquiring stocks with a higher

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contemporaneously and thus reduces their future expected returns.

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sensitivity to changes in market volatility. The demand for such stocks increases their prices

Following Ang et al. (2006), we consider changes in the Chicago Board Options

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Exchange (CBOE) volatility index (VIX) to proxy for innovations in aggregate volatility and estimate factor loadings on market implied volatility changes using individual stocks’ daily

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returns. We then sort stocks into quintile portfolios according to their factor loadings and

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other risk factors.

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examine their returns during high and low sentiment periods, separately, while controlling for

We find a substantial negative and significant return differential between the stocks

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with the highest and the lowest return sensitivity to aggregate volatility when sentiment is low whereas no evidence of a significant return differential is obtained when sentiment is high. This finding confirms the intuition that investors want to hedge against changes in aggregate volatility only during low sentiment periods. Using three sentiment proxies to forecast the returns of a long-short portfolio

conditional to the sensitivity to aggregate volatility risk, we find a significant impact of investor sentiment on the return of a hedge portfolio buying stocks with high and selling stocks with low sensitivities to innovations in aggregate volatility. Our results are robust to the incorporation of market, size, book-to-market, momentum and liquidity factors. 4

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Consistent with the results of the portfolio sorts, using Fama and MacBeth (1973) regressions, we also obtain a significant price of aggregate volatility risk, only in low sentiment periods, indicating that, during such periods, investors require a compensation in

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order to hold assets that depreciate when market volatility rises. Overall, our findings reveal that in high-sentiment periods, the relation between aggregate

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volatility risk and expected returns is weaker probably due to a higher participation by

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sentiment traders, whereas, during low-sentiment periods, prices reflect rational traders’ opinions and incorporate a premium that accounts for the sensitivity to changes in market

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volatility.

Our study contributes to a recent literature that emphasizes the importance of investor

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sentiment in asset pricing. One stream of this literature investigates the relationship between investor sentiment and market anomalies. Stambaugh, Yu and Yuan (2012, 2014) find that

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sentiment affects the degree of mispricing generated by a broad set of anomalies. Antoniou,

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Doukas and Subramanyam (2013) show that momentum profits arise only in optimistic

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periods and Livnat and Petrovits (2009) report that stock price reactions to earnings surprises and accruals are influenced by the level of investor sentiment. Other recent studies have focused on the relation between investor sentiment and

standard asset pricing models. Ho and Hung (2009) find that adding investor sentiment as conditioning information in asset pricing models improves the overall model performance in explaining the dynamics of stock returns. Antoniou, Doukas and Subrahmanyam (2015) show that although the CAPM beta appears not to be priced in the cross section of stocks, a significant positive relation between returns and the beta exists during periods of pessimistic sentiment. Yu and Yuan (2011) document the influence of investor sentiment on the market’s mean-variance tradeoff. They find that the stock market expected return is positively related 5

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to the market’s conditional variance in low-sentiment periods but unrelated to variance in high sentiment periods. Gao, Yu and Yuan (2012) find that investor sentiment plays a crucial role in the puzzling relation between idiosyncratic volatility and expected stock returns. They

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argue in favor of a strong negative relation between idiosyncratic volatility and expected stock returns during high-sentiment periods while there is no discernable relation during low-

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sentiment periods.

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Our study is also connected to Shen and Yu (2013). They explore the role of investor sentiment on the pricing of 10 macro-related risk factors, including aggregate volatility. They

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fail to find evidence of “rational” risk factors pricing but they argue that stocks with high exposure to macroeconomic shocks earn significantly higher returns than stocks with low

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exposure, only during low-sentiment periods. While they rely on monthly historical volatility as a proxy for aggregate market volatility and find no evidence of aggregate volatility pricing

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in the cross-section of stock returns, our study differs from theirs in that we follow Ang et al

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(2006) and use changes in the VIX index constructed by the CBOE to estimate the

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innovations in aggregate volatility. The VIX index represents a forward-looking proxy of market volatility and is hence consistent with the idea that a state variable ought to reflect changes in the future prospects, in order to be considered as a relevant risk factor (Chen, 2003). Several studies also provide strong evidence that the use of implied rather than historical volatilities improves the estimation precision (e.g. Jiang and Tian, 2005). Moreover, using the VIX index allows us to confirm the pricing of aggregate volatility risk in the cross-section of stock returns and to build on previous findings while incorporating the investor sentiment.

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The remainder of this paper is organized as follows. Section 2 describes the data. Section 3 explains the methodology and presents the empirical results from time series and cross-sectional analysis. Section 4 concludes.

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2. Data

The cross-sectional relation between aggregate volatility risk and expected returns is

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examined for all stocks traded in the New York Stock Exchange (NYSE) from August 2001

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to December 2008, using daily data collected from Thomson Reuters Datastream.5,6,7 Panel A of Table 1 provides some summary statistics of the monthly stock returns. Daily VIX index

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levels, used to measure the sensitivity to aggregate volatility innovations are collected from the Chicago Board Options Exchange (CBOE) website.

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In order to empirically test the proposed hypotheses, we use three distinct monthly sentiment measures that directly or indirectly reflect investor sentiment. The direct measures

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are the American Association of Individual Investors (AAII) sentiment index and Investors

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Intelligence Advisors’ (IIA) sentiment index.

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The AAII sentiment index is the result of a weekly survey conducted by the American Association of Individual Investors (AAII) to measure the sentiment of market participants about the direction of the stock market during the next six months. The answers are collected and labeled as bullish, bearish or neutral based on the expectation of future market movements. 5

Our sample was constrained by the availability of the sentiment proxies. The data was collected before the last update of Baker and Wurgler (BW) sentiment index in May 16, 2011. The index is now available until December 2010. The start date in 2001 corresponds to the last year of the sample used by Ang et al. (2006), providing an excellent setting to confirm the documented negative price of aggregate volatility risk. 6

We exclude securities that are not common stock from our sample.

7

Ince and Porter (2006) show that after a careful screening, which mainly consists in excluding securities that are not common shares, inferences drawn from Thomson Reuters Datastream data are similar to those drawn from CRSP (Center for Research in Security Prices) data.

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The IIA sentiment index reflects the outlook of over 130 independent financial market newsletter writers. Each week, the editors of Investors Intelligence read the advisors’ newsletters and label them as bullish, bearish or neutral based on their recommendations.

investors and the percentage of bearish investors (Bull–Bear).

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Both sentiment indices are computed as the spread between the percentage of bullish

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The indirect measure considered in this paper is the Baker and Wurgler (2007) (BW) sentiment index, which is computed as the first principal component of six proxies for

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sentiment: the trading volume as measured by the NYSE turnover, the dividend premium, the

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closed-end fund discount, the number and first-day returns on IPOs and the equity share in new issues.8 Figure 1 plots the monthly standardized time series of the three sentiment indices

indices as well as their correlations.

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over the sample period. Panel B of Table 1 provides some summary statistics of the sentiment

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(Insert here Figure 1)

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(Insert here Table 1)

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3. Methodology and Results

3.1. Cross-sectional returns and loadings on ΔVIX

We follow the portfolio formation procedure of Ang et al. (2006) which in turn is part of a long tradition in the asset pricing literature that consists in focusing on the relation between realized factor loadings and realized stock returns. We measure returns’ sensitivity to aggregate volatility changes by regressing daily stock excess returns on market excess returns

8

As explained in Baker and Wurgler (2007), each of the proxies has first been orthogonalized with respect to a set of macroeconomic indicators (growth in industrial production, real growth in durable, non-durable and services consumption, growth in employment, NBER recession indicator) to remove the influence of economic fundamentals. BW Index is obtained from Jeffrey Wurgler’s homepage .

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and the change in VIX index, which we denote by VIX.9 The resulting empirical model is as follows:

where

is the excess return for stock on day ,

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(1)

is the market excess return on day ,

and

risk, respectively, and

are stock

loadings on market risk and aggregate volatility

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volatility factor,

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is the daily change in VIX which is used as a proxy for innovations in the aggregate

is an error term.

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We estimate the above model separately for each stock-month using daily data.10 We

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then sort, at the end of each month, stocks into quintiles based on their in quintile 1 have the lowest values of the realized

coefficients, while stocks in quintile

coefficients. For each quintile portfolio, we calculate equal- and

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5 have the highest

loadings. Stocks

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value-weighted returns, and link them across months generating a single series of postranking returns. Table 2 provides some descriptive statistics for

loadings and quintile

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portfolios’ returns. The first and second columns report the average equal- and valueweighted pre-formation

coefficients, which are estimated for each portfolio. Since the

portfolios are formed by ranking the stocks based on their past equal- (value-) weighted pre-formation

coefficients, the average

loadings monotonically increase from -0.09 (-

0.02) for portfolio 1 to 1.97 (1.91) for portfolio 5. (Insert here Table 2) 9

Following Ang et Al. (2006) we measure daily innovations in aggregate volatility by using daily first differences in VIX because the VIX index is highly serially correlated. 10

For stocks to be included in the computation, we follow Ang et al. (2006) and Amihud (2002). We require at least 17 return and volume observations for each stock-month. The stock price must be greater than $5 at the end of the month. The stock must have market capitalization data at the end of the month and must be listed at the end of the year.

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The third and fourth columns, report the average equal- and value-weighted postformation

loadings for each quintile portfolio. They are obtained by using the loadings

estimated at the end of month t+1 for the stocks composing the portfolios formed at the end

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of month t. The post-formation coefficients are used to examine whether the loadings are stable over time. Table 2 indicates that the average equal- (value-) weighted post-formation

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loadings monotonically increase from 0.66 (0.68) for portfolio 1 to 1.2 (1.18) for

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portfolio 5. Comparing the average pre- and post-formation coefficients indicates that the loadings tend to maintain a good dispersion and ranking order.

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In the fifth and sixth columns, we report the post-formation average monthly returns for each of the equal- and value-weighted quintile portfolios. Consistent with the negative

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price of aggregate volatility risk documented by Ang et al. (2006), we find that higher past

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loadings generate lower average returns.

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Finally, the rows labeled “5-1” Return, CAPM Alpha, FF-3 Alpha, and Carhart-4 Alpha report the difference in mean returns between portfolios 5 and 1, the “5-1” capital asset

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pricing model alpha spread, the “5-1” Fama-French three-factor model alpha spread, and the Carhart four-factor model alpha spread respectively.11 We find a significant difference of -0.44% (-0.34%) between the average returns of

the equal- (value-) weighted quintile portfolios 5 and 1. CAPM alpha spreads, FF-3 alpha spreads and Carhart-4 alpha spreads are also all negative and significant for both equal- and value-weighted portfolios. Controlling for the CAPM/Fama-French/Carhart factors results in 11

CAPM, FF-3, and Carhart-4 alphas are obtained from the estimation of the CAPM, the Fama-French three-factor model, and the Carhart four-factor model, respectively, using the quintile portfolio returns. Fama-French Factors (MKT, SMB and HML) and the momentum factor (MOM) are collected from Kenneth French’s homepage < www.dartmouth.edu/~kfrench/>.

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even larger average return spreads of -1.03%/-0.97%/-0.90% per month for equal-weighted quintile portfolios and -1.29%/-1.25%/-1.14% per month for value-weighted portfolios. These findings confirm the expectation that stocks with high sensitivities to innovations in

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aggregate volatility should earn low returns as such stocks represent a good hedge for risk averse investors who dislike high volatility risk. Consistent with Ang et al (2006), our

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preliminary portfolio sorts results argue in favor of a negative market price of aggregate

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volatility risk.

3.2. Cross-sectional portfolio returns, investor sentiment and aggregate volatility

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risk

We pursue the analysis by examining quintile portfolio returns (both equal- and value-

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weighted) conditional on the state of sentiment. We use the three proxies of investor sentiment, namely AAII, IIA and BW indices, to identify high and low sentiment states as

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follows: the sentiment in month t is high (low) if the sentiment index at the beginning of the

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month is above (below) the median value. The obtained results reported in Panels A and B of

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Table 3 show a clear two-regimes pattern.

During low sentiment periods (see Table 3, Panel A), we find a strong negative

relation between stocks’ sensitivity to innovations in aggregate volatility and expected returns. Stock returns monotonically decrease as sensitivity to innovations in systematic implied volatility increases and the “5-1” returns, CAPM alpha spreads, FF-3 alpha spreads, and Carhart-4 alpha spreads are all negative and significant. Using the AAII (IIA) investor sentiment index, we find that the “5-1” return spread is a significant -1.48% (-2.37%) per month for equal-weighted portfolios. A similar pattern is apparent for value-weighted returns with a spread of -1.28% (-2.41%) per month. Using the BW investor sentiment index, the equal- (value-) weighted quintile portfolio with the highest aggregate volatility risk displays a 11

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monthly return 1.33% (1.44%) lower than that of the lowest quintile portfolio. CAPM alpha spreads, FF-3 alpha spreads, and Carhart-4 alpha spreads are also all negative and even larger and more significant using the three sentiment indices and for both equal- and value-weighted

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portfolios. These results clearly indicate the existence of a significant negative relation between

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loadings on VIX and subsequent returns during low sentiment periods that persists after

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controlling for the market factor, Fama-French factors and Carhart factors.

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(Insert here Table 3)

In contrast, in the high sentiment regime (Table 3, Panel B), the “5-1” equal- and

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value-weighted return spreads, CAPM alpha spreads, FF-3 alpha spreads, and Carhart-4 alpha spreads are mostly non-negative and are all non-significant at the 1, 5 and 10% levels. We

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investor sentiment is high.

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conclude that there is no relation between the loadings on VIX and subsequent returns when

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These findings confirm the existence of a two-regime pattern: the relation between sensitivity to innovations in systematic implied volatility and expected returns changes significantly from periods when sentiment is high to periods when sentiment is low. The obtained results confirm the intuition that “rational” asset pricing is only valid during the low sentiment state and that the presence of sentiment traders, during the high sentiment state, tends to weaken the relation between aggregate volatility risk and expected returns. This also suggests that Ang et al. (2006) results may only reflect a mean loading for both sentiment regimes which is mainly driven by sensitivities to innovations in aggregate volatility when investor sentiment is low. 3.3. Time-series regressions of long-short portfolio returns 12

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Another way to investigate the aggregate volatility risk effect across time is to use investor sentiment to forecast the returns of portfolios that are long on stocks with high sensitivities to innovations in systematic implied volatility and short on stocks with low exposure. As shown

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previously, in low sentiment periods, stocks with high exposure to innovations in systematic implied volatility earn lower expected returns than stocks with low sensitivity, so investor .

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sentiment seems likely to forecast the returns of long-short portfolios formed on

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Following Baker and Wurgler (2006) methodology, we examine the hypothesis that sentiment can predict the next period’s return of the long-short portfolios conditional on

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sensitivity to innovations in aggregate volatility. The adopted approach allows us to control for various sources of risk and to incorporate the sentiment both as a dummy and as a

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continuous variable.

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We first use the following regression to disentangle the effects of aggregate

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volatility risk from Fama-French factors along with the momentum and liquidity factors:

where

is the “5-1” long-short portfolio return constructed using the same quintile

portfolios as in Table 2. factors and

(2)

,

and

are the Fama-French market, size and value

is the momentum factor. As a liquidity proxy (

), we use the Pastor and

Stambaugh (2003) measure which is constructed from the least squares estimate of the parameter in the following regression:12 (3) 12

Pastor-Stambaugh model focuses on a particular dimension of liquidity associated with temporary price fluctuations induced by the order flow. Lower liquidity tends to correspond to stronger price reversals the next day resulting from the order flow in a given direction on a particular day.

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where

and

are respectively the return and excess return for stock i on day t and

month m,

is the signed indicator which is equal to 1 if the excess return

is

is the volume (in millions of dollars) for stock i on

positive and -1 if it is negative, and

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day t and month m. The signed volume is a proxy for the previous day order flow.

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The model in equation (3) is estimated for each stock-month using daily return data.

where

(4)

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The obtained liquidity measure is then averaged over all stocks month by month:

is the number of stocks and

is considered as a monthly measure of aggregate

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liquidity.

Systematic liquidity risk is usually measured as the sensitivity to innovations in aggregate , we run the following regression using the

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differenced liquidity series:

d

liquidity. To obtain the liquidity innovation

The estimated

is then multiplied by

(5) :13 (6)

Including the liquidity factor, estimated in (6), in our regressions allows to mitigate the concern that the sentiment effect might be related to market liquidity (e. g. Baker and Stein, 2004 and Liu, 2015).

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The scaling has no effect on the results and is merely used to produce a desirable range for the liquidity index and beta.

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Panel A of Table 4 reports the results of the time-series regression in equation 2 before including the sentiment variables. The negative and significant

coefficients, obtained for

both equal-weighted and value-weighted long-short portfolios, provide a formal support to

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our preliminary findings from the sorts and confirm the conclusion of Ang et al. (2006) that higher sensitivity to innovations in systematic implied volatility yields a lower subsequent

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return after controlling for market, size, value, momentum and liquidity risk factors.

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To check the robustness of our results to the choice of the liquidity factor proxy, we have also estimated the same regression using the market illiquidity measure proposed by Amihud

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(2002). This measure, which follows Kyle’s (1985) concept of illiquidity, has been used in

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several recent studies on liquidity14.

Amihud (2002) market illiquidity measure is computed as the equal- (value-) weighted

in month , Rtdi is the return on stock i on day d of month t and

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stock

is the number of days for which data are available for

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, where

as

d

average of individual stock illiquidity for each month. Individual stock illiquidity is obtained

is the

respective daily volume (measured in millions of dollars).15 Panel B of Table 4 reports the estimates of the regression in equation (2) when the market illiquidity shock (ILLIQ) is used

14

15

Examples are Acharya and Pederson (2005), Liu (2015) and Avramov, Cheng and Hameed (2015).

The market illiquidity shock ( process.

is measured as the residual of the logarithm of market illiquidity in an AR(1)

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in replacement of Pastor and Stambaugh (2003) liquidity factor. The obtained results show persistent negative and significant

coefficients providing further support to Ang et al

(Insert here Table 4)

as follows:

where

(7)

an

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To include investor sentiment as a dummy variable, we modify equation

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(2006) finding.

is a dummy variable equal to one if the sentiment proxy is higher than the median,

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and zero otherwise.

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d

We also run a predictive regression using a continuous investor sentiment variable:

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(8)

where

is the investor sentiment proxied by the American Association of Individual

Investors index, Investors Intelligence Advisors index, and Baker and Wurgler (2007) index.16

Table 5 reports the results of the regression including the high sentiment and low

sentiment as dummy variables without the intercept. For the equal-weighted portfolio, the results indicate that during high sentiment periods, there is no significant relation between the 16

Following Baker and Wurgler (2007), we use a sentiment-changes index (as opposed to a sentiment-levels index) to test for return predictability associated with changes in sentiment. The changes in AAII and IIA indices and the BW sentimentchanges index (measured as the first principal component of the changes in the six proxies) are considered here.

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sentiment index and the long-short portfolio return.17 However, when sentiment is low, AAII (IIA) sentiment index predicts a significant -1.9% (-1.3%) return per month, while BW sentiment index forecasts a significant return of -3.1%. We obtain similar results with value-

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(Insert here Table 5)

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weighted portfolios.

Table 6 reports the results when investor sentiment is measured as a continuous

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variable. As expected, investor sentiment significantly predicts the long-short portfolio return with a stronger predictive power associated with the IIA and the BW sentiment indices.

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coefficients also remain negative and highly significant and, with the exception of MKT and

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MOM, none of the other documented risk factors can be related to the long-short portfolio return.

d

(Insert here Table 6)

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Very similar results, reported in Tables 7 and 8, were obtained when we use Amihud

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(2002) illiquidity measure in replacement of Pastor and Stambaugh (2003) liquidity factor in equations (7) and (8). Overall, these findings indicate that the relation between the sensitivity to innovations in aggregate volatility and future returns significantly depends on investor sentiment. Furthermore, the role played by sentiment in the pricing of aggregate volatility risk is robust to various additional risk controls. (Insert here Table 7) (Insert here Table 8)

17

With the exception of a weakly significant Index.

coefficient (at the 10% level) when sentiment is measured with the AAII

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3.4. The price of aggregate volatility risk across high and low sentiment regimes The portfolio sorts and predictive regressions strongly show that aggregate volatility risk is

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negatively priced in the cross-section of stock returns but only during the low sentiment regime. The next step is then to estimate the price of cross-sectional aggregate volatility risk

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conditional on the state of sentiment using Fama and MacBeth (1973) regressions with firm-

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level data. Following DeLisle et al. (2011), we include in the cross-sectional regressions, , log of size (lnSize), book-to-market equity ratio (B/M), 12-month momentum, market and liquidity beta (

) as independent variables. The dependent variable is the

an

beta (

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subsequent monthly return.

The independent variables are constructed as follows: LnSize is the natural logarithm

d

of the market value of equity. B/M is the book value of equity divided by the market value of equity.18 12-month momentum is the cumulative return from the end of month .

te

end of month

to the

is estimated, using daily data, from a month by month rolling

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regression of the stock excess return on market excess return and the change in VIX index (equation (1)) over a 36 months period.19 Following Pastor and Stambaugh (2003),

is

also estimated using a rolling time-series regression that includes the Fama-French risk factors along with the aggregate liquidity measure in (6). The construction of

was

explained in the previous subsections.

18

The book value of equity assigned to a firm from July of year y to June of year (y+1) is the value at the end of the fiscal year in (y-1)

19

Following Delisle et al. (2011), we control for

innovations while estimating market

as

and

innovations

are highly correlated.

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The first column of Table 9 reports Fama-MacBeth regression results without considering investor sentiment regimes. In the subsequent columns, we consider the AAII, IIA and BW sentiment indices to classify the entire sample into high and low sentiment

ip t

periods and then estimate risk factors’ premiums separately for the two regimes. Nonconditional to sentiment regimes, we find a negative and highly significant coefficient on

cr

, representing the average price of aggregate volatility risk. The significance level and

us

magnitude of the price of aggregate volatility risk are close to those documented by Ang et al (2006) and DeLisle et al (2011). In line with asset pricing theory, this result confirms that

an

aggregate volatility risk is priced in the cross-section of stock returns and the market price of volatility risk is negative.

M

Results of the Fama-MacBeth regressions conditional on sentiment regimes show that the price of aggregate volatility risk is significant at the 1% level only in low sentiment

d

periods. Economically, when sentiment is low, one unit decrease in sensitivity to aggregate

te

volatility changes has a price of 60.5, 105.9 and 56.3 basis points per month, considering

Ac ce p

AAII, IIA and BW sentiment indices, respectively. When sentiment is high, the coefficient on is negative but insignificant. These results are consistent with those found in our

portfolio analysis and provide further evidence that the economically sound negative and significant relation between sensitivity to innovations in aggregate volatility and expected returns, is only valid during low sentiment periods. (Insert here Table 9)

We also notice that the coefficients of LnSize, B/M,

, and

are consistently

significant in almost all the regressions and across both sentiment regimes. The momentum coefficient appears however to be higher and more significant in high sentiment periods. This 19

Page 20 of 39

is consistent with Antoniou, et al. (2013) result that the momentum effect is stronger when sentiment is high as the spread of bad news during these periods is relatively slow. The coefficient of

also reveals a very interesting finding. The market price of liquidity risk is

ip t

always highly significant but its sign changes across sentiment regimes. When investor sentiment is low, we find a positive price of liquidity risk that is consistent with Pastor and

cr

Stambaugh (2003) argument that investors prefer assets whose returns are less sensitive to

us

aggregate liquidity. However, our results indicate that when sentiment is high, the liquidity risk premium becomes negative, suggesting that during high sentiment periods, investors do

an

not hedge against liquidity risk and prefer to hold stocks with high sensitivities to aggregate liquidity. This finding can be explained by the theoretical prediction that the stock market is

M

more liquid when investors are more bullish (DeLong et al, 1990; Baker and Stein, 2004). Liu (2015) also provides empirical evidence of the predicted positive relation between investor

d

sentiment and stock market liquidity.

te

Finally, and since stocks are equally weighted in the cross-sectional regressions, the

Ac ce p

results in Table 9 can be compared to those of Tables 2 and 3 in order to assess the extent to which sensitivity to innovations in implied systematic volatility accounts for the large spread in returns between the quintile portfolios with the highest and the lowest exposure to aggregate volatility risk during low sentiment periods. The mean spread in VIX betas ), reported in Table 2, is equal to 2.06.

between portfolios 5 and 1 (ranked by

Multiplying the mean “5-1” portfolio  VIX by the price of sensitivity to changes in VIX, when AAII, IIA and BW sentiment indices are low, yields a return of almost -125, -218 and 116 basis points per month, respectively. These obtained values are very close to the “5-1”

20

Page 21 of 39

return spreads reported for equal-weighted portfolios in Table 3.20 Therefore, the difference in mean returns between portfolios with the highest and lowest

loadings, when investor

sentiment is low, is essentially arising from the sensitivity to implied systematic volatility

ip t

innovations. Overall, our results suggest that aggregate volatility risk or how stock returns respond to

cr

innovations in implied systematic volatility is an independent risk factor and this risk is

us

priced in the cross-section of stock returns only during low sentiment periods. This finding confirms the intuition of Yu and Yuan (2011) that the active presence of sentiment traders

an

during high sentiment periods can undermine the risk-return tradeoff. In contrast, in low sentiment periods, “rationality” holds and the long-standing intuition that risk ought to be

M

compensated remains valid. It also suggests that investor sentiment should be incorporated in

te

4. Conclusion

d

asset pricing models and may play an important role in asset allocation decisions.

Taking the role of investor sentiment into account, we examine whether aggregate volatility

Ac ce p

is a priced risk factor. Prior studies document a negative premium associated with the sensitivity to innovations in market volatility. The evidence found in this paper confirms the pricing of aggregate volatility risk but only in low sentiment periods, periods during which sentiment traders have small impact. We use changes in the VIX index constructed by the CBOE to proxy for innovations

in market volatility and model the return process as a function of innovations in the VIX index. We estimate loadings on VIX changes, sort securities into portfolios based upon their estimated factor loadings and examine their future returns during high and low sentiment 20

The comparison between results in the first column of Table 9 and those in Table 2 (without distinction between high and low sentiment periods), leads to the same conclusion.

21

Page 22 of 39

periods separately. The results show a clear two-regime pattern. We find a large and significant return differential between the firms with the most and the least negative return sensitivity to aggregate volatility when sentiment is low, but when it is high, there is no

ip t

differential return requirement. We conclude that a low sentiment is a necessary condition for the negative relation between loadings on VIX innovations and expected returns suggesting

cr

that “rational” asset pricing is only valid during low sentiment regimes; i.e. when sentiment

us

traders are out of the market.

We pursue the analysis by using the investor sentiment to forecast the returns of a

an

long-short portfolio formed on exposure to aggregate volatility risk. Following Baker and Wurgler (2006), we conduct a predictive regression analysis and test whether the profits from

M

the long-short portfolio in each sentiment state are equal to zero. Again the results confirm that the relation between sensitivity to innovations in aggregate volatility and future returns is

d

strongly impacted by investor sentiment even after controlling for the comovement with

te

market return, size, book-to-market, momentum and liquidity factors. More specifically, high

Ac ce p

sensitivity to VIX innovations yields lower subsequent risk-adjusted returns only when sentiment is low.

We also estimate Fama and MacBeth (1973) regressions with firm-level data. The

obtained results are consistent with our portfolio analysis. Stocks’ sensitivities to innovations in implied systematic volatility are related to returns when investor sentiment falls, but not when it rises. Thus we conclude that aggregate volatility is a priced risk factor only in low sentiment periods, indicating that, during such periods, investors require compensation in order to hold assets that depreciate when market volatility rises. Fama-MacBeth regressions also reveals that market-wide liquidity risk is positively priced in the cross-section of stock

22

Page 23 of 39

returns, only when investor sentiment is low, confirming the intuition that rational pricing occurs when noise traders stay out of the market. Overall, the evidence provided in this paper strongly supports the hypothesis that

ip t

high market sentiment reduces market volatility risk premium by activating biased sentiment traders who demand a lower compensation for bearing risk. This result is important as it

cr

deepens our understanding of the relation between exposure to aggregate volatility risk and

us

future returns. It should also be of a great interest to asset managers since their asset allocation decisions will depend on the state of investor sentiment. During high sentiment

an

periods, for example, it will be profitable for them to reduce their holdings on stocks with

Ac ce p

te

d

M

high exposure to aggregate volatility risk, as this risk is not adequately compensated.

23

Page 24 of 39

References Acharya, V. V., & Pederson, L. H. (2005). Asset pricing with liquidity risk. Journal of

ip t

Financial Economics, 77 (2), 375-410. Amihud, Y. (2002). Illiquidity and Stock Returns: Cross Section and Time Series Effects.

cr

Journal of Financial Markets, 5, 31-56.

us

Ang, A., Hodrick, R., Xing, Y., & Zhang, X. (2006). The cross-section of volatility and expected returns. Journal of Finance, 51, 259–299.

an

Antoniou, C., Doukas, J., & Subrahmanyam, A. (2013). Cognitive dissonance, sentiment and momentum. Journal of Financial and Quantitative Analysis, 48, 245-275.

M

Antoniou, C., Doukas, J., & Subrahmanyam, A. (2015). Investor sentiment, beta and the cost

d

of equity capital. Management Science, Forthcoming.

te

Avramov, D., Cheng, S., & Hameed, A. (2015). Time-varying liquidity and momentum

Ac ce p

profits. Journal of Financial and Quantitative Analysis, Forthcoming. Baker, M., & Stein, J. (2004). Market liquidity as a sentiment indicator. Journal of Financial Markets, 7, 271–299.

Baker, M., & Wurgler, J. (2006). Investor sentiment and the cross-section of stock returns. Journal of Finance, 61, 1645-1680.

Baker, M., & Wurgler, J. (2007). Investor sentiment in the stock market. Journal of Economic Perspectives, 21, 129-151. Baker, M., Wurgler, J., & Yuan, Y. (2012). Global, local and contagious investor sentiment. Journal of Financial Economics, 104, 272-287. 24

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Brown, G., & Cliff, M. (2004). Investor sentiment and the near-term stock market. Journal of Empirical Finance, 11, 1-27. Brown, G., & Cliff, M. (2005). Investor sentiment and asset valuation. Journal of Business,

ip t

78, 405-440.

cr

Campbell, J. Y. (1993). Intertemporal asset pricing without consumption data. American

us

Economic Review, 83, 487–512.

Campbell, J. Y. (1996). Understanding risk and return. Journal of Political Economy, 104,

an

298-345.

Campbell, J. Y., & Hentschel, L. (1992). No news is good news: An asymmetric model of

M

changing volatility in stock returns. Journal of Financial Economics, 31, 281-318.

d

Campbell, J. Y., Giglio, S., Polk, C., & Turley, R. (2012). An intertemporal CAPM with

te

stochastic volatility. Working Paper, Harvard University. Chang, B. Y., Christoffersen, P., & Jacobs, K. (2013). Market skewness risk and the cross

Ac ce p

section of stock returns. Journal of Financial Economics, 107, 46-68.

Chen, J. (2003). Intertemporal CAPM and the cross-section of stock returns. Working Paper, University of Southern California.

Cremers, M., Halling, M., & Weinbaum, D. (2015). Aggregate jump and volatility risk in the cross-section of stock returns. Journal of Finance, 70, 489–924.

DeLisle, R. J., Doran, J. S., & Peterson, D. R. (2011). Asymmetric pricing of implied systematic volatility in the cross-section of expected returns. Journal of Futures Markets, 31, 34-54.

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DeLong, B., Shleifer, A., Summers, L. H., & Waldmann, R. (1990). Noise trader risk in financial markets. Journal of Political Economy, 90, 703-738. Fama, E. F., & MacBeth, J. D. (1973). Risk, return, and equilibrium: Empirical tests. Journal

ip t

of Political Economy, 81 (3), 607-636.

cr

Fama, E. F., & French, K. (1993). Common risk factors in the returns on stocks and bonds.

us

Journal of Financial Economics, 33, 3-56.

French, K. R., Schwert, G. W., & Stambaugh, R. F. (1987). Expected stock returns and

an

volatility. Journal of Financial Economics, 19, 3-29.

Gao, X., Yu, J., & Yuan, Y. (2012). Investor sentiment and idiosyncratic volatility puzzle.

M

Working Paper, University of Pennsylvania.

d

Ho, C., & Hung, C. H. (2009). Investor sentiment as conditioning information in asset

te

pricing. Journal of Banking and Finance, 33, 892‒903.

Ac ce p

Ince, O.S., & Porter, R. B. (2006). Individual equity return data from Thomson Datastream: Handle with Care!. Journal of Financial Research, 29 (4), 463-479.

Jiang, G. J., & Tian, Y. S. (2005). The model-free implied volatility and its information content. Review of Financial Studies, 18, 1305-1342.

Kyle, A. S. (1985). Continuous Auctions and Insider Trading. Econometrica, 53 (6), 13151335.

Liu, S. (2015). Investor sentiment and stock market liquidity. Journal of Behavioral Finance, 16 (1), 51-67.

26

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Livnat, J., & Petovits, C. (2009). Investor sentiment, post-earnings announcement drift, and accruals. Working Paper, New York University.

ip t

Merton, R. C. (1973). An intertemporal asset pricing model. Econometrica, 41, 867–887. Miller, E. M. (1977). Risk, uncertainty and divergence of opinion. Journal of Finance, 32,

cr

1151-1168.

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Pastor, L., & Stambaugh, R. F. (2003). Liquidity risk and expected stock returns. Journal of Political Economy, 111, 642–685.

an

Shen, J., & Yu, J. (2013). Investor sentiment and economic forces. Working Paper, University of Minnesota.

M

Shleifer, A., & Vishny, R., 1997, The limits of arbitrage, Journal of Finance, 52, 35-55.

d

Stambaugh R.F., Yu, J., & Yuan, Y. (2012). The short of it: Investor sentiment and

te

anomalies. Journal of Financial Economics, 104, 288-302.

Ac ce p

Stambaugh R.F., Yu, J., & Yuan, Y. (2014). The long of it: Odds that investor sentiment spuriously predicts anomaly returns. Journal of Financial Economics, 114, 613-

619.

Yu, J., & Yuan, Y. (2011). Investor sentiment and the mean-variance relation, Journal of Financial Economics, 100, 367-381.

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M

an

us

cr

ip t

Figure 1. Sentiment Indices

Ac ce p

te

d

Note. This figure plots monthly values of three distinct proxies of investor sentiment. The AAII sentiment index is the result of a weekly survey conducted by the American Association of Individual Investors. The IIA sentiment index reflects the outlook of over 130 independent financial market newsletter writers. Both sentiment indices are computed as the spread between the percentage of bullish investors and the percentage of bearish investors (Bull–Bear). The third measure is the BW sentiment index, which was introduced by Baker and Wurgler (2007) and is computed as the first principal component of the changes in six proxies for sentiment: the trading volume as measured by the NYSE turnover, the dividend premium, the closed-end fund discount, the number and first-day returns on IPOs and the equity share in new issues. Each of the proxies has first been orthogonalized with respect to a set of macroeconomic indicators (growth in industrial production, real growth in durable, non-durable and services consumption, growth in employment, NBER recession indicator).

28

Page 29 of 39

Table 1. Summary Statistics

ip t

Panel A reports summary statistics of the monthly stock returns. Our sample includes 1,594,728 stock-day observations. Panel B provides summary statistics of the sentiment indices (AAII, IIA and BW) as well as their correlations. AAII denotes the sentiment index computed by the American Association of Individual Investors, IIA sentiment index corresponds to Investors Intelligence Advisors’ index and BW is the sentiment index calculated by Baker and Wurgler (2007).

Table 1: Summary Statistics

Min

Max

0.000

0.083

-0.325

0.204

5th

25th

Median

-0.130

-0.380

Percentiles

Skewness

Panel B: Sentiment Indices

-0.866

7.203

75th

95th

0.006

0.048

IIA

BW

Mean

0.092

0.200

-0.070

Std. Dev.

0.213

0.153

0.878

% High

d

M

AAII

48.86

67.05

57.95

51.14

32.95

42.05

te

% Low

Kurtosis

us

Std. Dev.

an

Mean

cr

Panel A: Monthly Returns

0.113

Correlations

Ac ce p

AAII

1

IIA

0.438

1

BW

0.149

0.276

1

29

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Table 2. Quintile Portfolios Sorted by Sensitivity to Innovations in Aggregate Volatility

ip t

For each firm, we run the following regression:

where is the excess return for stock i on day t, is the excess return on the market on day t, is the change in VIX from the end of day (t-1) to the end of day t which we use as the proxy for innovations in the aggregate volatility factor, and are loadings on market risk and aggregate volatility risk respectively

while stocks in quintile 5 have the highest equal- and value-weighted pre-formation

us

cr

and is an error term. We require at least 17 return and volume observations for each stock-month. The stock price must be greater than $5 at the end of the month. The stock must have market capitalization data at the end of the month and must be listed at the end of the year. We obtain monthly parameter estimates for each firm in each month. We then sort, at the end of each month, firms into quintiles based on their VIX sensitivities coefficients, (measured by the VIX loadings). Stocks in quintile 1 have the lowest values of the realized coefficients. The first and second columns report the average

an

coefficients, which are estimated for each portfolio. The third

te

d

M

loadings for each and fourth columns, report the average equal- and value-weighted post-formation quintile portfolio. They are obtained by using the loadings estimated at the end of month t+1 for the stocks composing the portfolios formed at the end of month t. The fifth and sixth columns report the post-formation average monthly returns for each of the equal- and value-weighted quintile portfolios. The rows labeled “5-1” Return, CAPM Alpha, FF-3 Alpha and Carhart-4 Alpha report the difference in mean returns between portfolios 5 and 1, the “5-1” capital asset pricing model alpha spread, the “5-1” alpha spread using the Fama-French threefactor model, and the “5-1” alpha spread using the Carhart four-factor model, respectively. (*), (**), and (***) denote significance at the 10%, 5%, and 1% levels, respectively. Robust Newey-West (1987) p-values are reported in parentheses. The sample period ranges from September 2001 to December 2008. Table 2: Quintile portfolios sorted by

 VIX

Ac ce p

Mean of Pre-formation   VIX



Post-formation average monthly returns (%)

Equal

Value

Equal

Value

Equal

Value

1 (Low)

-0.09

-0.02

0.66

0.68

0.28

0.22

2

0.49

0.50

0.75

0.71

0.26

0.16

3

0.83

0.83

0.84

0.82

0.02

0.09

4

1.20

1.20

0.98

0.96

-0.06

-0.01

5 (High)

1.97

1.91

1.20

1.18

-0.15

-0.11

“5-1” Return

-0.44*** (0.000)

-0.34*** (0.000)

“5-1” CAPM Alpha

-1.03** (0.012)

-1.29*** (0.006)

“5-1” FF-3 Alpha

-0.97** (0.019)

-1.25*** (0.007)

“5-1” Carhart-4 Alpha

-0.90** (0.027)

-1.14** (0.012)

 VIX

Quintiles

Mean of Post-formation   VIX

30

Page 31 of 39

Table 3. Quintile Portfolios Sorted by

in Low and High Sentiment Periods

Ac ce p

te

d

M

an

us

cr

ip t

This table reports the post-formation average monthly returns when we examine -sorted quintile portfolios (both equal- and value-weighted) during high and low-sentiment periods separately. The sentiment in month t is considered as high (low) if the sentiment index at the beginning of the month is above (below) the median value. AAII denotes the sentiment index computed by the American Association of Individual Investors, IIA sentiment index corresponds to Investors Intelligence Advisors’ index and BW is the sentiment index calculated by Baker and Wurgler (2007). The rows labeled “5-1” Return, CAPM Alpha, FF-3 Alpha and Carhart-4 Alpha report the difference in mean returns between portfolios 5 and 1, the “5-1” capital asset pricing model alpha spread, the “51” alpha spread using Fama-French three-factor model, and the “5-1” alpha spread using Carhart four-factor model, respectively. (*), (**), and (***) denote significance at the 10%, 5%, and 1% levels, respectively. Robust Newey-West (1987) p-values are reported in parentheses.

31

Page 32 of 39

Table 3: Quintile portfolios sorted by

 VIX

Panel A: Quintile portfolios sorted by

in low and high sentiment periods

 VIX

in low sentiment periods

Post-formation average monthly returns (%)



BW Sentiment Index

Value

Equal

Value

Equal

1 (Low)

-0.64

-0.62

-2.22

-1.72

-0.04

2

-0.67

-0.83

-2.43

-2.04

-0.18

3

-1.15

-1.09

-2.88

-2.29

-0.54

4

-1.32

-1.08

-3.59

-2.90

-0.84

5 (High)

-2.12

-1.91

-4.59

-4.12

“5-1” Return

-1.48** (0.014)

-1.28** (0.030)

-2.37** (0.021)

“5-1” CAPM Alpha

-2.69*** (0.002)

-1.41* (0.051)

“5-1” FF-3 Alpha

-2.52*** (0.004)

“5-1” Carhart-4 Alpha -2.60*** (0.001)

Value -0.02 -0.22 -0.59 -0.73

cr

Equal

-1.46

-2.41** (0.011)

-1.33* (0.069)

-1.44* (0.053)

-3.73*** (0.007)

-2.53** (0.018)

-1.82** (0.022)

-1.35* (0.097)

-1.70** (0.032)

-3.09*** (0.008)

-3.17*** (0.009)

-2.42*** (0.001)

-2.07** (0.021)

-1.77** (0.020)

-3.36*** (0.002)

-3.05*** (0.009)

-2.42*** (0.001)

-2.45*** (0.001)

 VIX

in high sentiment periods

M

Panel B: Quintile portfolios sorted by 

us

-1.37

an

 VIX

Quintiles

IIA Sentiment Index

ip t

AAII Sentiment Index

Post-formation average monthly returns (%)



 VIX

Quintiles

Value

Equal

Value

Equal

Value

1.11

1.33

1.04

0.55

0.53

1.23

1.20

1.39

1.09

0.62

0.48

1.25

1.33

1.24

1.09

0.49

0.66

1.27

1.12

1.42

1.21

0.59

0.60

1.90

1.77

1.71

1.57

0.47

0.57

“5-1” Return

0.65 (0.233)

0.66 (0.289)

0.37 (0.326)

0.53 (0.235)

-0.09 (0.853)

0.04 (0.939)

“5-1” CAPM Alpha

0.80 (0.203)

0.83 (0.204)

0.42 (0.297)

0.63 (0.204)

-0.18 (0.794)

0.08 (0.914)

“5-1” FF-3 Alpha

-0.07 (0.916)

0.28 (0.719)

0.05 (0.914)

0.54 (0.313)

-0.22 (0.755)

0.11 (0.886)

“5-1” Carhart-4 Alpha

0.03 (0.965)

0.48 (0.507)

0.02 (0.962)

0.56 (0.300)

-0.17 (0.807)

0.18 (0.820)

2 3 4

Ac ce p

5 (High)

1.25

BW Sentiment Index

te

1 (Low)

Equal

IIA Sentiment Index

d

AAII Sentiment Index

32

Page 33 of 39

Table 4. Time series regression for long-short portfolios Panel A of this table reports the coefficients of the following regression:

Table 4: Time series regression for long-short portfolios 5

−

1

=

0

+

+





0

+ MKT



SMB

-0.015*** (0.005)

0.392*** (0.000)

0.077 (0.756)

Value-weighted

-0.019*** (0.002)

0.226** (0.018)

0.246 (0.344)

−

1

=

0

+



+



0

-0.018** (0.026)

Value-weighted

-0.026*** (0.004)

MKT



SMB



-0.067 (0.683) 0.114 (0.550) +

+

 LIQ

R

-0.042 (0.150)

0.536 (0.591)

0.175

0.113

-0.065** (0.034)

0.365 (0.307)

0.074

0.004

 HML



MOM

+ MOM



+ ILLIQ

R

2

2

Adj. R

Adj. R

2

2

0.389*** (0.000)

0.227 (0.366)

0.004 (0.979)

-0.031 (0.330)

0.010 (0.823)

0.218

0.159

0.226** (0.034)

0.311 (0.272)

0.154 (0.402)

-0.045 (0.216)

0.045 (0.373)

0.103

0.035

Ac ce p

te

Equal-weighted

+

d

5

+

 HML

M

Equal-weighted

Panel B:

+

an

Panel A:

us

cr

ip t

where is the “5-1” long-short portfolio monthly return constructed using the same quintile , and are the Fama-French market, size and value factors. portfolios as in Tables 2 and 3, is the momentum factor. Monthly time series of , , and are collected from Kenneth French’s homepage. The liquidity proxy ( ) is measured following Pastor and Stambaugh (2003). Panel B reports the coefficients of the same regression when we replace the liquidity proxy by Amihud (2002) illiquidity ). The number of monthly observations in the time series is 88. (*), (**), and (***) denote measure ( significance at the 10%, 5%, and 1% levels, respectively. Robust Newey-West (1987) p-values are reported in parentheses.

33

Page 34 of 39

Table 5. Predictive regressions for long-short portfolios with a dummy sentiment variable

ip t

Table 5 reports the results of the following regression:

us

cr

where is the “5-1” long-short portfolio return constructed using the same quintile portfolios as in is a dummy variable equal to one if the sentiment proxy is higher than the median, and zero Table 2, , and are the Fama-French market, size and value factors. is the momentum otherwise, factor. The liquidity proxy ( ) is measured following Pastor and Stambaugh (2003). AAII denotes the sentiment index computed by the American Association of Individual Investors, IIA sentiment index corresponds to Investors Intelligence Advisors’ index and BW is the sentiment index calculated by Baker and Wurgler (2007). The number of monthly observations in the time series is 88. (*), (**), and (***) denote significance at the 10%, 5%, and 1% levels, respectively. Robust Newey-West (1987) p-values are reported in parentheses.

5

−

1

=

1

× (1 −

−1 )

+

2

×

−1

+

an

Table 5: Predictive regressions for long-short portfolios with a dummy sentiment variable +

+

+

+

+

Equal-weighted

-0.013* (0.052)

-0.019*** (0.007)

0.408*** (0.001)

M

AAII Sentiment Index

0.268 (0.234)

0.008 (0.967)

-0.034 (0.143)

0.596 (0.177)

0.262

0.206

Value-weighted

-0.004 (0.534)

-0.016* (0.066)

0.351*** (0.001)

0.251 (0.336)

0.152 (0.414)

-0.065** (0.031)

0.354 (0.547)

0.031

0.000

1



2



MKT



SMB

d





HML



MOM



LIQ

R

2

Adj. R

2



1



te

IIA Sentiment Index

2



MKT



SMB



HML



MOM



LIQ

R

2

Adj. R

2

-0.008 (0.257)

-0.013* (0.059)

0.479*** (0.000)

0.231 (0.490)

0.007 (0.967)

-0.048** (0.045)

0.848* (0.073)

0.220

0.161

Value-weighted

-0.007 (0.378)

-0.019** (0.030)

0.326*** (0.001)

0.231 (0.422)

0.169 (0.364)

-0.076** (0.019)

0.769 (0.489)

0.096

0.028

Ac ce p

Equal-weighted



1



2



BW Sentiment Index MKT



SMB



HML



MOM



LIQ

R

2

Adj. R

2

Equal-weighted

-0.004 (0.510)

-0.031*** (0.000)

0.340*** (0.003)

0.127 (0.566)

-0.118 (0.500)

-0.052** (0.024)

0.309 (0.495)

0.281

0.226

Value-weighted

-0.009 (0.108)

-0.035*** (0.000)

0.163* (0.098)

0.258 (0.298)

0.070 (0.701)

-0.075** (0.010)

0.108 (0.826)

0.149

0.085

34

Page 35 of 39

Table 6. Predictive regressions for long-short portfolios using a continuous sentiment variable

ip t

Table 6 reports the results of the following regression:

us

cr

where is the “5-1” long-short portfolio return constructed using the same quintile portfolios as in is the investor sentiment proxied by the changes in AAII and IIA indices as well as the BW Table 2, , and are the Fama-French market, size and value factors. is sentiment-changes index, the momentum factor. The liquidity proxy ( ) is measured following Pastor and Stambaugh (2003). The number of monthly observations in the time series is 88. (*), (**), and (***) denote significance at the 10%, 5%, and 1% levels, respectively. Robust Newey-West (1987) p-values are reported in parentheses. Table 6: Predictive regressions for long-short portfolios with a continuous sentiment variable −

1

=

0

+

×

−1

+

+

+

+

+

an

5

+

AAII Sentiment Index 0



SENT





MKT

Equal-weighted

-0.016*** (0.002)

0.038* (0.058)

0.402*** (0.000)

Value-weighted

-0.020*** (0.002)

0.017 (0.475)

0.231** (0.017)

SMB



HML

M





MOM



LIQ

R

2

Adj. R

2

0.331 (0.152)

-0.033 (0.841)

-0.037 (0.158)

0.596 (0.178)

0.262

0.206

0.389 (0.131)

0.140 (0.457)

-0.062** (0.043)

0.402 (0.336)

0.103

0.035

0



SENT



MKT

te



d

IIA Sentiment Index



SMB



HML



MOM



LIQ

R

2

Adj. R

2

-0.016*** (0.004)

0.080** (0.021)

0.401*** (0.000)

0.158 (0.503)

0.042 (0.793)

-0.046* (0.055)

0.960** (0.026)

0.271

0.216

Value-weighted

-0.019*** (0.002)

0.074** (0.045)

0.234** (0.019)

0.268 (0.320)

0.194 (0.257)

-0.070** (0.012)

0.741* (0.098)

0.134

0.068

Ac ce p

Equal-weighted



0



SENT



BW Sentiment Index MKT



SMB



HML



MOM



LIQ

R

2

Adj. R

2

Equal-weighted

-0.017*** (0.003)

0.014** (0.028)

0.359*** (0.000)

0.238 (0.304)

-0.044 (0.807)

-0.044* (0.077)

0.295 (0.431)

0.245

0.187

Value-weighted

-0.022*** (0.001)

0.017*** (0.004)

0.173* (0.087)

0.409 (0.108)

0.150 (0.438)

-0.068** (0.024)

0.027 (0.948)

0.155

0.091

35

Page 36 of 39

Table 7. Predictive regressions for long-short portfolios with a dummy sentiment variable using Amihud (2002) illiquidity measure.

ip t

Table 7 reports the results of the following regression:

us

cr

where is the “5-1” long-short portfolio return constructed using the same quintile portfolios as in is a dummy variable equal to one if the sentiment proxy is higher than the median, and zero Table 2, , and are the Fama-French market, size and value factors. is the momentum otherwise, factor. The illiquidity proxy ( ) is measured following Amihud (2002). AAII denotes the sentiment index computed by the American Association of Individual Investors, IIA sentiment index corresponds to Investors Intelligence Advisors’ index and BW is the sentiment index calculated by Baker and Wurgler (2007). The number of monthly observations in the time series is 88. (*), (**), and (***) denote significance at the 10%, 5%, and 1% levels, respectively. Robust Newey-West (1987) p-values are reported in parentheses.

5

−

1

=

1

× (1 −

−1 )

+

2

×

−1

+

an

Table 7: Predictive regressions for long-short portfolios with a dummy sentiment variable using Amihud (2002) illiquidity measure

+

+

+

+

+

AAII Sentiment Index 1



2



MKT

-0.012 (0.123)

-0.019** (0.014)

0.400*** (0.000)

Value-weighted

0.003 (0.732)

-0.016* (0.054)

0.385*** (0.001)

SMB



HML



MOM



ILLIQ

R

2

Adj. R2

0.262 (0.267)

0.011 (0.953)

-0.034 (0.150)

-0,005 (0.868)

0.258

0.202

0.351 (0.225)

0,182 (0.353)

-0.077** (0.041)

-0,037 (0.363)

0.044

0.000

d

Equal-weighted



M







2



Value-weighted

MKT



SMB



HML



MOM



ILLIQ

R

2

Adj. R2

-0.013 (0.251)

-0.022** (0.027)

0.391*** (0.000)

0,190 (0.443)

0,010 (0.953)

-0.035 (0.270)

0.007 (0.894)

0.231

0.172

-0.007 (0.451)

-0.018** (0.045)

0.309*** (0.003)

0.235 (0.421)

0.174 (0.351)

-0.076** (0.024)

-0,013 (0.750)

0.092

0.023

Ac ce p

Equal-weighted

1

te

IIA Sentiment Index



1



2



BW Sentiment Index MKT



SMB



HML



MOM



ILLIQ

R

2

Adj. R2

Equal-weighted

-0.007 (0.502)

-0.031*** (0.004)

0.345*** (0.000)

0.263 (0.303)

-0.056 (0.743)

-0.045 (0.121)

-0.000 (0.999)

0.307

0.255

Value-weighted

-0.009 (0.252)

-0.029*** (0.001)

0.201* (0.054)

0.266 (0.351)

0.074 (0.682)

-0.072** (0.029)

0.007 (0.862)

0.151

0.086

36

Page 37 of 39

Table 8. Predictive regressions for long-short portfolios using a continuous sentiment variable using Amihud (2002) illiquidity measure Table 8 reports the results of the following regression:

cr

ip t

where is the “5-1” long-short portfolio return constructed using the same quintile portfolios as in is the investor sentiment proxied by the changes in AAII and IIA indices as well as the BW Table 2, , and are the Fama-French market, size and value factors. is sentiment-changes index, ) is measured following Amihud (2002). The number of the momentum factor. The illiquidity proxy ( monthly observations in the time series is 88. (*), (**), and (***) denote significance at the 10%, 5%, and 1% levels, respectively. Robust Newey-West (1987) p-values are reported in parentheses.

5

−

1

=

0

+

×

−1

+

+

+

+



0



SENT





MKT

SMB

-0.018** (0.023)

0.038** (0.041)

0.397*** (0.000)

0.311 (0.212)

Value-weighted

-0.026*** (0.004)

0.018 (0.399)

0.230** (0.032)

0.351 (0.223)



HML



MOM

+



ILLIQ

R

2

Adj. R2

-0.031 (0.848)

-0.031 (0.324)

0.012 (0.778)

0.259

0.203

0.138 (0.457)

-0.044 (0.218)

0.046 (0.363)

0.111

0.043





M

Equal-weighted

+

an

AAII Sentiment Index

us

Table 8: Predictive regressions for long-short portfolios with a continuous sentiment variable using Amihud (2002) illiquidity measure

IIA Sentiment Index 0



SENT





MKT

SMB

d





HML

MOM

ILLIQ

R

2

Adj. R2

0.074** (0.034)

0.392*** (0.000)

0.145 (0.558)

0.045 (0.778)

-0.042 (0.187)

0.001 (0.983)

0.262

0.206

Value-weighted

-0.024** (0.015)

0.067* (0.071)

0.228** (0.017)

0.237 (0.383)

0.191 (0.251)

-0.054 (0.129)

0.037 (0.469)

0.135

0.069





Ac ce p

te

Equal-weighted

-0.016** (0.041)



0



SENT



BW Sentiment Index

MKT



SMB



HML

MOM

ILLIQ

R

2

Adj. R2

Equal-weighted

-0.020** (0.036)

0.015** (0.020)

0.359*** (0.000)

0.427* (0.091)

0.032 (0.852)

-0.035 (0.247)

0.007 (0.898)

0.301

0.248

Value-weighted

-0.031*** (0.001)

0.018*** (0.002)

0.177* (0.071)

0.472* (0.056)

0.195 (0.274)

-0.044 (0.210)

0.069 (0.172)

0.197

0.136

37

Page 38 of 39

Table 9. Fama-MacBeth Regressions

ip t

This table reports the Fama and MacBeth (1973) regression estimates with firm-level data. Independent , log of size ( ), book-to-market equity ratio ( ), 12-month momentum, market variables include beta ( , and liquidity betas ( . The first column reports regression results without considering investor sentiment regimes. In the subsequent columns, we consider the AAII, IIA and BW sentiment indices to classify the entire sample into high and low sentiment periods. (*), (**), and (***) denote significance at the 10%, 5%, and 1% levels, respectively. Robust Newey-West (1987) p-values are reported in parentheses.

AAII High

Low

High

BW

Low

High

Low

-1.059*** (0.000)

-0.046 (0.433)

-0.563*** (0.000)

-0.033*** (0.000)

-0.474*** (0.006)

0.026 (0.809)

0.099*** (0.000)

0.133*** (0.000)

0.177*** (0.000)

0.075*** (0.000)

0.297*** (0.000)

0.033** (0.032)

0.370*** (0.000)

-0.006 (0.649)

us



IIA

cr

Table 9: Fama-MacBeth Regressions

-0.195*** (0.000)

-0.076 (0.358)

-0.605*** (0.000)

-0.021 (0.701)

LnSize

-0.150*** (0.000)

-0.260*** (0.000)

-0.099*** (0.003)

-0.050** (0.016)

B/M

0.111*** (0.000)

0.109*** (0.000)

0.115*** (0.000)

12-month momentum

0.126*** (0.000)

0.184*** (0.000)

0.043 (0.101)

1.698*** (0.000)

2.292*** (0.000)

1.749*** (0.000)

0.897** (0.045)

1.889*** (0.005)

1.108*** (0.004)

1.503* (0.096)

-0.156***

-0.641***

0.183***

-0.614***

0.094**

-1.300***

0.468***

(0.002)

(0.000)

(0.006)

(0.004)

(0.018)

(0.000)

(0.000)

0.113

0.111

0.115

0.096

0.149

0.111

0.118

0.076

0.130

0.092

0.099

LIQ

Avg. R

2 2

0.094

0.092

0.095

Ac ce p

Avg. Adj. R

M



d

 

te



an

 VIX

38

Page 39 of 39