stock price synchronicity, cognitive biases, and momentum · cognitive biases to the noisiness of...

Stock Price Synchronicity, Cognitive Biases, and Momentum

Chen Chen1 and John A. Doukas2

Abstract

The momentum anomaly is widely attributed to investor cognitive biases, but the trigger of

cognitive biases is largely unexplored. In this study, inspired by psychology studies linking

cognitive biases to the noisiness of information, we examine whether momentum returns are

associated with high stock price synchronicity, a manifestation of noisy firm-specific information.

Our results demonstrate that momentum is more pronounced in the presence of high stock price

synchronicity. This finding is robust to other explanations and firm characteristics. We also find

that stock price synchronicity boosts the profitability of momentum by amplifying investor

underreaction to new information.

JEL classification: G10; G12; G14; G41

Keywords: Momentum; Stock Price Synchronicity; Cognitive Biases; Capital Markets.

1 Corresponding Author. Affiliation: Strome College of Business, Old Dominion University, Constant Hall, Suite 2004, Norfolk, VA 23529, Email: [email protected], Phone: +1 (516) 606-8780 2 Affiliation: Strome College of Business, Old Dominion University, Constant Hall, Suite 2080, Norfolk, VA 23529, USA, and Judge Business School, University of Cambridge, Cambridge, UK, Email: [email protected], Phone +1 (757) 683-5521

Stock Price Synchronicity, Cognitive Biases, and Momentum

Abstract

The momentum anomaly is widely attributed to investor cognitive biases, but the trigger of

cognitive biases is largely unexplored. In this study, inspired by psychology studies linking

cognitive biases to the noisiness of information, we examine whether momentum returns are

associated with high stock price synchronicity, a manifestation of noisy firm-specific information.

Our results demonstrate that momentum is more pronounced in the presence of high stock price

synchronicity. This finding is robust to other explanations and firm characteristics. We also find

that stock price synchronicity boosts the profitability of momentum by amplifying investor

underreaction to new information.

JEL classification: G10; G12; G14; G41

Keywords: Momentum; Stock Price Synchronicity; Cognitive Biases; Capital Markets.

1

1. Introduction

The behavioral finance literature attributes the momentum anomaly to investor cognitive

biases (e.g., Hong and Stein 1999; Antoniou, Doukas, and Subrahmanyam 2013). Additionally,

previous psychology studies show that the rise of cognitive biases is related to the noisiness of

information (e.g., Tversky and Kahneman 1974; Hilbert 2012). These two strands of literature

naturally raise the question of whether the noisiness of information mirrored in stock price

synchronicity (Roll 1988), which has been shown to inhibit the incorporation of firm-specific

information into asset prices, amplifies the profitability of the momentum strategy. Therefore, this

study conjectures that stock price synchronicity, our proxy of noisy firm-specific information,

induces cognitive biases that lead non-momentum traders to underreact to news, which, in turn,

increases the profitability of the momentum strategy.1 Specifically, unlike previous studies, we

explore whether the momentum anomaly is prominent in the presence of stock price synchronicity,

a manifestation of noisy firm-specific information, and find results consistent with our hypothesis.

Momentum is a trading strategy that refers to buying past winners and selling past losers.

This simple trading strategy generates consistent returns that cannot be explained by classical asset

pricing models (e.g., the capital asset pricing model and the Fama–French three-factor model).

Previous studies provide different explanations for the momentum anomaly, ranging from rational

to behavioral paradigms. The rational explanations consider momentum a risk-based phenomenon

(e.g., Berk, Green, and Naik 1999; Johnson 2002). The behavioral paradigm attributes momentum

profitability to either overreaction (Daniel, Hirshleifer, and Subrahmanyam 1998) or underreaction

1 That is, non-momentum traders trade less (underreact) as they are unable to discern the true value of firm-specific information in high synchronicity (noisy) states while momentum traders, on the other hand, trade on past returns to exploit this underreaction. Thus, the underreaction of non-momentum traders gives rise to higher momentum gains in the presence of high-stock price synchronicity (noise). That is, these two trading patterns between non-momentum and momentum traders give rise to higher momentum gains in high-stock price synchronicity (noise) states.

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(Barberis, Shleifer, and Vishny 1998; Hong and Stein 1999). In this study, we posit that the

momentum anomaly is associated with the rise of noisy firm-specific information that induces

investor cognitive biases, leading to investor underreaction. Next, we briefly discuss how noisy

firm-specific information affects momentum within the theoretical framework of Hong and Stein

(1999).

According to Hong and Stein (1999), momentum emerges because the information is

gradually diffused by “newswatchers” while “momentum traders” trade based on past returns to

exploit this gradual diffusion of information. These trading patterns lead to greater momentum

profits. Although Hong and Stein (1999) do not justify why the information is gradually diffused,

subsequent studies attribute it to investor underreaction triggered by cognitive biases, such as

cognitive dissonance or conservatism (e.g. Grinblatt and Han 2005; Antoniou et al. 2013; Da,

Gurun, and Warachka 2014).

However, the source prompting those cognitive biases is rarely explored. Psychology

studies, meanwhile, indicate that complex, noisy information is the main source of cognitive

biases. In particular, they argue that cognitive biases result from limited information-processing

capacity (Simon 1955), information-processing shortcuts (Tversky and Kahneman 1974), and

noisy information processes (Hilbert 2012), all of which are associated with noisy information.

Inspired by these studies, we argue that noisy firm-specific information captured through stock

price synchronicity, accounting for other effects, boosts the profitability of the momentum strategy

by inducing investor cognitive biases.2

2 We do not link momentum to a specific type of cognitive biases. Our argument is valid for any kind of cognitive biases subject to noisy information.

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When firm-specific information is noisy, investors are unable to discern the true value of

firm-specific information, leading high stock price synchronicity. This makes the new

firm-specific information to diffuse gradually into prices because non-momentum traders’ (i.e.,

news watchers) cognitive biases make them trade less (underreact) in high synchronicity (noisy)

states. Momentum traders, on the other hand, trade based on past returns (not new information) to

exploit this underreaction. These two trading patterns between non-momentum and momentum

traders give rise to higher momentum gains in the presence of high stock price synchronicity

(noise). Although high stock price synchronicity may also reflect the lack of firm-specific

information, previous studies report a strong relation between stock price synchronicity and noisy

firm-specific information. For example, Morck, Yeung, and Yu (2000) infer that high stock price

synchronicity reflects noisy firm-specific information and show that high stock price synchronicity

is explained by poor protection of property rights instead of the fundamental co-movement, an

indicator of lack of firm-specific information. This inference is also supported by the evidence that

stock price synchronicity increases with financial opacity, measured by earnings management

(Hutton, Marcus, and Tehranian 2009), and the presence of transient institutional investors, who

tend to trade rather than monitor these firms (An and Zhang 2013). Also, stock price synchronicity

decreases with the adoption of eXtensible Business Reporting Language (XBRL) in the US, which

is designed to greatly decrease the difficulty and costs of firm-specific information processing

(Dong, Li, Lin, and Ni 2016).3 These empirical findings indicate that firm-specific information is

noisy in the presence of high stock price synchronicity. 4 Therefore, if noisy firm-specific

3 XBRL requires the same names for financial statement items, with the same economic implications, making financial statements machine readable. 4 Some studies challenge the link between stock price synchronicity and noisy firm-specific information by providing empirical evidence that more information leads to high price synchronicity (e.g., Dasgupta, Gan, and Gao 2010; Xing and Anderson 2011). Such evidence should not be used to dispute the link between stock price synchronicity and price informativeness, because more available information does not necessarily improve the price informativeness (e.g., Kondor 2012; Han, Tang, and Yang 2016; Goldstein and Yang 2019).

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information heightens the profitability of the momentum strategy, momentum is expected to be

more pronounced when stock price synchronicity is high. Consequently, following Durnev,

Morck, Yeung, and Zarowin (2003) and Durnev, Morck, and Yeung (2004), we use stock price

synchronicity, the 𝑅𝑅2 statistic from the regression of firm stock returns on market returns and

industry returns, to capture the noisiness of firm-specific information and determine whether

momentum is more pronounced in states of high stock price synchronicity.

In line with our conjecture, we find stocks with higher price synchronicity are associated

with greater momentum profits than stocks with lower price synchronicity. Specifically, the

11-month/12-month equal-weighted momentum strategy based on stocks with high (low) price

synchronicity yields a 0.7166% (0.1200%) average monthly return with a t-statistic of 2.74 (0.60).

The momentum returns for stocks with high price synchronicity significantly outperform those of

their low-price synchronicity counterparts by 0.5966 percentage point. This effect is mainly driven

by loser stocks, consistent with the evidence of previous studies, which show that momentum

profit is attributed to loser stocks (e.g., Antoniou et al. 2013; Da et al. 2014). This pattern also

supports the underreaction framework by showing that the return continuation is more likely to

arise in loser stocks, the ones with higher arbitrage costs. Fama–French three-factor (FF3) and

Fama–French five-factor (FF5) adjusted returns (Fama and French 1993; Fama and French 2015)

are even more pronounced and this finding cannot be explained by time-varying beta models used

by Daniel and Moskowitz (2016) and Grundy and Martin (2001).5 On the other hand, momentum

portfolios with high price synchronicity have significantly greater exposure to two underreaction

factors proposed by Stambaugh and Yuan (2017) and Daniel, Hirshleifer, and Sun (2020) than

their low price synchronicity counterparts, supporting our hypothesis that the underreaction is

5 See Tables 1A in Appendix for the results of these tests.

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pronounced among high synchronicity stocks.6 We find a similar pattern using a broader sample

and a variety of settings.7 The main pattern of our findings is still unchanged after including

delisting returns as well as using value-weighted portfolios and alternative formation periods.8

Additionally, our findings are robust after conditioning on the disposition effect, limited investor

attention, market information delay, share turnover, firm capitalization, idiosyncratic risk, market

states, and investor sentiment, respectively. Consistent with our main findings, Fama–Macbeth

regression results show that the positive impact of stock price synchronicity on momentum profits

is highly significant. We also check the sensitivity of our results to the concern that strategies that

enhance momentum may be due to defining momentum using extreme percentile cut-offs in the

cross-section of past stock returns (Bandarchuk and Hilscher 2013) and our evidence shows that

this is not the case.

Furthermore, we find that the profitability of momentum triggered by mental accounting

(Grinblatt and Han 2005), limited investor attention (Da et al. 2014), and cognitive dissonance

(Antoniou et al. 2013) is more (less) pronounced in the presence of high (low) stock price

synchronicity. In addition, the effect of stock price synchronicity on momentum profits is stronger

during states of high and mild share turnover, an indicator of a high turnout of irrational investors

(Baker and Stein 2004). Moreover, through post-earnings announcement drift (PEAD), we show

that loser (winner) stocks with high price synchronicity respond less strongly to bad (good) news

during the “impact” period, but more strongly during the “adjustment” period during

high-sentiment (low-sentiment) periods, suggesting that noisy firm-specific information fuels

6 See Tables 5A in Appendix for the results of these tests. 7 Following Jegadeesh and Titman (1993), our main sample incudes NYSE/AMEX stocks. Our results remain robust to a broader sample involving NYSE/AMEX/NASDAQ stocks. We also find a similar pattern for FF3 adjusted returns using different holding period and order settings. These results are reported Tables 2A, 3A, and 4A of the Appendix. 8 See Table 4A in Appendix for the results of these tests.

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investor underreaction through the cognitive dissonance channel.9,10 This finding gains additional

support from the data when we examine the short interest positions of losers (winners) and find

that they increase (decrease) with stocks with high price synchronicity.

Also, we use bid-ask spread and stock turnover as well as the first principal component

factor of stock price synchronicity, bid-ask spread and stock turnover as alternative measures of

stock price informativeness. Our baseline results remain robust. The effect of stock price

synchronicity on momentum profits is also robust to the adoption of XBRL, a disclosure policy

that was introduced to reduce the noise level of firm-specific information. Finally, momentum

profitability is still pronounced in the presence of higher stock price synchronicity, even after we

purge stock price synchronicity from the effects of firm characteristics and systematic risks.

The literature shows the importance of stock price informativeness in asset pricing (e.g.,

Vega 2006; Epstein and Schneider 2008) and corporate policy (e.g., Chen, Goldstein, and Jiang

2007; De Cesari and Huang-Meier 2015). This paper contributes to this literature by investigating

the link between stock price informativeness and momentum, an important stock price anomaly.

Moreover, although momentum is widely credited to investor cognitive biases (Grinblatt and Han

2005; Antoniou et al. 2013; Da et al. 2014), to the best of our knowledge, there is no evidence on

how or why investor cognitive biases emerge. By investigating the link between stock price

synchronicity and momentum profits, we provide a noisy information–based explanation to this

question. Furthermore, our study provides new evidence in support of the underreaction

explanation of momentum profits (Hong and Stein 1999).

9 Cognitive dissonance, which strengthens investor underreaction, is more likely to emerge in the presence of bad (good) news during high-sentiment (low-sentiment) periods. 10 This result is consistent with the findings of Antoniou et al. (2012), who show that, given bad earnings surprises, the PEAD for losers during the “adjustment” period is stronger in high-sentiment periods than in low-sentiment periods. They also interpret this finding as evidence in support of cognitive dissonance.

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It is worth noting that our findings differ with the results of Bandarchuk and Hilscher

(2013) and Hou, Xiong, and Peng (2006). We find that the differences are largely driven by the

extreme past returns associated with their sorting method (i.e., sequential sorting by price

synchronicity and past returns) and single month holding approach. 11 This contradiction should

not be considered as a repudiation of previous empirical results, but as evidence of security markets

populated by heterogeneous traders (i.e., newswatchers and momentum) as suggested by Hong

and Stein (1999), where newswatchers underreact when firm-specific information is noisy and

momentum traders trade merely based on past returns without being able to detect the

underreaction of newswatchers. Therefore, momentum traders will trade more when a stock has

stronger past returns regardless of its state of informativeness. However, without the underreaction

caused by noisy firm-specific information, momentum gains will be less sustainable due to

overpricing.

An interesting implication of our analysis is that the strong association between stock price

synchronicity and momentum returns mirrors the information inefficiency of the markets when

they are mostly populated by uninformed or partially informed traders who fail to learn the true

asset value when fully informed traders are not present in the market. Intuitively, trades involving

fully informed investors carry substantially more information than trades involving partially

informed investors, thus facilitating Bayesian inference and the faster transmission of private

information into prices, which should reduce the momentum anomaly.12 Hence, our results also

11 See Tables 2A and 3A in Appendix for the sensitivity of results to different holding period and sorting order. We can get similar results of Bandarchuk and Hilscher (2013) by using their approach. In addition, Hou et al. (2006) argue that investor overaction strengthens momentum. This conjecture is inconsistent with recent evidence that shows that strong momentum does not precede reversal (e.g., Da et al. (2014) and Conrad and Yavuz (2017)). 12 This point of information efficiency, however, cannot be tested with archival data (Fama 1991).

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suggest that the thin presence of fully informed traders in the market leads to increased stock price

synchronicity and momentum returns.

The remainder of the paper is organized as follows. Section 2 describes the data and

methodology. Section 3 presents the results. Section 4 concludes the paper.

2. Data and methodology

Our main sample includes data on common stocks (share codes 10 and 11) listed on the

New York Stock Exchange (NYSE) and the American Stock Exchange (AMEX), obtained from

the monthly files of the Center for Research in Security Prices (CRSP). The main sample period

of this study ranges from March 1964 to December 2018 based on the availability of the investor

sentiment data. Firm financial data are collected from Compustat. We also examine the effect of

stock price synchronicity using a broader sample that involves stocks listed on NYSE, AMEX,

and Nasdaq Stock Exchange (NASDAQ).

We follow the conventional momentum studies (e.g., Jegadeesh and Titman 1993, 2001;

Eisdorfer 2008; Antoniou et al. 2013) to construct the overlapping momentum portfolios instead

of the one-month holding period portfolios used by Asness (1995) and Fama and French (1996),

since the one-month holding period approach is difficult to differentiate the underreaction-driven

momentum from momentum trading activities that affect all stocks in short term, and , therefore,

naturally favor detecting the effect of past return alone. Specifically, in each month, all stocks are

sorted into 10 deciles based on their past J months’ returns. Based on the ranking, we create 10

equally weighted portfolios. The portfolio with the highest past returns is labeled the portfolio of

winners and the portfolio with the lowest past returns is labeled the portfolio of losers. The

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momentum strategy buys the winners and sells the losers and then holds them for K months. To

increase the power of our tests, we construct overlapping portfolios. Specifically, we take a new

position in month t and close the position that was initiated in month t - K. Therefore, in any given

month t, the strategies hold a set of positions created in month t and in the previous K - 1 months.

Following the literature (Antoniou et al. 2013; Da et al. 2014), we allow a one-month gap between

the formation period and the holding period. To avoid the noise of penny stocks, we exclude all

stocks that trade at less than $1.

Our main research purpose is to examine the relation between momentum profits and stock

price synchronicity. Following Durnev et al. (2003) and Durnev et al. (2004), we use a market

model to compute stock price synchronicity. Specifically, we estimate the following model for

each firm within the J-month formation period:

𝑟𝑟𝑖𝑖,𝑡𝑡 = 𝑎𝑎𝑖𝑖 + 𝛽𝛽𝑚𝑚𝑟𝑟𝑚𝑚,𝑡𝑡 + 𝛽𝛽𝑖𝑖𝑖𝑖𝑖𝑖𝑟𝑟𝑖𝑖𝑖𝑖𝑖𝑖,𝑡𝑡 + 𝜀𝜀𝑖𝑖,𝑡𝑡, (1)

where 𝑟𝑟𝑖𝑖,𝑡𝑡, 𝑟𝑟𝑚𝑚,𝑡𝑡, and 𝑟𝑟𝑖𝑖𝑖𝑖𝑖𝑖,𝑡𝑡 are, respectively, weekly stock, market, and industry returns. Our stock

price synchronicity proxy (SYNCH) is 𝑅𝑅2, which is the coefficient of determination of Eq. (1). The

market return is defined as the CRSP value-weighted index return and the industry return is

calculated based on two-digit Standard Industrial Classification (SIC) codes.13

To examine the sensitivity of momentum profitability to SYNCH, we construct 10 × 5

sequential double sorts. In detail, at the beginning of holding period t, we sort all stocks into 10

groups based on their past J-month performance, and then sort the stocks in each decile into

quintiles by their SYNCH values. We identify the stocks in the top SYNCH quintile as high-SYNCH

13 We use weekly returns to mitigate the effect of short-term trading behavior. Our findings are also robust to SYNCH based daily returns and different industry classifications. See Panel B, Table 1 for the results.

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stocks and the stocks in the bottom SYNCH quintile as low-SYNCH stocks. Subsequently, we

calculate the momentum profits in each SYNCH quintile. This approach yields five momentum

portfolios with different levels of SYNCH. Unlike some previous studies (e.g., Hou et al. 2006;

Bandarchuk and Hilscher 2013) that sort stocks by their characteristics first, our baseline approach

sorts stocks by PRET first for keeping the strength of the past returns similar in each PRET group,

which is important given the strong relation between PRET and future returns (Bandarchuk and

Hilscher 2013). Although this sorting approach may lead to wider variation of SYNCH within each

SYNCH group, it should not be a critical concern because the main pattern of our findings remains

robust when independent sorting and SYNCH × PRET sorting are used.14 This corroborates that

our sorting approach is appropriate. To evaluate the performance of the momentum portfolios, we

report both unadjusted and risk-adjusted average monthly returns using the FF3 model. To gauge

the difference between high- and low-SYNCH momentum profits, we create a high–low SYNCH

portfolio by buying the high-SYNCH momentum portfolio and selling the low-SYNCH momentum

portfolio, and we calculate its unadjusted and risk-adjusted returns as well. To control for

autocorrelation and heteroskedasticity, we estimate standard errors, using Newey–West

adjustment with K lags.

Prior literature suggests that momentum profits are sensitive to several factors. Therefore,

we also check whether our findings are robust to factors reported in previous studies, by using

sequential three-way sorts. Specifically, we examine the sensitivity of our main findings to the

disposition effect (Grinblatt and Moskowitz 2004; Grinblatt and Han 2005), information

discreteness (Da et al. 2014), market information delay (Hou and Moskowitz 2005), stock

14 See Panel B, Table 1 and Tables 2A and 3A in Appendix for the results of these tests. The exception is that the results based on SYNCH × PRET sorting are different from other two sorting methods when K is small because high-SYNCH quintile has lower strength of the past returns than their low-SYNCH counterpart.

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turnover, firm size (Jegadeesh and Titman 1993), market states (Cooper, Gutierrez, and Hameed

2004), and sentiment (Antoniou et al. 2013), respectively.

3. Empirical results

Our main hypothesis posits that noisy firm-specific information induces investor cognitive

biases that lead to investor underreaction, which, in turn, amplifies momentum returns. This

argument builds on two streams of research. First, Hong and Stein (1999) suggest that momentum

is caused by the slow diffusion of news, and that the slow diffusion is attributed to cognitive biases,

as suggested by Antoniou et al. (2013). Second, a series of psychological studies point out that

cognitive biases are more likely to arise when information is noisy (Festinger 1957; Egan, Bloom,

and Santos 2010; Hilbert 2012). Therefore, we hypothesize that noisy firm-specific information,

which is captured by SYNCH, should strengthen momentum profits.

3.1 Momentum and stock price synchronicity

In this section, we examine the relation between stock price synchronicity and the

profitability of the momentum strategy. Specifically, all stocks are sequentially sorted by their past

J-month cumulative returns (PRET) and SYNCH at the beginning of the holding period. Then, we

construct the momentum portfolio in each SYNCH quintile and obtain five momentum portfolios,

ranging from the high-SYNCH to the low-SYNCH quintile. In our main analysis, we let J = 11 and

let K = 12 months, respectively.15 The results are reported in Panel A of Table 1. All the returns

are reported as percentage returns. Panel B presents the momentum performance and the formation

15 Tables 2A and 3A in the Appendix, report results conditional on different settings.

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period performance with different sorting methods for the main sample. The results based on

different SYNCH estimation methods are also reported in Panel B of Table 1.

The results in Table 1 indicate that momentum profits are sensitive to SYNCH. In Panel A,

the average monthly momentum profit for high-SYNCH stocks is 0.7166%, with a t-statistic of

2.74, significant at the 1% level. The average monthly momentum profit, however, for low-SYNCH

stocks is 0.1200%, with a t-statistic of 0.60, which is statistically insignificant at conventional

levels. Additionally, the momentum profits of the high-SYNCH quintile significantly outperform

the low-SYNCH quintile by 0.5966 percentage point, which accounts for a large portion of the

momentum profits. It is worth noting that the average monthly returns decrease monotonically by

0.7166%, 0.6593%, 0.3621%, 0.2713%, and 0.1200% as we move from the high-SYNCH

momentum portfolios to the low-SYNCH momentum portfolio, with t-statistics of 2.74, 2.70, 1.54,

1.16, and 0.60, respectively. The results based on the FF3 adjusted returns are similar and even

stronger than the unadjusted returns because the Fama-French three factors explain the variation

rooted in other risk characteristics but have low explanatory power on momentum. Similar patterns

are also found in previous studies that create momentum portfolios based on some cross-sectional

characteristics (e.g., Hou et al. 2006; Bandarchuk and Hilscher 2013; Da et al. 2014). The FF5

adjusted returns are reported in Panel B of Table 1 and lead to a similar conclusion.16

Interestingly, as shown in Panel A of Table 1, the average monthly returns increase

monotonically and double in magnitude as we move from the quintile of the high-SYNCH losers

(0.5185%) to the low-SYNCH losers (1.0269%). The average monthly returns, however, for the

high- and low-SYNCH winners are, respectively, 1.2351% and 1.1468%, and quite similar in terms

16 Several studies extend Fama–French three-factor model (e.g., Fama and French 2015; Hou, Xue, and Zhang 2015). We select to use of the Fama–French three-factor model because of its great data availability that fits our main sample.

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of magnitude. The asymmetric effect of SYNCH on winner and loser returns suggests that the

difference between high- and low-SYNCH momentum profits is mainly driven by loser stocks.

This loser-driven momentum pattern is consistent with the findings in previous momentum studies

(e.g., Antoniou et al. 2013; Da et al. 2014) and is more likely to fit the underreaction paradigm

than the overreaction or rational risk–based explanation. If the stock price movement is driven by

investor underreaction, arbitrageurs should engage in trading to wipe out the mispricing. However,

arbitrage is riskier in losers than winners because of costly short selling (D’Avolio 2002). Thus,

the return continuation caused by investor underreaction should be more pronounced among losers

than winners. Our findings confirm this prediction and demonstrate that the return continuation is

due to high-SYNCH losers rather than high-SYNCH winners. Also, based on the results reported in

Table 4A, our findings are robust to the inclusion of CRSP delisting returns, which can impact

momentum returns according to Eisdorfer (2008). An alternative explanation for the higher

momentum profits in high-SYNCH stocks documented in this study could be that low-SYNCH loser

stocks experience reversals due to time-varying betas in certain periods, as documented by Daniel

and Moskowitz (2016). To examine the sensitivity of our main results to time-varying betas we

performed a similar test, as in Daniel and Moskowitz (2016) and find, as shown in the Table 1A

in the Appendix, that our main result remains robust to time-varying betas.17 Specifically, high

SYNCH momentum portfolios generate the high alphas than low SYNCH momentum portfolios.

The difference (0.7053%) between high- and low-SYNCH momentum portfolios is also significant.

This result implies that, in line with the main point of our paper, higher momentum profits in

high-SYNCH stocks are driven by higher idiosyncratic firm-specific characteristics that investors

17 In a unreported results, we also use Korajczyk and Sadka (2004)’s approach to capture the conditional factor risk exposures (i.e., Market, SMB, and HML factors) shown by Grundy and Martin (2001). Our result remains robust to their approach as well. The conditional FF3 adjusted return of high–low portfolio is 0.6661% with a t-statistic of 3.53.

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are unable to identify, but not by time-varying betas. The results for NYSE/AMEX/NASDAQ

Stocks in Table 4A are similar with the results reported in Panel A of Table 1, showing that our

findings hold for a broader sample.

We also test the sensitivity of our results to the concern that strategies that increase

momentum may be due to using extreme percentile cut-offs in the cross-section of past stock

returns (Bandarchuk and Hilscher 2013). Specifically, the formation period returns, reported in

Panel B of Table 1, indicate that high-SYNCH momentum portfolios do not have more extreme

returns than their low-SYNCH counterparts. In fact, the formation period high–low return is

significantly negative (-2.4615%, t-statistic = -11.55), indicating that high-SYNCH stocks have

less extreme past returns. Therefore, SYNCH per se enhances the profits of momentum rather than

the use of more extreme past returns. This conclusion is also confirmed by the plot of the

distribution of past returns for the portfolios sorted on SYNCH, which shows that top and bottom

ends of the whiskers (i.e., the average past return for winners and losers) are similar across the

SYNCH quintiles.18 The evidence that high-SYNCH stocks have less extreme past returns and

stronger return continuation in top and bottom deciles also implies that, as long as the difference

of the momentum strength between high-SYNCH stock and low-SYNCH stock is not huge, the

effect of high SYNCH can overcome the low magnitude of past-returns. Also, consistent with the

finding of Bandarchuk and Hilscher (2013), for a given level of SYNCH, the positive relation

between past and future returns still holds. Given that most existing characteristics enhance

momentum profits by sorting out a portfolio with more extreme past returns (Bandarchuk and

Hilscher 2013), the effect of SYNCH is more striking than it seems.

18 See Figure 1A in Appendix.

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It is also worth noting that effect of SYNCH is more pronounced in top and bottom deciles.

One possible explanation for this result is that the signs of past returns in top and bottom deciles

are more likely to reflect the arrival direction of firm-specific news (i.e., good or bad news). If the

SYNCH strengthens the positive relation between past returns and momentum due to the

underreaction of firm-specific information, we can only observe momentum when newswatchers’

initial interpretation of information is at the right direction. Given the interpretation error of the

newswatchers, they are more likely to mistakenly interpret the direction of information in middle

deciles because the arrival of new information is not crucial.

To test the sensitivity of our results to portfolio construction approach, we report the results

for different sorting methods in Panel B of Table 1. The results indicate that our findings are robust

to different sorting methods. It is worth noting that sequential sorting by SYNCH and PRET, as

shown in Tables 2A and 3A in the Appendix, generates insignificant or even negative high–low

FF3 adjusted returns when K is small (i.e., K=1 or K=3).19 This result is consistent with the finding

of Bandarchuk and Hilscher (2013) and could be explained by more extreme past returns

associated with sequential sorting stocks by SYNCH and PRET, which offset the effect of

high-SYNCH.20 In Tables 2A and 3A, the overall momentum returns decrease when extending the

holding horizon from K=1 to K =12, consistent with the evidence from previous literature.

However, the high-SYNCH momentum return decreases much slower than their low-SYNCH

counterpart, supporting that the momentum caused purely by past return is less sustainable.21

19 Even under this condition, high–low risk adjusted returns are significant positive when the holding period equals 12 months. 20 In Panel B of Table 1, the magnitude of formation period high–low return is more than double under sequential sorting by SYNCH and PRET (-5.7761%, t-statistic = -13.44). 21 This pattern is consistent with Gutierrez Jr and Prinsky (2007)’s finding that momentum caused purely by past return experience significant reversal.

16

Additionally, our main findings remain robust to the value-weighted portfolios and a

different formation period setting (i.e., J = 6 and J = 9), as shown in Table 4A in the Appendix.

The value-weighted approach does not weaken the difference between high-SYNCH and

low-SYNCH portfolio, although it reduces the overall profitability of momentum strategy because

momentum profitability decreases with firm size (Hong, Lim, and Stein 2000).

To further examine whether our findings fit the behavioral paradigm, we analyze the

returns of SYNCH-momentum portfolios by using two behavioral mispricing factor models

proposed by Stambaugh and Yuan (2017) and Daniel et al. (2020). These results, reported in Table

5A in the Appendix, show that high-SYNCH momentum portfolios have significantly greater

exposure to the underreaction factor (i.e., the PEAD factor) in Stambaugh and Yuan (2017)’s

model and the mispricing factor (i.e., the PERF factor) in Daniel et al. (2020)’s model than their

low-SYNCH counterparts, supporting our hypothesis that the underreaction is pronounced among

high synchronicity stocks.

We also explore the effect of SYNCH on time-series momentum (TSMOM), initially

introduced by Moskowitz, Ooi, and Pedersen (2012), and report results in Table 6A of the

Appendix. According to these results, the relation between SYNCH and TSMOM is not significant.

Moreover, they are consistent with the argument of Goyal and Jegadeesh (2018) that

cross-sectional momentum is more suitable to test the behavioral models than the TSMOM.

In sum, the results in Table 1 demonstrate that high-SYNCH momentum portfolios

consistently outperform low-SYNCH momentum portfolios, and this result is robust to different

sorting methods. The findings in this section also indicate that momentum profits are driven by

investor underreaction, which is more pronounced in stocks with a high SYNCH value (i.e., noisy

firm-specific information). In the following sections, we examine whether our main findings are

17

the robust to other factors that cause momentum and discuss how stock price synchronicity affects

their effects.

[Insert Table 1 about here]

3.2 Momentum, stock price synchronicity, and the disposition effect

Grinblatt and Moskowitz (2004) and Grinblatt and Han (2005) propose an explanation of

momentum through the disposition effect, a phenomenon where investors tend to hold on to their

losing stocks while selling their gaining stocks. According to mental accounting and prospect

theory, investors tend to be loss averse (gain seeking) when they realize a paper capital gain (loss)

and, therefore, underreact to good (bad) news. The authors use two proxies to capture the

disposition effect: return consistency (RC) and unrealized capital gains (UCG). In this section, we

examine (1) whether the findings reported in Table 1 are robust to the disposition effect and

(2) whether disposition effect–based momentum is sensitive to SYNCH. First, RC is used to capture

the disposition effect. Following Grinblatt and Moskowitz (2004), we identify a stock as a high-RC

stock through a dummy that is set equal to one if eight of its 12 monthly returns before the

formation date have the same sign as their PRET value, and zero otherwise. According to the

disposition effect, stocks with a high RC value should be more likely to generate momentum profits.

To examine the sensitivity of our findings to the disposition effect, we sort stocks sequentially by

using PRET, SYNCH, and RC. The results are reported in Table 2.


Panel A of Table 2 reports the results for stocks with high RC values, while Panel B reports

the results for stocks with low RC values. It is worth pointing out that the FF3 adjusted returns of

18

the high–low SYNCH portfolios are 0.7908% (t-statistic = 3.38) and 0.7505% (t-statistic = 3.17)

in Panels A and B, respectively. Thus, regardless of RC, high-SYNCH momentum portfolios

always outperform their low-SYNCH counterparts. These results indicate that the effect of SYNCH

on momentum profits is robust to the disposition effect. In line with the findings of Grinblatt and

Moskowitz (2004), the results also show that momentum portfolios with high-RC stocks

outperform those with low-RC stocks. In addition, given stocks with a high RC, the FF3 adjusted

return of high-SYNCH momentum portfolio is 1.2938% (t-statistic = 5.28), while the FF3 adjusted

return of low-SYNCH momentum portfolio is 0.5030% (t-statistic = 2.27). These results suggest

that the disposition effect is prevalent among high-SYNCH stocks, supporting our hypothesis that

cognitive bias is rooted in high-SYNCH stocks. To further test the robustness of our results, we

replace RC with UCG and replicate the previous analysis to examine the performance of

momentum portfolios. Following Grinblatt and Han (2005), we estimate UCG by using weekly

stock trading data in the past five years:

𝑈𝑈𝑈𝑈𝐺𝐺𝑡𝑡−1 =𝑃𝑃𝑡𝑡−2 − 𝑅𝑅𝑡𝑡−1

𝑃𝑃𝑡𝑡−2, (2)

where 𝑃𝑃𝑡𝑡−2 is the one-week-lagged price and 𝑅𝑅𝑡𝑡−1 is the relevant reference price for the mental

accounting one week before the formation date. The relevant reference price, R, is estimated as

𝑅𝑅𝑡𝑡−1 =1𝑘𝑘��𝑉𝑉𝑡𝑡−1−𝑖𝑖�[1 − 𝑉𝑉𝑡𝑡−1−𝑖𝑖+𝜏𝜏]

𝑖𝑖−1

𝜏𝜏=1

�𝑃𝑃𝑡𝑡−1−𝑖𝑖

260

𝑖𝑖=1

, (3)

where 𝑉𝑉𝑡𝑡 is the stock’s turnover ratio on date t and 𝑃𝑃𝑡𝑡 is the stock price at time t. The term in

parentheses multiplied by 𝑃𝑃𝑡𝑡−𝑖𝑖 is the probability that a stock share was last purchased on date t - n

and has not been traded since. The term k is a constant that makes the sum of probabilities equal

to one. We sort all the stocks sequentially by PRET, SYNCH, and UCG to construct 10×5×3

portfolios. The three UCG terciles are, respectively, defined as high, mid, and low values of UCG.

19

A high UCG reflects high levels of investors’ unrealized capital gains. In contrast, a low UCG

indicates that investors’ unrealized capital gains are low (i.e., unrealized capital loss). The results

are reported in Table 3.

Panels A to C of Table 3 report the momentum performance for high-, mid-, and low-UCG

stocks, respectively. In Panels A, B and C, the FF3 adjusted returns (t-statistic) of the high–low

SYNCH portfolio are 0.6591% (2.50), 0.6937% (3.09), and 0.8653% (3.44), respectively. The

results indicate that the effect of SYNCH on momentum profits is robust to high, mid, and low

UCG values.


Jointly, the results in Tables 2 and 3 reveal that our main findings reported in Table 1

remain robust to the disposition effect. Moreover, finding that stock price synchronicity

strengthens disposition effect–based momentum profits suggests that cognitive bias arises when

firm-specific information is noisy.

3.3 Momentum, stock price synchronicity, and limited attention

Da et al. (2014) suggest that momentum profits are due to investors’ limited attention,

because they underreact to information that arrives continuously in small amounts over a long

horizon. The authors construct an information discreteness (ID) measure to capture the relative

frequency of small signals, defined as follows:

𝐼𝐼𝐼𝐼 = 𝑠𝑠𝑠𝑠𝑠𝑠(𝑃𝑃𝑅𝑅𝑃𝑃𝑃𝑃)𝑋𝑋[%𝑠𝑠𝑛𝑛𝑠𝑠 − %𝑝𝑝𝑝𝑝𝑠𝑠], (4)

20

where %neg and %pos are the percentages of days during J months with negative and positive

returns, respectively. The authors report that momentum portfolios with a low ID outperform

momentum portfolios with a high ID.

In this section, we examine whether the effect of SYNCH on momentum profits is robust

to ID and whether the momentum profits among low-ID stocks are sensitive to SYNCH. To explore

the sensitivity of our results to ID, we sequentially sort stocks by PRET, SYNCH, and ID, resulting

in 10×5×3 portfolios. We define the three ID terciles as high-, mid- and low-ID terciles. The results

are reported in Table 4.

Panels A to C of Table 4 present the average monthly returns of SYNCH momentum

portfolios with high-, mid-, and low-ID values, respectively. According to the results, our main

findings in Section A hold in the three panels. From high- to low-ID values, the FF3 adjusted

returns of the high–low SYNCH portfolios are, respectively, 0.8614% (t-statistic = 3.91), 0.7412%

(t-statistic = 3.23), and 0.8605% (t-statistic = 3.10), showing that, regardless of ID, momentum

profits for high-SYNCH stocks are higher than for low-SYNCH stocks. These results indicate that

SYNCH strengthens momentum performance in addition to the effect of ID, suggesting that the

investor limited attention is not the only factor causing momentum.22 Furthermore, consistent with

the results of Da et al. (2014), the momentum profits for low-ID stocks are higher than for high- and

mid-ID stocks within each SYNCH quintile. In line with our prediction, the FF3 adjusted return for

high-SYNCH low-ID momentum portfolio, in Panel C, is 1.6781%, which is 105% higher than the

FF3 adjusted return for low-SYNCH low-ID momentum portfolio, indicating that momentum

returns caused by investor limited attention are higher in high-SYNCH stocks than in low-SYNCH

22 This result may also suggest that the ID is not a perfect measure that captures all investors limited attention.

21

stocks. This pattern provides additional support for our hypothesis that the effects of investor

cognitive biases on momentum profits are consistently more pronounced in stocks with noisy

firm-specific information.


3.4 Momentum, stock price synchronicity, and market information delay

Stock prices reflect two components of information: market-based information and

firm-specific information. Our hypothesis posits that momentum profits emanate from noisy

firm-specific information. However, it is also possible that the information noise is due to the

market component, rather than the firm-specific component. In the other words, it could be more

difficult to incorporate market-based information in some stocks than in others. Hou and

Moskowitz (2005), using a measure that captures the average delay with which stock prices

respond to market-based information, report that the speed of the response of stock prices to market

information can explain the cross-sectional variation of expected returns.

In this section, we examine whether our results are robust to market information delay.

Although both stock price synchronicity and market information delay reflect information quality,

they represent different components of information, market information versus firm-specific

information. Therefore, it is worth seeing whether our results still hold after we control for market

information delay. Based on the approach of Hou and Moskowitz (2005), we use a market

information delay proxy (D) to capture the average delay with which a firm’s stock responds to

market-based information:

𝐼𝐼 = 1 −𝑅𝑅𝑐𝑐2

𝑅𝑅𝐿𝐿2, (5)

22

where 𝑅𝑅𝑐𝑐2 is the 𝑅𝑅2 of Eq. (1) and 𝑅𝑅𝐿𝐿2 is the 𝑅𝑅2 of the extended Eq. (1), which includes original

terms and lagged market and industry returns over the previous four weeks. Then, we form our

10×5×3 portfolios by using PRET, SYNCH, and D. The results are presented in Table 5.

These results show that our main findings are robust to market information delay.

Specifically, the FF3 adjusted returns of the high–low SYNCH portfolio for high-, mid-, and low-D

terciles are 0.8598% (t-statistic = 3.68), 0.8867% (t-statistic = 4.36), and 0.7287% (t-statistic =

2.90), respectively. Furthermore, for any D terciles, both unadjusted and risk-adjusted momentum

portfolio returns are significantly positive for stocks with high SYNCH values, but nonsignificant

for stocks with low SYNCH values. Therefore, our hypothesis that momentum profits are related

to noisy firm-specific information holds, regardless of the delay with which stock prices respond

to market-based information. Moreover, there is no evidence that market information delay

strengthens the momentum profits. In sum, our main findings are robust to market information

delay.


3.5 Momentum, stock price synchronicity, and stock turnover

Previous studies (e.g., Lee and Swaminathan 2000; Baker and Stein 2004) interpret stock

turnover as a proxy for the presence of irrational investors. Thus, higher share turnover is taken to

imply the greater participation of noise traders. In the context of our hypothesis, investor cognitive

bias is expected to be more prevalent when firm-specific information is noisy and the market is

populated with noise traders. Therefore, we expect momentum profits to be more pronounced in

stocks with a high turnover due to the higher turnout of noise traders. We explore the validity of

23

this prediction by exploring how turnover affects momentum among the five SYNCH quintiles.

Specifically, we compute stock turnover (TURN) during the formation period and form our 10×5×3

portfolios based on PRET, SYNCH, and TURN. The results are reported in Table 6.

Panels A to C of Table 6 report the momentum performance for high-, mid-, and low-TURN

stocks, respectively. In line with our expectations, the momentum profits are higher for high-TURN

stocks, indicating that greater market participation by noise traders generates higher momentum

profits.23 The results in Table 6 show that SYNCH significantly influences momentum profits

within all TURN terciles. For example, in the high-TURN tercile (Panel A), high-SYNCH

momentum portfolios generate a FF3 adjusted return of 1.3074% (t-statistic = 4.36) that is

significantly positive, whereas low-SYNCH momentum portfolios yield only a FF3 adjusted return

of 0.3877% (t-statistic of 1.65) that is nonsignificant. Additionally, the FF3 adjusted return of the

high–low SYNCH portfolio is 0.9197% (t-statistic = 3.12) and highly significant, indicating that

high-SYNCH momentum portfolios significantly outperform their low-SYNCH counterparts in the

presence of high TURN values. This finding provides additional support for the view that SYNCH,

which manifests the level of firm-specific noise information, remains an important determinant of

momentum profits, even in the presence of high-levels of noise trader participation. Panels B and

C report similar results.

The findings in this section show that our main results in Table 1 are robust to stock

turnover. More importantly, they indicate that (1) the effect of SYNCH on momentum profits is

more pronounced when more irrational investors participate in the market, and (2) without high

SYNCH values, the presence of irrational investors alone does not generate significant momentum

23 In unreported results, the FF3 adjusted momentum returns for high (low) turnover portfolio is 0.9995% (0.5037%) and t-statistics is 4.81 (2.37).

24

profits, confirming that stock price synchronicity induces cognitive biases. These two results

corroborate our hypothesis that noisy firm-specific information gives rise to investor cognitive

biases that, in turn, boost momentum profits.


3.6 Momentum, stock price synchronicity, and firm capitalization

Prior studies have documented a higher degree of stock price return predictability among

small firms because of the greater (lower) participation of individual (institutional) investors and

higher arbitrage costs (D’Avolio 2002; Nagel 2005), which allow stock mispricing to persist.24

Therefore, the stock prices of small firms are expected to be more sensitive to investors’ cognitive

biases. In this section, we investigate whether our results are sensitive to firm capitalization.

Specifically, we assign stocks to two groups by using the size breakpoints on Kenneth French’s

website. 25 We also sequentially sort stocks by PRET and SYNCH and replicate our baseline

analysis. The results are displayed in Table 7.

Panels A and B of Table 7 present the results for small and large firms, respectively. As

expected, our main finding is more significant among small-cap stocks (i.e., stocks with greater

short-sale constraints). Specifically, in both Panels A and B, the momentum returns and their

significance (t-statistics) decrease monotonically as we move from the high-SYNCH quintile to the

low-SYNCH quintile, indicating that momentum profits are more pronounced among stocks with

higher SYNCH values. Additionally, in Panel A, the high–low SYNCH FF3 adjusted return is

24 In the presence of short-sale constraints, stocks can become overpriced if some investors are too optimistic (Miller 1977). If so, return predictability should be most pronounced among small-cap stocks, which that are subject to higher short-sale constraints (arbitrage costs) than large-cap stocks. 25 See http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/det_me_breakpoints.html.

25

0.7771% (t-statistic = 3.09) and highly significant. However, as shown in Panel B, the effects of

SYNCH on momentum profits are weak among large-cap firms. Although the FF3 adjusted

momentum returns of the high-SYNCH stocks are higher than those of the low-SYNCH stocks, the

difference between the two groups is small (0.4143%) and statistically insignificant (t-statistic =

1.05). The weaker effect of SYNCH on momentum profits among large-cap firms suggests that

large-cap stocks are less sensitive to investor biases. In addition, this result appears to be consistent

with the lack of noisy traders (i.e., greater institutional investor participation) and/or low arbitrage

costs (i.e., low short-sale constraints/high supply of stock loans). Collectively, our findings are

consistent with our hypothesis that stock price synchronicity affects momentum performance

through investor cognitive biases that are more pronounced among individual investors than

among institutional investors.


3.7 Fama–MacBeth regression

In this section, we comprehensively examine the effect of SYNCH on return continuation

(i.e., momentum) after controlling for the disposition effect, investor limited attention, and other

factors that explain cross-sectional stock return variation. Therefore, we use Fama-MacBeth

regressions (Fama and MacBeth 1973) to evaluate the impact of SYNCH on return continuation.

Specifically, we estimate

𝐹𝐹𝑅𝑅𝑃𝑃𝑃𝑃 = 𝛽𝛽0 + 𝛽𝛽1𝑃𝑃𝑅𝑅𝑃𝑃𝑃𝑃 + 𝛽𝛽2(𝑆𝑆𝑆𝑆𝑆𝑆𝑈𝑈𝐻𝐻𝑋𝑋) + 𝛽𝛽3𝑆𝑆𝑆𝑆𝑆𝑆𝑈𝑈𝐻𝐻 + 𝛼𝛼𝛼𝛼 + 𝜖𝜖, (6)

where FRET and PRET, respectively, are the cumulative returns of individual stocks during the

holding period (i.e., t + 1 to t + 12) and formation period (i.e., t - 11 to t - 1). SYNCH is the measure

26

of stock price synchronicity, SYNCHX is an interaction term between SYNCH and PRET, and Z is

an array of control variables. If SYNCH strengthens return continuation, 𝛽𝛽2 is expected to be

positive. The term Z includes the market beta (𝛽𝛽𝑚𝑚), the industry beta (𝛽𝛽𝑖𝑖𝑖𝑖𝑖𝑖), the book-to-market

ratio (BM), and the logarithm of market capitalization (SIZE). In the extended model, we also

include limited attention (ID), the disposition effect (RC), firm age (AGE), illiquidity measure

(ILLQ) developed by Amihud (2002), idiosyncratic risk (IVOL), stock turnover (TURN), and their

interaction terms with PRET (i.e., IDX, RCX, SIZEX, BMX, AGEX, ILLIQX, IVOLX, and,

TURNX).26, 27 We winsorize the data for all the valuables at the 1% and 99% levels. The results

are reported in Table 8. Models 1, 2, 3, and 7 present the results for a sample involving

NYSE/AMEX stocks. Models 4, 5, 6, and 8 show the result for a sample involving

NYSE/AMEX/NSADAQ stocks. Since both samples yield similar results, our focus is mainly on

the NYSE/AMEX sample.

To examine whether momentum is generally present in our sample, we use Model 1 in

Table 8 as the benchmark model that includes only the intercept and PRET. We find that the

coefficient of PRET is 0.0297 and significant at 10%, indicating return continuation (i.e.,

momentum) in our sample. Then, we extend Model 1 by adding SYNCHX and SYNCH in Model 2

and find that 𝛽𝛽2 is 0.0952 and significant at 1%, indicating that SYNCH strengthens the return

continuation. Interestingly, the coefficient of PRET is weakened relative to Model 1 and turns out

to be statistically nonsignificant, suggesting that the explanatory power of PRET drops when

SYNCH is low. This finding is consistent with our reported results in previous sections. In Model 3,

we extend Model 2 by including 𝛽𝛽𝑖𝑖𝑖𝑖𝑖𝑖, 𝛽𝛽𝑚𝑚, SIZE, and BM. These regression results are similar with

26 The variable IVOL is measured by the standard deviation of daily stock return residuals for the 11-month formation period, which are estimated by using the Fama–French three-factor model. 27 In untabulated results, RC is replaced by UCG, an alternative proxy for the disposition effect. The results are similar.

27

the results of Model 2. Specifically, SYNCHX is significantly positive (0.0907, t-statistics = 2.91),

and the coefficient of PRET remains statistically nonsignificant, corroborating that SYNCH

increases momentum profits. Model 7 includes all the control variables. As before, the coefficient

of SYNCHX in Model 7 is significantly positive (0.1249, t-statistics = 3.88), indicating that

SYNCH-based momentum is robust to the disposition effect, investor limited attention, firm age,

size, book-to-market ratio, and liquidity measures (i.e., ILLIQ, IVOL, and TURN). It is also worth

noting that, in Models 7 and 8, SYNCHX is significantly positive after controlling for IVOL,

distinguishing our findings from firm-level risks captured by idiosyncratic volatility. Therefore,

this result clearly demonstrates that the effect of SYNCHX is robust to the disposition effect,

investor limited attention, and other common factors used in the previous literature to explain the

cross-sectional stock return variation.28

Jointly, we infer that stock price synchronicity strengthens return continuation, controlling

for existing explanations such as the disposition effect, investor limited attention, and common

factors.


3.8 Momentum, stock price synchronicity, market states, and sentiment

We have shown, thus far, that stock price synchronicity has significant explanatory power

for cross-sectional momentum profits and that this result is robust to other cross-sectional

explanations. In this section, we discuss whether the effect of stock price synchronicity on

28 To make our results comparable with those in Table 15, in an untabulated test, we also replace SYNCH with LnSYNCH, which is 𝐿𝐿𝑠𝑠𝑆𝑆𝑆𝑆𝑆𝑆𝑈𝑈𝐻𝐻 = 𝐿𝐿𝑠𝑠[𝑆𝑆𝑆𝑆𝑆𝑆𝑈𝑈𝐻𝐻/(1 − 𝑆𝑆𝑆𝑆𝑆𝑆𝑈𝑈𝐻𝐻)]. The results are consistent with those reported in Table 8.

28

momentum performance is robust to two time series explanations, namely, (i) the market state and

(ii) investor sentiment.

Cooper et al. (2004) suggest that momentum profits are related to the past market state.

Following their approach, we identify the market state by, respectively, using 12-month (Panel A),

24-month (Panel B), and 36-month (Panel C) CRSP value-weighted index returns prior to the

portfolio holding period. If the cumulative return is positive (negative), we classify such a market

state as UP (DOWN) market. We replicate our baseline SYNCH momentum analysis in UP and

DOWN markets and report the results in Table 9.

Based on FF3 adjusted returns, the results show that high-SYNCH momentum portfolios

outperform low-SYNCH momentum portfolios, regardless of market states, suggesting that our

main finding holds, conditional on the market state. However, in DOWN markets, the effect of

SYNCH is weak and the difference between high- and low-SYNCH momentum portfolios is

nonsignificant. Furthermore, in UP markets, the momentum portfolios for higher-SYNCH stocks

generate significantly positive returns, whereas those for lower-SYNCH stocks generate smaller

and less significant returns. In DOWN markets, while high-SYNCH momentum portfolios

outperform their low-SYNCH counterparts, their profitability is not reliably significantly positive.

These results confirm the finding of Cooper et al. (2004), who show that momentum profits are

only significant during UP markets, and provide new evidence that, even in DOWN markets,

high-SYNCH momentum portfolios still outperform their low-SYNCH counterpart portfolios, even

though the difference is not significant.


29

The second time series explanation is sentiment. Antoniou et al. (2013) find that

momentum profits are pronounced when investor sentiment is high, and they attribute their finding

to cognitive dissonance. According to our hypothesis, SYNCH induces cognitive dissonance,

which leads to higher momentum profits in high investor sentiment periods. Therefore, it is worth

checking whether momentum portfolios with high-SYNCH stocks outperform those with

low-SYNCH stocks across sentiment states. Following previous studies, we use the Michigan

Consumer Sentiment Index to estimate our sentiment proxy (Fisher and Statman 2003; McLean

and Zhao 2014). As Antoniou et al. (2013), we regress our original sentiment index on growth in

industrial production; real growth in durable consumption, real growth in nondurable consumption,

real growth in service consumption, growth in employment, and a National Bureau of Economic

Research recession indicator to purge the effects of macroeconomic conditions. The residuals from

this regression are saved to calculate our sentiment proxy. Following the approach of Antoniou et

al., we create a time-weighted sentiment index based on the residuals as our sentiment proxy.29

We also classify our sample into three sentiment terciles (i.e., high, mid, and low) and assess the

effect of SYNCH on momentum profits across the three sentiment states. The results are presented

in Table 10.

Panels A to C of Table 10 present the momentum returns during high, mid, and low-

sentiment periods, respectively. First, the FF3 adjusted returns of momentum portfolios

monotonically decrease as we move from the high-SYNCH to the low-SYNCH quintile, regardless

of investor sentiment. Additionally, high-SYNCH momentum portfolios consistently outperform

low-SYNCH momentum portfolios in each different sentiment period, demonstrating that our main

results are robust to investor sentiment. Second, our results are consistent with the findings of

29 Our sentiment proxy is calculated as 3/6 × 𝑟𝑟𝑛𝑛𝑠𝑠𝑟𝑟𝑟𝑟𝑟𝑟𝑎𝑎𝑟𝑟(𝑡𝑡) + 2/6 × 𝑟𝑟𝑛𝑛𝑠𝑠𝑟𝑟𝑟𝑟𝑟𝑟𝑎𝑎𝑟𝑟(𝑡𝑡 − 1) + 1/6 × 𝑟𝑟𝑛𝑛𝑠𝑠𝑟𝑟𝑟𝑟𝑟𝑟𝑎𝑎𝑟𝑟(𝑡𝑡 − 2).

30

Antoniou et al. (2012), who show that momentum profits are significant higher during

high-sentiment periods. In addition, given high investor sentiment that represents an optimistic

marketwide belief, the momentum is significantly stronger among stocks with noisy firm-specific

information (i.e., high SYNCH values), indicating stronger cognitive dissonance in high-SYNCH

stocks, supporting our hypothesis that stock price synchronicity improves momentum profits by

intensifying cognitive bias.


Next, we examine whether the returns of SYNCH momentum portfolios can be explained

by investor sentiment and market states together. Specifically, we estimate the following

multivariate regression specification for each SYNCH momentum portfolio:

𝑀𝑀𝑀𝑀𝑀𝑀𝑅𝑅𝑃𝑃𝑃𝑃𝑡𝑡 = 𝛽𝛽0 + 𝛽𝛽1𝑆𝑆𝑃𝑃𝑆𝑆𝑃𝑃𝐼𝐼𝑀𝑀𝑃𝑃𝑆𝑆𝑃𝑃𝑡𝑡 + 𝛽𝛽2𝑀𝑀𝑎𝑎𝑟𝑟𝑘𝑘𝑛𝑛𝑡𝑡𝑆𝑆𝑡𝑡𝑎𝑎𝑡𝑡𝑛𝑛𝑡𝑡 + 𝛽𝛽3𝑀𝑀𝑎𝑎𝑟𝑟𝑘𝑘𝑛𝑛𝑡𝑡𝑆𝑆𝑡𝑡𝑎𝑎𝑡𝑡𝑛𝑛𝑡𝑡2 + 𝛽𝛽4𝑀𝑀𝑀𝑀𝑃𝑃𝑅𝑅𝐹𝐹𝑡𝑡

+ 𝛽𝛽5𝑆𝑆𝑀𝑀𝐵𝐵𝑡𝑡 + 𝛽𝛽6𝐻𝐻𝑀𝑀𝐿𝐿𝑡𝑡 + 𝜀𝜀𝑡𝑡, (7)

where MOMRET is the time series of monthly average returns for the corresponding SYNCH

momentum portfolio in month t; MKTRF, SMB, and HML are the three Fama–French factors;

SENTIMENT is our investor sentiment proxy in month t; and MarketState is the 12-month

cumulative market returns used to identify the market state in month t. Following Antoniou et al.

(2013), we include the squared term of MarketState in our model. If investor sentiment and market

states are unable to fully explain the SYNCH momentum profits, 𝛽𝛽0 should be significantly

positive. The results are shown in Table 11.

In Table 11, 𝛽𝛽0 is significantly positive for the top three SYNCH momentum portfolios and

nonsignificant for the other SYNCH momentum portfolios. The difference in 𝛽𝛽0 values between

the high- and low-SYNCH momentum portfolios is also significantly positive, supporting our main

31

finding that high-SYNCH momentum portfolios outperform low-SYNCH portfolios after investor

sentiment and market states are controlled for, indicating that our main result is robust to investor

sentiment and market states.

In sum, this section shows that the effects of stock price synchronicity on momentum are

robust to market states and investor sentiment. High-SYNCH momentum portfolios outperform

their low-SYNCH counterparts, regardless of market state or investor sentiment.


3.9 Stock price synchronicity and PEAD

According to our stock price synchronicity hypothesis of momentum, noisy firm-specific

information breeds investor cognitive biases that induce investor underreaction, which, in turn,

increases the profitability of the momentum strategy. If momentum gains are attributed to investor

underreaction fueled by high SYNCH, high-SYNCH losers and winners are more likely to

underreact to unexpected earnings announcements than their low-SYNCH counterparts are.

Specifically, to examine whether the profitability of the momentum strategy stems directly

from the underlying link between investor underreaction and noisy firm-specific information, we

use the PEAD to examine how high-SYNCH/low-SYNCH loser and winner stocks respond to the

most recent quarterly standardized unexpected earnings (SUE). If the loser (winner) stocks

underreact to “bad news” (“good news”) because of noisy firm-specific information, high-SYNCH

loser (winner) portfolios are expected to underreact to low (high) SUE values, in comparison to

their low-SYNCH counterparts. Therefore, high-SYNCH losers (winners) with low (high) SUE

values should perform better (worse) during the “impact” period (from one day before to one day

32

after the earnings announcement date), but worse (better) during the “adjustment” period (from

two to 60 days after the earnings announcement date). Following Sadka (2006), we calculate SUE

as

(𝑃𝑃𝑎𝑎𝑟𝑟𝑠𝑠𝑟𝑟𝑠𝑠𝑠𝑠𝑠𝑠𝑡𝑡 − 𝑃𝑃𝑛𝑛𝑎𝑎𝑟𝑟𝑠𝑠𝑟𝑟𝑠𝑠𝑠𝑠𝑠𝑠𝑡𝑡−1 − 𝜇𝜇𝑒𝑒𝑒𝑒𝑒𝑒𝑖𝑖𝑖𝑖𝑖𝑖𝑒𝑒𝑒𝑒,𝑡𝑡)/𝜎𝜎𝑒𝑒𝑒𝑒𝑒𝑒𝑖𝑖𝑖𝑖𝑖𝑖𝑒𝑒𝑒𝑒,𝑡𝑡, (8)

where 𝑃𝑃𝑎𝑎𝑟𝑟𝑠𝑠𝑟𝑟𝑠𝑠𝑠𝑠𝑡𝑡 is the most recent quarterly earnings, 𝑃𝑃𝑛𝑛𝑎𝑎𝑟𝑟𝑠𝑠𝑟𝑟𝑠𝑠𝑠𝑠𝑠𝑠𝑡𝑡−1 is earnings for the prior

four quarters, and 𝜇𝜇𝑒𝑒𝑒𝑒𝑒𝑒𝑖𝑖𝑖𝑖𝑖𝑖𝑒𝑒𝑒𝑒,𝑡𝑡 and 𝜎𝜎𝑒𝑒𝑒𝑒𝑒𝑒𝑖𝑖𝑖𝑖𝑖𝑖𝑒𝑒𝑒𝑒,𝑡𝑡 are, respectively, the mean and standard deviation of

𝑃𝑃𝑎𝑎𝑟𝑟𝑠𝑠𝑟𝑟𝑠𝑠𝑠𝑠𝑠𝑠𝑡𝑡 − 𝑃𝑃𝑛𝑛𝑎𝑎𝑟𝑟𝑠𝑠𝑟𝑟𝑠𝑠𝑠𝑠𝑠𝑠𝑡𝑡−1 at the end of quarter t. Because of the availability of SUE, the tests

in this section cover the period from January 1973 to December 2018. We independently sort

stocks into terciles by SUE and identify the top (bottom) SUE tercile as the high (low) SUE tercile.

Additionally, we identify winners and losers by using the 11-month PRET in month t and classify

them into SYNCH quintiles. Then, we calculate the cumulative abnormal returns in the “impact”

and the “adjustment” periods for low-SUE losers and high-SUE winners across the SYNCH

quintiles.30 Furthermore, we examine the PEAD across different sentiment periods to provide

additional evidence that SYNCH increases underreaction by fueling of cognitive dissonance. If

noisy firm-specific information helps shape preexisting beliefs and fuels cognitive dissonance,

high-SYNCH loser stocks are more likely to underreact during high-sentiment (i.e., optimistic)

periods, whereas high-SYNCH winner stocks are more likely to underreact during low-sentiment

(i.e., pessimistic) periods. The results of PEAD are presented in Table 12. Panel A shows the

PEAD for both losers with low SUE values and winners with high SUE values. Panels B and C

report the PEAD for losers with low SUE values and winner with high SUE values, respectively,

across different sentiment periods.

30 The cumulative abnormal returns are estimated by using Fama-French three-factor model. The estimation period for parameters covers 120 trading days. The gap between event date and end of estimation period is 20 trading days.

33

The results are consistent with the prediction of our hypothesis. First, during the “impact”

period (one day before to one day after the earnings announcement date), as shown in Panel A of

Table 12, low-SYNCH losers with low SUE values exhibit more pronounced negative drift in

comparison to high-SYNCH losers and the drift difference between high- and low-SYNCH losers

is 1.0191% and statistically significant. During the “adjustment” period (two to 60 days after the

earnings announcement date), the drift difference between high- and low-SYNCH losers

is -3.0707% and statistically significant. Therefore, high-SYNCH losers respond less strongly than

their low-SYNCH counterparts to “bad news” at the beginning, but respond more strongly

subsequently, indicating that they are associated with greater underreaction. The results are the

opposite for winners with high SUE values, suggesting that we can draw the same inference as

before. The drift differences between high- and low-SYNCH winners are -0.6418% (t-statistic

= -2.96) during the “impact” period and 7.4536% (t-statistic = 8.46) during the “adjustment”

period. Moreover, in Panel B, we find that this phenomenon is pronounced for losers during the

optimistic period, but nonsignificant during the pessimistic period, indicating that the

underreaction among losers is more likely for high-SYNCH stocks during optimistic times than

during pessimistic times. Panel C reports the opposite results for winners, indicating that the

underreaction is pronounced during pessimistic periods. The results in Panels B and C confirm our

prediction that high-SYNCH loser stocks (winner stocks) are more likely to underreact during

optimistic (pessimistic) periods. Generally, the responses of the losers and winners to standardized

unexpected earnings, SUE, indicate that high-SYNCH stocks underreact more, implying that

cognitive dissonance is more likely among high-SYNCH stocks.


34

In sum, the results of this section show that high-SYNCH losers (winners) are more likely

to underreact to the most recent quarterly standardized unexpected earnings than their low-SYNCH

counterparts, consistent with the prediction of our hypothesis that noisy firm-specific information

fuels investor underreaction. In addition, we find that the underreaction in high-SYNCH losers

(winners) is more pronounced during optimistic (pessimistic) periods, indicating that cognitive

dissonance surfaces in firms with noisy firm-specific information.

3.10 Stock price synchronicity and short-selling activity

To investigate further the relation between noisy firm-specific information, high stock

price synchronicity, and investor underreaction, we explore the short-selling activity of winners

and losers during the formation and holding periods of the SYNCH momentum portfolios. Short

selling is known to arbitrage overpriced stocks. Hence, if a stock is overpriced, arbitrageurs are

expected to short the stock and, therefore, increase its short interest positions. If a stock is

underpriced, however, arbitrageurs should close their short positions and thus decrease its short

interest positions. Therefore, change in short interest position can be considered a signal of whether

a stock is overpriced or underpriced. Accordingly, if SYNCH increases underreaction, we expect

high-SYNCH loser (winner) stocks to be overpriced (underpriced) and associated with an increase

(decrease) in short-selling interest, since they are more likely to underreact to “bad news” (“good

news”). Additionally, if SYNCH strengthens underreaction through cognitive dissonance we

expect to observe a greater short interest increase (decrease) among high-SYNCH losers (winners)

in high-sentiment (low-sentiment) periods than in low-sentiment (high-sentiment) periods. To

address this issue, we obtain short interest data from the Compustat Supplemental Short Interest

File. Due to the availability of short interest data, the tests in this section cover the period from

35

January 1973 to December 2018. We use shares held short scaled by total outstanding shares to

measure short interest. The results are presented in Table 13, with the reported short interest

positions in percentages.

Panel A of Table 13 reports the average short interest for high- and low-SYNCH winners

and losers from t - 11 to t + 11. We exclude the last month of holding period (i.e., t + 12) when the

stock price is close to its intrinsic value and the short interest changes in the opposite direction.

Panel B presents the change in short interest for high- and low-SYNCH winners and losers during

the formation and holding periods, respectively. In line with our predication, in Panel A, we

observe short interest positions of high-SYNCH losers (winners) monotonously increase (decrease)

from t - 11 to t + 11, indicating that the stock prices of high-SYNCH losers (winners) are overpriced

(underpriced). However, this pattern is not observed for low-SYNCH losers (winners).

Furthermore, according to Panel B, we observe a significantly positive (negative) change in short

interest positions in the formation period [-11, 0] and holding period [0, 11] for high-SYNCH losers

(winners). However, as expected, this pattern does not hold for low-SYNCH winners and losers.

These results suggest that high-SYNCH losers (winners) are overpriced (underpriced), providing

additional evidence in support of the pronounced underreaction among high-SYNCH losers

(winners). Panel B also presents the change in short interest during different sentiment periods.

The results are consistent with our prediction that the change in short interest for high-SYNCH

losers is more pronounced during high-sentiment periods, indicating that cognitive dissonance is

more likely to be manifested when SYNCH is high. Specifically, for high-SYNCH losers, the

average holding period change in short interest positions during high-sentiment periods is 0.4669

percentage point with a t-statistic of 3.34, which is much stronger than the change of 0.2482

percentage point with a t-statistic of 1.82 during the low-sentiment period. We do not observe a

36

similar pattern for winners, consistent with the conjecture of Antoniou et al. (2013) that investor

cognitive dissonance is more pronounced among losers.


Overall, we document a pronounced increase (decrease) in short interest positions among

high-SYNCH losers (winners), suggesting that high-SYNCH losers (winners) are overpriced

(underpriced). We also show that the increase (decrease) in short interest positions among

high-SYNCH losers is more pronounced during periods of high sentiment, indicating cognitive

dissonance arises when SYNCH is high. The findings in this section provide additional support that

high-SYNCH stocks realize high-momentum profits because of being more susceptible to cognitive

biases that induce underreaction to information, based on change in short interest positions.

3.11 Robustness tests

3.11.1 Stock price synchronicity and other informativeness measures

In this study, we focus on SYNCH as our proxy for the level of firm-specific information

noisiness because it has several advantages in terms of both empirical application and theoretical

interpretation. SYNCH can be estimated by just using stock returns, which require no additional

databases. Second, unlike other characteristics (i.e., the ones that are positively associated with

extreme past returns) used to strengthen momentum (Bandarchuk and Hilscher 2013), stock price

synchronicity is negatively related to the extremeness of formation period returns. Therefore, the

high SYNCH-momentum return is not linked to extreme past returns. It is a standalone

characteristic of momentum returns. In addition, comparing to the measures that directly reflect

the information availability (e.g., analyst coverage and news coverage), SYNCH also has its

37

advantages in terms of measuring the overall noisiness of firm-specific information. Although

unable to link the noisiness to a specific type of information, SYNCH, as a measure based on

investors’ ultimate response (i.e., stock return), captures all kinds of information that investors

respond to. This is an important feature for our study because the momentum portfolio exposes to

all kinds of information and we focus on whether and how the level of firm-specific information

noisiness affects momentum performance instead of trying to identify any specific type of

information. The direct information availability measures, such as analyst coverage, only reflect

the availability of a specific type/source of information and cannot capture whether and how much

investors incorporate it into stock prices. Moreover, given that the more available information does

not necessarily improve the price informativeness (e.g., Kondor 2012; Han, Tang, and Yang 2016;

Goldstein and Yang 2019), the direct measures are not appropriate for capturing information

noisiness. It is also worth emphasizing that we study the momentum performance under the

firm-specific information noisiness rather than examine the role of any specific information and

for that reason we do not try to distinguish the role of public information and private information.

According to Roll (1988), SYNCH can reflect the traders’ action based on noisy private

information, which is unable to be captured by most direct informativeness measures if not all of

them. For these reasons, the direct measures are problematic to reflect the firm-specific

information noisiness.

In addition to SYNCH, there are other stock price informativeness measures used in

previous studies. To mitigate the concern about the validity of SYNCH as a stock price

informativeness measure, we examine momentum performance conditional on other stock price

informativeness measures. Although there is a variety of stock price informativeness measures,

most of them can be classified in three categories, the stock return volatility measure, the trading

38

volume measure, or the bid-ask information measure. Because SYNCH is linked to the stock return

volatility, we use measures from other two categories as our alternative measures. Specifically, we

use bid-ask spread (Bid_Ask_Spread) and stock turnover (TURN) as our alternative measures,

which are widely used to capture stock price informativeness and have a great data availability

that fits our main sample. Bid-ask spread is positively associated with price informativeness (i.e.,

low information noisiness) because market makers protect themselves by charging a spread when

they are trading against informed individuals (Bagehot 1971). Previous studies also show that

firm-specific information noisiness can stimulate trading volume (Kandel and Pearson 1995;

Bamber, Barron, and Stober 1999; Banerjee and Kremer 2010) so that we use the TURN during

the formation period to measure the trading volume.

To evaluate the validity of SYNCH, we first examine the correlation coefficient between

SYNCH and our alternative measures. Then we calculate the difference between high and low

characteristic momentum returns for each of the measures, respectively. Finally, we extract the

first principle component factor (First_factor) of SYNCH, Bid_Ask_Spread, and TURN, and

calculate the momentum performance conditional on it. We estimate the Bid_Ask_Spread by using

the Corwin and Schultz (2012)’s approach. The results are presented in Table 14. Panels A, B, and

C report the correlation coefficients between stock price informativeness measures, the results of

principle component analysis, and, the difference between high and low characteristic momentum

returns, respectively.

According to the correlation coefficients, reported in Panel A, SYNCH is negatively

correlated to Bid_Ask_Spread (correlation coefficients = -0.1455), and positively correlated to

TURN (correlation coefficients = 0.2590), consistent with the theoretical prediction we discussed

above. We also include the PRET and its absolute value (|PRET|) in Panel A, to examine the

39

correlation between each measure and PRET. If the correlation between the two variables is high,

the coefficient of interaction term between SYNCH and PRET in the Fama–MacBeth regression

may not be reliable. The correlation between SYNCH and PRET is -0.0379, which is low. Therefore,

our Fama–MacBeth regression results are not contaminated by the correlation between SYNCH

and PRET. In addition, except SYNCH, Bid_Ask_Spread and TURN are positively related to |PRET|.

Therefore, unlike Bid_Ask_Spread and TURN, the high-SYNCH momentum is not associated with

extreme past returns.

In Panel B, the eigenvector indicates that the First_factor is positively related to SYNCH

and TURN and negatively related to Bid_Ask_Spread, which are consistent with the predicted

relations between stock price informativeness and each measure. Therefore, we also use

First_factor as our alternative measure of stock price informativeness. In Panel C, the FF3 adjusted

returns of High–Low portfolios are -0.6468, 0.4958, and 0.9373 (t-statistic = -3.55, 2.22, and 4.20)

for Bid_Ask_Spread, TURN, and First_factor, indicating that high firm-specific information

noisiness lead to high momentum returns. This finding is consistent with our main result based on

SYNCH, suggesting SYNCH is a valid measure of firm-specific information noisiness.

In sum, the results in this section show that our main result is robust to three alternative

firm-specific information noisiness measures (i.e., Bid_Ask_Spread, TURN, and First_factor)

suggesting that SYNCH is a reliable measure of the level of firm-specific information noisiness.


3.11.2 Momentum, stock price synchronicity, and XBRL

Even though we have shown that momentum profits are more pronounced in stocks with

40

high price synchronicity, there is a concern that this effect could have been reduced by the

introduction of recent regulations that are supposed to reduce information complexity and the

processing costs of firm-specific information. To mitigate this concern, we examine whether the

relation between noisy firm-specific information and momentum profits is robust to the adoption

of XBRL, a regulatory policy that standardizes financial data and makes them computer readable.

The U.S. Securities and Exchange Commission (SEC) initiated voluntary XBRL adoption after

April 2005, and then mandated firms with a public float above $5 billion to submit XBRL data

after June 2009. The adoption of XBRL decreases the complexity and processing costs of

firm-specific information and thus reduces the noise level of firm-specific information. Dong et

al. (2016) find that, after the SEC required firms to adopt XBRL, stock price synchronicity

decreased.

To examine whether the effect of SYNCH on momentum profits is robust to the adoption

of XBLR, we regress monthly average returns for each SYNCH momentum portfolio on its

corresponding SYNCH rank. Specifically, we first divide our sample into three periods according

to the adoption stages of XBRL.31 Then, we estimate the following equation for each subsample

period:

𝑀𝑀𝑀𝑀𝑀𝑀𝑅𝑅𝑃𝑃𝑃𝑃 = 𝛽𝛽0 + 𝛽𝛽1𝑆𝑆𝑆𝑆𝑆𝑆𝑈𝑈𝐻𝐻_𝑅𝑅𝑎𝑎𝑠𝑠𝑘𝑘 + 𝛽𝛽2𝑆𝑆𝑃𝑃𝑆𝑆𝑃𝑃𝐼𝐼𝑀𝑀𝑃𝑃𝑆𝑆𝑃𝑃𝑋𝑋 + 𝛽𝛽3𝑀𝑀𝑎𝑎𝑟𝑟𝑘𝑘𝑛𝑛𝑡𝑡𝑆𝑆𝑡𝑡𝑎𝑎𝑡𝑡𝑛𝑛𝑋𝑋

+ 𝛽𝛽4𝑀𝑀𝑎𝑎𝑟𝑟𝑘𝑘𝑛𝑛𝑡𝑡𝑆𝑆𝑡𝑡𝑎𝑎𝑡𝑡𝑛𝑛2𝑋𝑋 + 𝛽𝛽5𝑀𝑀𝑀𝑀𝑃𝑃𝑅𝑅𝐹𝐹𝑋𝑋 + 𝛽𝛽6𝑆𝑆𝑀𝑀𝐵𝐵𝑋𝑋 + 𝛽𝛽7𝐻𝐻𝑀𝑀𝐿𝐿𝑋𝑋 + 𝛽𝛽8𝑆𝑆𝑃𝑃𝑆𝑆𝑃𝑃𝐼𝐼𝑀𝑀𝑃𝑃𝑆𝑆𝑃𝑃

+ 𝛽𝛽9𝑀𝑀𝑎𝑎𝑟𝑟𝑘𝑘𝑛𝑛𝑡𝑡𝑆𝑆𝑡𝑡𝑎𝑎𝑡𝑡𝑛𝑛 + 𝛽𝛽10𝑀𝑀𝑎𝑎𝑟𝑟𝑘𝑘𝑛𝑛𝑡𝑡𝑆𝑆𝑡𝑡𝑎𝑎𝑡𝑡𝑛𝑛2 + 𝛽𝛽11𝑀𝑀𝑀𝑀𝑃𝑃𝑅𝑅𝐹𝐹 + 𝛽𝛽12𝑆𝑆𝑀𝑀𝐵𝐵 + 𝛽𝛽13𝐻𝐻𝑀𝑀𝐿𝐿

+ 𝜀𝜀, (9)

where MOMRET is the time series of the monthly average returns for each SYNCH momentum

portfolio in month t; SYNCH_Rank is the rank based on SYNCH, which equals five, four, three,

31 The three stages are pre-XBRL period, which is the period before April 2005; the voluntary period, which is the period from April 2005 to June 2009; and the mandatory period, which is the period after July 2009.

41

two, and one from high SYNCH to low SYNCH values, respectively; SENTIMENT is our investor

sentiment proxy in month t; MarketState is the cumulative market return used to identify the

market state in month t; and MKTRF, SMB, and HML are the three Fama–French factors. To allow

for change in the coefficients of control variables across different SYNCH portfolios, we include

the interaction terms between controls and SYNCH_Rank (i.e., SENTIMENTX, MarketStateX,

MKTRFX, SMBX, and HMLX). Then, we estimate the following equation for our full sample period

(March 1964 to December 2018):

𝑀𝑀𝑀𝑀𝑀𝑀𝑅𝑅𝑃𝑃𝑃𝑃 = 𝛽𝛽0 + 𝛽𝛽1𝑆𝑆𝑆𝑆𝑆𝑆𝑈𝑈𝐻𝐻𝑅𝑅𝑒𝑒𝑖𝑖𝑅𝑅 + 𝛽𝛽3𝑋𝑋𝐵𝐵𝑅𝑅𝐿𝐿𝑃𝑃𝑒𝑒𝑒𝑒𝑖𝑖𝑃𝑃𝑖𝑖 + 𝛽𝛽3𝑆𝑆𝑃𝑃𝑆𝑆𝑃𝑃𝐼𝐼𝑀𝑀𝑃𝑃𝑆𝑆𝑃𝑃𝑋𝑋 + 𝛽𝛽4𝑀𝑀𝑎𝑎𝑟𝑟𝑘𝑘𝑛𝑛𝑡𝑡𝑆𝑆𝑡𝑡𝑎𝑎𝑡𝑡𝑛𝑛𝑋𝑋

+ 𝛽𝛽5𝑀𝑀𝑎𝑎𝑟𝑟𝑘𝑘𝑛𝑛𝑡𝑡𝑆𝑆𝑡𝑡𝑎𝑎𝑡𝑡𝑛𝑛2𝑋𝑋 + 𝛽𝛽6𝑀𝑀𝑀𝑀𝑃𝑃𝑅𝑅𝐹𝐹𝑋𝑋 + 𝛽𝛽7𝑆𝑆𝑀𝑀𝐵𝐵𝑋𝑋 + 𝛽𝛽8𝐻𝐻𝑀𝑀𝐿𝐿𝑋𝑋 + 𝛽𝛽9𝑆𝑆𝑃𝑃𝑆𝑆𝑃𝑃𝐼𝐼𝑀𝑀𝑃𝑃𝑆𝑆𝑃𝑃

+ 𝛽𝛽10𝑀𝑀𝑎𝑎𝑟𝑟𝑘𝑘𝑛𝑛𝑡𝑡𝑆𝑆𝑡𝑡𝑎𝑎𝑡𝑡𝑛𝑛 + 𝛽𝛽11𝑀𝑀𝑎𝑎𝑟𝑟𝑘𝑘𝑛𝑛𝑡𝑡𝑆𝑆𝑡𝑡𝑎𝑎𝑡𝑡𝑛𝑛2 + 𝛽𝛽12𝑀𝑀𝑀𝑀𝑃𝑃𝑅𝑅𝐹𝐹 + 𝛽𝛽13𝑆𝑆𝑀𝑀𝐵𝐵 + 𝛽𝛽14𝐻𝐻𝑀𝑀𝐿𝐿

+ 𝜀𝜀, (10)

where 𝑋𝑋𝐵𝐵𝑅𝑅𝐿𝐿_𝑃𝑃𝑛𝑛𝑟𝑟𝑟𝑟𝑝𝑝𝑟𝑟 is a dummy variable that equals one if the end of the formation period is

after April 2005, and zero otherwise. We report the results in Table 15.

In Table 15, SYNCH_Rank is positively significant across the three subsamples, indicating

that SYNCH significantly strengthens the momentum profits, regardless of the adoption of XBRL.

In the full-period test, the coefficient of SYNCH_Rank consistent with the subsample results is also

positive and significant, implying that SYNCH remains an important determinant of momentum

profitability, despite the adoption of the XBRL regulation designed to reduce firm-specific

information noise. A noteworthy result is that the coefficient of XBRL_Period is negative and

statistically significant. While this finding suggests that the adoption of XBRL has a negative effect

on the profitability of the momentum strategy by reducing firm-specific noise, it fails to remove

the significant effect of SYNCH on momentum. This result suggests that the decrease in

information complexity and information processing costs, due to the adoption of XBRL, weaken

42

the profitability of the momentum strategy. However, although the adoption of XBRL decreases

information complexity and information processing costs, it is unable to fully remove noise from

firm-specific information. Therefore, stock price synchronicity, SYNCH, remains an important

factor in the profitability of the momentum strategy.

In sum, the results in Table 15 document that SYNCH still significantly strengthens

momentum profits after controlling for the adoption of XBRL, a financial data filing policy

designed to decrease stock price synchronicity. An interesting interpretation of these results is that

the reduction of noise from firm-specific information through regulatory changes is limited.


3.11.3 Momentum and excess SYNCH

One concern about stock price synchronicity is that SYNCH can reflect other effects in

addition to noisy firm-specific information. High SYNCH values can be driven by firm

characteristics such as systematic risks, firm size (market capitalization), the book-to-market ratio,

firm profitability (return on assets), the volatility of firm profitability (standard deviation of the

return on assets), and the firm’s financial leverage (Dasgupta et al. 2010; Crawford, Roulstone,

and So 2012; Dong et al. 2016). These firm characteristics might not reflect the noise level of

firm-specific information and could simultaneously affect SYNCH and momentum profits, leading

to endogeneity problems. To purge the effect of systematic risks and other firm characteristics

from SYNCH, we regress SYNCH on the following firm characteristics: the market beta, the

industry beta, the logarithm of the firm’s market capitalization, the book-to-market ratio, the return

on assets (ROA), the standard deviation of ROA, and the ratio of total liability to total assets. Since

43

SYNCH is not suitable as a dependent variable (Morck et al. 2000), we transform it into its

logarithmic form,

𝐿𝐿𝑠𝑠𝑆𝑆𝑆𝑆𝑆𝑆𝑈𝑈𝐻𝐻 = 𝐿𝐿𝑠𝑠 �𝑆𝑆𝑆𝑆𝑆𝑆𝑈𝑈𝐻𝐻

1 − 𝑆𝑆𝑆𝑆𝑆𝑆𝑈𝑈𝐻𝐻� , (11)

and replace SYNCH with LnSYNCH as the dependent variable in the regression analysis. Then, we

use the residuals from this regression as our excess SYNCH (EX_SYNCH) and re-estimate Eq. (6).

The results reported in Table 16 are consistent with those in Table 8. Models 1, 2, and 5 present

the results for a sample involving NYSE/AMEX stocks. Models 3, 4, and 6 show the result for a

sample involving NYSE/AMEX/NSADAQ stocks. Since both samples yield similar results, our

presentation focus below is based on the NYSE/AMEX sample. Specifically, the coefficients of

interaction term between EX_SYNCH and PRET (EX_SYNCHX) are positive and statistically

significant in all the regression models, indicating that, after exclusion of the effects of systematic

risks and other firm characteristics from SYNCH, its purged version, EX_SYNCH, is positively and

significantly associated with momentum stock return predictability. In model 5, which includes all

the controls, the coefficient of EX_SYNCHX is 0.0163, with a t-statistic of 3.20, demonstrating that

the effect of EX_SYNCH on momentum remains robust after controlling for investor attention, the

disposition effect, systematic risks, firm age, firm size, the book-to-market ratio, illiquidity,

idiosyncratic risk, and stock turnover.


In sum, these findings show that the effect of SYNCH on momentum profitability is not

driven by systematic risks or firm characteristics. After we exclude these effects from SYNCH,

EX_SYNCH significantly increases return continuation, as well as its predecessor, SYNCH.

44

4. Conclusion

The behavioral finance literature attributes the momentum anomaly to investor cognitive

biases, and psychology studies claim that cognitive biases are related to the noisiness of

information. Motivated by these two strands of literature, we infer that the noisiness of

firm-specific information, manifested in stock price synchronicity, heightens the profitability of

the momentum strategy by inducing investor cognitive biases that lead investors to underreact to

news.

Our evidence demonstrates that momentum profitability is significantly prominent in states

of high stock price synchronicity (high SYNCH), and this finding remains robust to existing

explanations, firm characteristics, and the adoption of an information disclosure (XBRL) policy.

Moreover, our results reveal that, under circumstances that favor the rise of cognitive biases—

such as low levels of information discreteness, return consistency, small firm capitalization, high

market information delays, high sentiment, and high share turnover during the formation period

(i.e., ID, RC, SIZE, D, SENTIMENT, and TURN, respectively)—high-SYNCH momentum

portfolios still significantly outperform their low-SYNCH counterparts, implying that high stock

price synchronicity boost investors’ cognitive biases. Furthermore, our results show that

high-SYNCH momentum profits are largely driven by loser stocks, fitting the prediction of the

underreaction paradigm. The underreaction explanation gains additional support from the data on

the PEAD and short-selling activity among winner and loser stocks.

Overall, this study demonstrates that momentum profitability is significantly stronger in

states of high stock price synchronicity, providing an inefficient information–based explanation

for the emergence of cognitive biases. An interesting implication of our analysis is that the strong

link between stock price synchronicity and momentum returns mirrors the information inefficiency

45

of the markets when they are mostly populated by uninformed or partially informed traders who

fail to discover the true value of assets.

46

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TABLE 1 Momentum Profit Conditional on Stock Price Synchronicity This table reports the average monthly returns (%) of SYNCH momentum portfolios involving the NYSE/AMEX stocks for the period Mar. 1964–Dec. 2018. Panel A presents our main results. At each t, all the stocks are sorted into deciles by their PRET, the past J-month cumulative returns, and then into quintiles by their SYNCH, 𝑅𝑅2 from the regression of Eq. (1) in the past J months. For each SYNCH level, we report the average monthly returns of the PRET portfolios and the momentum portfolio, an overlapping strategy that buys (sells) the highest (lowest) PRET portfolio and holds for K-month after skipping the most recent month. High–Low is a portfolio that buys (sells) the high (low) SYNCH momentum portfolio. Both the unadjusted returns, Buy-Sell, and the Fama-French three-factor adjusted returns, FF3, are presented. Panel B presents momentum portfolio returns based on different sorting order and SYNCH proxies. SYNCH_SIC4 is the SYNCH proxy estimated by using 4-digit SIC classification. SYNCH_ff48, SYNCH_ff30, and SYNCH_ff17 are SYNCH proxies estimated by using Fama-French 48, 30, and 17 industry classifications, respectively. SYNCH_SIC2_Daily is the SYNCH proxy estimated by using daily returns and 2-digit SIC classification. Hi. SYNCH and Lo. SYNCH are momentum returns of high-SYNCH and low-SYNCH stocks. High–Low, FF3, and FF5 are the monthly return, the Fama-French three-factor adjusted returns, and the Fama-French five-factor adjusted returns of High–Low portfolio. All t-statistics are Newey–West adjusted with K lags.

Sell 1 2 3 4 5 6 7 8 9 Buy 10 Buy-Sell t-Stat. FF3 t-Stat. Panel A. J=11, K=12 NYSE/AMEX stocks High SYNCH 0.5185 0.8673 0.9945 1.0101 1.0299 1.0818 1.0841 1.0955 1.1766 1.2351 0.7166 2.74 1.2068 5.52

4 0.5927 0.9471 1.0774 1.0907 1.1420 1.1331 1.1671 1.1955 1.2255 1.2520 0.6593 2.70 1.1398 5.75 3 0.8329 1.0839 1.0912 1.1371 1.1535 1.1627 1.1912 1.2581 1.2656 1.1950 0.3621 1.54 0.7544 3.84 2 0.9329 1.1168 1.1526 1.2165 1.2502 1.2398 1.3030 1.3034 1.3298 1.2042 0.2713 1.16 0.6501 3.66

Low SYNCH 1.0269 1.1697 1.2571 1.2918 1.2812 1.3094 1.2875 1.3382 1.3241 1.1468 0.1200 0.60 0.3908 2.09 High–Low 0.5966 3.31 0.8160 4.22

Panel B. SYNCH-Momentum based on different settings (J=11, K=12) Hi. SYNCH t-Stat. Lo. SYNCH t-Stat. High–Low t-Stat. FF3 t-Stat. FF5 t-Stat.

SYNCH-Momentum portfolios with different sorting methods PRET × SYNCH 0.7166 2.74 0.1200 0.60 0.5966 3.31 0.8160 4.22 0.7301 3.58

Independent sorting 0.7843 2.74 0.1599 0.78 0.6244 2.93 0.8276 3.66 0.7505 3.17 SYNCH × PRET 0.5466 2.30 0.1610 0.73 0.3857 2.01 0.4913 2.27 0.4723 2.11

Formation period performance of SYNCH-Momentum portfolios with different sorting methods PRET × SYNCH 10.4996 44.12 12.9612 47.51 -2.4615 -11.55 -2.3130 -11.92 -2.4706 -12.25

Independent sorting 10.3398 41.27 12.8524 47.90 -2.5126 -11.18 -2.3755 -11.69 -2.5298 -12.12 SYNCH × PRET 8.7502 33.33 14.5263 39.59 -5.7761 -13.44 -5.6277 -14.04 -5.7396 -13.87

SYNCH-Momentum portfolios with different SYNCH proxies SYNCH_SIC4 0.6337 2.51 0.1832 0.86 0.4505 2.43 0.6847 3.44 0.7050 3.43 SYNCH_ff48 0.7329 2.71 0.1434 0.70 0.5895 3.05 0.8085 4.09 0.7520 3.59 SYNCH_ff30 0.6830 2.56 0.1703 0.82 0.5127 2.60 0.7303 3.60 0.6524 3.07 SYNCH_ff17 0.6684 2.48 0.1892 0.90 0.4793 2.42 0.6891 3.41 0.5911 2.84

SYNCH_SIC2_Daily 0.6976 2.79 0.0074 0.03 0.6902 3.46 0.9429 4.23 0.9051 4.01

50

TABLE 2 Momentum Profit Conditional on Stock Price Synchronicity and Return Consistency This table reports the average monthly returns (%) of RC-SYNCH momentum portfolios involving all NYSE/AMEX stocks for the period Mar. 1964–Dec. 2018. At each t, all the stocks are sequentially sorted into 10 × 5 × 2 equal-weighted portfolios by their PRET, SYNCH and RC. The PRET is the lagged J-month cumulative returns. The SYNCH is 𝑅𝑅2 from the regression of Eq. (1) in the past 12 months. The RC is a dummy, which equals one if eight of the 12 monthly returns have the same sign as PRET, otherwise zero. We identify a stock as a high-RC stock if its RC equals one, otherwise a low-RC stock. The returns of portfolios with high-RC (low-RC) stocks are reported in Panel A (Panel B). For each SYNCH level, we report the average monthly returns of the PRET portfolios and the momentum portfolio, an overlapping strategy that buys (sells) the highest (lowest) PRET portfolio and holds for K-month after skipping the most recent month. High–Low is a portfolio that buys (sells) the high (low) SYNCH momentum portfolio. Both the unadjusted returns, Buy-Sell, and the Fama-French three-factor adjusted returns, FF3, are presented. All t-statistics are Newey–West adjusted with K lags.

Sell 1 2 3 4 5 6 7 8 9 Buy 10 Buy-Sell t-Stat. FF3 t-Stat. Sequential sorts: 𝑃𝑃𝑅𝑅𝑃𝑃𝑃𝑃 × 𝑆𝑆𝑆𝑆𝑆𝑆𝑈𝑈𝐻𝐻 × 𝑅𝑅𝑈𝑈

Panel A. stocks with RC =1; J=11, K=12 High SYNCH 0.5061 0.8038 1.0293 1.0038 1.0435 1.0495 1.0727 1.1036 1.1891 1.2583 0.7522 2.63 1.2938 5.28

4 0.4827 1.0340 1.0992 1.2080 1.2018 1.0976 1.1702 1.1796 1.1832 1.2925 0.8098 3.03 1.3264 6.01 3 0.7163 1.0303 1.1237 1.0799 1.1734 1.1343 1.2434 1.2793 1.2736 1.2253 0.5090 1.95 0.9556 4.27 2 0.8059 1.1127 1.1903 1.2100 1.2645 1.2634 1.3469 1.3461 1.3469 1.2278 0.4219 1.54 0.8342 3.95


Panel B. stocks with RC =0; J=11, K=12 High SYNCH 0.4285 0.8537 0.9710 1.0026 1.0229 1.0956 1.0628 1.0515 1.0779 1.0783 0.6498 2.57 0.9820 4.35

4 0.6709 0.9067 1.0752 1.0755 1.1106 1.1281 1.1483 1.1581 1.1715 1.0257 0.3548 1.32 0.7525 3.38 3 0.9031 1.1222 1.0978 1.1314 1.1406 1.1582 1.1214 1.2221 1.1592 1.0189 0.1159 0.48 0.3899 1.58 2 1.0219 1.1281 1.1544 1.2338 1.2527 1.2001 1.2504 1.2247 1.2372 1.1521 0.1303 0.61 0.4343 2.31

Low SYNCH 1.0218 1.2575 1.3038 1.3364 1.2940 1.3192 1.2432 1.2608 1.2051 1.0036 -0.0182 -0.09 0.2315 1.25 High–Low 0.6680 2.74 0.7505 3.17

51

TABLE 3 Momentum Profit Conditional on Stock Price Synchronicity and Unrealized Capital Gain This table reports the average monthly returns (%) of UCG-SYNCH momentum strategies involving all NYSE/AMEX stocks for the period Mar. 1964–Dec. 2018. At each t, all the stocks are sequentially sorted into 10 × 5 × 3 equal-weighted portfolios by their PRET, SYNCH and UCG. The PRET is the lagged J-month cumulative returns. The SYNCH is 𝑅𝑅2 from the regression of Eq. (1) in the past J months. The UCG is calculated by using Grinblatt and Han (2005)’s procedure. The three UCG terciles are, respectively, defined as high-, mid-, and low-UCG. The returns of portfolios with high-, mid-, and low-UCG stocks are reported in Panels A to C, respectively. For each SYNCH level, we report the average monthly returns of the PRET portfolios and the momentum portfolio, an overlapping strategy that buys (sells) the highest (lowest) PRET portfolio and holds for K-month after skipping the most recent month. High–Low is a portfolio that buys (sells) the high (low) SYNCH momentum portfolio. Both the unadjusted returns, Buy-Sell, and the Fama-French three-factor adjusted returns, FF3, are presented. All t-statistics are Newey–West adjusted with K lags.

Sell 1 2 3 4 5 6 7 8 9 Buy 10 Buy-Sell t-Stat. FF3 t-Stat. Sequential sorts: 𝑃𝑃𝑅𝑅𝑃𝑃𝑃𝑃 × 𝑆𝑆𝑆𝑆𝑆𝑆𝑈𝑈𝐻𝐻 × 𝑈𝑈𝑈𝑈𝐺𝐺

Panel A. High UCG; J=11, K=12 High SYNCH 0.5473 0.8336 0.9037 0.9978 0.9774 1.0222 1.0693 1.0722 1.2318 1.4433 0.8961 3.22 1.3520 5.78

4 0.6371 0.9137 1.0472 1.0258 1.1187 1.1224 1.1915 1.2247 1.2751 1.4175 0.7803 3.23 1.2005 5.90 3 0.7514 1.0765 1.1578 1.1291 1.1063 1.1931 1.1881 1.2872 1.3352 1.3724 0.6209 2.86 0.9497 5.25 2 0.9310 1.0618 1.1227 1.1793 1.2162 1.2085 1.2846 1.3442 1.4267 1.3526 0.4216 1.88 0.7577 4.55


Panel B. Mid UCG; J=11, K=12 High SYNCH 0.5432 0.8798 1.0314 1.0197 1.0261 1.0889 1.0624 1.0736 1.1805 1.2942 0.7510 2.91 1.2391 5.92

4 0.6941 1.0230 1.0879 1.0252 1.1695 1.1652 1.1179 1.1669 1.1745 1.2079 0.5138 2.04 0.9655 4.80 3 0.8513 1.0928 1.0107 1.1311 1.1316 1.1606 1.1893 1.1979 1.2809 1.1805 0.3292 1.27 0.7286 3.61 2 0.9102 1.0661 1.1085 1.2096 1.2209 1.2023 1.2783 1.2492 1.3374 1.0704 0.1602 0.60 0.5180 2.60


Panel C. Low UCG; J=11, K=12 High SYNCH 0.7983 1.0083 1.0397 1.0520 1.1116 1.0987 1.1463 1.0882 1.0892 1.0567 0.2584 0.86 0.7672 2.94

4 0.8163 1.0838 1.0840 1.1700 1.1301 1.1478 1.1253 1.1059 1.1497 1.0974 0.2811 0.94 0.7881 3.22 3 1.1091 1.1214 1.1640 1.1796 1.1915 1.0978 1.1132 1.1924 1.1906 0.9982 -0.1109 -0.38 0.3176 1.25 2 1.1017 1.3368 1.1960 1.2184 1.2295 1.1849 1.2691 1.2057 1.2235 1.1263 0.0246 0.08 0.3472 1.29

Low SYNCH 1.2448 1.1843 1.2904 1.3518 1.3061 1.2435 1.1952 1.3609 1.2245 0.9068 -0.3380 -1.20 -0.0981 -0.39 High–Low 0.5964 2.23 0.8653 3.44

52

TABLE 4 Momentum Profit Conditional on Stock Price Synchronicity and Information Discreteness This table reports the average monthly returns (%) of ID-SYNCH momentum strategies involving all NYSE/AMEX stocks for the period Mar. 1964–Dec. 2018. At each t, all the stocks are sequentially sorted into 10 × 5 × 3 equal-weighted portfolios by PRET, SYNCH and ID. The PRET is the lagged J-month cumulative returns. The SYNCH is 𝑅𝑅2 from the regression of Eq. (1) in the past J months. The ID is defined as 𝑠𝑠𝑟𝑟𝑠𝑠𝑠𝑠(𝑃𝑃𝑅𝑅𝑃𝑃𝑃𝑃) × [%𝑠𝑠𝑛𝑛𝑠𝑠 − %𝑝𝑝𝑝𝑝𝑠𝑠], where the %𝑝𝑝𝑝𝑝𝑠𝑠 and %𝑠𝑠𝑛𝑛𝑠𝑠 are the respective percentages of positive and negative daily returns during the J months. The three ID terciles are, respectively, defined as high-, mid-, and low-ID. The returns of portfolios with high-, mid-, and low-ID stocks are reported in Panels A to C, respectively. For each SYNCH level, we report the average monthly returns of the PRET portfolios and the momentum portfolio, an overlapping strategy that buys (sells) the highest (lowest) PRET portfolio and holds for K-month after skipping the most recent month. High–Low is a portfolio that buys (sells) the high (low) SYNCH momentum portfolio. Both the unadjusted returns, Buy-Sell, and the Fama–French three-factor adjusted returns, FF3, are presented. All t-statistics are Newey–West adjusted with K lags.

Sell 1 2 3 4 5 6 7 8 9 Buy 10 Buy-Sell t-Stat. FF3 t-Stat. Sequential sorts: 𝑃𝑃𝑅𝑅𝑃𝑃𝑃𝑃 × 𝑆𝑆𝑆𝑆𝑆𝑆𝑈𝑈𝐻𝐻 × 𝐼𝐼𝐼𝐼

Panel A. High ID; J=11, K=12 High SYNCH 0.7213 0.9231 1.0043 1.0023 0.9885 1.0594 1.0728 1.0441 1.1303 1.1632 0.4419 1.76 0.7858 3.64

4 0.9219 0.9526 1.1222 1.1155 1.1598 1.0852 1.1557 1.1530 1.1225 1.0374 0.1155 0.47 0.5005 2.47 3 1.2444 1.3158 1.1291 1.0936 1.1326 1.0517 1.1201 1.1723 1.0885 0.9881 -0.2563 -1.20 0.0344 0.18 2 1.2035 1.3389 1.2580 1.2098 1.2009 1.1601 1.2194 1.1537 1.0879 1.0414 -0.1621 -0.73 0.1298 0.67


Panel B. Mid ID; J=11, K=12 High SYNCH 0.5524 0.8748 1.0241 1.0300 1.0512 1.0852 1.0846 1.1373 1.1834 1.2383 0.6859 2.56 1.1764 5.26

4 0.5754 1.0434 1.1068 1.1078 1.1478 1.1782 1.1655 1.2359 1.2787 1.2822 0.7068 2.80 1.1649 5.67 3 0.8939 1.1257 1.1035 1.1564 1.1919 1.2459 1.2260 1.3040 1.3677 1.2424 0.3485 1.39 0.7546 3.47 2 1.0546 1.1109 1.1819 1.2382 1.3538 1.3180 1.3759 1.3845 1.4014 1.2374 0.1828 0.73 0.5251 2.68


Panel C. Low ID; J=11, K=12 High SYNCH 0.2544 0.7986 0.9509 0.9983 1.0594 1.1120 1.0915 1.0905 1.2241 1.3051 1.0506 3.35 1.6781 6.19

4 0.2902 0.8536 1.0156 1.0588 1.1073 1.1242 1.1648 1.1990 1.2627 1.4312 1.1409 3.97 1.7403 7.25 3 0.3508 0.8011 1.0337 1.1435 1.1459 1.1974 1.2241 1.2818 1.3312 1.3444 0.9937 3.43 1.4881 6.26 2 0.5531 0.9291 1.0168 1.1935 1.1972 1.2369 1.2907 1.3706 1.5034 1.3498 0.7967 2.47 1.2996 5.20


53

TABLE 5 Momentum Profit Conditional on Stock Price Synchronicity and Market Information Delay This table reports the average monthly returns (%) of D-SYNCH momentum strategies involving all NYSE/AMEX stocks for the period Mar. 1964–Dec. 2018. At each t, all the stocks are sequentially sorted into 10 × 5 × 3 equal-weighted portfolios by PRET, SYNCH and D. The PRET is the lagged J-month cumulative returns. The SYNCH is 𝑅𝑅2 from the regression of Eq. (1) in the past J months. The D is calculated by using Hou and Moskowitz (2005)’s procedure. The three D terciles are, respectively, defined as high-, mid-, and low-D from top D value tercile to bottom D value tercile. The returns of portfolios with high-, mid-, and low-D stocks are reported in Panels A to C, respectively. For each SYNCH level, we report the average monthly returns of the PRET portfolios and the momentum portfolio, an overlapping strategy that buys (sells) the highest (lowest) PRET portfolio and holds for K-month after skipping the most recent month. High–Low is a portfolio that buys (sells) the high (low) SYNCH momentum portfolio. Both the unadjusted returns, Buy-Sell, and the Fama–French three-factor adjusted returns, FF3, are presented. All t-statistics are Newey–West adjusted with K lags.

Sell 1 2 3 4 5 6 7 8 9 Buy 10 Buy-Sell t-Stat. FF3 t-Stat. Sequential sorts: 𝑃𝑃𝑅𝑅𝑃𝑃𝑃𝑃 × 𝑆𝑆𝑆𝑆𝑆𝑆𝑈𝑈𝐻𝐻 × 𝐼𝐼

Panel A. High D; J=11, K=12 High SYNCH 0.5611 0.8309 0.9934 1.0029 1.0518 1.1199 1.1760 1.1441 1.2356 1.1883 0.6272 2.36 1.1029 4.88

4 0.6573 0.9686 1.0753 1.1015 1.1251 1.1102 1.1583 1.1758 1.2405 1.2958 0.6385 2.57 1.1300 5.35 3 0.8971 1.1254 1.1003 1.1318 1.1517 1.1488 1.1645 1.2596 1.2461 1.1788 0.2817 1.15 0.6898 3.30 2 0.9527 1.1088 1.1632 1.2303 1.2452 1.2559 1.3073 1.2898 1.3479 1.1447 0.1920 0.78 0.5778 2.97

Low SYNCH 1.1478 1.1713 1.2275 1.2724 1.3448 1.3060 1.1873 1.3501 1.3136 1.1446 -0.0032 -0.01 0.2432 1.15 High–Low 0.6303 2.66 0.8598 3.68

Panel B. Mid D; J=11, K=12 High SYNCH 0.4644 0.9079 0.9957 1.0020 1.0439 1.0788 1.0464 1.1480 1.1565 1.2141 0.7497 2.90 1.2392 5.70

4 0.6400 0.9044 1.0393 1.0835 1.1542 1.1324 1.1822 1.2311 1.2157 1.2549 0.6149 2.40 1.0986 5.12 3 0.8136 1.0844 1.1261 1.1520 1.1356 1.1437 1.2058 1.2303 1.2025 1.2119 0.3983 1.63 0.7750 3.64 2 0.9811 1.1603 1.1252 1.2453 1.2171 1.2456 1.3125 1.2944 1.3140 1.1830 0.2019 0.79 0.5922 2.95


Panel C. Low D; J=11, K=12 High SYNCH 0.5188 0.8609 0.9914 1.0281 0.9927 1.0471 1.0293 0.9911 1.1352 1.3108 0.7920 2.74 1.2959 5.17

4 0.4802 0.9716 1.1195 1.0853 1.1454 1.1589 1.1630 1.1793 1.2219 1.2043 0.7241 2.92 1.1915 6.05 3 0.7854 1.0459 1.0482 1.1266 1.1728 1.1976 1.2006 1.2815 1.3499 1.1957 0.4103 1.59 0.7984 3.69 2 0.8644 1.0746 1.1735 1.1768 1.2901 1.2207 1.2881 1.3189 1.3245 1.2906 0.4262 1.81 0.7880 4.28


54

TABLE 6 Momentum Profit Conditional on Stock Price Synchronicity and Stock Turnover This table reports the average monthly returns (%) of TURN-SYNCH momentum strategies involving all NYSE/AMEX stocks for the period Mar. 1964–Dec. 2018. At each t, all the stocks are sequentially sorted into 10 × 5 × 3 equal-weighted portfolios by PRET, SYNCH and TURN. The PRET is the lagged J-month cumulative returns. The SYNCH is 𝑅𝑅2 from the regression of Eq. (1) in the past J months. The TURN is the formation period stock turnover, which is trading volume divided by shares outstanding. The three TURN terciles are, respectively, defined as high-, mid-, and low-TURN. The returns of portfolios with high-, mid-, and low-TURN stocks are reported in Panels A to C, respectively. For each SYNCH level, we report the average monthly returns of the PRET portfolios and the momentum portfolio, an overlapping strategy that buys (sells) the highest (lowest) PRET portfolio and holds for K-month after skipping the most recent month. High–Low is a portfolio that buys (sells) the high (low) SYNCH momentum portfolio. Both the unadjusted returns, Buy-Sell, and the Fama–French three-factor adjusted returns, FF3, are presented. All t-statistics are Newey–West adjusted with K lags.

Sell 1 2 3 4 5 6 7 8 9 Buy 10 Buy-Sell t-Stat. FF3 t-Stat. Sequential sorts: 𝑃𝑃𝑅𝑅𝑃𝑃𝑃𝑃 × 𝑆𝑆𝑆𝑆𝑆𝑆𝑈𝑈𝐻𝐻 × 𝑃𝑃𝑈𝑈𝑅𝑅𝑆𝑆

Panel A. High TURN; J=11, K=12 High SYNCH 0.2748 0.6523 0.9183 0.9381 0.9548 1.0962 1.0933 1.0530 1.0707 1.0351 0.7603 2.39 1.3074 4.36

4 0.2963 0.8381 0.9602 0.9708 1.0582 1.0939 1.1077 1.1242 1.0753 1.0127 0.7164 2.74 1.2260 5.13 3 0.3960 0.8973 0.9258 0.9969 1.0479 1.1013 1.0680 1.1482 1.0660 0.9200 0.5241 2.16 0.9134 4.19 2 0.5814 0.8317 1.0108 1.0357 1.1708 1.1025 1.1205 1.1701 1.0419 0.7936 0.2122 0.80 0.6548 3.08


Panel B. Mid TURN; J=11, K=12 High SYNCH 0.5594 0.8951 1.0682 1.1084 1.0592 1.0855 1.1361 1.1550 1.2895 1.3221 0.7626 2.69 1.2568 5.35

4 0.6114 0.9727 1.1244 1.1607 1.1639 1.1754 1.2004 1.2637 1.3297 1.3013 0.6899 2.39 1.1649 4.90 3 0.9317 1.1237 1.1047 1.1655 1.2632 1.2301 1.2365 1.2670 1.3326 1.2339 0.3022 1.11 0.7354 3.35 2 0.8847 1.1212 1.2225 1.2753 1.2727 1.2760 1.3554 1.3896 1.4356 1.2878 0.4031 1.61 0.8099 4.24


Panel C. Low TURN; J=11, K=12 High SYNCH 0.7500 1.0279 0.9955 1.0243 1.0199 1.0640 1.0669 1.1081 1.2034 1.3034 0.5535 2.04 1.0036 4.51

4 0.7726 1.0244 1.1337 1.1486 1.2034 1.1979 1.2011 1.2720 1.2785 1.4242 0.6516 2.60 1.1047 5.63 3 1.1953 1.2235 1.2815 1.2465 1.1940 1.1704 1.2786 1.3848 1.4133 1.5095 0.3142 1.17 0.6782 2.83 2 1.3462 1.3961 1.2206 1.4020 1.3400 1.3379 1.4453 1.3920 1.5669 1.5207 0.1746 0.64 0.4469 1.84


55

TABLE 7 Momentum Profit Conditional on Stock Price Synchronicity and Firm Capitalization This table reports the average monthly returns (%) of SIZE-SYNCH momentum strategies involving all NYSE/AMEX stocks for the period Mar. 1964–Dec. 2018. At each t, all the stocks are sequentially sorted into 10 × 5 × 2 equal-weighted portfolios by PRET, SYNCH, and SIZE. The PRET is the lagged J-month cumulative returns. The SYNCH is 𝑅𝑅2 from the regression of Eq. (1) in the past J months. The SIZE is firm’s market capitalization. Panel A displays the result for small firms, which are identified as the stocks in the smaller five SIZE deciles. Panel B displays the result for large firms, which are identified as the stocks in the larger five SIZE deciles. SIZE decile breakpoints come from Kenneth French’s data library. For each SYNCH level, we report the average monthly returns of the PRET portfolios and the momentum portfolio, an overlapping strategy that buys (sells) the highest (lowest) PRET portfolio and holds for K-month after skipping the most recent month. High–Low is a portfolio that buys (sells) the high (low) SYNCH momentum portfolio. Both the unadjusted returns, Buy-Sell, and the Fama–French three-factor adjusted returns, FF3, are presented. All t-statistics are Newey–West adjusted with K lags.

Sell 1 2 3 4 5 6 7 8 9 Buy 10 Buy-Sell t-Stat. FF3 t-Stat. Sequential sorts: 𝑃𝑃𝑅𝑅𝑃𝑃𝑃𝑃 × 𝑆𝑆𝑆𝑆𝑆𝑆𝑈𝑈𝐻𝐻 × 𝑆𝑆𝐼𝐼𝛼𝛼𝑃𝑃

Panel A. Small Market Capitalization; J=11, K=12 High SYNCH 0.5653 1.0744 1.2339 1.2632 1.3403 1.3103 1.4639 1.4348 1.5687 1.4016 0.8363 2.68 1.1712 4.02

4 0.6020 1.0776 1.2129 1.2077 1.2345 1.2341 1.2882 1.2836 1.3867 1.2966 0.6946 2.67 1.1082 4.90 3 0.8663 1.1570 1.1722 1.2381 1.2393 1.2076 1.2506 1.2758 1.3174 1.2338 0.3675 1.46 0.7175 3.36 2 0.9435 1.1460 1.1973 1.2671 1.3176 1.2840 1.3681 1.3429 1.3513 1.2142 0.2707 1.12 0.6360 3.36


Panel B. Large Market Capitalization; J=11, K=12 High SYNCH 0.5560 0.8219 0.9310 0.9421 0.9691 1.0203 1.0159 1.0033 1.0854 1.1373 0.5813 2.31 1.0195 4.89

4 0.6380 0.7977 0.9719 1.0100 1.0692 1.0473 1.0645 1.1114 1.1317 1.1820 0.5440 2.36 0.9163 4.46 3 0.8136 0.9410 0.9623 0.9563 1.0305 1.0965 1.0927 1.1706 1.1622 1.0882 0.2747 1.05 0.6128 2.39 2 1.0028 1.1173 0.8968 1.1013 1.0887 1.0701 1.0265 1.1363 1.2247 1.0879 0.0909 0.31 0.4251 1.49


.

56

TABLE 8 Fama–MacBeth regressions This table reports the results of Fama–MacBeth regression for individual stock returns (%) during Mar.1964–Dec.2018. The dependent variable is FRET, which is the cumulative returns of individual stock during the holding period. The PRET is the lagged 11-month cumulative returns. The SYNCH, 𝛽𝛽𝑚𝑚, and 𝛽𝛽𝑖𝑖𝑖𝑖𝑖𝑖 are estimated by Eq. (1). IVOL is standard deviation of daily stock return residuals during the 11-month formation period, which are estimated by using FF3 model. Other control variables are ID (Information Discreteness), RC (Return Consistency), SIZE (the log of market capitalization), BM (Book to market ratio), IVOL (idiosyncratic risk), IILLIQ (Illiquidity factor), AGE (the log of the listed months), TURN (stock turnover), and interaction terms with PRET (e.g., SYNCHX, IDX, RCX etc.). t-statistics are shown in parentheses and Newey–West adjusted with K lags. ***, **, and * indicate that the coefficients are significantly different from zero at the 1%, 5%, and 10% level. Panel A: Basic specifications

NYSE/AMEX NYSE/AMEX/NASDQ Model 1 Model 2 Model 3 Model 4 Model 5 Model 6

Intercept 0.1244*** 0.1249*** 0.1263*** 0.1259*** 0.1272*** 0.1080*** (5.80) (4.75) (3.45) (5.75) (4.85) (2.91) PRET 0.0297* 0.0008 -0.0022 0.0291** 0.0045 -0.0017 (1.73) (0.06) (-0.16) (2.03) (0.45) (-0.19) SYNCHX 0.0952*** 0.0907*** 0.0955*** 0.1008*** (2.86) (2.91) (3.10) (3.78) SYNCH -0.0235 0.0679*** -0.0247 0.0551*** (-0.87) (4.14) (-0.85) (3.28) 𝜷𝜷𝒎𝒎 -0.0099 -0.0090 (-1.28) (-1.14) 𝜷𝜷𝒊𝒊𝒊𝒊𝒊𝒊 -0.0207** -0.0186* (-2.19) (-1.96) SIZE -0.0070 -0.0048 (-1.47) (-0.98) BM 0.0219*** 0.0352*** (3.69) (4.76) Adj. 𝑹𝑹𝟐𝟐 0.0133 0.0242 0.0580 0.0103 0.0179 0.0498 Pane B: All interactions PRET SYNCHX IDX RCX SIZEX BMX Model 7 0.1265*** 0.1249*** -0.3342*** 0.0037 -0.0111*** -0.0100 (NYSE/AMEX) (4.45) (3.88) (-4.20) (0.54) (-2.68) (-1.04) Model 8 0.0881*** 0.1065*** -0.3629*** 0.0041 -0.0064* -0.0116 (NYSE/AMEX/NASDQ) (4.62) (4.43) (-5.63) (0.67) (-1.80) (-1.35) AGEX ILLIQX IVOLX TURNX ID RC Model 7 (continued) -0.0236*** 0.0005 -0.9494* -0.0129 0.1175*** -0.0032 (-5.20) (0.35) (-1.95) (-1.27) (5.24) (-1.38) Model 8 (continued) -0.0197*** 0.0012 -0.8629* -0.0076 0.1347*** -0.0030* (-5.11) (0.98) (-1.92) (-0.96) (6.82) (-1.65) ILLIQ IVOL TURN AGE SYNCH 𝜷𝜷𝒎𝒎 Model 7 (continued) 0.0048*** -1.7199** -0.0307*** 0.0039 0.0326** 0.0114** (4.07) (-2.50) (-4.49) (1.59) (2.18) (2.07) Model 8 (continued) 0.0019** -1.3326** -0.0250*** 0.0084*** 0.0185 0.0109** (2.33) (-2.05) (-3.94) (3.20) (1.21) (2.23) 𝜷𝜷𝒊𝒊𝒊𝒊𝒊𝒊 SIZE BM Intercept Adj. 𝑹𝑹𝟐𝟐 Model 7 (continued) 0.0095 -0.0130*** 0.0137** 0.1985*** 0.0970 (1.44) (-3.88) (2.51) (6.26) Model 8 (continued) 0.0097* -0.0129*** 0.0228*** 0.1775*** 0.0775 (1.80) (-3.97) (3.68) (5.74)

57

TABLE 9 Momentum Profit Conditional on Stock Price Synchronicity and Market States This table reports the average monthly returns (%) of SYNCH momentum portfolios involving all NYSE/AMEX stocks across the market states for sample period Mar. 1964–Dec. 2018. At each t, all the stocks are sequentially sorted into 10 × 5 equal-weighted portfolios by PRET and SYNCH. The PRET is the lagged J-month cumulative returns. The stocks in top (bottom) PRET portfolio are defined as winners (losers). The SYNCH is the 𝑅𝑅2 from the regression of Eq. (1) in the past J months. The market state is defined as a UP (DOWN) market if the past M-month CRSP value-weighted index return is positive (negative). From Panels A to C, the M equals to 12, 24 and 36, respectively. For each SYNCH level, we report the average monthly returns of the momentum portfolio, an overlapping strategy that buys (sells) the winner (loser) portfolio and holds for K-month after skipping the most recent month. High–Low is a portfolio that buys (sells) the high (low) SYNCH momentum portfolio. Both the unadjusted returns, Buy-Sell, and the Fama–French three-factor adjusted returns, FF3, are presented. All t-statistics are Newey–West adjusted with K lags.

UP Market DOWN Market Loser winner Buy-Sell t-Stat. FF3 t-Stat. Loser winner Buy-Sell t-Stat. FF3 t-Stat. Panel A. 12-Month; J=11, K=12 High SYNCH 0.1829 1.1263 0.9434 4.43 1.2210 5.96 High SYNCH 1.4973 1.4220 -0.0752 -0.16 1.2109 2.73

4 0.2302 1.1302 0.90 4.57 1.2003 7.07 4 1.6641 1.6566 -0.0074 -0.02 1.2530 3.24 3 0.4014 1.0696 0.6681 3.85 0.8776 5.98 3 1.9498 1.7539 -0.1959 -0.44 0.8692 2.13 2 0.5257 1.112 0.5863 3.63 0.7003 4.85 2 2.2207 1.5544 -0.6662 -1.44 0.5537 1.43

Low SYNCH 0.6597 1.0219 0.3622 2.44 0.4475 3.15 Low SYNCH 2.1516 1.8095 -0.3421 -0.80 0.6014 1.42 High–Low 0.5813 2.89 0.7736 3.74 High–Low 0.2668 0.87 0.6095 1.69

Panel B. 24-Month; J=11, K=12 High SYNCH 0.2957 1.1926 0.8969 3.78 1.3358 6.48 High SYNCH 1.9220 1.4701 -0.4520 -0.55 0.5432 0.79

4 0.4304 1.2279 0.7975 3.54 1.1977 6.62 4 2.1449 1.5727 -0.5722 -0.79 0.3970 0.60 3 0.6403 1.1586 0.5183 2.39 0.8035 4.45 3 2.6633 1.7108 -0.9525 -1.19 0.0528 0.07 2 0.7196 1.1774 0.4578 2.16 0.7281 4.49 2 3.0203 1.7508 -1.2695 -1.67 -0.3247 -0.44

Low SYNCH 0.8029 1.0805 0.2777 1.75 0.4223 2.74 Low SYNCH 2.8630 1.8544 -1.0086 -1.40 -0.1379 -0.18 High–Low 0.6193 3.22 0.9135 4.47 High–Low 0.5566 1.59 0.6811 1.84

Panel C. 36-Month; J=11, K=12 High SYNCH 0.2813 1.1503 0.869 3.61 1.3269 6.05 High SYNCH 2.1220 1.5251 -0.597 -0.61 0.3721 0.58

4 0.3553 1.1348 0.7795 3.33 1.1953 5.77 4 2.1793 1.5685 -0.6107 -0.77 0.3166 0.62 3 0.5722 1.0633 0.4911 2.34 0.8109 4.28 3 2.6175 1.6083 -1.0091 -1.08 -0.0572 -0.08 2 0.6173 1.0853 0.4680 2.45 0.7739 4.91 2 2.8280 1.4607 -1.3673 -1.38 -0.4186 -0.59

Low SYNCH 0.7754 0.9836 0.2081 1.25 0.3979 2.40 Low SYNCH 2.4286 1.5440 -0.8846 -1.00 -0.0824 -0.11 High–Low 0.6609 3.45 0.929 4.62 High–Low 0.2876 0.76 0.4545 1.08

58

TABLE 10 Momentum Profit Conditional on Stock Price Synchronicity and Sentiment This table reports the average monthly returns (%) of SYNCH momentum portfolios involving all NYSE/AMEX stocks across SENTIMENT states for the period Mar. 1964–Dec. 2018. At each t, all the stocks are sequentially sorted into 10 × 5 equal-weighted portfolios by PRET and SYNCH. The PRET is the lagged J-month cumulative returns. The SYNCH is the 𝑅𝑅2 from the regression of Eq. (1) in the past J months. The SENTIMENT is the weighted residual of Michigan Consumer Sentiment Index, which is calculated by using Antoniou et al. (2012)’s procedure. Our full sample period is evenly divided into high-, mid- and low-sentiment period by SENTIMENT. For each SYNCH level, we report the average monthly returns of the PRET portfolios and the momentum portfolio, an overlapping strategy that buys (sells) the highest (lowest) PRET portfolio and holds for K-month after skipping the most recent month. High–Low is a portfolio that buys (sells) the high (low) SYNCH momentum portfolio. Both the unadjusted returns, Buy-Sell, and the Fama–French three-factor adjusted returns, FF3, are presented. All t-statistics are Newey–West adjusted with K lags.

Sell 1 2 3 4 5 6 7 8 9 Buy 10 Buy-Sell t-Stat. FF3 t-Stat. Sequential sorts: 𝑃𝑃𝑅𝑅𝑃𝑃𝑃𝑃 × 𝑆𝑆𝑆𝑆𝑆𝑆𝑈𝑈𝐻𝐻

Panel A. High SENTIMENT; J=11, K=12 High SYNCH 0.2786 0.7040 0.9490 0.9838 0.9227 0.9879 1.0320 1.0066 1.0839 1.0227 0.7441 2.49 1.1243 3.94

4 0.2834 0.5337 0.7589 0.9119 1.0143 0.9758 1.0498 1.0328 1.1184 1.0326 0.7492 2.38 1.1719 4.38 3 0.2819 0.6034 0.7928 0.9328 0.8829 0.9802 0.9894 1.0488 0.9823 0.9574 0.6755 2.72 0.9030 4.10 2 0.5423 0.6880 0.8342 1.0027 0.9435 1.0403 1.0827 1.1382 1.1186 0.8949 0.3526 1.38 0.6083 2.83


Panel B. Mid SENTIMENT; J=11, K=12 High SYNCH 0.4820 0.9136 1.0177 1.0338 1.1187 1.1344 1.0462 1.0250 1.1157 1.2330 0.7510 2.20 1.4112 4.75

4 0.6140 1.0628 1.0655 1.1112 1.2053 1.1341 1.1407 1.1860 1.2051 1.2391 0.6251 1.98 1.2213 4.26 3 0.8850 1.0542 1.0989 1.1781 1.0948 1.1740 1.1936 1.2770 1.2515 1.1125 0.2275 0.76 0.6824 2.58 2 0.8532 1.0941 1.0769 1.1554 1.2527 1.1726 1.2196 1.2625 1.2214 1.1408 0.2877 0.95 0.7277 2.96


Panel C. Low SENTIMENT; J=11, K=12 High SYNCH 0.8694 1.0221 1.0292 1.0311 1.0189 1.0652 1.0417 1.0867 1.1067 1.1772 0.3079 0.75 1.0999 3.34

4 0.9010 1.2883 1.3186 1.1785 1.1645 1.1548 1.1929 1.2379 1.2440 1.1829 0.2819 0.70 1.0260 2.95 3 1.2592 1.4668 1.3728 1.2487 1.2822 1.2910 1.2754 1.2753 1.3284 1.2114 -0.0478 -0.12 0.6181 1.79 2 1.4566 1.4784 1.4023 1.5276 1.4541 1.4682 1.4399 1.3159 1.4236 1.3263 -0.1303 -0.32 0.5339 1.66


59

TABLE 11 Regression of Momentum profits on Market returns and Investor Sentiment This table reports regression of average monthly SYNCH momentum returns (%) on sentiment, past market returns and the three Fama–French factors for each SYNCH momentum portfolio. The dependent variable, MOMRET, is the average monthly returns for each SYNCH momentum portfolio in month t. At each t, all the stocks are sequentially sorted into 10 × 5 equal-weighted portfolios by PRET, and SYNCH. The PRET is the lagged 11-month cumulative returns. The SYNCH is the 𝑅𝑅2 from regression of Eq (1) in the past 11 months. For each SYNCH level, we create momentum portfolio that buys (sells) the highest (lowest) PRET portfolio and holds for 12 months after skipping the most recent month. The SENTIMENT is the weighted residual of Michigan Consumer Sentiment Index at the end formation date, which is calculated by using Antoniou et al. (2012)’s procedure. The MarketState is the 12-month cumulative returns of CRSP value-weighted index at the end of formation date. Other control variables are the three Fama–French factors, which are MKTRF (market excess returns), SMB and HML. t-statistics are shown in parentheses and Newey–West adjusted with K lags. ***, **, and * indicate that the coefficients are significantly different from zero at the 1%, 5%, and 10% level.

High SYNCH 4 3 2 Low SYNCH High–Low Intercept 1.1049*** 0.9596*** 0.6180** 0.4987* 0.3324 0.7725*** (3.89) (3.45) (2.11) (1.84) (1.08) (3.49) SENTIMENT -0.0024 0.0101 0.0012 0.0011 0.0147 -0.0171 (-0.12) (0.61) (0.07) (0.07) (0.88) (-1.27) 𝑀𝑀𝑎𝑎𝑟𝑟𝑘𝑘𝑛𝑛𝑡𝑡𝑆𝑆𝑡𝑡𝑎𝑎𝑡𝑡𝑛𝑛 0.0793** 0.0751** 0.0985** 0.1027*** 0.0842* -0.0049 (2.33) (2.58) (2.57) (2.61) (1.94) (-0.34) 𝑀𝑀𝑎𝑎𝑟𝑟𝑘𝑘𝑛𝑛𝑡𝑡𝑆𝑆𝑡𝑡𝑎𝑎𝑡𝑡𝑛𝑛2 -0.0023** -0.0021*** -0.0027*** -0.0027** -0.0022* -0.0001 (-2.54) (-2.81) (-2.64) (-2.55) (-1.95) (-0.24) MKTRF -0.3288* -0.1493 -0.1861 -0.2223 -0.2989* -0.0299 (-1.71) (-0.95) (-1.08) (-1.39) (-1.73) (-0.29) SMB -0.1596 -0.1114 -0.0740 -0.1943 -0.0689 -0.0908 (-0.84) (-0.71) (-0.45) (-1.07) (-0.40) (-0.62) HML -0.4077** -0.5020*** -0.4851*** -0.4739*** -0.3076* -0.1001 (-2.03) (-2.97) (-2.85) (-2.65) (-1.71) (-0.80) Adj. 𝑅𝑅2 0.2806 0.3096 0.3497 0.3966 0.2902 0.0013

60

TABLE 12 PEAD for Winner and Loser Stocks This table reports the PEAD, which is measured by average cumulative abnormal returns (CAR), for winner and loser stocks. Specifically, at each t, all the stocks are sequentially sorted into 10 × 5 equal-weighted portfolios by PRET and SYNCH. The PRET is the lagged 11-month cumulative stock returns. The SYNCH is the 𝑅𝑅2 from regression of Eq (1). We identify the stocks in top (bottom) PRET portfolio as winners (losers) and independently sort them into terciles by SUE and identify the top (bottom) SUE tercile as the high (low) SUE. The CAR reported is estimated by Fama–French three-factor model. We report the CARs during “impact” period (-1 to 1 days) and “adjustment” period (2 to 60 days). The sample period is from Jan. 1973 to Dec 2018. The whole sample period is evenly classified into high-, mid- and low-sentiment periods by SENTIMENT. Panel A reports the PEAD of loser stocks and winner stocks. Panels B and C display the PEAD across different sentiment periods for loser stocks with Low SUE and winner stocks with high SUE, respectively. Panel A: PEAD (CAR) for loser stocks and winner stocks

SYNCH Loser stocks with Low SUE

SYNCH Winner stocks with high SUE

(-1, 1) t-Stat. (2, 60) t-Stat. (-1, 1) t-Stat. (2, 60) t-Stat. High -0.5585 -2.01 10.7027 9.95 High 0.2523 1.16 -10.958 -12.43

4 -0.8387 -3.02 11.9191 11.08 4 0.8839 4.08 -12.575 -14.26 3 -0.7483 -2.70 13.3465 12.41 3 1.2318 5.68 -13.285 -15.07 2 -1.2079 -4.35 12.3963 11.53 2 0.6887 3.18 -15.735 -17.85

Low -1.5775 -5.69 13.7734 12.81 Low 0.8941 4.12 -18.411 -20.89 High–Low 1.0191 3.67 -3.0707 -2.85 High–Low -0.6418 -2.96 7.4536 8.46

Panel B: PEAD (CAR) for loser stocks with Low SUE across different sentiment states

SYNCH High SENTIMENT Mid SENTIMENT Low SENTIMENT

(-1, 1) t-Stat. (2, 60) t-Stat. (-1, 1) t-Stat. (2, 60) t-Stat. (-1, 1) t-Stat. (2, 60) t-Stat. High -0.4880 -1.00 10.0929 5.48 -0.0089 -0.01 12.0192 5.92 -0.7533 -1.43 8.9679 4.90

4 -0.9478 -1.95 10.8083 5.87 -0.7699 -1.24 13.4646 6.64 -0.4316 -0.82 11.0905 6.06 3 -0.7461 -1.54 13.3399 7.24 -0.0732 -0.12 12.1714 6.00 -1.0824 -2.05 11.7365 6.42 2 -1.6284 -3.35 12.7671 6.93 -1.8840 -3.03 14.2200 7.01 -0.5729 -1.09 9.5754 5.24

Low -2.3233 -4.78 14.0656 7.64 -0.9541 -1.53 17.4428 8.60 -1.1684 -2.21 11.0566 6.05 High–Low 1.8353 3.78 -3.9728 -2.16 0.9452 1.52 -5.4236 -2.67 0.4151 0.79 -2.0887 -1.14

Panel C: PEAD (CAR) for winner stocks with high SUE across different sentiment states

SYNCH High SENTIMENT Mid SENTIMENT Low SENTIMENT

(-1, 1) t-Stat. (2, 60) t-Stat. (-1, 1) t-Stat. (2, 60) t-Stat. (-1, 1) t-Stat. (2, 60) t-Stat. High 0.4078 1.06 -11.310 -8.10 0.1155 0.29 -11.569 -8.34 -0.0456 -0.08 -10.139 -5.25

4 0.9799 2.55 -12.125 -8.68 0.6893 1.75 -12.971 -9.35 1.2148 2.14 -11.430 -5.92 3 1.8543 4.83 -14.121 -10.11 0.9571 2.43 -12.767 -9.20 1.5775 2.78 -13.486 -6.99 2 0.5907 1.54 -16.887 -12.09 1.0331 2.62 -14.779 -10.65 1.0372 1.83 -13.545 -7.02

Low 0.6170 1.61 -18.320 -13.12 0.6373 1.62 -18.726 -13.50 0.9390 1.65 -18.536 -9.60 High–Low -0.2093 -0.54 7.0109 5.02 -0.5218 -1.32 7.1578 5.16 -0.9846 -1.73 8.3975 4.35

61

TABLE 13 Short interest for Momentum Portfolios This table reports the short interest for loser and winner stocks, which are identified by their PRET, the lagged 11-month cumulative stock returns. Specifically, at each t, all the stocks are sequentially sorted into 10 × 5 equal-weighted portfolios by PRET and SYNCH. The SYNCH is the 𝑅𝑅2 from regression of Eq (1). We identify the stocks top (bottom) PRET portfolio as winners (losers). The short interest is calculated by using shares held short scaled by total outstanding shares. The sample period is from Jan. 1973 to Dec. 2018. Our whole sample period is evenly classified into high-, mid- and low-sentiment periods by SENTIMENT, the weighted residual of Michigan Consumer Sentiment Index calculated by using Antoniou et al. (2012)’s procedure. [-11,0] and [0,11] indicate the formation period and the holding period, respectively. Panel A reports the average monthly short interests (%) for loser- and winner-portfolios. Panel B reports the average changes in short interests in the whole sample period and the sample periods with different sentiment state. t-statistics are reported in parentheses.

Panel A: Short interest for Loser and Winner portfolios

SYNCH -11 -9 -7 -5 -3 -1 1 3 5 7 9 11

High

Losers 4.2931 4.2925 4.4024 4.6331 4.8752 5.0837 5.2902 5.4628 5.4829 5.4703 5.3763 5.4005 [t-stat.] (38.07) (36.50) (35.99) (35.31) (34.55) (33.59) (33.50) (34.14) (34.41) (33.43) (33.09) (33.25) winners 6.8850 7.0055 6.8024 6.7093 6.6974 6.4900 6.3581 6.1571 6.0710 6.0351 6.0108 5.9881 [t-stat.] (34.61) (26.73) (37.30) (37.92) (35.22) (36.97) (36.15) (34.15) (33.01) (31.40) (31.47) (31.31)

Low

Losers 2.1591 2.1586 2.2493 2.2310 2.2502 2.2631 2.2341 2.1708 2.0679 2.0143 1.9508 1.8666 [t-stat.] (23.80) (28.04) (28.02) (29.87) (29.63) (27.29) (28.42) (26.68) (26.46) (26.66) (26.21) (25.91) winners 2.2304 2.2663 2.2215 2.1541 2.1627 2.2542 2.3071 2.3204 2.3600 2.2824 2.2883 2.3387 [t-stat.] (8.15) (9.34) (11.46) (16.10) (18.75) (18.87) (21.79) (23.23) (23.82) (32.39) (33.55) (34.12)

Panel B: Change in short interest during formation [-11,0] period and holding [0,11] period

SYNCH Full sample High SENTIMENT Mid SENTIMENT Low SENTIMENT [-11,0] [0,11] [-11,0] [0,11] [-11,0] [0,11] [-11,0] [0,11]

High

Losers 0.8437 0.2617 0.5168 0.4669 1.5346 0.0697 0.4727 0.2482 [t-stat.] (7.58) (2.86) (3.30) (3.34) (6.41) (0.36) (2.88) (1.82) winners -0.5447 -0.3765 -0.0351 -0.8412 -0.9229 -0.0547 -0.6505 -0.2484 [t-stat.] (-3.05) (-2.46) (-0.16) (-2.87) (-2.40) (-0.17) (-2.15) (-1.46)

Low

Losers 0.0891 -0.3279 0.4146 -0.4804 0.0269 -0.3201 -0.1768 -0.1921 [t-stat.] (1.45) (-5.46) (5.58) (-6.60) (0.18) (-2.52) (-2.38) (-1.84) winners 0.1387 0.0855 0.4829 0.2850 0.4376 -0.2780 -0.4703 0.2384 [t-stat.] (0.71) (0.76) (4.70) (2.53) (1.31) (-0.96) (-1.02) (1.80)

62

TABLE 14 Momentum Profit Conditional on stock price informativeness measures This table reports the correlation coefficients and principal component analysis results of stock price informativeness measures as well as the High–Low characteristic momentum performances based on corresponding stock price informativeness measure. The sample includes the NYSE/AMEX stocks for the period Mar. 1964–Dec. 2018. Panel A presents the correlation coefficients between price informativeness measures, which includes SYNCH, 𝑅𝑅2 estimated by Eq. (1), Bid_Ask_Spread, stock’s bid ask spread estimated by using Corwin and Schultz (2012)’s approach, and TURN, stock turnover during formation period. The First_factor, Second_factor, and Third_factor are first-, second- and third-principle component factors extracted from principle component analysis based on SYNCH, Bid_Ask_Spread, and TURN. The PRET and |𝑃𝑃𝑅𝑅𝑃𝑃𝑃𝑃| are the lagged 11-month cumulative returns and its absolute value. Panel B shows the eigenvalues and eigenvector from principal component analysis. Panel C presents average monthly returns (%) of the High–Low characteristic momentum returns based on corresponding Informativeness measure. High–Low is a portfolio that buys (sells) momentum portfolio with the high (low) Informativeness measure. High-Low, FF3, and FF5 are the monthly return, the Fama-French three-factor adjusted returns, and the Fama-French five-factor adjusted returns of High–Low portfolio. All t-statistics are Newey–West adjusted with K lags. ***, **, and * indicate that the coefficients are significantly different from zero at the 1%, 5%, and 10% level. Panel A. Correlation coefficients between the stock price informativeness measures

SYNCH Bid_Ask_Spread TURN First_factor PRET |𝑷𝑷𝑹𝑹𝑷𝑷𝑷𝑷| SYNCH -0.1455*** 0.2590*** 0.8178*** -0.0379*** -0.0933***

Bid-Ask Spread 0.1181*** -0.1117*** -0.0021* 0.1735*** TURN 0.7613*** 0.0355*** 0.1221***

Panel B. Principal component analysis Eigenvalues Eigenvectors Eigenvalue Proportion SYNCH Bid_Ask_Spread TURN

First_factor 1.2609 0.4203 0.7284 -0.0995 0.6779 Second_factor 1.0957 0.3652 -0.2532 0.8803 0.4638 Third_factor 0.6434 0.2145 0.6367 0.4638 -0.6160

Panel C. Momentum portfolio conditional on corresponding stock price informativeness measure Informativeness measure High–Low t-Stat. FF3 t-Stat. FF5 t-Stat.

SYNCH 0.5966 3.31 0.8160 4.22 0.7301 3.58 Bid_Ask_Spread -0.6331 -.3.39 -0.6468 -3.55 -0.6855 -3.50

TURN 0.3122 1.43 0.4958 2.22 0.6331 2.80 First_factor 0.7076 3.35 0.9373 4.20 0.9863 4.21

63

Table 15 Momentum profit and the Adoption of XBRL This table reports the analysis of the adoption of XBRL. The dependent variable, MOMRET, is the average monthly returns for momentum portfolio during the holding period. At each t, all the stocks are sequentially sorted into 10 × 5 equal-weighted portfolios by PRET, and SYNCH. The PRET is the lagged 11-month cumulative returns. The SYNCH is the 𝑅𝑅2 from regression of Eq (1). For each SYNCH level, we create momentum portfolio that buys (sells) the highest (lowest) PRET portfolio and holds for 12 months after skipping the most recent month. SYNCH_Rank equals, respectively, 1, 2, 3, 4 and 5 from low SYNCH level to high SYNCH level. XBRL_Period equals one if the formation date is after Apr. 2005; zero otherwise. The SENTIMENT is the time-weighted residuals of Michigan Consumer Sentiment Index, which is calculated by using Antoniou et al. (2012)’s procedure. 𝑀𝑀𝑎𝑎𝑟𝑟𝑘𝑘𝑛𝑛𝑡𝑡𝑆𝑆𝑡𝑡𝑎𝑎𝑡𝑡𝑛𝑛 and 𝑀𝑀𝑎𝑎𝑟𝑟𝑘𝑘𝑛𝑛𝑡𝑡𝑆𝑆𝑡𝑡𝑎𝑎𝑡𝑡𝑛𝑛2, respectively, are the 12-month cumulative returns of CRSP value-weighted index prior formation date t and its squared term. Other control variables are the three Fama–French factors, which are MKTRF (market excess returns), SMB and HML. t-statistics are reported in parentheses and Newey–West adjusted with K lags. ***, **, and * indicate that the coefficients are significantly different from zero at the 1%, 5%, and 10% level.

Before 2005/04 Pre-XBRL Period

2005/04-2009/06 Voluntary Period

After 2009/06 Mandatory Period Full Period

Intercept 0.7035*** 2.98 -1.8370** -2.05 -0.7243 -1.49 0.7048** 2.20 SYNCH_Rank 0.1545** 2.04 0.4919* 1.72 0.3558** 2.07 0.2018** 2.17 𝑋𝑋𝐵𝐵𝑅𝑅𝐿𝐿_𝑃𝑃𝑛𝑛𝑟𝑟𝑟𝑟𝑝𝑝𝑟𝑟 -1.2002*** -5.18 𝑀𝑀𝑀𝑀𝑃𝑃𝑅𝑅𝐹𝐹𝑋𝑋 0.0021 0.34 0.0023 0.07 -0.0395*** -2.97 0.0001 0.01 𝑆𝑆𝑀𝑀𝐵𝐵𝑋𝑋 0.0013 0.19 -0.0213 -0.35 -0.0003 -0.01 -0.0014 -0.18 𝐻𝐻𝑀𝑀𝐿𝐿𝑋𝑋 -0.0022 -0.82 0.0109 0.24 0.0335 1.01 -0.0023 -0.57

𝑆𝑆𝑃𝑃𝑆𝑆𝑃𝑃𝐼𝐼𝑀𝑀𝑃𝑃𝑆𝑆𝑃𝑃𝑋𝑋 -0.0017 -0.31 0.0191 0.70 -0.0087 -0.97 -0.0022 -0.41 𝑀𝑀𝑎𝑎𝑟𝑟𝑘𝑘𝑛𝑛𝑡𝑡𝑆𝑆𝑡𝑡𝑎𝑎𝑡𝑡𝑛𝑛𝑋𝑋 0.0023 0.49 -0.0171 -1.10 0.0152* 1.84 -0.0036 -0.38 𝑀𝑀𝑎𝑎𝑟𝑟𝑘𝑘𝑛𝑛𝑡𝑡𝑆𝑆𝑡𝑡𝑎𝑎𝑡𝑡𝑛𝑛2𝑋𝑋 -0.0001 -0.80 0.0001 0.07 -0.0004** -2.39 0.0000 0.17

MKTRF -0.0242 -1.44 -0.2143** -2.27 0.1240*** 2.92 -0.0460 -1.47 SMB -0.0506** -2.28 0.0363 0.22 -0.1346 -1.27 -0.0312 -1.23 HML -0.0408*** -4.43 0.0080 0.06 -0.2545*** -2.90 -0.0573*** -4.18

SENTIMENT 0.0096 0.61 0.0872 1.11 -0.0008 -0.03 0.0071 0.43 𝑀𝑀𝑎𝑎𝑟𝑟𝑘𝑘𝑛𝑛𝑡𝑡𝑆𝑆𝑡𝑡𝑎𝑎𝑡𝑡𝑛𝑛 0.0222* 1.69 0.1644*** 3.48 -0.0275 -1.02 0.0922*** 2.70 𝑀𝑀𝑎𝑎𝑟𝑟𝑘𝑘𝑛𝑛𝑡𝑡𝑆𝑆𝑡𝑡𝑎𝑎𝑡𝑡𝑛𝑛2 -0.0008*** -2.72 -0.0027 -1.23 0.0009* 1.76 -0.0025*** -2.62

𝑅𝑅2 0.1865 0.8754 0.2084 0.3897

64

Table 16 Fama-MacBeth regressions-Excess SYNCH This table reports Fama–MacBeth regressions of FRET on the EX_SYNCH during Mar. 1964–Dec. 2018. The dependent variable is FRET, which is the cumulative returns of individual stock during the holding period. The PRET is the lagged 11-month cumulative returns. The EX_SYNCH is the residuals of cross-sectional regression of LnSYNCH on firm’s size, book to market ratio, Return on assets (ROA), standard deviation of ROA, financial leverage, 𝛽𝛽𝑚𝑚,𝑖𝑖, and 𝛽𝛽𝑖𝑖𝑖𝑖𝑖𝑖,𝑖𝑖. 𝛽𝛽𝑚𝑚,𝑖𝑖 and 𝛽𝛽𝑖𝑖𝑖𝑖𝑖𝑖,𝑖𝑖 are estimated by Eq. (1). VOL is the idiosyncratic risk estimated by using FF3 model. Other control variables are ID (Information Discreteness), RC (Return Consistency), SIZE (the log of market capitalization), BM (Book to market ratio), IVOL (idiosyncratic risk), IILLIQ (Illiquidity factor), AGE (the log of the listed months), TURN (stock turnover), and interaction terms with PRET (e.g., EX_SYNCHX, IDX, RCX etc.). t-statistics are shown in parentheses and Newey–West adjusted with K lags. ***, **, and * indicate that the coefficients are significantly different from zero at the 1%, 5%, and 10% level. Panel A: Basic specifications

NYSE/AMEX NYSE/AMEX/NASDQ Model 1 Model 2 Model 3 Model 4

Intercept 0.1270*** 0.1379*** 0.1303*** 0.1359*** (6.01) (3.87) (6.07) (3.85) PRET 0.0313* 0.0255 0.0273* 0.0213* (1.79) (1.60) (1.89) (1.67) EX_SYNCHX 0.0214*** 0.0233*** 0.0113*** 0.0135*** (3.98) (5.13) (2.71) (4.18) EX_SYNCH 0.0103*** 0.0098*** 0.0079*** 0.0077*** (4.93) (4.74) (4.56) (4.44) 𝜷𝜷𝒎𝒎 0.0002 -0.0026

(0.03) (-0.35)

𝜷𝜷𝒊𝒊𝒊𝒊𝒊𝒊 -0.0040 -0.0076 (-0.49) (-0.91) SIZE -0.0055 -0.0046 (-1.21) (-1.02) BM 0.0153*** 0.0186*** (3.80) (4.08) Adj. 𝑹𝑹𝟐𝟐 0.0163 0.0523 0.0119 0.0461 Pane B: All interactions PRET EX_SYNCHX IDX RCX SIZEX BMX Model 5 0.1574*** 0.0163*** -0.3372*** 0.0072 -0.0053 -0.0167* (NYSE/AMEX) (5.29) (3.20) (-4.27) (1.07) (-1.22) (-1.85) Model 6 0.1110*** 0.0097*** -0.4256*** 0.0080 -0.0013 -0.0141* (NYSE/AMEX/NASDQ) (4.98) (2.68) (-5.92) (1.34) (-0.35) (-1.66) AGEX ILLIQX IVOLX TURNX ID RC Model 5 (continued) -0.0260*** -0.0001 -1.4333** -0.0099 0.1078*** -0.0032 (-5.09) (-0.05) (-2.32) (-1.03) (4.63) (-1.44) Model 6 (continued) -0.0238*** 0.0006 -1.1133* -0.0106 0.1225*** -0.0025 (-5.39) (0.55) (-1.90) (-1.28) (5.88) (-1.44) ILLIQ IVOL TURN AGE EX_SYNCH 𝜷𝜷𝒎𝒎 Model 5 (continued) 0.0038*** -1.2126* -0.0254*** 0.0029 0.0052** 0.0127** (3.65) (-1.85) (-3.99) (1.13) (2.27) (2.45) Model 6 (continued) 0.0015** -0.9272 -0.0193*** 0.0072** 0.0038* 0.0102** (2.07) (-1.52) (-3.37) (2.54) (1.87) (2.17) 𝜷𝜷𝒊𝒊𝒊𝒊𝒊𝒊 SIZE BM Intercept Adj. 𝑹𝑹𝟐𝟐 Model 5 (continued) 0.0132** -0.0121*** 0.0084** 0.2021*** 0.0828 (2.27) (-3.72) (2.03) (6.25) Model 6 (continued) 0.0099** -0.0121*** 0.0129*** 0.1863*** 0.0727 (2.11) (-3.83) (2.87) (6.10)

65

Appendix

Table 1A: Market Timing Regression Results This table reports monthly time-series regression results based on the Daniel and Moskowitz (2016) approach.

𝑃𝑃𝑀𝑀𝑅𝑅𝑃𝑃𝑅𝑅𝑃𝑃𝑃𝑃𝑡𝑡 = 𝛼𝛼0 + 𝛼𝛼𝐵𝐵𝐼𝐼𝐵𝐵,𝑡𝑡−1 + [𝛽𝛽0 + 𝐼𝐼𝐵𝐵,𝑡𝑡−1(𝛽𝛽𝐵𝐵 + 𝐼𝐼𝑈𝑈,𝑡𝑡𝛽𝛽𝐵𝐵,𝑈𝑈)]𝑀𝑀𝑀𝑀𝑃𝑃𝑅𝑅𝐹𝐹𝑡𝑡 + 𝜀𝜀𝑡𝑡 In all regressions, the dependent variable is the return on the corresponding SYNCH momentum portfolio. At each t, all the stocks are sorted into deciles by their PRET, the past J-month cumulative returns, and then into quintiles by their SYNCH, 𝑅𝑅2 from the regression of Eq. (1) in the past J months. For each SYNCH level, we calculate the returns of the momentum portfolio, an overlapping strategy that buys (sells) the highest (lowest) PRET portfolio and holds for 12 months after skipping the most recent month. The independent variables are a constant, an indicator for bear markets, which equals one if the cumulative past two-year return on the market is negative, the excess market return, and a contemporaneous upmarket indicator, which equals one if excess market return is greater than zero. The coefficients ×100 (i.e., are in percent per month). ***, **, and * indicate that the coefficients are significantly different from zero at the 1%, 5%, and 10% level.

SYNCH-MOM MOM (D&M like) Coef. High 4 3 2 low H-L

𝛼𝛼0� 1.0314*** 0.9603*** 0.6794*** 0.6446*** 0.3261** 0.7053*** 0.7335***

(3.94) (4.59) (3.98) (4.34) (2.31) (3.01) (4.47) 𝛼𝛼𝐵𝐵� 0.1694 -0.4345 -0.4663 -0.7467 0.3375 -0.1682 -0.2258

(0.18) (-0.50) (-0.53) (-0.93) (0.42) (-0.20) (-0.29) 𝛽𝛽0� 0.0575 0.0721 0.0967 0.0884 0.0779 -0.0204 0.0794

(0.58) (0.82) (1.33) (1.22) (1.19) (-0.28) (1.06) 𝛽𝛽𝐵𝐵� -0.3288* -0.3831** -0.3826** -0.4137*** -0.1458 -0.1830 -0.3323**

(-1.69) (-2.18) (-2.13) (-2.91) (-0.94) (-1.03) (-2.17) 𝛽𝛽𝐵𝐵,𝑈𝑈� -0.4747 -0.2191 -0.2479 -0.2068 -0.4443 -0.0304 -0.3180

(-1.20) (-0.65) (-0.66) (-0.54) (-1.32) (-0.13) (-0.90) Adj. 𝑹𝑹𝟐𝟐 0.0498 0.0450 0.0602 0.0685 0.0359 0.0058 0.0636

66

TABLE 2A SYNCH-Momentum with NYSE/AMEX stocks (10 × 5 portfolios) This table reports the Fama-French three-factor adjusted returns of Winner-, Loser-, and MOM-portfolios conditional on SYNCH with different J and K settings. At each t, all the stocks are sorted into deciles by their PRET, the past J-month cumulative returns, and into quintiles by their SYNCH, 𝑅𝑅2 estimated by Eq. (1), according to the corresponding soring order. The sample includes the NYSE/AMEX stocks for the period Mar. 1964–Dec. 2018. The stocks with price lower than $1 at the end of formation period are excluded. Winner and Loser are the equal weighted portfolios for stocks in top- and bottom-PRET deciles, respectively. MOM is the momentum portfolio that buys (sells) the Winner (Loser) portfolio. High–Low is a portfolio that buys (sells) the high (low) SYNCH portfolio within each group. All the portfolios are constructed by using overlapping strategy and held for K months after skipping the most recent month. t-statistics are shown in parentheses and Newey–West adjusted with K lags.

Sorting Order PRET × SYNCH Independent Sorting SYNCH × PRET

J K SYNCH Winner Loser MOM Winner Loser MOM Winner Loser MOM

11 1 High 0.4594 -1.3567 1.8160 0.4747 -1.3477 1.8224 0.5300 -0.8959 1.4260

(2.83) (-5.67) (5.63) (2.81) (-4.64) (4.90) (3.45) (-3.73) (4.48)

Low 0.4926 -1.0425 1.5350 0.4667 -1.1608 1.6275 0.3450 -1.2950 1.6400

(3.33) (-4.96) (6.05) (3.38) (-6.10) (6.95) (2.28) (-5.80) (6.10)

High-low -0.0332 -0.3142 0.2810 0.0080 -0.1869 0.1949 0.1851 0.3991 -0.2140

(-0.19) (-1.19) (0.90) (0.05) (-0.64) (0.57) (1.07) (1.43) (-0.66)

11 3 High 0.3806 -1.3245 1.7051 0.4156 -1.2980 1.7135 0.4434 -0.9102 1.3536

(2.52) (-5.94) (5.68) (2.65) (-4.91) (4.98) (3.01) (-4.02) (4.50)

Low 0.3985 -0.9517 1.3501 0.3701 -0.9950 1.3651 0.2636 -1.1448 1.4084

(3.09) (-4.77) (5.93) (2.99) (-5.35) (6.21) (1.94) (-5.57) (5.69)

High-low -0.0178 -0.3728 0.3550 0.0455 -0.3029 0.3484 0.1798 0.2346 -0.0548

(-0.12) (-1.52) (1.26) (0.31) (-1.13) (1.12) (1.25) (0.91) (-0.18)

11 6 High 0.2781 -1.2454 1.5235 0.3129 -1.2733 1.5862 0.3390 -0.8927 1.2317

(1.96) (-6.13) (5.61) (2.07) (-5.24) (5.07) (2.42) (-4.37) (4.52)

Low 0.3048 -0.6976 1.0024 0.2895 -0.7633 1.0528 0.2068 -0.9150 1.1218

(2.63) (-3.52) (4.49) (2.62) (-4.05) (4.93) (1.73) (-4.29) (4.69)

High-low -0.0267 -0.5478 0.5211 0.0235 -0.5100 0.5334 0.1322 0.0223 0.1099

(-0.19) (-2.58) (2.11) (0.16) (-2.09) (1.90) (0.98) (0.09) (0.40)

11 9 High 0.2231 -1.1768 1.3999 0.2718 -1.2688 1.5406 0.2695 -0.8578 1.1272

(1.74) (-6.09) (5.69) (2.02) (-5.52) (5.48) (2.14) (-4.71) (4.77)

Low 0.1511 -0.4899 0.6410 0.1634 -0.5586 0.7219 0.1021 -0.6842 0.7864

(1.36) (-2.61) (3.11) (1.55) (-3.05) (3.60) (0.92) (-3.40) (3.62)

High-low 0.0720 -0.6869 0.7589 0.1084 -0.7102 0.8186 0.1673 -0.1736 0.3409

(0.54) (-3.44) (3.47) (0.79) (-3.03) (3.26) (1.35) (-0.78) (1.44)

11 12 High 0.1273 -1.0795 1.2068 0.1727 -1.1177 1.2904 0.1842 -0.7873 0.9715

(1.05) (-6.03) (5.52) (1.33) (-5.37) (5.08) (1.54) (-4.69) (4.62)

Low 0.0022 -0.3886 0.3908 0.0220 -0.4408 0.4628 -0.0502 -0.5305 0.4803

(0.02) (-2.28) (2.09) (0.22) (-2.62) (2.53) (-0.47) (-2.87) (2.39)

High-low 0.1251 -0.6909 0.8160 0.1507 -0.6769 0.8276 0.2344 -0.2569 0.4913

(1.00) (-3.81) (4.22) (1.17) (-3.17) (3.66) (1.96) (-1.24) (2.27)

67

TABLE 3A SYNCH-Momentum Profit with NYSE/AMEX/NASDAQ stocks (5 × 5 portfolios) This table reports the Fama-French three-factor adjusted returns of Winner-, Loser-, and MOM-portfolios conditional on SYNCH with different J and K settings. At each t, all the stocks are sorted into quintiles by their PRET, the past J-month cumulative returns, and into quintiles by their SYNCH, 𝑅𝑅2 estimated by Eq. (1), according to the corresponding soring order. The sample includes NYSE/AMEX/NASDAQ stocks for the period Mar. 1964–Dec. 2018. The stocks with price lower than $1 at the end of formation period are excluded. Winner and Loser are the equal weighted portfolios for stocks in top- and bottom-PRET deciles, respectively. MOM is the momentum portfolio that buys (sells) the Winner (Loser) portfolio. High–Low is a portfolio that buys (sells) the high (low) SYNCH portfolio within each group. All the portfolios are constructed by using overlapping strategy and held for K months after skipping the most recent month. t-statistics are shown in parentheses and Newey–West adjusted with K lags.

Sorting Order PRET × SYNCH Independent Sorting SYNCH × PRET

J K SYNCH Winner Loser MOM Winner Loser MOM Winner Loser MOM

11 1 High 0.4304 -1.0166 1.4470 0.4352 -1.0075 1.4427 0.4805 -0.7794 1.2599

(4.16) (-5.41) (5.79) (4.14) (-4.86) (5.38) (4.60) (-4.03) (4.89)

Low 0.5739 -0.6813 1.2551 0.5664 -0.6741 1.2405 0.5142 -0.7478 1.2620

(4.89) (-3.94) (6.87) (4.88) (-3.98) (6.87) (4.41) (-4.28) (6.85)

High-low -0.1435 -0.3354 0.1919 -0.1312 -0.3334 0.2022 -0.0337 -0.0316 -0.0021

(-1.08) (-1.70) (0.98) (-0.98) (-1.53) (0.94) (-0.25) (-0.14) (-0.01)

11 3 High 0.3229 -0.9804 1.3033 0.3228 -0.9881 1.3109 0.3416 -0.7468 1.0884

(3.28) (-5.90) (5.85) (3.22) (-5.35) (5.50) (3.39) (-4.41) (4.75)

Low 0.4840 -0.5388 1.0228 0.4756 -0.5242 0.9998 0.4312 -0.6183 1.0495

(4.29) (-3.34) (6.39) (4.29) (-3.28) (6.34) (3.97) (-3.73) (6.51)

High-low -0.1611 -0.4416 0.2805 -0.1528 -0.4639 0.3111 -0.0897 -0.1286 0.0389

(-1.28) (-2.32) (1.54) (-1.20) (-2.19) (1.56) (-0.72) (-0.60) (0.19)

11 6 High 0.2519 -0.8992 1.1511 0.2512 -0.9157 1.1668 0.2659 -0.7098 0.9757

(2.59) (-5.86) (5.44) (2.53) (-5.45) (5.21) (2.70) (-4.73) (4.65)

Low 0.3520 -0.3282 0.6802 0.3480 -0.3323 0.6803 0.3323 -0.4055 0.7377

(3.34) (-2.05) (4.48) (3.32) (-2.10) (4.56) (3.24) (-2.45) (4.84)

High-low -0.1001 -0.5710 0.4709 -0.0968 -0.5834 0.4865 -0.0663 -0.3043 0.2380

(-0.84) (-3.34) (2.91) (-0.80) (-3.09) (2.74) (-0.56) (-1.55) (1.31)

11 9 High 0.1915 -0.8363 1.0278 0.1947 -0.8589 1.0537 0.1961 -0.6569 0.8530

(2.17) (-6.01) (5.47) (2.18) (-5.64) (5.36) (2.20) (-5.00) (4.68)

Low 0.2539 -0.1752 0.4292 0.2577 -0.1964 0.4541 0.2470 -0.2534 0.5004

(2.45) (-1.11) (2.88) (2.51) (-1.27) (3.13) (2.49) (-1.56) (3.37)

High-low -0.0624 -0.6610 0.5986 -0.0629 -0.6625 0.5996 -0.0509 -0.4035 0.3526

(-0.53) (-4.18) (4.36) (-0.54) (-3.81) (4.02) (-0.45) (-2.26) (2.36)

11 12 High 0.1146 -0.7328 0.8474 0.1213 -0.7640 0.8853 0.1218 -0.5665 0.6883

(1.37) (-5.60) (5.10) (1.43) (-5.39) (5.14) (1.47) (-4.65) (4.34)

Low 0.1675 -0.0464 0.2139 0.1733 -0.0682 0.2415 0.1672 -0.1200 0.2872

(1.68) (-0.30) (1.48) (1.76) (-0.44) (1.71) (1.72) (-0.74) (1.97)

High-low -0.0529 -0.6864 0.6335 -0.0520 -0.6958 0.6439 -0.0454 -0.4465 0.4011

(-0.46) (-4.58) (5.44) (-0.45) (-4.20) (5.07) (-0.41) (-2.60) (3.08)

68

TABLE 4A Momentum Profit Conditional on Stock Price Synchronicity This table reports the average monthly returns (%) of SYNCH momentum portfolios involving the NYSE/AMEX stocks for the period Mar. 1964–Dec. 2018. At each t, all the stocks are sorted into deciles by their PRET, the past J-month cumulative returns, and then into quintiles by their SYNCH, 𝑅𝑅2 estimated by Eq. (1) in the past J months. For each SYNCH level, we report the average monthly returns of the PRET portfolios and the momentum portfolio, an overlapping strategy that buys (sells) the highest (lowest) PRET portfolio and holds for K-month after skipping the most recent month. High–Low is a portfolio that buys (sells) the high (low) SYNCH momentum portfolio. Hi. SYNCH and Lo. SYNCH are momentum returns of high-SYNCH and low-SYNCH stocks. High–Low, FF3, and FF5 are the monthly return, the Fama-French three-factor adjusted returns, and the Fama-French five-factor adjusted returns of High–Low portfolio. All t-statistics are Newey–West adjusted with K lags. SYNCH-Momentum based on different settings (J=11, K=12, NYSE/AMEX stocks if not specified)

Hi. SYNCH t-Stat. Lo. SYNCH t-Stat. High–Low t-Stat. FF3 t-Stat. FF5 t-Stat. 5×5 SYNCH-Momentum portfolio with different sorting methods

PRET × SYNCH 0.4686 2.29 0.1707 1.01 0.2979 2.10 0.4500 2.98 0.3640 2.26 Independent sorting 0.4787 2.25 0.1613 0.97 0.3175 2.10 0.4538 2.79 0.3723 2.15

SYNCH × PRET 0.3445 1.86 0.1848 1.00 0.1596 1.08 0.2147 1.35 0.1997 1.19 SYNCH-Momentum portfolio with different settings

Value-weighted 0.3847 1.38 -0.5897 -1.90 0.9744 4.49 1.0731 5.07 1.1831 5.30 With delisted return 0.7997 3.12 0.3670 1.81 0.4327 2.41 0.6446 3.29 0.5676 2.71

J = 9, K=12 0.7377 2.90 0.1706 0.89 0.5671 3.27 0.7739 4.22 0.6499 3.41 J = 6, K=12 0.7247 3.27 0.2910 1.63 0.4337 2.59 0.5867 3.31 0.4690 2.60

NYSE/AMEX/NASDAQ Stocks 0.6535 2.49 -0.0043 -0.02 0.6578 3.84 0.9315 5.91 0.7399 3.29

69

TABLE 5A SYNCH-Momentum Risk-Adjusted Returns based on Behavioral Factor Models This table reports the risk-adjusted returns and factor loadings of SYNCH momentum portfolios based on Stambaugh and Yuan (2017) and Daniel et al. (2020)’s behavioral factor models. At each t, all the NYSE/AMEX stocks are sorted into deciles by their PRET, the past 11-month cumulative returns, and then into quintiles by their SYNCH, 𝑅𝑅2 from the regression of Eq. (1) in the past 11 months. For each SYNCH level, we construct the momentum portfolio by buying (selling) the highest (lowest) PRET portfolio. All the portfolios are constructed by using overlapping strategy and held for 12 months after skipping the most recent month. We present the results for Hi. SYNCH, Lo. SYNCH and High–Low Portfolios. Hi. SYNCH and Lo. SYNCH are high- and low-SYNCH momentum portfolios, respectively. High–Low is a portfolio that buys (sells) the high (low) SYNCH momentum portfolio. Due to the availability of data, the sample periods for Stambaugh and Yuan (2017)’s and Daniel et al. (2020)’s models are Mar.1964–Dec. 2016, and Jan. 1972–Dec. 2018, respectively. All t-statistics are Newey–West adjusted with K lags.

Stambaugh and Yuan (2017) model Daniel, Hirshleifer, and Sun (2020) model Parameter Hi. SYNCH Lo. SYNCH High-Low Parameter Hi. SYNCH Lo. SYNCH High-Low Intercept 0.3392 -0.0503 0.3894 Intercept -0.1372 -0.3799 0.2427

(1.21) (-0.20) (1.95) (-0.42) (-1.54) (1.12) MKTRF 0.0304 0.0590 -0.0287 MKTRF -0.0992 -0.0050 -0.0942

(0.40) (1.00) (-0.50) (-0.86) (-0.08) (-1.07) SMB -0.4256 -0.3574 -0.0682 PEAD 1.2298 0.6253 0.6045

(-3.38) (-2.98) (-0.61) (3.91) (3.27) (2.54) MGMT -0.3015 -0.0556 -0.2459 FIN 0.0855 0.1190 -0.0335

(-1.96) (-0.43) (-1.76) (0.63) (1.63) (-0.26) PERF 1.0727 0.4659 0.6068

(7.77) (6.69) (5.14)

70

TABLE 6A TSMOM Conditional on Stock Price Synchronicity This table reports the risk-adjusted returns of TSMOM conditional on SYNCH. The sample includes the NYSE/AMEX stocks for the period Mar. 1964–Dec. 2018. We follow Moskowitz et al. (2012)’s approach to construct TSMOM portfolio. For Each stock, we buy the stock if its J-month cumulative excess return is positive and short if it is negative, skipping the most recent month. Then, we assign the stocks into quintiles for buying and selling groups, respectively. Finally, we construct SYNCH-TSMOM equal weighted portfolio for each SYNCH quintiles and hold them for K months. Panels A and B present the FF3 and the FF5 returns for high-SYNCH and low-SYNCH TSMOM. Panel C presents the FF3 and FF5 returns for high-low SYNCH TSMOM that buys (sells) TSMOM portfolio with the high (low) SYNCH. All t-statistics are Newey–West adjusted with K lags. Panel A. TSMOM FF3 adjusted return

High SYNCH Low SYNCH J K K 3 6 9 12 3 6 9 12

3 0.1314 0.1088 0.1568 0.1418 0.2590 0.1898 0.1963 0.1509 (1.29) (1.35) (2.09) (2.07) (2.56) (2.15) (2.41) (2.13)

6 0.1504 0.1889 0.2163 0.2135 0.2749 0.2548 0.2332 0.1932 (1.26) (1.68) (2.07) (2.43) (2.22) (2.04) (2.10) (2.10)

9 0.2525 0.2542 0.2631 0.2275 0.3300 0.2759 0.2352 0.1682 (1.87) (2.01) (2.28) (2.33) (2.30) (2.00) (1.92) (1.62)

11 0.2909 0.2821 0.2696 0.2099 0.3517 0.2667 0.2175 0.1184 (2.17) (2.24) (2.32) (2.12) (2.49) (1.93) (1.74) (1.10)

Panel B. TSMOM FF5 adjusted return High SYNCH Low SYNCH J K K 3 6 9 12 3 6 9 12

3 0.0590 0.0503 0.1005 0.0870 0.1966 0.1287 0.1500 0.1067 (0.56) (0.55) (1.12) (1.11) (1.85) (1.32) (1.62) (1.34)

6 0.0751 0.1142 0.1423 0.1474 0.1985 0.1838 0.1703 0.1344 (0.56) (0.86) (1.17) (1.45) (1.46) (1.31) (1.37) (1.28)

9 0.1707 0.1732 0.1892 0.1637 0.2447 0.1914 0.1603 0.0997 (1.12) (1.22) (1.49) (1.48) (1.58) (1.28) (1.20) (0.86)

11 0.1980 0.1985 0.1944 0.1447 0.2550 0.1724 0.1367 0.0422 (1.33) (1.45) (1.54) (1.32) (1.69) (1.17) (1.01) (0.35)

Panel C. High-Low TSMOM adjusted return FF3 adjusted return FF5 adjusted return J K K 3 6 9 12 3 6 9 12

3 -0.1276 -0.0810 -0.0396 -0.0090 -0.1376 -0.0784 -0.0495 -0.0197 (-1.99) (-1.55) (-0.89) (-0.24) (-2.09) (-1.42) (-1.07) (-0.50)

6 -0.1245 -0.0659 -0.0169 0.0203 -0.1233 -0.0696 -0.0280 0.0130 (-1.61) (-0.98) (-0.30) (0.43) (-1.53) (-0.98) (-0.47) (0.26)

9 -0.0775 -0.0217 0.0279 0.0593 -0.0740 -0.0182 0.0289 0.0640 (-0.92) (-0.29) (0.45) (1.11) (-0.86) (-0.24) (0.44) (1.12)

11 -0.0608 0.0154 0.0521 0.0914 -0.0570 0.0262 0.0577 0.1025 (-0.72) (0.21) (0.84) (1.67) (-0.65) (0.35) (0.88) (1.74)

71

Figure 1A. The Distribution of past returns for SYNCH sorts. This figure plots average log past returns of winners and losers for a conditional double sort on SYNCH. For each SYNCH quintile (1=low SYNCH, 5= high SYNCH), The top and bottom ends of the whiskers are the winner and loser cutoffs.

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