The effects of investor attention on stock returns

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The effects of investor attention on stock returns

By

Yan He

S3100111

University of Groningen Faculty of Economics and Business

Msc. Finance

Supervisor: Prof. Roelof Salomons Date: 08-06-2017

Abstract

This study examines the relationship between investor attention and stock returns in the US market. The investor attention is measured by online ticker searches on Google. The sample consists of 408 companies selected from the S&P 500 index. And the time period focused in the research is from the start of 2012 to the end of 2016. This study finds that in the short term, stocks with higher search intensity have higher returns, but a reversal is expected in the medium or longer horizon. This finding is consistent with the ‘price pressure hypothesis’. Furthermore, the impacts of past search intensity are also examined in the paper. But different indicators end up with divergent results.

Keywords: Investor attention, Stock returns, Google trends, Price pressure

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1 1. Introduction

One of the most focused and controversial research topic in finance is possibly evaluating and forecasting stock returns, while concerns and views of scholars have been changing over time. Traditional asset pricing models are based on efficient market hypothesis (EMH), which is first developed by Fama (1965). EMH assumes that investors are rational and all information is available instantaneously to all investors. This assumption requires that investors allocate sufficiently high attention to the investing assets. In reality, attention is a scarce cognitive resource as discussed in Kahneman (1973). Investors have limited time and energy to collect massive information. The limited attention will result in different information subsets obtained by different investors, which will inevitably lead to a certain probability of decision-making errors or mistakes. Some remarkable phenomenon, such as herding behavior, calendar effect, and abnormal volatility, imply that stock prices contain a certain degree of investors’ irrational factors. Therefore, the impact of investor attention should be considered when evaluating stock prices.

Two theories of the relationship between investor attention and stock markets have been developed. Merton (1987) builds up the ‘investor recognition hypothesis’, which states that new information of a company would increase investor recognition and persuade investors to buy stocks of the company. Thus, investor attention is relevant for the determination of stock prices and liquidity. More recently, Barber and Odean (2008) propose the ‘price pressure hypothesis’ or ‘attention theory’, which notes that investors do not have enough resources and time to select investment targets among thousands of stocks. This formidable decision problem makes investors tend to buy stocks that catch their attention. As such, an increase in investor attention is associated with an increase in buying pressure, probably leading to abnormally high returns and trading activities.

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2 crucial since there is no direct measure of it. In today’s digital information era, the forecasting ability of data collected from various digital platforms has received increasing interest and recognition. One of the most studied predictive data is online searching queries. As discussed in Beatty and Smith (1987), the theory of buyer behavior assumes that consumers’ act of searching and collecting information happens before their buying decision. Therefore, the analysis of consumers’ searching activities can provide insights of predicting sales of products and thus offer relevant marketing suggestions such as when is appropriate to launch promotions. Also, searching activities provide a new way to read economy. Hal Varian, the chief economist of Google, states that the changes in search volumes of certain keywords such as ‘unemployment office’ and ‘jobs’ predict the promising increase in initial jobless claims Tuna (2010). Researching the relationship between online searches and the potential predictive power has become the marketplace trends.

Nowadays, there are several internet search engines provide real-time information on searching behavior, among which google is most widely used. Actually, from 2017, Google accounts for 79.6% of all search engines on desktop, 95.73% on mobile and tablet, and 95.48% on console in the world1. And since 2004, Google Trend provides Search Volume Index (SVI) and forecasts future trends based on Google search volume. Recently several researchers in diverse areas have used Google Trends in their empirical researches, demonstrating that it can provide some useful insights. For example,Carneiro & Mylonakis (2009) study the spreading of epidemics and diseases using Google Trends as the tool. Therefore, the Search Volume Index (SVI) provided by Google trend is likely to be representative of investor attention.

The figure below depicts an example of keyword searching in Google trends, where ‘S&P 500’ is the search item. In panel A where the daily SVI is displayed, the remarkable periodic search volume change is in line with the fact that people tend to

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Panel A: daily SVI over the past 90 days

Panel B: S&P 500 index and weekly SVI from the start of 2012 to the end of 2016

Fig. 1 Google trend data (SVI) of S&P 500

The figure shows the search volume index (SVI) of the keyword ‘S&P 500’ obtained from google trends. Panel A exhibits the interface of google trends when searching ‘S&P 500’ over the past 90 days. In panel B, weekly SVI of S&P 500 over a five-year period from 2012 to 2016 is compared with the S&P 500 index during the same period. The left vertical axis shows the measure of S&P 500 index and the right vertical axis displays the measure of logarithm of SVI.

In financial field, after the Google trends data are first employed by Da, Engelberg, and Gao (2011) and Mondria, Wu, and Zhang (2010) as an active measure of investor attention, a few attempts are made to forecast financial markets based on search

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5 intensity, but with mixed results. In this paper, relationships between investor attention and stock returns in US market are investigated, using a sample of 408 companies selected from the S&P 500 index. This study not only tests the theory of limited attention, but also examines the effects of investor attention over both the short-term period and medium or longer horizon and thus examines the ‘price pressure hypothesis’ proposed by Barber and Odean (2008).

The rest of the paper is organized as follows. Section 2 provides the background information and related literature review. Section 3 elaborates data issues as well as the preliminary data processing. Section 4 describes the models and methods. Section 5 discusses the results, including assessments of robustness. Finally, a conclusion is provided in Section 6.

2. Literature Review 2.1 Limited attention

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6 According to Merton (1987), investor attention is relevant for stock pricing and the determination of market liquidity. The ‘investor recognition hypothesis’ states that in a world of costly information, investors are informational constrained, thus investors tend to buy and hold only the securities that capture their attention and about which they have enough information. More recently, Barber and Odean (2008) propose the ‘price pressure hypothesis’ or ‘attention theory’, which notes that investors are net buyers of stocks that catch their attention. Because the buying decision of retail investors can be made through thousands of stocks while the selling decision of them can only be limited in what they already own. Therefore, the limited attention should result in net buying behavior of the informational constrained individual investors As such, the stocks that catch investor attention are expected to have higher buying pressure, thus leading to higher stock returns in the short-term and price reversals in the long run.

2.2 Proxy of investor attention

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7 and Wurgler (2007)), trading volume (Gervais, Kaniel, and Mingelgrin (2001)), advertising expenditure (Chemmanur and Yan (2009)) and limits of stock price (Seasholes and Wu (2007)) are also commonly used in various researches.

However, these indirect proxies mainly capture the passive attention of investors and inherit some defects. According to Da et al. (2011) and Tantaopas, Padungsaksawasdi, and Treepongkaruna (2016), these passive measures mentioned above are based on the assumption that if a stock presented abnormal return or trading volume, or its name was covered in the news report or any kind of medias, then investors should have noticed it. In reality, there is no guarantee that investors actually read or watch them, thus making them not a good measure of investor attention. Furthermore, the spikes on stock prices and trading volumes might attribute to the market manipulations or interventions made by a small or a particular group of investors, intuitively making these proxies problematic.

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8 outbreaks of influenza 1 to 2 weeks before Centers for Disease Control and Prevention (CDC) reports.

In financial field, a few attempts are also made to study the relationship between investor attention and financial markets. Takeda and Wakao (2014) examine the correlation between investor attention, which is measured by search intensity, and returns and trading volumes of stocks in the Japanese Nikkei 225 index, concluding that investor attention has strongly positive correlation to trading volumes and weakly positive relationship with stock returns. Goddard, Kita, and Wang (2015) use SVI as investors’ active attention and provide evidence that investor attention is able to forecast the future volatility of currency returns. Arditi, Yechiam, and Zahavi (2015) focus on the periods when stocks are extensively searched and illustrate that investors exhibit different sensitivity to positive and negative returns. In general, all of these literatures provide concrete basis of using SVI as the direct measure for investor attention.

2.3 Hypotheses development

Based on the ‘price pressure hypothesis’ proposed by Barber and Odean (2008), the effects of investor attention over both the short-term period and medium or longer term horizon are examined. With the theoretical background, I list two hypotheses that are transformed from the research questions.

H1: Investor attention is positively related to stock returns in the short-term. H2: Investor attention is negatively related to stock returns in the medium or longer term horizon, i.e., a reversal is expected in the long run.

3. Data

Thomson Reuters Datastream and Google Trends2 are the main source of data used in

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9 this paper. The data obtained from Thomson Reuters Datastream include daily opening prices, closing prices, and trading volumes for companies in the S&P 500 index from January 1, 2011 to December 31, 2016. The Google Trends data used for analysis are from 2012 to 2016. Stock data for the year 2011 are needed to calculate 52 weeks rolling betas and moving averages for stocks in 2012. And the search volume collected from google trends are from November 1, 2011 to December 31, 2016. Companies in the S&P 500 index are selected because of the liquidity and because most of these companies have frequent searching data.

3.1 Sample selection

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10 to download daily data, the time period is limited. In this paper, the downloaded Google Trends data are across recent 5 years, from November 1, 2011 to December 31, 2016. The data interval is weekly, and the results are updated every Sunday.

According to the research objective, the search volumes of companies in S&P 500 index are required. However, the choice of the keyword for a specific company can be subjective and case-sensitive. There are two main branches of keyword selection among existing research papers when it comes to equity study. One is to use the name of the company, and the other is to use the ticker. And the correlation between the two indicators is low. According to Da et al. (2011), the number is about 9%. For the possible causes, Da et al. (2011) and Joseph, Wintoki, and Zhang (2011) mention two potential problems when the company names are used for studying financial issues. First, there are many different ways to spell the name of a company, including various abbreviations. Users may adopt different spellings according to their own habits. Second, a user who search the name of a company on the internet may not intend to acquire financial information about the company. For example, a user who searches ‘Amzon’ might purely want to buy stuff on the website. Other possible reasons that people search company names might be collecting product information, looking for stores addresses, or even seeking job opportunities. Therefore, using company name as searching item may result in a large amount of search noise in the data, especially for companies that are in retail industry, have online shops, sell products that apply their company names, and companies whose names can be used for general objects, such as Apple.

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11 their owner trading platforms are more likely to access and analyze the investing information through their proprietary information databases. The less sophisticated individual investors who are constrained by the limited information accessibility are prone to gather information through online search engines. And the financial tickers are easily accessible through internet. Therefore, the majority of ticker searches is expected to reflect the behavior of retail investors. Although tickers may also generate some ambiguity, such as the common abbreviations, the noise included in tickers are apparently less than that generated from searching company names. And several measures are taken to minimize the influence of these noise. Firms are deleted if their tickers are in following categories:

1) Firms whose tickers are single or double alphabets. For example, AT&T Inc. has a ticker with single alphabet ‘T’, and Ford Motor Co has the single ‘F’ as the ticker.

2) Firms whose tickers have general meanings. For example, tickers of the companies Costco Wholesale Corp and Caterpillar Inc are ‘COST’ and ‘CAT’ respectively.

3) Firms whose tickers might unintentionally imply other companies. For example, users who search ‘HP’ online might want to collect information of the company Hewlett-Packard rather than the Company Helmerich & Payne Inc. that happens to have a ticker ‘HP’.

4) Firms that are in retail industry or provide commonly used online service and whose tickers are the same with their company names. For example, Ebay Inc. has a ticker ‘EBAY’. And people who search ‘YAHOO’ may not intend to search the ticker, but rather the website of Yahoo.

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12 following table exhibits the detailed screening process.

Table 1

Sample Selection.

This table elaborates how the sample in the paper is selected form companies in S&P 500 index during the period from January 1, 2011 to the end of 2016.

No. of firms included in S&P 500 index 496

No. of firms with incomplete stock data 28

No. of firms whose SVIs are 0 for more than 5 weeks 8

No. of firms whose tickers are not appropriate 52

No. of firms in the sample 408

3.2 Stock return 3.2.1 Weekly return

Weekly return is computed as the log price of the stock on Friday minus the log price on Monday. 𝑃𝑟𝑖𝑐𝑒_{𝐹𝑟𝑖𝑑𝑎𝑦 𝑖,𝑡} and 𝑃𝑟𝑖𝑐𝑒_{𝑀𝑜𝑛𝑑𝑎𝑦 𝑖,𝑡} represent closing market price of stock i on Friday and Monday respectively during the week t. If Friday or/and Monday is not trading day, 𝑃𝑟𝑖𝑐𝑒_{𝐹𝑟𝑖𝑑𝑎𝑦 𝑖,𝑡} or/and 𝑃𝑟𝑖𝑐𝑒_{𝑀𝑜𝑛𝑑𝑎𝑦 𝑖,𝑡} will equal to the closing prices on the closest trading days during the week. And 𝑅𝑖,𝑡 stands for the weekly return of stock i during week t.

𝑅𝑖,𝑡 = ln (𝑃𝑟𝑖𝑐𝑒𝐹𝑟𝑖𝑑𝑎𝑦 𝑖,𝑡) − 𝐿𝑛(𝑃𝑟𝑖𝑐𝑒𝑀𝑜𝑛𝑑𝑎𝑦 𝑖,𝑡) (1)

3.2.2 Excess return

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13 which is the difference between return of the underlying asset and the risk free rate.

ER_𝑖,𝑡 = 𝑅_𝑖,𝑡− 𝑅_𝑓,𝑡 (2)

Besides this definition, the other one uses a particular benchmark instead of risk free rate. In this paper, the two types of excess return are both applied. And for the second definition, a 52-week rolling beta for each stock is incorporated to adjust for individual risk, hence the excess returns are calculated by subtracting the product of 52-week rolling betas of individual companies and corresponding market returns from the weekly stock returns, see equation (3).

ER𝑖,𝑡 = 𝑅𝑖,𝑡− 𝛽𝑖,𝑡𝑅𝑚,𝑡 (3)

Where ER_𝑖,𝑡 represents excess return for company i at time t. 𝑅_𝑖,𝑡 is the weekly log return calculated as equation (1). The corresponding weekly market return is denoted as 𝑅_𝑚,𝑡. And 𝛽_𝑖,𝑡 is the 52-week rolling beta of the stock.

3.2.3 Abnormal return

Besides weekly return and excess return, abnormal return is also taken into consideration. The validity and robustness of the three-factor model developed by Fama and French (1993) have been widely demonstrated. Thus, the abnormal returns are defined by carrying out the following regression:

𝑅 − 𝑅_𝑓 = 𝛼 + 𝛽_𝑚(𝑅_𝑚− 𝑅_𝑓) + 𝛽_𝑠𝑆𝑀𝐵 + 𝛽_ℎ𝐻𝑀𝐿 + 𝜀 (4)

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14 is the value of the simple average return of high book-to-market stocks minus that of low book-to-market stocks. As for the source of data, Tuck School of Business provides the calculated up-to-date three factors. Since this paper studies stocks from S&P 500 index, the US research returns data are obtained from its website3.

3.3 Three indicators of search intensity

Several different indicators of search intensity are adopted in various researches. In this paper, following Takeda and Wakao (2014), three indicators are examined and compared to represent investor attention.

First, the logarithm of basic SVI is employed, denoted as ln (𝑆𝑉𝐼_𝑖,𝑡). However, this indicator may involve some problems when comparing search intensity of multiple stocks. For instance, consider the situation in which the search volume 𝑆𝑉𝐼𝑗,𝑝 is extremely high at time p for stock j due to some news outbreak. This situation would make search intensity 𝑆𝑉𝐼𝑗,𝑞 (q ≠ p) for stock j relatively low compared with other stocks and for other periods.

Next, the change in SVI is introduced as the second indicator, which is defined as follow:

∆SVI𝑖,𝑡 = ln (𝑆𝑉𝐼𝑖,𝑡) − ln (𝑆𝑉𝐼𝑖,𝑡−1) (5)

However, if searching volumes of some certain companies remain high for several weeks, this indicator may not be able to capture the lasting impact.

To avoid the problems discussed above, the third indicator abnormal search volume index (ASVI) is also applied. Following Da et al. (2011), it is defined as the difference between the log SVI during the week and the median of log SVIs during the previous

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15 8 weeks.

𝐴𝑆𝑉𝐼𝑖,𝑡 = ln (𝑆𝑉𝐼𝑖,𝑡) − 𝑀𝑒𝑑𝑖𝑎𝑛 (ln (𝑆𝑉𝐼𝑖,𝑡−1), ln (𝑆𝑉𝐼𝑖,𝑡−2), … ln( 𝑆𝑉𝐼𝑖,𝑡−8)) (6)

Where 𝐴𝑆𝑉𝐼_𝑖,𝑡 stands for the abnormal search volume index for stock i during the week t. ln (𝑆𝑉𝐼_𝑖,𝑡) and ln (𝑆𝑉𝐼_{𝑖,𝑡−1}), … ln( 𝑆𝑉𝐼_{𝑖,𝑡−8}) are logarithm of SVI for stock i during the corresponding week t, t-1,…t-8. Using ASVI, the problem mentioned above can be efficiently avoided since the median value of a time period reflects the normal level of attention and thus can be robust to recent drastic ups and downs. Another advantage of ASVI is that the time trends and other low-frequency seasonality can be removed. Therefore, ASVI is a more stable and robust measure of attention, and can be compared both in cross-section and time-series ways. Clearly, a positive ASVI means a rise in investor attention, and the larger the number, the higher the degree of increasing. On the contrary, a large and negative ASVI represents a severe decreased attention over the week.

4. Methodology

4.1 Search intensity and short-term return

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16 Where 𝑅_𝑖,𝑡 is the weekly return of stock i at week t, N is the number of all sample stocks, which is 408, and k ranges from 1 to 10, representing Q1, Q2, Q3, … Q10 ten

subsets of the entire sample. And Rank (𝑆𝐼𝑖,𝑡) is the order of the search intensity, which is represented by three indicators, ln (𝑆𝑉𝐼𝑖,𝑡), ∆SVI𝑖,𝑡, and 𝐴𝑆𝑉𝐼𝑖,𝑡, among the sample companies. Apparently, Q1 is composed of stocks with lowest search intensity, while Q10 comprises companies with the highest search intensity. The companies in the

corresponding sorted portfolios are held for the entire trading week, then new portfolios will be generated at the beginning of next trading week according to the new rank of the search intensity.

The average weekly return of portfolio 𝑄_𝑘 (k = 1, 2, 3, … 10) at time t is defined as follow:

𝑅𝑄𝑘,𝑡 =

∑ 𝑄𝑘,𝑡

𝑛_𝑄𝑘 (8)

Where 𝑄_𝑘,𝑡 is the returns of stocks included in the portfolio 𝑄_𝑘 as defined in the model (7), 𝑛𝑄𝑘 is the number of stocks within the portfolio 𝑄𝑘.

Next, the impact of investor attention on abnormal stock returns of the portfolio 𝑄𝑘 is examined based on the three-factor model of Fama and French (1993).

𝑅_𝑄_𝑘,𝑡− 𝑅_𝑓,𝑡 = 𝛼 + 𝛽_𝑚(𝑅_𝑚,𝑡− 𝑅_𝑓,𝑡) + 𝛽_𝑠𝑆𝑀𝐵_𝑡+ 𝛽_ℎ𝐻𝑀𝐿_𝑡+ 𝜀_𝑄_𝑘,𝑡 (9)

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17 4.2 Search intensity and longer term return

Next, the long-run relationship between search intensity and stock returns is investigated. The ‘price pressure hypothesis’ assumes a positive short-run relationship between investor attention and stock returns and a negative correlation over a medium or long term horizon. Almost all the prior studies reach the consistent conclusion about the shot-term relationship that search intensity is positively related to stock returns or abnormal returns, whereas divergent findings exist over a longer term horizon. Some researches such as Da et al. (2011) and Joseph et al. (2011) demonstrate a negative relationship between search intensity and stock returns, while others such as Takeda and Wakao (2014) fail to provide evidence of a reversal that appears in the long run. In theory, if the increase of stock prices is due to the fundamental change in company value, no long-term reversal is expected. However, if the increase of stock prices is caused by sentimental factor, that is, investor attention in this paper, a long-term reversal is likely to happen.

4.2.1 Forecasting ability of investor attention

As in prior analysis, the sample is sorted into 10 portfolios on the first trading day of every week, according to the three indicators of search intensity illustrated in equation (7). Then a portfolio that has long position in the subset with highest attention and short position in the subset with lowest attention, i.e., (Q10 - Q1), is formed and updated each

week. Instead of focusing on the portfolio returns only over a one-week period, I track the performance of the portfolio over an eight-week horizon following the portfolio construction. The average weekly returns and abnormal returns over the eight-week period are examined to verify whether a reversal of the short-term positive returns exists in the medium and longer term. The results are shown in table 4.

4.2.2 Lagged effects of investor attention

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18 is also investigated. Based on Fama-French three-factor model, another factor, search intensity, which is represented by the three indicators is added as an explanatory variable. The multivariate regression is shown as bellow:

𝑅𝑖,𝑡− 𝑅𝑓,𝑡 = 𝛼 + ( ∑8𝑗=0𝐿𝑗𝜃𝑗 )𝑆𝐼𝑖,𝑡+ 𝛽𝑚(𝑅𝑚,𝑡− 𝑅𝑓,𝑡) + 𝛽𝑠𝑆𝑀𝐵𝑡+

𝛽ℎ𝐻𝑀𝐿𝑡+ 𝜀𝑖,𝑡 (10)

Where a lag operator, 𝐿𝑗 (j = 0, 1, … 8) is defined to transform the variable 𝑆𝐼𝑖,𝑡, which stands for search intensity, to a row vector including both the 𝑆𝐼_𝑖,𝑡 itself and the eight lags of it, that is, 𝐿₁𝑆𝐼_𝑖,𝑡 = 𝑆𝐼_{𝑖,𝑡−1}, 𝐿₂𝑆𝐼_𝑖,𝑡 = 𝑆𝐼_{𝑖,𝑡−2}, and so on. And three indicators (ln (𝑆𝑉𝐼_𝑖,𝑡), ∆SVI_𝑖,𝑡, and 𝐴𝑆𝑉𝐼_𝑖,𝑡) are employed respectively to represent the search intensity.

Since the regressions involve panel data, Durbin–Wu–Hausman test is first conducted to determine the specification of the model. For all the three indicators, the test result fails to reject the null hypothesis and thus random effects model is appropriate to estimate equation (10).

4.3 Model for robustness check

Since divergent results exist for the longer term effects, following Bijl et at. (2016) and Tetlock (2007), another model based on VAR estimates is introduced to check the robustness of the longer term effects. This model is specified as follow:

ER_𝑖,𝑡 = 𝛼 + ( ∑5_𝑗=1𝐿_𝑗𝛽_𝑗 ) 𝐸𝑅_𝑖,𝑡+ ( ∑5_𝑗=0𝐿_𝑗𝛾_𝑗 ) 𝑆𝐼_𝑖,𝑡+ 𝜃𝜎_{𝑤 𝑖,𝑡−1}+

𝜑𝜎_{𝑙 𝑖,𝑡−1} + 𝜀_𝑖,𝑡 (11)

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19 And five lags are applied to all VAR estimates. Considering the unlagged variables may also have significant impact on the excess return, unlike the models used by Bijl, Kringhaug, Molna_{́r and Sandvik (2016) and Tetlock (2007) in which only the lagged} items are included, the unlagged VAR estimates are added to the model. In addition, based on the results of Corsi (2009), a short-term and long-term volatility, 𝜎𝑤 𝑖,𝑡−1 and 𝜎_{𝑙 𝑖,𝑡−1} are also included in the regression. 𝜎_{𝑤 𝑖,𝑡−1} is the weekly volatility for stock i, and 𝜎_{𝑙 𝑖,𝑡−1} is the corresponding long-term volatility that is simply calculated as the average of the weekly volatilities for the last 5 weeks:

𝜎_{𝑙 𝑖,𝑡−1} = 1

5 ∑ 𝜎𝑤 𝑖,𝑗 𝑡

𝑗=𝑡−4 (12)

The dataset in model (11) for each indicator is a panel with 408 companies for a 5-year (256 weeks) observation period, therefore Hausman test is conducted. However, for all the three indicators, the result rejects the null hypothesis and thus makes random effects model inappropriate. Then the redundant fixed effects test is conducted and the result rejects the null hypothesis at 5% significance level. Therefore, the panel data model with fixed effects estimator is used for this regression.

5. Results 5.1 Stationary test

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20 Table 2

Results of unit root test.

This table exhibits results of the stationary test. The null hypothesis of the test is defined as the presence of a unit root, which means non-stationary. And the alternative hypothesis is therefore stationarity. The results using different proxies of investor attention are presented in panel A, B, and C respectively. And the three forms of ADF test, i.e., plain, with constant, and with constant and trend are conducted subsequently. The t-statistics marked ∗∗∗ denote that the coefficients are significant at the 1% level.

Panel A: ln (𝑆𝑉𝐼𝑖,𝑡)

Variables T-statistics Results

plain with constant with constant and

trend 𝑅𝑄1− 𝑅𝑓 -17.3335 *** _-17.3112*** _-17.6894*** _stationary 𝑅𝑄2− 𝑅𝑓 -17.7935 *** _-17.7806*** _-18.0105***. _stationary 𝑅𝑄₃− 𝑅𝑓 -17.3458 *** -17.3903 *** -17.5786 *** stationary 𝑅𝑄₄− 𝑅𝑓 -16.9489 *** -16.9659 *** -17.1460 *** stationary 𝑅𝑄₅− 𝑅𝑓 -17.0144 *** -17.0326 *** -17.1612 *** stationary 𝑅𝑄₆− 𝑅𝑓 -16.9392 *** -16.9417 *** -17.0232*** stationary 𝑅𝑄7− 𝑅𝑓 -17.1380 *** _-17.1751*** _-17.5176*** _stationary 𝑅𝑄8− 𝑅𝑓 -18.1566 *** _-18.2405*** _-18.3111*** _stationary 𝑅𝑄9− 𝑅𝑓 -17.6213 *** _-17.6796*** _-17.8904*** _stationary 𝑅𝑄10− 𝑅𝑓 -17.2526 *** _-17.2550*** _-17.3968*** _stationary 𝑅𝑚− 𝑅𝑓 -17.2618 *** -17.7168 *** -17.7307 *** stationary SMB -16.1668 *** _-16.1360*** _-16.1100*** _stationary HML -15.1395 *** _-15.1677*** _-15.1702*** _stationary Panel B: ∆SVI𝑖,𝑡

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21 𝑅𝑄₁− 𝑅𝑓 -17.2164 *** -17.1832 *** -17.2957 *** stationary 𝑅𝑄₂− 𝑅𝑓 -17.4222 *** -17.3941 *** -17.7278 *** stationary 𝑅𝑄₃− 𝑅𝑓 -18.0760 *** -18.0522 *** -18.1687 *** stationary 𝑅𝑄4− 𝑅𝑓 -17.2300 *** _-17.2001*** _-17.4139*** _stationary 𝑅𝑄5− 𝑅𝑓 -17.3604 *** _-17.4130*** _-17.6207*** _stationary 𝑅𝑄6− 𝑅𝑓 -17.4401 *** _-17.4707*** _-17.6815*** _stationary 𝑅𝑄7− 𝑅𝑓 -16.8187 *** _-16.8431*** _-17.1069*** _stationary 𝑅𝑄8− 𝑅𝑓 -17.7825 *** _-17.8326*** _-17.9271*** _stationary 𝑅𝑄9− 𝑅𝑓 -17.4454 *** _-17.5216*** _-17.7494*** _stationary 𝑅𝑄₁₀− 𝑅𝑓 -16.9566 *** -17.2068 *** -17.3424 *** stationary 𝑅𝑚− 𝑅𝑓 -17.2618 *** -17.7168 *** -17.7307 *** stationary SMB -16.1668 *** _-16.1360*** _-16.1100*** _stationary HML -15.1395 *** _-15.1677*** _-15.1702*** _stationary Panel C: 𝐴𝑆𝑉𝐼𝑖,𝑡

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22

HML -15.1395 *** _-15.1677*** _-15.1702*** _stationary

It is clear from the table 2 that all variables are stationary and thus the regression outputs can be reliable. And the results of this analysis are presented in table 3.

5.2 Short-term effects

Table 3 shows the analysis results of equation (9)，where three indicators of search intensity are employed. Alongside the focus on abnormal returns that denoted by 𝛼, weekly raw returns of each portfolio 𝑄𝑘 are also included in the table. The average and abnormal return of the ten portfolios are plotted in fig. 2. We can see from the table that although panel A, where the first indicator ln (𝑆𝑉𝐼𝑖,𝑡) is used, does not provide a clear pattern, in panel B and panel C, investor attention is in general positively correlated with both returns and abnormal returns. This trend can be clearly seen in figure 2. Although the values of 𝛼 are negative for all the ten portfolios, it is clear that abnormal returns associated with corresponding portfolios increase as the degree of investor attention goes up. This positive relationship also exists for portfolio returns. In addition, the table also shows a significant difference between companies that have high investor attention and those with low investor attention. This result is represented in the last row of each panel, where a portfolio consists of a long position in high attention stocks (Q10) and short position in low attention stocks (Q1), denoting as (Q10 - Q1).

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23 finding is consistent with the ‘price pressure hypothesis’ that abnormal returns are positively related to investor attention.

Table 3

Returns of portfolios formed according to investor attention.

This table reports weekly raw returns of the portfolio 𝑄𝑘 (k = 1, 2, 3, … 10) and the regression

outputs of equation (9). The portfolio 𝑄𝑘 is formed based on the investor attention according

to equation (7), where three indicators of search intensity is applied. Panel A shows the results of indicator ln (𝑆𝑉𝐼𝑖,𝑡), panel B exhibits the results when ∆SVI𝑖,𝑡 is employed, and the results of indicator 𝐴𝑆𝑉𝐼𝑖,𝑡 is presented in panel C. At every week, Q1 is composed of stocks

with lowest search intensity, while Q10 comprises companies with the highest search intensity.

And following Fama-French three-factor model, 𝛼 the constant variable represents the abnormal return of portfolio 𝑄𝑘. 𝑅𝑚,𝑡− 𝑅𝑓,𝑡 is the market risk premium. 𝑆𝑀𝐵𝑡 is the

difference between the simple average return of small-cap stocks and large-cap stocks. And 𝐻𝑀𝐿𝑡 is the value of the simple average return of high book-to-market stocks minus that of

low book-to-market stocks. There are 261 observations for each regression. Figures represent in parenthesis are White heteroskedasticity-consistent standard errors. Coefficients marked ∗∗∗, ∗∗ and ∗ denote statistical significance at 1%, 5%, and 10% level respectively.

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24 Q5 0.25 -0.0019 *** (0.0004) 1.0698 *** (0.0238) -0.0003 (0.0006) -0.0005 (0.0004) 90.36 Q6 0.23 -0.0020 *** (0.0004) 1.0078 *** (0.0226) 0.0005 (0.0004) 0.0010 ** (0.0004) 89.18 Q7 0.26 -0.0016 *** (0.0004) 0.0126 *** (0.0278) -0.0002 (0.0005) 0.0003 (0.0004) 88.62 Q8 0.28 -0.0014 *** (0.0004) 1.0010 *** (0.0240) -0.0002 (0.0004) 0.0010 ** (0.0004) 88.84 Q9 0.27 -0.0016 *** (0.0004) 0.9957 *** (0.0233) -0.0006 (0.0005) 0.0010 *** (0.0004) 88.30 Q10 0.22 -0.0020 *** (0.0004) 0.9897 *** (0.0258) 0.0004 (0.0005) 0.0006 (0.0004) 87.34 Q10 - Q1 0.03 0.0003 (0.0004) -0.0207 (0.0278) 0.0005 (0.0004) 0.0011 (0.0005) ** 2.57 Panel B: ∆SVI𝑖,𝑡

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25 Q7 0.25 -0.0017 *** (0.0004) 0.9964 *** (0.0228) -0.0006 * (0.0003) -0.0000 (0.0004) 90.60 Q8 0.26 -0.0016 *** (0.0003) 1.0205 *** (0.0257) -0.0002 (0.0004) 0.0001 (0.0004) 89.25 Q9 0.29 -0.0015 *** (0.0003) 1.0808 *** (0.0229) -0.0001 (0.0004) -0.0000 (0.0004) 91.61 Q10 0.40 -0.0003 (0.0005) 1.0845 *** (0.0264) 0.0011 ** (0.0005) -0.0006 (0.0005) 85.11 Q10 - Q1 0.25 0.0023 *** (0.0005) 0.0978 *** (0.0323) 0.0015 * (0.0008) -0.0001 (0.0007) 7.00 Panel C: 𝐴𝑆𝑉𝐼𝑖,𝑡

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26 Q9 0.31 -0.0012 *** (0.0004) 1.0540 *** (0.0238) 0.0004 (0.0005) 0.0000 (0.0005) 89.19 Q10 0.39 -0.0006 (0.0005) 1.1088 *** (0.0267) 0.0006 (0.0005) -0.0006 (0.0005) 86.41 Q10 - Q1 0.23 0.0020 *** (0.0005) 0.1076 *** (0.0320) 0.0009 (0.0007) -0.0006 (0.0006) 6.82

Panel A: average weekly return

Panel B: weekly abnormal return

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27 Fig. 2 Average and abnormal return of ten portfolios.

In this figure, average weekly return and weekly abnormal return of the ten portfolios are presented in panel A and panel B respectively. Three variables are used as the indicators of search intensity, based on which the ten portfolios are constructed. Q1 is composed of stocks

with lowest search intensity, while Q10 comprises companies with the highest search intensity.

Next, the performance of the portfolios formed based on investor attention is further examined. Hereby three portfolios, portfolio with the lowest search intensity Q1,

portfolio with the highest search intensity Q10, and portfolio with long position in Q10

and short position in Q1, that is Q10 - Q1, are employed to compare their performance.

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28

Panel B: ∆SVI𝑖,𝑡

Panel C: 𝐴𝑆𝑉𝐼𝑖,𝑡

Fig. 3 Cumulative holding period portfolio performance.

The figure shows cumulative values for portfolio with the lowest search intensity Q1, portfolio

with the highest search intensity Q10, portfolio with long position in Q10 and short position in Q1, that is Q10 - Q1, and S&P 500 index respectively. Portfolios are formed based on different

indicators of search intensity every week. Panel A, panel B, and panel C exhibit the performance of portfolios determined by the three indicators ln (𝑆𝑉𝐼_𝑖,𝑡), ∆SVI𝑖,𝑡, and 𝐴𝑆𝑉𝐼𝑖,𝑡

respectively.

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29 different degree of investor attention present significantly diverse performance. Although in panel A, the relationship between search intensity and portfolio returns is not explicit, panel B and panel C clearly show that the performance of portfolio with high attention far exceeds that of the portfolio with low attention. In panel B, after the 5-year holding period, the value of portfolio Q10 reaches 2.71, almost double the final

value of portfolio Q1, which is only 1.42. And the discrepant performance exists for the

whole observation period. Also, the long-short portfolio (Q10 - Q1) outperforms the

market, ending at a value of 1.92 against to the value of index investing of 1.72. Similar result can be found in panel C. Although the long-short portfolio only slightly outperforms the market, the portfolio with high search intensity Q10 has much better

return than that of the low attention portfolio Q1 as well as that of the market. As for

the relatively disappointing result in panel A for both the regression outputs in table 3 and the investing performance in fig. 3, the possible reason is the internal problem associated with the indicator ln (𝑆𝑉𝐼𝑖,𝑡). As what has been discussed in section 3.3, an abnormal high search volumes in certain period for certain stock can make the SVI in other periods for this stock relatively low, thus making the SVI incomparable in both cross-section and time-series ways. In general, the results support the ‘price pressure hypothesis’ that high investor attention can lead to high stock returns.

5.3 Longer term effects

Table 4 shows the longer term effects of investor attention over an eight-week period, where the performance of the long-short portfolio (Q10 - Q1) is reported. As the results

shown in section 5.1, the raw returns for only one week are positive under all three indicators, which means that in the short-term, the portfolio with high attention (Q10)

has better returns than the portfolio with low attention (Q1). Similar results can be

obtained through abnormal returns. However, from week 2 to 4, the average weekly returns as well as abnormal returns turn to be negative in all three panels, which means that the portfolio with high attention (Q10) does not outperform the portfolio with low

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30 negative returns that there is a reversal after week 2. According to the ‘price pressure hypothesis’, a negative relationship between investor attention and stock returns is expected in the medium and longer term. Thus, the results from table 4 support the ‘price pressure hypothesis’ that a reversal appears in the medium and longer term.

Table 4

Forecasting ability of investor attention.

This table reports the longer term effects of investor attention. The abnormal and raw returns of a portfolio (Q10 - Q1) are shown in the table. This portfolio is formed as follow: On the first

trading day of every week, the 408 stocks in the sample is sorted according to the search intensity, which has three indicators (ln (𝑆𝑉𝐼𝑖,𝑡), ∆SVI𝑖,𝑡, and 𝐴𝑆𝑉𝐼𝑖,𝑡). Then ten subsets are

determined according to equation (6), where Q10 is comprised of stocks with highest search

intensity and Q1 constitutes stocks with lowest attention. The portfolio (Q10 - Q1) is formed with

long position in Q10 and short position in Q1. The portfolio is updated every week and the

performance of each portfolio is tracked for eight weeks after its formation. The raw returns reported in the table are average weekly returns. The α represents abnormal returns, which are obtained from the regression of Fama-French three factor model. There are 255 observations for each regression. Figures represent in parenthesis are White heteroskedasticity-consistent standard errors. Coefficients marked ∗∗∗, ∗∗ and ∗ denote statistical significance at 1%, 5%, and 10% level respectively.

Holding periods 1 week 2-4 weeks 5-8 weeks 1-8 weeks

α -0.0010 ** (0.0005) -0.0022 *** (0.0003) -0.0018 *** (0.0003) -0.0019 *** (0.0002) Raw returns (%) 0.03% -0.09% -0.05% -0.06% Panel B: ∆SVI𝑖,𝑡

Holding periods 1 week 2-4 weeks 5-8 weeks 1-8 weeks

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31

Raw returns (%) 0.26% -0.01% 0.00% 0.03%

Holding periods 1 week 2-4 weeks 5-8 weeks 1-8 weeks

α 0.0008 (0.0005) -0.0015 *** (0.0003) -0.0016 *** (0.0003) -0.0013 *** (0.0002) Raw returns (%) 0.24% -0.02% -0.04% 0.01%

Table 5 represents the results of regression (11). In all three panels, the effect of unlagged search intensity is significant and positive, which is in line with the result shown in table 3 and again supports the short-term effect of ‘price pressure hypothesis’. After that, we can see from the table that the impact of search intensity from the previous week is significant and negative. However, next, a positive effect for the two-week lag is observed. In general, the effects of investor attention become weaker, and the signs of coefficient fluctuate over time. In order to further clarify the longer term relationship between past search intensity and stock returns, the coefficients of search intensity with different lags are added to examine the medium and longer term effects, shown in table 6.

Table 5

Lagged effects based on Fama-French three-factor model.

This table reports the regression outputs of equation (9). In panel A, B, and C, three indicators are applied to represent investor attention, which also includes 1 to 8 lagged variables of each indicator. And following Fama-French three-factor model, 𝑅𝑚,𝑡− 𝑅𝑓,𝑡 is the market risk

premium. 𝑆𝑀𝐵𝑡 is the difference between the simple average return of small-cap stocks and

large-cap stocks. And 𝐻𝑀𝐿𝑡 is the value of the simple average return of high book-to-market

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32

Variables Coefficient T-statistics

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33

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34

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35 Table 6

Medium and longer term effects of past investor attention.

This table shows the influence of investor attention with different lags. The numbers are simply the sum of corresponding coefficients that reported in table 5. The figure of one-week lag is the coefficient of search intensity SI t- 1 in each panel, the figure of a lag of 2-4 weeks is the sum of coefficients of SI t- 2, SI t- 3, and SI t- 4 in each panel. The other values can be calculated as such.

Lags 1 week 2-4 weeks 5-8 weeks 1-8 weeks

-0.0015 -0.0011 0.0001 -0.0025

0.0010 0.0022 0.0013 0.0025

-0.0012 -0.0004 -0.0002 -0.0015

Although it is clear from table 4 that the forecasting ability of all three indicators of search intensity is in line with the ‘price pressure hypothesis’, the effects of past investor attention are not consistent for the three indicators. We can see from the panel A and panel C that the past search intensity have negative influence for current stock returns, and this impact becomes weaker over time, which is shown by the decreasing absolute value of longer term horizon. However, panel B ends up with positive values for all the time periods, meaning that the change of SVI in the past still has positive impact on current stock returns.

5.4 Robustness check

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36 idiosyncratic risk. Table 7 presents the regression results of equation (11). The coefficients of unlagged variables of search intensity are significantly positive, which again supports the short-term effects of ‘price pressure hypothesis’. However, like the results in table 5 and 6, the lagged effects differ for different search intensity. In panel A and panel C, the influences of previous search intensity on stock returns are similar. In general, the negative impacts are observed in both panels. But all the positive coefficients of lagged search intensity in panel B show opposite effect, which is also consistent with the results in table 6. So the lagged logarithm of SVI and abnormal search volume in general have negative effects on stock returns while the former change in SVI has positive influence. Also, it is worth noting that the impact of search intensity is weaker than that of lagged excess returns and volatility.

Table 7

Lagged effects based on VAR model.

This table reports the regression outputs of equation (11). In panel A, B, and C, three indicators are applied to represent investor attention, which also includes 1 to 5 lagged variables of each indicator.The total panel observations are 104448, including 256 period observations and 408 cross-section variables in each panel. Figures represent in parenthesis are White period standard errors. Coefficients marked ∗∗∗, ∗∗ and ∗ denote statistical significance at 1%, 5%, and 10% level respectively.

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37 (0.0004) ln (SVI) t- 3 -0.0008 ** (0.0003) -2.3169 ln (SVI) t- 4 -0.0008 ** (0.0003) -2.3442 ln (SVI) t- 5 -0.0003 (0.0004) -0.7750 Excess return t - 1 -0.0185 *** (0.0047) -3.9619 Excess return t - 2 -0.0164 *** (0.0039) -4.1820 Excess return t - 3 -0.0249 *** (0.0078) -3.1848 Excess return t - 4 -0.0118 *** (0.0045) -2.6541 Excess return t - 5 -0.0070 (0.0059) -1.1709

Past week volatility -0.5439 ***

(0.0529)

-10.2892

Past 5-week volatility 0.1727 ***

(0.0264)

6.5378

Adjusted R2 _0.0070

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38 (0.0005) ΔSVI t- 2 0.0016 *** (0.0005) 3.3340 ΔSVI t- 3 0.0001 ** (0.0004) 2.2185 ΔSVI t- 4 0.0004 (0.0004) 1.0324 ΔSVI t- 5 0.0005 (0.0003) 1.5970 Excess return t - 1 -0.0185 *** (0.0047) -3.9730 Excess return t - 2 -0.0165 *** (0.0039) -4.2002 Excess return t - 3 -0.0250 *** (0.0078) -3.1944 Excess return t - 4 -0.0119 *** (0.0045) -2.6643 Excess return t - 5 -0.0071 (0.0060) -1.1955

(0.0528)

-10.3748

Past 5-week volatility 0.1709

(0.0266)

6.4179

Adjusted R2 _0.0070

Intercept 0.0050 ***

(0.0005)

9.6099

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39 (0.0006) ASVI t- 1 -0.0016 *** (0.0004) -3.6174 ASVI t- 2 0.0006 * (0.0003) 1.7731 ASVI t- 3 -0.0004 (0.0003) -1.1850 ASVI t- 4 -0.0004 (0.0003) -1.1243 ASVI t- 5 0.0000 (0.0004) 0.0263 Excess return t - 1 -0.0185 *** (0.0047) -3.9607 Excess return t - 2 -0.0164 *** (0.0039) -4.1766 Excess return t - 3 -0.0250 *** (0.0079) -3.1790 Excess return t - 4 -0.0118 *** (0.0045) -2.6580 Excess return t - 5 -0.0070 (0.0060) -1.1713

(0.0528)

-10.3539

Past 5-week volatility 0.1711***

(0.0266)

6.4231

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40 6. Conclusion

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