Divergence of sentiment and stock market trading

Abstract

This paper introduces the concept of divergence of sentiment to the behavioral finance literature. We measure the distance between people with positive and negative sentiment on a daily basis for 20 countries by using data from status updates on Facebook. The prediction is that a higher divergence of sentiment leads to more diverging views on prospects and risks, and thus to more diverging views on the value of a stock. In line with this prediction, divergence of sentiment is positively related to trading volume. We further predict and find a positive relation between divergence of sentiment and stock price volatility. The observed relations are stronger when individual investors are more likely to trade. We compare the effect of our country-specific measures to a global measure of divergence of sentiment. We find that the separate effects of country-specific and global divergence measures depend on a country's level of market integration.

Introduction

Sentiment is a relatively generic term that has been used extensively in the behavioral finance literature. As discussed in detail by Liu (2015), sentiment can affect choices in unconscious ways and covers both emotions and mood. Based on evidence from psychology (Johnson and Tversky, 1983, Loewenstein et al., 2001), sentiment influences judgment of a potential prospect and the assessment of risk. Investor sentiment, defined as a belief about future cash flows and investment risk that is not justified by the facts at hand, is important for stock markets (Baker and Wurgler, 2007). Kaplanski et al. (2015) show that happy investors are not only positive on expected stock returns, but they also believe that the risks involved are relatively low.

The relations between the level of sentiment and stock markets are well documented (Baker and Wurgler, 2007). However, the average sentiment level hides a significant variation on a given day. A day in which each person in a country has a neutral sentiment obtains the same average sentiment level score as a day in which half the country is happy and the other half is equally unhappy. Our paper contributes to the literature by investigating divergence of sentiment rather than the average level of sentiment.

We predict that divergence of sentiment affects trading volume. Imagine that particular information reaches investors, for example a firm's announcement about a particular project or merger. Investors with positive sentiment would be more optimistic about the potential benefits and risks of the newly arrived information than investors with negative sentiment. Consequently, on days with high divergence of sentiment, investors differ in how they interpret public information, which leads to a difference of opinion. When investors transact in line with their diverging beliefs on firms’ value, days with high divergence in sentiment are expected to be related to high contemporaneous trading volume.

Our predictions are in line with theoretical models developed in the disagreement literature. Karpoff, 1986, Harris and Raviv, 1993, Banerjee and Kremer, 2010, and Atmaz and Basak (2016) predict that higher disagreement is associated with more trading. For example, in Banerjee and Kremer (2010), investors disagree about the interpretation of public information. In their model, trading volume reflects revisions to the level of disagreement, and periods of high disagreement are related to higher volume. Hong and Stein (2007) stress that heterogeneous priors can generate disagreement of the “value” of new information even when that information is available to investors simultaneously.

This paper also examines the relation between divergence of sentiment and stock price volatility. Because higher disagreement can lead to higher absolute price changes (e.g., Banerjee and Kremer, 2010), one might expect a positive relation between divergence of sentiment and stock price volatility. We treat the relation between divergence of sentiment and stock price volatility mostly as an empirical question, because the expected strength of this relation depends on the extent to which investors affected by sentiment are able to move prices.

To capture divergence of sentiment, we use data from Facebook. Sentiment levels have previously been established by household survey data (Brown and Cliff, 2004, Lemmon and Portniaguina, 2006, Qiu and Welch, 2006, Schmeling, 2009, Kaplanski et al., 2015), economic and financial variables (Lee et al., 1991, Baker and Wurgler, 2007, Brown et al., 2008, Firth et al., 2015), social media (Das and Chen, 2007, Bollen et al., 2011, Karabulut, 2014, Siganos et al., 2014), the weather (Saunders, 1993, Hirshleifer and Shumway, 2003), and sport results (Edmans et al., 2007, Kaplanski and Levy, 2010). We use data from Facebook and exploit the percentage of positive and negative terms used by Facebook users when updating their status. Facebook users write their status updates in a box that contains an open question such as “What's on your mind?”. Siganos et al. (2014) and Karabulut (2014) validate the Facebook sentiment index by showing that the level of sentiment on Facebook is positively related to other sentiment indexes, including the US Gallup index and the Google sentiment index of Da et al. (2014).

Using Facebook data has both advantages and disadvantages. A first advantage is the availability of both positive and negative sentiment scores. The availability of both positive and negative sentiment estimates allows us to measure divergence of sentiment as the absolute distance between positive and negative sentiment levels. Second, Facebook's data are available at the daily frequency, which allows us to explore the relation between divergence of sentiment and stock markets in a contemporaneous setting. Third, Facebook is the world's largest social network site (Wilson et al., 2012), with approximately 55 million status updates per day; its sheer size makes it very likely that many investors are represented on Facebook. Fourth, Facebook's status updates are likely to reflect external phenomena that could affect individuals to different degrees, creating a divergence of sentiment. Examples are a national sports event dividing the nation, the weather varying within the nation, or the nation experiencing high temperatures that are preferred by some but not by others. Fifth, divergence of sentiment could be driven by relatively random factors, such as an individual investor having had a good night's sleep, and social media sentiment proxies are the only proxies that could potentially capture these types of factors. Finally, Facebook data are available for 20 international markets, which allow us to test some hypotheses that exploit differences between countries. We obtain one divergence of sentiment score per day per country.

The data from Facebook also come with limitations. One limitation is that the measurement of sentiment depends on the quality of the word analysis. Linguistic programs typically fail to cope with double negatives (e.g., Baker, 1970), and the sentiment of non-English-speaking communities might be relatively difficult to capture with word analysis (Mihalcea et al., 2007). A second limitation is the relatively short sample period available, from November 2007 to March 2012. Third, even though the average age of Facebook users is increasing over time, stock investors are likely to be underrepresented on Facebook. We believe that our approach is still valuable, because some of the factors that make Facebook users’ sentiment more diverse are also likely to have differential effects on the sentiment of investors. Facebook sentiment reflects investor sentiment because some investors are active on Facebook, and because factors that make Facebook users’ sentiment more diverse, such as the outcome of the Super Bowl, are also likely to have differential effects on investor sentiment. Fourth, there is a great deal of noise in Facebook posts. Our tests could have been sharper if one could filter posts based on relevance and/or obtain sentiment scores combined with demographic information. We do not have access to this demographic information. Consequently, we need to interpret our results with the appropriate caution.

Our empirical analysis shows that high divergence of sentiment is positively related to contemporaneous trading volume and stock price volatility. These findings are in line with groups of investors with diverging sentiment levels within a day disagreeing on the value of stocks, which could make them trade. The increase in stock price volatility is in line with higher disagreement leading to higher absolute price changes and with traders affected by sentiment being able to move prices.

In line with other behavioral studies (e.g., Kumar and Lee, 2006), it is important to control for macroeconomic news to ensure that the established relations are not simply due to macroeconomic information driving sentiment. We exploit data on economic uncertainty and macroeconomic surprises in the US and find that our results are robust. Limitations are that we cannot control for the arrival of all news and that our macroeconomic variables are only available for the US.

We examine additional predictions regarding the extent to which divergence of sentiment on Facebook may matter for international stock markets. Given that Facebook users also update their status after the close of trading, an interesting prediction is that divergence of sentiment on day t relates to trading volume and stock price volatility on day t +1. We find evidence in line with this prediction, which reduces concerns about reverse causality. We further hypothesize that our relations are stronger when trading is more frequent by individual investors and find some evidence in line with this prediction. Further, our results in this paper depend on how accurately we can capture sentiment in status updates. This approach is expected to be more accurate for English than for other languages (Mihalcea et al., 2007). In line with this expectation, we find stronger results for English-speaking countries.

We exploit the international dimension of our study by contrasting the effects of country-specific and global divergence of sentiment. In a truly globally integrated world, stocks are priced in a global rather than a local equilibrium (e.g., Bekaert and Harvey, 2003). We use the standard deviation of individual countries’ sentiment levels on a given day as a measure of global divergence of sentiment and find that this measure also matters for international stock markets. We predict that while local sentiment may matter more for relatively poorly integrated countries, globally integrated markets are likely to be affected by global sentiment. By using interaction terms between local and global divergence of sentiment and a de facto measure of market integration, we find evidence in line with this prediction.

We contribute to the finance literature in various ways. We first contribute to empirical studies on sentiment levels. We introduce the concept of divergence of sentiment and show that its effect on financial markets goes beyond the effect of the level of sentiment.

Second, we contribute to empirical studies on divergence of opinion. Most of these studies confirm the positive relation between differences of opinion and the probability of trade, using measures based on, for example, the dispersion of analyst forecasts (Ajinkya et al., 1991, Diether et al., 2002, Berkman et al., 2009), open interest on index futures (Bessembinder et al., 1996), and macroeconomic variables based on a household investor survey (Li and Li, 2011). We differ from these studies by specifically focusing on differences in sentiment. Because we find evidence in line with theories of trade based on differences of opinion, our results suggest that previously developed propositions in the disagreement literature apply to the behavioral field.

The remainder of the paper is structured as follows. Section 2 describes our data, and we discuss our main results and robustness tests in Section 3. We examine further predictions in Section 4. Section 5 concludes this study.