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Social Media and Disagreement

Updated: Dec 3, 2022

Under the semi-strong form of market efficiency, information diffusion through all social media should be inconsequential. The information circulated there are considered to be stale or becomes stale almost instantly after the initial post. Rational traders should not react to them, and the transmission of news via social media should not affect trading volume and price.

Yet in a striking rejection of this null, many previous studies convincingly show that investors do react to stale news. One remarkable example of this phenomenon comes from Huberman and Regev (2001), who examine the stock-market behaviour of a single biotechnology firm, EntreMed. On May 3, 1998, the Sunday New York Times carried a front-page story on recent innovations in cancer research, and featured EntreMed prominently. The next day, Monday, May 4, EntreMed stock, which had closed the previous Friday at $12 per share, shot up on heavy volume, ending the day at $52 per share. What is ironic about this episode is that the front-page Times story contained essentially no real news: the substance of the story had been reported five months earlier, in November 1997, in the scientific journal Nature. As we step into the era of mobile internet, with online social networks complementing, and at times replacing traditional media and even offline networks, investors’ belief formation are heavily affected by the contents circulated in their personalized networks. This reality, allows disagreement about the market to spread much more widely (Chawla et al., 2022). If one thinks of the arrival of public news as creating the raw fodder for disagreement as shown in the case of EntreMed, then the increase heterogeneous information coverage caused by social media, can indeed act as a new stimulus to trade.

Another important feature is that, the development of communication technology also fundamentally transforms market participates. Most of retail investors nowadays become increasingly prone to be manipulated, especially for those younger generations who use the internet from their very early age. In the past, people worked offline every day and spend their spare time surfing the Internet for fun. Today, many users live and exist in the digital world and only go offline for eating and sleeping. There has never been a time in human history when so many people are fetching information primarily online 24/7. More likely, more and more investors are eventually reluctant to dive into effortful researches, but instead, to herding interpretations of online analysts (Dim, 2021) or many other user-generated-contents (UGC). In sum, it will be interesting to investigate the aggregated effect of social media interactions on the stock market. In particular, we argue that contents in social media exaggerate market volatility and price distortion to another level. We start by discussing the mechanisms that explain why the interactions between social media and disagreement are crucial. We then show how these mechanisms can influence prices in addition to volume and volatility.

Does contents in social media exaggerate disagreement? And if so, will this harm market efficiency? Below we briefly discuss three theoretical aspects that we think social media tend to change the game thoroughly.

a) Gradual information flow Gradual information flow is an important reason that leads to under-reaction and over-reaction in asset markets (Hong and Stein, 1999). When new information is generated, many factors prevent investors receiving it at a timely manner. Either because of the technology of broadcasting, or investor segmentation and specialization, certain pieces of value-relevant news will arrive in the hands of investors, almost certainly, at different time points. Therefore, even if we assume the piece of information arrives intact at investors and they will process it instantly and uniformly upon receipt, disagreements arise since valuation of each individual shall only be updated sequentially, in the order in which they were received.

The idea of gradual information flow is very established in explaining under-reaction and over-reaction related anomalies. Under-reaction happens when a group of investors receive a valuable information earlier than the industry, but is either small in numbers or they fail to fully aware their information advantage. Over-reaction happens when a group of investors who trade based on stale news because they do not fully realize that they may be at an informational disadvantage. In this sense, a key theoretical subtlety is that disagreement may come from a simple lack of understanding about the structure of the information flow. Thus, we often observe price drift after an eye catching announcement like the front page New York Times story. Even five months after the original Nature article, stock price can rally to $ 52 per share and closed $ 30 per share in the following three weeks. This implies that a large fraction of the impact of the front page Times story was permanent. Although it contains no real news, it feels like information flow slowly across different types of investors and make them draw incorrect inferences.

b) Overloaded attention A lot of existing literature (e.g. see Hirshleifer and Teoh, 2003; Peng and Xiong, 2006; Ben- Rephael et al., 2017) stress the idea that, since human have a limited processing power, investors are incapable to pay attention to all relevant information in a timely manner. Albeit the label “limited attention”often predicts similar effect as gradual information flow does, it further hints at the opposite: if distracted investors tend to under-response to news, they may also over-response to the news which is packaged in an “attention-grabbing”manner. Many social apps, are in nature, designed to be highly propagable around users. And, the way of content creators being compensated also ensures that they are strongly motivated to feed users with contents that creates maximum exposure. As a result, social media is incredibly effective in clustering market sentiments because it is designed to generate overloaded attention (sentiment). We witnessed an extreme impact of social media during the GameStop episode in January 2021 whereby retail traders coordinated using social media and pushed GameStop’s price blindly rocketed into the sky.

c) Heterogeneous priors and selective exposure Even a given news is made publicly available to all investors simultaneously, and even due to an unknown magic, all investors pay adequate attention to it, the news can nevertheless increase the degree of disagreement about the fundamental value of the stock when investors interpret the news differently. This intuitive idea are wide spread and can be dated back to Harris and Raviv (1993) and Kandel and Pearson (1995).

Nowadays, driven by algorithmic recommendations, social media contents are becoming increasingly personalized based on users’ preferences. Such personalization has led to selective exposure in a much bigger scale than those ordinary social interactions where the spread of noise and disinformation are only clustered regionally (Huang et al., 2021). This “innovation”causes investors being overwhelmingly exposed to stale news they are interested in, and the specific perspective they identify with. It becomes clear that, heterogeneous priors held by different investors are inevitably exaggerated and create sharp disagreement.

We now turn to the disagreement as coming from the heterogeneous priors, whereby different investors may reach different conclusions even when simultaneously exposed to the same public news. In a world without constraints on short-selling, the stock price should loosely reflect the value- weighted average opinion of all market participants. However, when investors cannot (will not) short stocks, the price will be systematically biased upward. The reason is evident: if an investor thinks that a given stock is overvalued, given the investor does not sell the stock short, the only thing he can do is just sitting out of the market. In other words, the valuation of optimists will always be reflected in stock prices, whereas the valuations of pessimist will not. As argued in Miller (1977), overpricing is indeed driven by the optimists: prices only go up when the optimist become more optimistic, even if at the same time the pessimists become more pessimistic. Using different proxies for disagreement, both Chen et al. (2002), Diether et al. (2002) and Hong and Stein (2003) develop cross-sectional evidence supporting the Miller’s theory that the degree of overpricing increases as the dispersion of valuations rises.

The original model of Miller (1977) cannot speak to the volume, because it is a static model in which disagreement among investors is fixed so that investors never take further actions until the stock liquidates. Presumably, trading volume in any given interval does not come from the existing level of disagreement, but rather from changes in the level of disagreement. This idea is only testable in a dynamic setting. Following this idea, Harrison and Kreps (1978) is the first to studying the joint behaviour of volume and overpricing. Recent contributions include Scheinkman and Xiong (2003) and Hong et al. (2006). In these models, investors continually update their valuations based on their personal interpretations of incoming news, and trade between any two investors occurs whenever their valuations “cross”—that is, whenever the more optimistic of the two switches to being the more pessimistic. The central prediction of these dynamic models is that a positive correlation exists between trading volume and the degree of overpricing. With this regard, the greater news stimulus associated with this stock, say, a darling in social media should lead to more time-series variance in investors’disagreement, and hence trigger more trading volume and overpricing via the “crossing”effect outlined above.

One way to connect above hypothesis is to think those circulated, explosive and highly selective information may spark increased disagreement among those investors who were already following the stock, and is also likely to grab the attention of those who were not. In either case, in the presence of a short-sales constraint, more trading volume, upwards pressure on the price and overpricing are well expected.


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