How noise trading affects informational efficiency: Evidence from an order-driven market

Highlights

• We investigate how noise trading affects informational efficiency.

• We use full limit order book data from the Australian Securities Exchange.

• In aggregate - noise trading harms price efficiency.

• Noise trading harms informational efficiency of large liquid stocks.

• However, noise traders can be beneficial in small illiquid stocks.

• Our study also has important policy implications.

Abstract

We use full order book data from the Australian Securities Exchange to investigate how noise trading affects informational efficiency of securities prices. In aggregate, noise trading harms price efficiency. However, this is driven mainly by higher levels of noise trading, indicating a non-linear effect. Further, behind the aggregate effects lies rich heterogeneity in how noise trading affects informational efficiency cross-sectionally. Noise trading harms informational efficiency of large and liquid stocks but can be beneficial in small and illiquid stocks, indicating that noise trading affects different stocks differently.

Introduction

An important indicator of financial market quality is informational efficiency, which reflects how well and fast asset prices incorporate new information. Having an informationally efficient financial market has many benefits. For instance, such a market provides accurate price signals that guide market participants. Informationally efficient financial markets also attract more investors and capital, thereby improving liquidity and reducing trading costs. Given the importance of informational efficiency, it is imperative that we understand what drives informational efficiency. One such driver is trading activity,¹ which is critical in the transition to new prices that ultimately reflect information (Hasbrouck, 2017). Without trading, prices become stale and sluggish in impounding new information, resulting in a deterioration in informational efficiency. Therefore, there is a strong expectation that the trading process is a crucial driver of variation in the informational efficiency of asset prices.

One stream of literature considers the market impact of a specific type of investors' trading behavior. For instance, some authors focus on the effects of sophisticated traders such as institutional investors (e.g., Boehmer and Kelley, 2009; Yan and Zhang, 2009; Hendershott et al., 2015; Chen et al., 2020). Other authors investigate the impact of retail traders (e.g., Kaniel et al., 2008; Barber et al., 2009b; Foucault et al., 2011; Fong et al., 2014). Despite the valuable insights, these studies do not provide a holistic view of how the trading process affects financial markets. One apparent reason is that financial markets aggregate information from all market participants, not a selected few. Having a holistic understanding of the trading process can help regulators make unbiased policies.

In this study, we ask the question of whether the aggregate trading process affects the informational efficiency of asset prices. Our first empirical goal is to summarize the aggregate trading process. We focus on one prominent feature of the trading process, which is cross-sectional heterogeneity.² This is because different traders have different trading motives. To measure this cross-sectional dispersion in trading activity, we employ the noise trading proxy of Berkman and Koch (2008), which measures dispersion in daily net-initiated order flow across brokers. This noise trading measure is different from the traditional view of “noise trading” or “noise traders” in several aspects. First, while the term “noise traders” is generally used in the literature to refer to retail/uninformed traders, our noise trading proxy infers the aggregate level of noise trading by examining the trading activity by all traders in the entire market. Second, this noise trading proxy represents a broader concept. For instance, noise trading in an individual/retail investor-dominated market may be viewed as “noise trading” in the context of Glosten and Milgrom (1985) and Kyle (1985). In contrast, noise trading among sophisticated professional investors may create uncertainty about asset fundamentals and reduces transparency of the information environment. In other words, noise trading may be interpreted differently and thus has different effects on informational efficiency.

We study how noise trading affects equity price efficiency in the Australian Securities Exchange (ASX), an order-driven central limit order book market. We measure the noise trading proxy using the ASX full order book data. We choose the ASX setting and full order book data for several reasons. First, the data identify the participating stockbrokers on both sides of each transaction, which allows us to track the trading activity of individual brokers over time. Second, the data contain qualifiers that directly identify the initiator of each transaction, which allows us to calculate net initiated order flow for each broker without relying on a trade classification algorithm. Third, the full order book data are practically error-free as its granularity allows us to trace any outlier record to its original order submission. Therefore, our order flow calculation is highly accurate. Finally, the Australian stock market is more centralized than the U.S. stock market,³ which is more suited to our study because we aim to capture the trading activity in the entire market.

Using a battery of high-frequency informational efficiency metrics and relating them to our proxy for noise trading, our analyses reveal two key findings. First, noise trading is harmful to the informational efficiency of equity prices in aggregate. This aggregate effect leans towards the view that noise trading reflects differences of opinion across market participants, which creates uncertainty about asset valuation and impedes price efficiency. To address the potential endogeneity concern that our results are driven by greater noise trading when the informational efficiency of equity prices is low, we use instrumental variables to isolate the exogenous variation of noise trading. Results based on the two different sets of instruments are largely consistent with the baseline OLS results. This, along with the endogeneity test, suggests a causal link from greater noise trading to the deterioration in equity price efficiency. We also show that the effect of noise trading is non-linear. Specifically, high levels of noise trading tend to harm informational efficiency, while low levels do not. In other words, the reported aggregate (harmful) effect is primarily driven by high levels of noise trading.

Second, further cross-sectional investigation reveals that the aforementioned aggregate effect conceals rich heterogeneity in how noise trading affects informational efficiency cross-sectionally. Specifically, noise trading unequivocally harms the informational efficiency of large and most liquid stocks in our sample. In comparison, this harmful effect is much smaller in magnitudes and only occurs at high levels of noise trading for medium-sized and less liquid stocks. In stark contrast, noise trading is benign in most cases or could even benefit the informational efficiency of small and illiquid stocks in our sample. This observed cross-sectional heterogeneity in the impact of noise trading suggests that noise trading has different effects on different stocks, which merits further elaboration. We then propose and test two potential explanations of this phenomenon.

One plausible explanation for the cross-sectional heterogeneity in the impact of noise trading is variation in the liquidity level across stocks. Empirically, we find that the largest (smallest) stocks in our sample are also the most liquid (illiquid) stocks. Extant studies show that liquidity comes hand in hand with market efficiency (e.g., Chordia et al., 2008). If liquidity is crucial for the increase in market efficiency, the benign or beneficial impact of noise trading observed in small stocks may reflect that noise trading has a stronger effect on small stocks' liquidity. This is because noise trading improves liquidity (Glosten and Milgrom, 1985), which small stocks need the most. For large stocks, however, this liquidity effect is marginal as they are already very liquid. Therefore, the observed cross-sectional heterogeneity in the impact of noise trading on informational efficiency could be caused by its differential impact on stocks' liquidity. In other words, this explanation highlights a “liquidity channel” through which noise trading enhances the informational efficiency of small stocks. It also predicts that noise trading improves small stocks' liquidity more than that of large stocks. Indeed, our empirical tests of this “liquidity channel” document a stronger impact of noise trading on small stocks' liquidity, supporting our first explanation.

Alternatively, the heterogeneity in the types of traders contributing to noise trading may explain the observed cross-sectional heterogeneity in its impact on informational efficiency. Consistent with prior studies (e.g., Boehmer and Kelley, 2009; Yan and Zhang, 2009), we show that institutional investors are predominant in large-cap stocks, whereas retail investors are predominant in small-cap stocks. In such a case, institutional noise trading is interpreted by the market differently than retail noise trading. Noise trading in large-cap stocks is interpreted as belief dispersion among sophisticated institutional investors. Since institutional investors typically have superior information about stock fundamentals, belief dispersion among institutions creates uncertainty about the precision of information or its impact on asset valuation. Uncertainty increases the adverse selection risk for market participants and renders the information environment opaque, leading to a deterioration in large-cap stocks' informational efficiency.

In contrast, noise trading in small-cap stocks can be benign or beneficial to market efficiency. This is because noise trading in small-cap stocks primarily reflects retail traders' behavior. Because retail traders are typically uninformed “noise” traders, financial markets may interpret noise trading in small-cap stocks as “noise trading” in the spirit of Glosten and Milgrom (1985) and Kyle (1985). In such circumstances, noise trading motivates information acquisition and provides camouflage, allowing informed traders to trade private information into prices (e.g., Grossman and Stiglitz, 1980; Kyle, 1985). Thus, noise trading in small-cap stocks can be beneficial to market efficiency. We conduct placebo tests and show that institutional noise trading harms informational efficiency only for large-cap stocks, whereas retail noise trading improves informational efficiency only for small-cap stocks. This additional test lends further support to our alternative explanation of the differential impact of noise trading.

Overall, our study shows that cross-sectional dispersion in trading can significantly affect equity prices' informational efficiency. The dispersion in trading activity reflects traders' unique trading needs. Since trading motives are unobservable in most cases, financial markets can only infer them at best. If financial markets interpret dispersion in trading activity differently on different occasions, then the dispersion in trading activity can have different effects. Indeed, our cross-sectional results provide empirical evidence in support of this theory. We show that dispersion in trading activity is beneficial to the informational efficiency of small-cap stocks but harms the informational efficiency of large-cap stocks, suggesting that financial markets interpret dispersion in trading activity differently across stocks.

Our study contributes to several strands of literature. First, we add to the broad literature on trading activity and order flow. The novelty of our approach is twofold. On one hand, instead of focusing on a particular type of investor (e.g., Huang et al., 2021), we investigate the trading activity in the entire market thereby providing a holistic view of the stock trading process. On the other hand, while most studies focus on how the aggregate trading activity/order flow affects financial markets,⁴ we examine the heterogeneity in trading activity across market participants. Our empirical analyses show that dispersion in trading across market participants also significantly affects stock market efficiency.

Second, our study is related to the empirical literature on measuring belief dispersion. For instance, some studies use analyst forecast dispersion as a proxy for differences of opinion (e.g., Diether et al., 2002; Lee et al., 2019). Jiang and Sun (2014) use mutual funds' active holdings to measure dispersion in fund managers' beliefs. Andreou et al. (2018) use dispersion in options' trading volume across different moneynesses to capture differences in investors' expectations. We show that dispersion in trading activity across investors also has the potential to capture investors' belief dispersion.

Third, our study is also related to recent literature on the effects of belief dispersion. Theoretical models for instance by Banerjee and Kremer (2010), Banerjee (2011), and Atmaz and Basak (2018) predict that investors' belief dispersion affects return volatility and trading volume. Empirically, Carlin et al. (2014) show that disagreement among Wall Street mortgage dealers about prepayment speeds leads to larger trading volume in the mortgage-backed security market, and such volume increase is induced by uncertainty due to dealers' disagreement. Siganos et al. (2017) use positive and negative sentiments from Facebook status updates to construct a daily measure of divergence of sentiment. Utilizing a dataset covering 20 countries, the authors find that a higher divergence of sentiment is positively related to trading volume and stock price volatility. We add to the empirical literature and show specifically that belief dispersion among sophisticated professional investors (measured by dispersion in trading activity) is harmful to equity price efficiency.

Finally, our results are important from a policy perspective. Our cross-sectional evidence shows that taking a “one-size-fits-all” approach to regulating stock trading could have unintended consequences. Instead, it suggests that regulators should take potential cross-sectional differences into account. For instance, the current Financial Transaction Tax (FTT) implemented in European countries is heavily criticized due to its unintended market impact. Our study also calls for a reassessment of this tax policy, especially of the impact of such a tax on different stocks (e.g., market-cap, stock liquidity, ownership structure).

The remainder of this paper is structured as follows. In the next section, we provide arguments and review related literature. Section 3 presents data and the main empirical metrics used in this paper. The empirical approach and main results are discussed in section 4. Finally, section 5 concludes.