Price formation on the Tesla stock market

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Master thesis, 15 hp

Master program in Economics / Master Thesis in Economics 1, 60 hp

Spring term 2021

Price formation on the

Tesla stock market

A study on market impact and

trader types

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Abstract

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2 analyzed data is presented, and methodology is introduced. Later, the empirical results are reviewed and analyzed. Last, a conclusion and a summary will together serve as the link between all the previous sections. This study uses transaction information, from the Eikon database, of all trades that were executed on the Nasdaq stock market, during market open, February – April 2021, and compares it to market close prices. The data is analyzed through two price impact models as well as a method of isolating the economies of each of the trader groups, based on classical price theory. Some empirical evidence from the results of this study can be interpreted to be consistent with many parts of the theory and previous findings presented. To some degree, they indicate a stronger correlation between temporary price movements and the impact of the uninformed individual trader group, than between temporary price movements and the impact of the informed institutional trader group. There are also some clues in the empirical findings, which could suggest that the informed institutional trader group contributes to more long-lasting effects on price movements, although with a negative coefficient. This finding could highlight the difference in information processing that divides the two groups.

2. LITERATURE REVIEW

This section is divided into subsections, where each subsection discusses the theory and empirical findings within its branch of literature. The branches, which are introduced, are the branches relevant to the scope of this thesis. Fields discussed are informational advantage and decision rationality, the efficient market hypothesis, market manipulation, the price-volume relationship, limited arbitrage, proxies of trader type and trade direction, market impact, and classical price theory.

2.1 Informational Advantage and Decision Rationality

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3 Hendershott et al. 2015; Badrinath et al 1995; Gompers and Metrick 2001; Barber and Odean 2000; Odean 1999) attributes the informed characteristic to institutions and the uninformed characteristic to individual traders. It serves as an important assumption for the rest of this thesis.

Using a rational expectation framework, Grossman, and Stiglitz (1980) argue that investors will trade when the marginal benefit of doing so is equal to or exceeds the marginal cost of the trade. In contrast, there is empirical evidence that not all traders are rational, and instead trade when the believed marginal benefit exceeds the marginal cost (Barber and Odean 2000). A trader is determined, by the traditional finance paradigm, to be rational when demonstrating behavior consistent with two principles. First, updating beliefs, after new information is gathered, must happen in accordance with Bayes’ Law. Second, guided by current beliefs, the trader must demonstrate behavior that is acceptable through the lens of Savage’s notion of subjective expected utility (SEU). Individual rationality, along with consistent beliefs, has been assumed in models using the Rational Expectations Equilibrium framework, suggesting that investors can correctly estimate the effect of all information, moreover, has access to all information relevant for accurate estimation. These assumptions have been criticized by behavioral finance literature, which provides empirical findings that contradict these statements on an aggregate level as well as on the level of individual investors (Barberis and Thaler 2002; Sargent 1993). The next few paragraphs address the question of whether the degree of rationality differs between types of investors.

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4 behavior between 1997 and 2002 according to Griffin et al. (2012). Neither can institutions be classified as informed about takeovers, by analysis of Ancerno’s institutional client trade data from 1998 to 2008 (Jegadeesh and Tang 2010; Busse et al. 2012). Hendershott et al. (2015) discuss the results of previous work, that the wit of institutional traders is shown in some studies but not others. They consider the possibility that these results arise because institutional trades are much more prevalent on the NYSE venue than on Nasdaq. The suspicion that institutional traders are informed, is further supported by studies outside the realm of order flow. Stocks with a higher percentage of institutional ownership yield higher returns and are more efficiently priced (Badrinath et al 1995; Sias and Starks 1997; Boehmer and Kelley 2009). Firm and market-level returns can also be predicted using institutional trading (Bohemer and Wu 2008; Boulatov et al. 2013). Compared to stocks with resembling features, Baker et al. (2010) found that the stocks that were bought by institutions performed extraordinarily well, while stocks that were sold by institutions underperformed notably. Other studies that have found evidence that institutions should be classified as informed include (e.g., Gompers and Metric 2001; Chakravarty 2001; Griffin et al. 2003). Hendershott et al. (2015) reason that access to information differs between institutions and non-institutions. Furthermore, the channels by which institutions receive their information, combined with economies of scale, may also contribute to an advantage.

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5 representative bias, belief perseverance, and availability bias. Representative bias means that when attempting to estimate the probability that A belongs to B, the individual focuses too much on the similarities between A and B. Although similarity may indeed matter, the extent, to which it is relevant, is overestimated by the individual falling victim to representative bias. Belief perseverance is the phenomenon where an individual is too invested in her original belief. Irrationality arises when contradicting information has a smaller effect on behavior than information of the individual’s hypothesis. The bias can even cause an individual to think that certain information supports her belief, while in reality, it does the opposite. It is then referred to as confirmation bias. Important to note is that some psychological bias has shown to be prevalent in the behavior of professionals as well (Wermer 2000; Barberis and Thaler 2002; Lord et al. 1979; Kahneman and Tversky 1974).

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to be associated with.

2.2 The Efficient Market Hypothesis and Market Manipulation

The efficient market hypothesis discusses price formation. It provides important implications about how the price should arise, by a theoretical framework that makes assumptions about how agents on the market should behave, and the consequences of those behaviors with regards to price formation. The conclusions about which behaviors should control the price provide insight into the type of trader that should be responsible for those behaviors. According to Fama (1970), the efficient market hypothesis defines an efficient market as a market where the price of the asset “fully reflect available information”. This means that when all the information about an asset is accounted for in the price, the effective market price will arise. Fama (1970) determines the following sufficient, but not necessary, conditions for an efficient market to arise.

1. No transaction costs. 2. All information is costless.

3. Distributions of prices, and implications of current information, are agreed upon by all. Fama (1970) continues by describing situations where these conditions would not be considered necessary. It is inferred that transaction costs do not restrict prices from “fully reflecting available information”. The other two conditions, however, are subtracted with constraints. The number of investors, which possess available information must be sufficient. Furthermore, the implication constraint does not qualify as necessary “unless there are investors who can consistently make better evaluations of available information than are implicit in market prices.” (Fama, 1970). An argument that Cootner (8, p. 232) makes for why the market should always be efficient is the following. “If any substantial group of buyers thought prices were too low, their buying would force up the prices. The reverse would be true for sellers. Except for appreciation due to earnings retention, the conditional expectation of tomorrow’s price, given today’s price, is today’s price”. If the price does not “fully reflect available information”, the investors who hold the information, which is not reflected in the price, will make decisions based on the discrepancy between the information and the price. If the group of investors who have that information available is substantial enough, the price will follow, until it fully reflects available information.

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7 the information as historical prices and returns. In the semi-strong form tests, information is modeled as all the information that has been made public. Finally, the strong form tests include controlling for the possibility of information, where only a select group of investors have access (Fama 1970). Hence, markets, where prices reflect historical prices and returns, are deemed efficient on the weak level. Markets where prices reflect, not only past prices and returns but also all public information, are determined to be efficient on the semi-strong level. For markets to be strongly efficient, prices must reflect all the stated information, furthermore, they even reflect information only a few investors would have. A previously stated argument by Cootner (8, p. 232) is that if a substantial enough group of investors holds a specific type of information, the price will, by that group, be driven to the point where the information held by the group is reflected in the price. Logically, the market should therefore be efficient to the level that corresponds to the information that is available to the substantial group of traders. If different groups possess different sets of information, the groups might drive the price in opposite directions. Using the Fama (1970) framework, the price would settle closer to the price that is, by the most influential group, estimated to be the value. The efficient market hypothesis framework is traditionally used to argue for a natural steer of prices toward fundamentals, however, maybe the logic of Fama (1970) and Cootner (8, p. 232) can be used differently. If it is observed that prices steer away from fundamentals, as Strauss and Smith (2019) claim that the Tesla stock price did in 2016, could that instead mean that the substantial group of investors is investors informed to a lesser degree? Nevertheless, this would require agreeing on the value of the stock within the group. Dispersion of beliefs literature, which is later presented, suggests that this trait is unlikely for the uninformed individual trader group to acquire. The lack of skill and resources, attributed to the group in the previous subsection, should also be an issue in understanding how to exploit perceived arbitrage. There is no important evidence that markets are not always efficient on the semi-strong level according to Fama (1970), however, consensus on whether the effective market hypothesis holds or not does not appear in this subsection-section, since complexity only continues to increase as other areas of the literature are introduced.

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8 efficiency. More recent studies have conflicting results. Some found evidence that suggests rejecting the Random Walk hypothesis (e.g Worthington and Higgs 2004, Smith and Ryoo 2003), while others found evidence supporting the Random Walk hypothesis (e.g., Borges 2010).

An alternative hypothesis that regained popularity after Fama and French (1988) is the mean-reverting hypothesis. The notion that the price of an asset contains a long-term equilibrium price as well as a temporary component, that is decreasing, was discussed as early as in Crowles and Jones (1937). According to Gallagher and Taylor (2002) studies such as (e.g., Granger and Mortensen 1963; Fama 1965, 1970; LeRoy 1982) failed to reject the rejectable hypothesis of unpredictability in price movement. Predictable components have later been found in (e.g., Lo and McKinlay 1988; Cochrane 1994; Lee 1995; Fama and French 1988; Gallagher and Taylor 2002). The empirical results of De Bondt and Thaler (1985) suggest that the fundamental effects are only applicable over very long time periods. Important to remember is that all criticism of the Random Walk hypothesis is not necessarily a criticism of the efficient market hypothesis. A Random Walk, as stated, implies a larger set of assumptions than what is necessary for the price to “fully reflect available information” (Fama 1970). Gallagher and Taylor (2002) further confirm that the mean-reverting price can exist on an efficient market. To complicate things, the mean-reverting hypothesis has been met with some criticism as well, directed towards the most popular models as well as the claimed discontinuation of the phenomenon (Richardson and Stock 1989; Jegadeesh 1990; Kim, Nelson, and Startz 1991).

In this subsection, the possibility that one type of trader has the resources to manipulate the market price is also explored. If one type of trader could endogenously direct the market price at their wish, that could have vital implications for this thesis.

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9 stocks than it is in the context of high-volume expensive stocks. This is the technique where an informed investor impacts the price by executing trades themselves. The change in price that is caused by this behavior is meant to impact the analysis and decision-making of other traders to allow for arbitrage (e.g., Vila 1989, Benabou and Laroque 1992, Allen and Gale 1992). According to this literature, informed traders may have a resource for impacting the price, that is inaccessible to uninformed individual traders. Models that are used, to view price impact in this thesis, include the impact of such trades. However, the impact that is caused by attempted market manipulation is not distinguished from the impact of other trades. It will consequently not be directly observed, though it could influence the results.

2.3 The Price-Volume Relationship and Limited Arbitrage

This subsection aims to summarize the literature, which revolves around the relationship between price and volume. Many papers claim there exists a positive relationship between price and volume. It is even regarded as a stylized fact within the financial literature and Karpoff (1987) refers to eighteen separate studies, which show evidence of this correlation. This relationship is argued by some to be bidirectional, although not all empirical evidence supports

this hypothesis. In any case, evidence at least suggests that

volume is positively correlated with price changes in high order (Karpoff 1987; Baeck and Brock 1992; Tauchen et al.1996; Liu et al. 2015). Since this thesis aims to predict price from the volume of two different investor types, the literature, which discusses how these variables interact with each other, will be important to the analysis of the results. The theory on this subject stems from the mixture of distribution hypothesis (MDH) and has since been complemented by adding sequential arrival of information hypothesis (SAIH), dispersion of beliefs, and noise trading.

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10 and Daigler (2008), using artificial data. MDH models are criticized for not having the capacity to reason whether the relationship arises through volume of trades or size of trades, especially looking at empirical studies on real data. After all, MDH literature seems to have reached a consensus regarding the hypothesis that the cause of the correlation is information flow. However, opinions differ as to where the effect of information flow manifests itself. Xu and Wu (1999) argue that informed traders trade in bulk, and hence the correlation would be impacted by the size of trades. In contrast, Giot et al. (2010) and Louichi (2011) raised the argument that an informed investor has the option to instead make many small trades in an effort to disguise herself. In such situations, trade volume would instead be the root. Despite this argument, the view that informed traders choose to trade in larger quantities, than uninformed traders, is supported by Easley and O’Hara (1987) and Saglam et al. (2018).

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11 informed trade and increase possibilities of arbitrage, which hence should increase the performance of the informed group (Kyle 1985). This point is connected to the discussion of market impact, which is held later in this thesis. Further adding to the discussion of asymmetries in the impact of information flow, Admati and Pfleiderer (1988) argue that recent trade volume impacts the way volume interacts with volatility. The argument aligns with the empirical claim by Bessembinder and Seguin (1993), that the nature of an informational shock will affect the correlation between volume and volatility. Studying the behavior of eight separate future markets, Bessembinder and Seguin (1993) find that unexpected informational shocks that lead to increased expected volatility have a higher effect on actual volatility than informational shocks that lead to decreased expected volatility. The expectation is based on, for example, how fundamental analysis of the price is affected by the new information. Therefore, unexpected volatility would be volatility after new information that deviates from what fundamental analysis would suggest. Positive volume shocks have a greater impact on the price-volume relationship compared to negative volume shocks. Nevertheless, a market with a deep market depth is affected less by these shocks. Therefore, market depth is a factor that is negatively correlated with the effect of volume changes on volatility. Market depth has a negative correlation with unexpected order flows since unexpected order flows are associated with deviations from intrinsic value. Despite the fact that in the study, unexpected volume is inferred to primarily arise from less informed trading, and unexpected volume is more heavily correlated with price changes, they highlight that market depth can mitigate the effect of unexpected volume on volatility. (Chen and Daigler 2008; Daigler and Wiley 1993; Bessembinder and Seguin 1993). It is important to note that the methodology of Bessembinder and Seguin (1993), may to a small degree limit the relevancy of their discoveries in the context of this thesis. Because their empirical results are within the scope of futures markets, open interest is modeled as the activity of uninformed hedgers. Informed traders are modeled as speculators. This thesis discusses the situation of the Tesla stock spot market, where hedgers do not exist in the same sense. Accordingly, market depth will not have the same implications across these two papers. However, the inference that a heightened price-volume relationship is associated with behavior that is unexpected rather than rational, will be vital in constructing hypotheses.

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12 According to the theory of dispersion of beliefs, these differences are contributors to unexpected volume and excess volatility. Additionally, the greater the dispersion of beliefs is, within a group of traders, the greater is that group’s contribution to the disparities between actual volume/volatility and their respective equilibriums. The dispersion of beliefs within the uninformed group of traders is specifically identified as the cause for these circumstances within Shalen’s model. Price movements are exaggerated by uninformed traders (Shalen 1993; Harris and Raviv 1993; Chen and Daigler 2008). Evidence for the impact of dispersion of beliefs on the volume-price relationship was presented by Daigler and Wiley (1999). Chen and Daigler (2008) increase precision by observing that excessive volume, caused by dispersion of beliefs within the uninformed group, was the only form of excess volatility that could be explained in their study. In Chen and Daigler (2008), controlling for this even resulted in a rejection of the hypothesis that volume should cause excess volatility.

The last discussion to be held about the volume-price relationship has been briefly touched on already. It is the one about noise traders. Theory on noise traders originated from DeLong, Shleifer, Summers, and Waldmann (1990a, 1990b), however, as stated, the characteristic, of uninformed traders, to contribute to noise in the price formation process, was already to some extent reviewed by Kyle (1985). It rests on the assumption that a sufficiently dominant group in the market will make trades that causes the market price to deviate from fundamentals. A contribution of noise trading theory is that noise not only confuses market makers, but also triggers a response from informed traders. Informed traders will begin to deviate from fundamentals to instead direct efforts towards exploiting the arbitrage that has been created in the market. Empirical evidence of the presence of this phenomenon, in the market of stock index futures, is found in Chen and Daigler (2008). Next, a discussion of limited arbitrage questions the ability of informed investors to exploit the noise created by the presence of uninformed traders. Limited arbitrage literature does so by providing alternatives to the claims

of the traditional efficient market hypothesis.

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13 seen to cause mispricing to the extent to where informed traders are unable to drive the price back to fundamentals. The phenomenon is heavily related to noise trading. A central point of limited arbitrage literature is to show that noise trading in some cases controls the price to a larger extent than rational trading does. In contrast, some have argued that such a circumstance could never sustain the pressure of informed traders. Since opportunity will remain when the asset remains mispriced, informed traders will always exploit mispricing until the asset is no longer mispriced. However, insight, as to what strategies for exploiting mispricing may entail, has left behavioral finance literature questioning the accuracy of the argument. Behavioral finance literature argues that some deviations from fundamental value, in real asset prices, can remain because of the riskiness and costliness of addressing them. The existence of riskiness in the perfectly rational strategy for exploitation is contradictory to the existence of arbitrage. Hence, rational behavior is, instead, in some circumstances the characteristic that prevents the actions EMH literature would predict. Accordingly, behavioral finance literature argues that a lack of arbitrage is not a definite indicator that the real price matches the fundamental price (Barberis and Thaler 2002).

An important piece of evidence in favor of limited arbitrage is the analysis in Froot and Dabora (1999). It is executed on the difference in price movements between the Shell Transport stock and Royal Dutch stock. These two companies merged in a 60:40 contract in 1907, while they remained to be traded separately on different stock exchanges. A simple arbitrage strategy would be able to take advantage of mispricing. Although various hedge funds attempted this, as prices deviated heavily from parity, disparities between parity and real prices remained over a long time, furthermore, escalated over a period of six months in 1983. Another indication of mispricing is found in Harris and Gurel (1986) and Schleifer (1986), who find that inclusion in S&P 500 on average boosts stock price by 3.5 percent. In some cases, inclusion in the index has had a much more considerable effect.

2.4 Proxies of Trader Type and Trade Direction

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14 Approaches, such as this one, are beyond the scope of this thesis. As an alternative, the solution will be to use proxies of trader type characteristics and define the groups according to these proxies. In this paragraph, the aim is to discuss the literature behind the proxies that could define each type of trader. These proxies are needed to support the choices made in the methodology section.

A fair summary of the subsection about informational advantage and decision making would indicate that there exists a strong link between informed traders and institutional traders. Though controversy has arisen around estimating the degree of power that this advantage brings, it can be derived that differences in information, skill, and capital contribute to vastly different actions, taken on the market, between the two types of traders. One perspective presented is that uninformed traders contribute more to market depth and noise than informed traders do. Meanwhile, informed traders, according to some theory, trade larger quantities and experience higher returns. Easley and O’Hara (1987) suggest that the probability that a trade is initiated by an informed trader is positively correlated with the trade size of the transaction. Kyle (1985) also points towards a relationship between trade size and informational advantage. Empirical evidence of this relationship is provided by Saglam (2018) in studying skill differences of institutional traders. Liu et al. (2015) find evidence, consistent with theory, that the group of investors, which lacks private information, is in the majority on the market.

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15 Lee and Radhakrishna (2000) stress that they do not mean to say that the cutoff of $10 000 is perfect. The amount of money involved in a trade varied in both categories depending on firm size, in their study. Furthermore, sizes do not immediately adjust to price volatility, which means that price changes can cause misspecification. Finally, they proposed a revised model for trader type proxy that introduces a zone of uncertainty. In the new model, introduced by Lee and Radhakrishna (2000) and supported by their dataset, sizes below $5000 belong to individuals, and sizes above $50 000 belonging to institutions. Sizes in between do not belong to either category, as this measure limits the risk of transactions being incorrectly specified.

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16 2.5 Market Impact

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17 of relevance to strategy between the two groups, all trades have a temporary market impact to some extent. Though interestingly, block trades (trades with significantly large sizes) seem to alter the price permanently. The temporary market impact of an arbitrary trade has been shown to be affected by absolute sizes. The relationship seems to be concave and has many times been estimated to follow the square root model, which estimates the relationship to have a 0,5 exponent. This means that using a higher trade size will drive up the transaction cost of market impact, however, the increase will decrease on the margin (Easley and O’Hara, 1986; Stoll, 1979; Ho and Stoll, 1981; O’Hara and Oldfield, 1986; Fraenkle et al., 2011; Almgren, 2005).

Fraenkle et al. (2011) conduct a study to mitigate the problem of the market impact transaction cost through a VWAP algorithm. To this thesis, the most relevant aspect of their work is the definition and measurement characteristics of market impact. Market impact is according to Fraenkle et al. (2011) determined to be the influence that an investor’s order has on price change. They find that the variable that most heavily contributes to market impact is by far participation rate, which is measured as the ratio between the transaction size and the total trade volume during the period. Theory from papers such as Almgren (2005) suggests that plotting the relationship between participation rate and market impact yields a concave graph. Fraenkle et al. (2011) use both a linear model and a power-law model in their study. Nevertheless, it is important to note that the rationale for the linear model is heavily influenced by the practicality of such a model in constructing optimal strategies for lowering transaction costs. The linear model used is the one below. Market impact is measured per stock in basis points (0,01%) of the execution price.

M(v) = m ∗ v + b

M stands for market impact, v is the participation rate, and m and b are parameters. The power-law model alternative, which perhaps has more support in the literature, is presented here.

M(x) = m ∗ v^a + b

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18 They determine ‘a’ to be 0,534 +/- 0,115 across all markets. It is consistent with many other papers within the literature, which estimate the exponent to be close to 0,5. Nevertheless, their model is based on Almgren (2005). Almgren (2005) refutes the square root model, analyzing 700 000 stock trades through Citigroup Equity Trading

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19 orders by skilled investors have permanent price impact to a larger extent. One reason why market impact is modeled to increase with the size is, as discussed, the probability increase in that the transaction is executed from an informed position, making it more indicative of future prices. Nevertheless, the results of Saglam et al. (2019) show that the heterogeneity in skill among institutional investors contributes to bias in the estimate. To measure price impact properly, they suggest a skill-term should be included.

2.6 Classical and Neoclassical Price Theory

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20 that a purchase will be realized when the perceived benefits from the purchase, for the purchaser, exceeds the value of what is yielded by the agent. It will be within her willingness to pay. If the perceived value does not exceed the value that is yielded (the price), it will not be purchased. In that case, the price is beyond her willingness to pay. The increase or decrease in utility that is experienced by the agent when purchasing a good cannot be observed through the classical model, however, the point where the difference in utility shifts from being positive to being negative can in some cases be observed. It is the point where the decision shifts from being in favor of purchase to be avoiding the purchase. If the price of a good, that belongs to the agent, exceeds the price, which the agent perceives the good to have, the agent would want to trade it, since a trade would increase the utility of the agent. This is the interpretation of the supplier in the classical model. Since the willingness to pay is the extreme point for the choice to purchase, it is the same as the value. Hence, when the agent is faced with the decision of the supplier, she is willing to accept any price beyond the extreme point of where the agent’s willingness to pay would be had she faced the choice of the consumer.

3. PROBLEM AND HYPOTHESIS

Many different branches of literature are related to the subject of price formation in the financial markets. Different branches may answer slightly different questions, however, the way they interact with each other to form overall conclusions regarding how price is formed may not always be crystal clear. Some arguments may be great complements to each other, while other arguments are directly contracting to each other. The contradicting arguments may make consensus, in how the price of a stock is formed, notably difficult. The specific case of the Tesla stock price may exacerbate this difficulty. It might fit the hypotheses of some theory perfectly, while this situation would have to be considered an exception to other standpoints. Critical issues to consider with regards to the Tesla stock are deep market depth and the unexpected reactions of the stock price to certain information. Gaining further understanding of whether the large traders, such as institutions, are the most influential to price formation on the Tesla stock market, or whether small traders, such as individual investors can dominate, may bring insight that is important to future transaction decisions made by both private individuals and institutions.

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22 Speculatively, a potential consequence could be that price effects from the uninformed group largely cancel out, whereas effects from the informed group work in unison.

In conclusion, there are compelling arguments for hypothesizing in either direction. Be that as it may, it is inferred that the relevant literature provides slightly more evidence for the case that uninformed, individual, traders, as a group, contribute more to price formation on a temporary basis than informed, institutional, investors, do as a group. Although deep market depth may limit unexpected volatility, this is the first hypothesis of the current thesis. An important assumption of the efficient market hypothesis that is needed to conclude that price will form based on fundamentals, is that the group, driving the price back to fundamentals, is substantial enough (Fama, 1970). It may be that compared to noise traders present in the Tesla stock market, this assumption does not hold. Nevertheless, SAIH literature demonstrates that the uninformed group receives information later than the informed group, and consequently has a lagged response to the same information. It is further acknowledged, by the literature of informational advantage, that informed traders make better predictions about future prices, and therefore reach higher returns with their portfolios. Hence, the second hypothesis is that the behavior of the informed, institutional, trader group correlates more with long-run changes in the Tesla stock, than the behavior of the uninformed, individual, trader group. One predicted reason for this being that lagged behavior of the informed group is by this thesis predicted to correlate with the behavior of the uninformed, individual, trader group, while the opposite is predicted not to hold. Another predicted reason is that there is heterogeneity in permanent market impact within theinstitutional trader group (Saglam et al. 2019), where skilled investors impact the price more heavily on a permanent basis. This relationship is predicted to translate to the relationship between institutions and individual investors, where institutions, in general, have shown to exhibit a higher skill level than individual traders.

4. DATA

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23 5. METHODOLOGY

The methodology will feature two models that are going to be tested on the data. First, a price impact method. Then, a method that isolates the economy of individual traders from that of institutional traders and vice versa. The trades are divided into two groups. One group will serve as the proxy for individual traders, and one will serve as the proxy for the institutional traders. Each trade will be appointed a group depending on the USD turnover of each trade, which it is inferred to be most consistent with. If turnover exceeds the amount, decided on, the trade is put into the “institutional trader” category. If turnover is less than the cutoff, the trade is put into the “individual trader” category. This study has elected to feature both turnover models that are reviewed in the literature review section. It means that all regressions are performed with proxies where trades below $10 000 are determined to belong to an individual, whereas a trade on or above $10 000 is determined to be initiated by an institution. Likewise, all regressions are performed with proxies where a trade on or below $5 000 is attributed to the “individual trader” category, and trades on or above $50 000 are put in the “institutional trader category”. Where the latter is issued, transactions that are in between $5 000 and $50 000 are excluded. The model of Lee and Ready (1991) is adopted to dictate whether the stocks in a transaction are bought or sold by the type that the trade has been determined to belong to.

5.1 Price Impact Method

The first model chosen to measure the impact of each trader type on the price of the Tesla stock uses a measurement of market impact. As the market impact measurement estimates the impact of a particular trade on the price, it seems intuitive that aggregated market impact for a specific group gives the aggregated change which that group has caused by the execution of the trades they have initiated. The values will be aggregated one day at a time. This assumes that during a given day, the fundamental or perceived actual value of the stock does not change. It is important to note that this assumption does not always hold, which limits the accuracy of the results. The current study will use both the linear model and the power-law model by (e.g., Fraenkle, 2010; Almgren, 2005; Saglam, 2019) to estimate price impact.

Linear Model: M(v) = m ∗ v + b

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24 Since the model used in this thesis is not meant to be used for making future predictions but is rather meant for making inferences on past events, this study would have the liberty of selecting market return and relative tick size to develop a proxy for parameters ‘m’ and ‘b’. as suggested by Fraenkle (2010). However, as the perfect relationship, between our parameters and their proxies, remains uncertain, the current thesis bases market impact on participation rate solely. This might limit the accuracy somewhat. Furthermore, including other variables, such as a skill-term, would probably be wise. However, this is beyond the scope of this thesis, as it requires information of which our data set does not carry. Saglam (2019) for instance uses trader ID to attribute a skill-term to a trader. The data used in this thesis does not include any identification of traders. Without such a skill variable, the results of Saglam (2019) imply that our results may hold some bias. Tick direction will still be included to determine the direction of the impact. Functions for market impact per trade thereby become,

Linear Model: M(v) = tick direction* participation rate*size

Power-law model: M(x) = tick direction* participation rate^0,5*size

Aggregated market impacts of each day of the two groups form a new dataset that is used to model market return during the analyzed period. The objective is to investigate whether there is a difference in the significance of the effects, running from market impact to price fluctuations, between the two groups. Price fluctuations are first modeled as the difference in close price between one day to the next. However, as the difference between close prices depends not only on the transactions made in market open hours but also on pre-market orders, this model might have low explanatory value. The solution opted for in that case is to use return, i.e., the difference between open and close prices each day, as an alternative to the dependent variable. Correlation between return and lagged market impact will also be estimated to investigate whether any group has a more long-lasting impact on price.

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25 for the goodness of fit, a Durbin-Watson test for autocorrelation in residuals, a VIF test for checking multicollinearity, and a Ramsey Reset test for misspecification. When lags are included, the Durbin-Watson test might not be reliable, and therefore residual plots are therefore provided instead. This may provide further reason to believe those same day transactions executed by the uninformed, individual, group, explain price formation most accurately.

5.2 Isolated Economies Method

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27 6. RESULTS AND ANALYSIS

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28 influence the price at any given day, the price effect that is seen through the market impact of individual investors may be caused by information that institutional investors had one day earlier. The negative effect might then be explained by dispersion on beliefs literature, and informational advantage literature, which both provide reasons for why individuals respond to information differently from institutions. This is supported by results presented in tables 21-24 in the appendix, where there is a significantly negative relationship between the market impact of individual investors, and lagged market impact of institutional investors. The relationship holds for both proxy alternatives in the power rule model, as well as in the linear model. The results of the power rule models are largely consistent with those of the linear model. However, they cannot be trusted to the same extent since the power rule models fail the Ramsey-Reset test of misspecification in their original form. Models that rely solely on lags have much less explanatory power than models including variables of the same-day return, judged on adjusted R^2 values. This indicates that same-day transactions carry more information of the return, than

past transactions do.

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29 institutional investors in the modeled economy may change inferences about the group, as these investors tend to demonstrate behavior that is inconsistent with the behavior of the rest of the group.

7. SUMMARY AND CONCLUSION

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Appendix

Table #1. Dickey-Fuller test for unit root of dependent variable 1. (Close-price difference).

Dickey-Fuller test for unit root Number of obs = 61 Interpolated Dickey-Fuller ---

Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value Z(t) -9.286 -3.565 -2.921 -2.596 MacKinnon approximate p-value for Z(t) = 0.0000

D.dclose Coef. Std. Err. t P>t [95% Conf. Interval]

dclose

L1. -1.187116 .127841 -9.29 0.000 -1.442926 -.9313071 _cons -3.177285 3.756392 -0.85 0.401 -10.69381 4.339239

Table #2. Dickey-Fuller test for unit root test of dependent variable 2. (Daily return)

D.nreturn Coef. Std. Err. t P>t [95% Conf. Interval] nreturn

L1. -1.228796 .127591 -9.63 0.000 -1.484016 -.9735762 _cons -3.306563 3.297827 -1.00 0.320 -9.903199 3.290073

Table #3. Dickey-Fuller test for unit root test of independent variable 1. (institutions). Trader type proxies: $5 000, $50 000. Market impact model: Linear.

D.large Coef. Std. Err. t P>t [95% Conf. Interval] large

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Table #4. Dickey-Fuller test for unit root test of independent variable 2. (individuals). Trader type proxies: $5 000, $50 000. Market impact model: Linear.

D.small Coef. Std. Err. t P>t [95% Conf. Interval] small

L1. -.7681407 .1248696 -6.15 0.000 -1.017917 -.5183642 _cons -.0013149 .0003828 -3.44 0.001 -.0020806 -.0005493

Table #5. Dickey-Fuller test for unit root test of independent variable 1. (institutions). Trader type proxies: $5 000, $50 000. Market impact model: Power-rule.

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Table #6. Dickey-Fuller test for unit root test of independent variable 2. (individuals). Trader type proxies: $5 000, $50 000. Market impact model: Power-rule.

L1. -.7582807 .1247238 -6.08 0.000 -1.007765 -.508796 _cons -.820039 .235685 -3.48 0.001 -1.291479 -.3485987

Table #7. Dickey-Fuller test for unit root test of independent variable 1. (institutions). Trader type proxies: $10 000, $10 000. Market impact model: Linear.

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Table #8. Dickey-Fuller test for unit root test of independent variable 2. (individuals). Trader type proxies: $10 000, $10 000. Market impact model: Linear.

L1. -.9387891 .12731 -7.37 0.000 -1.193447 -.6841312 _cons -.0068654 .0018765 -3.66 0.001 -.0106189 -.0031118

Table #9. Dickey-Fuller test for unit root test of independent variable 1. (institutions). Trader type proxies: $10 000, $10 000. Market impact model: Power-rule.

L1. -1.093862 .1304215 -8.39 0.000 -1.354835 -.8328892 _cons 3478.43 1113.202 3.12 0.003 1250.918 5705.942

Table #10. Dickey-Fuller test for unit root test of independent variable 2. (individuals). Trader type proxies: $10 000, $10 000. Market impact model: Power-rule.

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Table #11. OLS regression. Dependent variable: One day difference in close price. Independent variables: institutional trader transactions (large), individual trader transactions (small).

Trader type proxies: $50 000, $5 000. Market impact model: Linear.

Diagnostics corresponding to table #11.

Prob > F = 0.2225 F(3, 56) = 1.51 Ho: model has no omitted variables

Ramsey RESET test using powers of the fitted values of dclose

_cons 11.13392 2.865733 3.89 0.000 5.3996 16.86824 small 8965.887 862.3577 10.40 0.000 7240.314 10691.46 large .0043667 .001957 2.23 0.029 .0004508 .0082827 dclose Coef. Std. Err. t P>|t| [95% Conf. Interval] Total 53444.36 61 876.13705 Root MSE = 16.774 Adj R-squared = 0.6788 Residual 16601.3774 59 281.379277 R-squared = 0.6894 Model 36842.9827 2 18421.4913 Prob > F = 0.0000 F(2, 59) = 65.47 Source SS df MS Number of obs = 62

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Table #12. OLS regression. Dependent variable: One day difference in close price. Independent variable individual trader transactions (small). Trader type proxies: $50 000, $5 000. Market impact model: Linear.

Diagnostics corresponding to table #12

Table #13. OLS regression. Dependent variable: One day difference in close price. Independent variables: institutional trader transactions with one day lag (large_1), individual trader transactions with one day lag (small_L1). Trader type proxies: $50 000, $5 000. Market impact model: Linear.

_cons 5.575951 4.612427 1.21 0.232 -3.653494 14.8054 small_L1 1124.832 1382.02 0.81 0.419 -1640.584 3890.247 large_L1 -.0119586 .0031649 -3.78 0.000 -.0182916 -.0056257 dclose Coef. Std. Err. t P>|t| [95% Conf. Interval] Total 53444.36 61 876.13705 Root MSE = 27.005 Adj R-squared = 0.1676 Residual 43027.7299 59 729.283558 R-squared = 0.1949 Model 10416.6301 2 5208.31505 Prob > F = 0.0017 F(2, 59) = 7.14 Source SS df MS Number of obs = 62 _cons 13.97547 2.650997 5.27 0.000 8.672688 19.27826 small 9413.198 866.098 10.87 0.000 7680.744 11145.65 dclose Coef. Std. Err. t P>|t| [95% Conf. Interval] Total 53444.36 61 876.13705 Root MSE = 17.322 Adj R-squared = 0.6575 Residual 18002.3514 60 300.03919 R-squared = 0.6632 Model 35442.0086 1 35442.0086 Prob > F = 0.0000 F(1, 60) = 118.12 Source SS df MS Number of obs = 62 . regress dclose small

Prob > F = 0.5808 F(3, 57) = 0.66 Ho: model has no omitted variables