The effect of short selling on return momentums : an empirical analysis of the SEC’s Reg SHO pilot

(1)

MSc Finance, Quantitative Finance

The Effect of Short Selling

on Return Momentums

An empirical analysis of the SEC’s Reg SHO pilot

Author: Elke Schreur

Student number: 11363754

Supervisor: dr. T. Caskurlu

01-07-2018

ABSTRACT

This article investigates the effect of short selling on return momentums. The effect of short selling is proxied by the pilot announced by the Securities and Exchange Commission (SEC) in 2004. The pilot implies removing price tests for a set of pilot stocks. Although, the results are insignificant, they present a relationship between short selling and momentum. The winner portfolio indicates that pilot firms have a lower return during the pilot than control firms. This implies that the pilot portfolio show less momentum than the control portfolio. Further research on this topic based on additional variables or a different methodology is necessary to fully understand the relationship between short selling and momentum. Besides, the significance in this research has improvements.

(2)

ii

Statement of Originality

This document is written by Elke Schreur who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

(3)

iii

1. Introduction

Stock market anomalies have been the focal point of many prior studies. One of those anomalies is the momentum effect in stock returns. The reason behind momentum is still unexplained. Daniel, Klos & Rottke (2017) argue that the momentum effect is caused by short-sale constraints. This research uses the Regulation Short sale pilot, in short Reg SHO pilot, of the Securities and Exchange Commission (SEC) to further examine the effects of short selling on return momentums. The empirical environment of the SEC’s Reg SHO pilot is used as a randomized experiment to investigate the effect of short selling on return momentums.

The momentum effect consists of returns and prices that follow a certain positive or negative trend so that past returns are positively correlated with future returns. Momentum investment strategies are proven to be highly profitable. Many different regions and firm size groups show momentum effects (Fama & French, 2012). These momentum investment strategies can also be based on firm, industry or country specific characteristics. Research has shown that investors are able to make profits from investment strategies based on momentum (Fama & French, 2012; Grinblatt & Moskowitz, 1999; Jegadeesh & Titman, 1993), but why and how this seasonal movement is happening remains unexplained.

One explanation is that momentum occurs because the fundamentals of companies change in a positive manner. New information can be announced which has a positive effect on the company. For example, a company is doing well in expanding or introducing more efficient ways to make production. Besides, a company could have successfully acquired a business line which increases company value. Or, a company appoints a new CEO from who is believed to have the power and ability to change things. This news can affect the fundamental value of a company. Though, advocating that momentum is caused by this would imply that investors do not act rational as the Efficient Market Hypothesis suggests and that emotions cloud investors’ judgement.

Another explanation for momentum is that short sale constraints cause momentum patterns to occur (Daniel, Klos & Rottke, 2017). Their research focuses on US stock markets and investigates the effect of short sale constraints and optimism on overpricing. Firms which are short sale constraint show more over pricing and this effect is present for a longer period than firms which are not short sale constraint. Therefore, being short sale constraint can be a cause of momentum. To further analyze this hypothesis, this research makes use of the SEC’s Reg SHO pilot to investigate the effect of short selling on return momentums.

(5)

2 The Regulation short sale pilot was announced by the SEC in 2004. The aim of the pilot is testing the effect on market quality by removing the NASDAQ bid test and uptick rule for a sample of listed firms. These price restrictions are rules for short selling. The bid test implies that short sales are restricted if the bid is less than the previous selling price. The uptick rule is similar to the bid test. The removal of these price tests in the pilot are used to test the effect on market quality measured by liquidity, price efficiency and market volatility. There has been other research using this pilot as a randomized experiment to test other relationships, like the relationship between corporate behavior and stock prices (Grullon, Michenaud & Weston, 2015).

The pilot firms are chosen from the Russell 3000 Index. The Russell 3000 Index tracks the performance of the largest 3000 stocks of the entire U.S. stock market. For the pilot, the Russell 3000 Index is sorted by market capitalization. From then on, every third firm is placed in the pilot sample, starting at the second firm. So, the second, fifth, eighth and so on are placed in the pilot sample. Consequently, all other firms of the Russell3000 are placed in the control sample. The pilot firms are not subject to the price restrictions and are thus the treated firms.

This research focuses on the relationship between short selling and momentum. The SEC’s Reg SHO pilot provides the opportunity to test this and eliminate the endogeneity problem. Endogeneity concerns are caused by omitted variables and cause wrong results (Roberts & Whited, 2013). This research investigates the momentum effect which is measured by the cumulative abnormal return, in short CAR. Changes in CARs can be the result of many different reasons. Stock prices can change because interest rates are changing or news which affects the company is announced. The use of the Reg SHO pilot shows the effect of removing the price tests on return momentums. The identified change can now be appointed to the pilot and thus short selling. The pilot lasts from May 2005 until July 2007. This causes the use of three time periods; before the pilot, during the pilot and after the pilot. The total time frame for which returns are collected is 2003 until 2009.

The portfolios are created by adapting the research methodology of Jegadeesh and Titman (1993). The control and pilot sample are both used to construct investment portfolios. The best and worst performing 10% of each sample are placed in the winner portfolio, the long position, and loser portfolio, the short position. The formation of the portfolios is based on the performance of the past 3 or 6 months. Then each portfolio is either held for 3 or 6 months. The effect of short selling on momentum returns is investigated by using difference-in-difference methodology. This methodology allows to investigate the different effects on the CARs from treatment and the time periods. Besides, it presents treatment effects which show the effect of being treated. Three time periods are used in this research, which results in a treatment effect during the pilot and a treatment effect after the pilot.

(6)

3 Previous literature advocates that short selling constraints cause momentum effects. This gives rise to the hypothesis that the control sample should present more momentum than the pilot sample. The restrictions are lifted for the pilot sample, so that the prices should reflect the fundamental value of a firm. First, returns themselves need to be different from zero, after which can be discussed if the CARs from the control and treated sample are different. The Wilcoxon signed-rank test is used to examine the returns. The results show that the returns are not statistically different from zero, some returns are, but this is only true for a small portion of the results. Besides, CARs of the pilot sample are in a smaller range than those of the control sample. This could imply that the pilot sample is less sensitive, which indicates that short selling has an effect on the momentum effect.

The main objective of this paper is to investigate the relationship between short selling and momentum. This relationship is studied by a difference-in-difference methodology. The winner portfolio displays a negative treatment effect during the pilot of -2.28% to -.92%. After the pilot, the treatment effect reverses and becomes 3.91% to 12.0%. Only for the F6H3 portfolio a negative effect of -1.62% is shown. The loser portfolio displays a positive treatment effect during the pilot of 1.80% to 4.84%. After the pilot, the treatment effect reverses and becomes -62.3% to -14.5%. The combined portfolio is a combination of the winner and loser portfolio. This portfolio presents similar results to those of the loser portfolio. The treatment effect during the pilot falls in the range of .88% to 2.61%, while after the pilot the effect turns negative. The value of this effect is -50.3% to -10.6%.

To conclude, the treatment effects show that being treated has a negative effect on the CARs of the winner portfolio, so that the CARs are smaller. This implies that being treated decreases the return and thus a decrease of the momentum effect. After the pilot, this effect is reversed and becomes positive which implies higher returns. The results are insignificant which makes further research necessary. The robustness checks, based on a different variable, smaller portfolios and the removal of financial firms, do not alter the results. The effects are slightly changed, but the direction of the results stays the same. Further research should focus on multiple variables, like firm size, relative short interest and short stock rebate rates. Also, a more critical view on the Reg SHO pilot, as the pilot has some randomization problems, improves existing knowledge in this field of study.

This article is organized as follows. Section 2 presents a literature review which discusses the relevant theories and prior research. Section 3 discusses the portfolio construction and difference-in-difference methodology. The data and descriptive statistics are stated in section 4. Section 5 examines the effect of short selling on momentum returns. Section 6 performs robustness checks based on a different variable, smaller portfolios and removal of financial firms. Lastly, a conclusion and discussion of the research is given, as well as further research opportunities.

(7)

4

2. Literature review

Many prior research focuses on the predictability of stock prices. Academics have created new models to predict them, but also investors use them for investing strategies. There is still no model that can predict stock prices in a proper manner despite of the overwhelming attention these models get. However, investing strategies based on predictions of seasonal movements ignoring business cycles, have a high probability of success (Wachtel, 1942). Stock market anomalies provide information about the trend of stock prices. This section discusses traditional finance and behavioral finance theories, as well as prior research about the momentum effect, short selling and the SEC’s Reg SHO pilot.

2.1 Traditional Finance Theory

The Efficient Market Hypothesis, or in short EMH, reflects a market in which all available information is reflected in the prices (Fama, 1970). This theory is the fundament to a variety of research on stock prices. Fama (1970) describes three forms of market efficiency.

Firstly, the weak form EMH reflects a market in which all market information is reflected in the prices. This implies that past returns do not reflect future returns. So, investors cannot use historical prices to predict future prices. Momentum strategies would therefore not yield positive returns in the weak-form efficiency. Secondly, the semi-strong form EMH implies an efficient market in which prices reflect all publicly available information. News and annual reports are included in public information. As soon as new information comes out, this will be reflected in the prices, which makes it impossible for investors to gain profits by trading on the news. Finally, the strong form EMH is a market in which prices reflect all information. Not just publicly available information, but also inside information. As a result, insider trading will not be profitable (Fama, 1970).

EMH has been the vocal point of different academic research. The EMH is supported by empirical evidence, especially the weak form of efficiency. The definition of public information is debatable and differs among articles. This makes it harder to state that the semi-strong form is rejected or not, because it depends on the definitions used. The strong form can be seen as a full embodiment of the EMH with little evidence that rejects this hypothesis (Jensen, 1978). EMH depends on three pillars. First, investors behave rational. They value securities for their fundamental value. New information changes the fundamental value of a security and thus its price. Second, irrational investors trade randomly. When there are many irrational traders, it is likely that these trades cancel each other out. In other words, there is no correlation between the trading strategies of these investors. Lastly, there is unlimited arbitrage. Even if there is a correlation between irrational trades, the irrational investors meet rational arbitrageurs who eliminate price effects (Shleifer, 2000).

(8)

5 In modern finance theory, the meaning of the EMH is still under debate. The trading conditions nowadays perfectly fit the EMH, due to the fast trades and continuous information flow. In contrast to the stock price patterns, which are not explained by EMH (Degustis & Novickyte, 2014). EMH fails to explain seasonality in stock returns, investor overreaction, etc., because EMH considers stock returns to be random. Besides, investors are uncapable of earning excess returns over a long period. The Capital Asset Pricing Model, in short CAPM, is another dominant theory within finance. The roots of CAPM lie in the work of Markowitz. In 1952, he introduced a mathematical solution for modern portfolio theory: the mean-variant efficient portfolio. He assumes that investors maximize returns and minimize risk. This is done by creating a diversified portfolio or a minimum variance portfolio. The goal of this portfolio is to pick the best of both worlds, so maximize return, while minimizing risk (Markowitz, 1952). This portfolio can also be called the market portfolio.

Portfolios are constructed based on investors’ preferences for risk. Investors can decrease the risk they are taking by combining the market portfolio with a risk-free asset, such as government bonds. Especially the U.S. treasury bills are often used as a risk-free asset. Risk averse investors would create a portfolio with many risk-free assets and assign a lower weight to the market portfolio. Similarly, risk seeking investors would choose a portfolio with a small portion of, or even excluding, the risk-free asset and a high amount of the market portfolio. This results in the following equation:

𝐸(𝑅) = 𝑅𝑓+ 𝑤(𝑅𝑝− 𝑅𝑓) (1)

The risk-free rate is denoted by 𝑅𝑓, the market return is denoted by 𝑅𝑝 and 𝑤 stands for the portion invested in the market portfolio. This equation shows that if 𝑤 = 0, so there is nothing invested in the market portfolio, the expected return is equal to the risk-free rate. The variance of this portfolio is completely determined by the variance of the market portfolio, because the risk-free asset does not have any risks. This variance looks like:

𝜎2= 𝑤2𝜎_𝑝2 (2)

Sharpe (1966) combined the two equations for expected return and variance to a new equation. The expected return is now also dependent on the variances, as seen in the next equation:

𝐸(𝑅) = 𝑅𝑓+

(𝑅_𝑝−𝑅_𝑓)

𝜎_𝑝 𝜎 (3)

According to CAPM, the expected return of an individual asset is a function of the risk-free rate, the market return and the beta, 𝛽. CAPM states that the only risk present is the risk between the individual asset and the market. This implies that 𝛽𝑖 is equal to the covariance between the individual

(9)

6 asset and the market divided by the variance of the market (Jagannathan & Wang, 1996). This model can also be used for predictions of future returns. The CAPM equation is depicted below:

𝐸(𝑅𝑖) = 𝑅𝑓+ 𝛽𝑖(𝐸(𝑅𝑚) − 𝑅𝑓) (4)

2.2 Behavioral Finance Theory

Behavioral finance theories appeared in response to the puzzles which traditional finance theory could not solve. The traditional paradigm assumes investors to be rational. This implies that when new information arrives investors update their beliefs concerning the value of securities in a correct manner. Besides, given the beliefs they have, investors make decisions which will maximize their utility (Barberis & Thaler, 2003). Behavioral finance argues that investors are not always rational and irrational behavior causes market changes. Barberis and Thaler define two main streams of behavioral finance, namely limits to arbitrage and psychology.

Limits to arbitrage focuses on market efficiency. As EMH stated, if investors behave accidentally irrational, these trades will get canceled out through arbitrage. According to traditional theories there is a limit to arbitrage, because prices only deviate from their fundamental value for a short period. However, from a behavioral finance perspective one argues that investors do trade irrationally. So, if a price deviation occurs, an arbitrage opportunity emerges. Besides, rational traders are powerless against the price deviations. Psychology focuses on investors’ beliefs and preferences. It is crucial for models of financial markets to understand how investors form expectations. Psychologists found different characteristics of how expectations are formed. One of them is overconfidence. This implies that investors are too confident that their decision is the right one. Further, individual preferences play a role in market models.

2.2.1 Characteristics of Investors

As said before, investors’ behavior decides how stock markets work. Understanding the behavior of investors is essential to understand how markets work. Expected utility theory states that investors always choose the outcome with the most utility. Each outcome is given a probability and a utility level. The utility function, which shows the expected utility, can be created by multiplying the probability by the utility. In risky situations expected utility theory does not seem to work (Barberis & Thaler, 2003). This implies that investors act irrational in risky situations.

The prospect theory from Kahneman and Tversky (1979) explains the failure of expected utility theory in risky situations. Certainty, probability and possibility are important factors for prospect theory. Individuals seem to overweigh outcomes which they consider certain despite of the utility level. This is called the certainty effect. However, for losses individuals are risk seeking. Instead of

(10)

7 choosing for the certain loss, one will choose a riskier option. This is referred to as the reflection effect. Thus, individuals are risk averse for gains and risk seeking for losses. Two prospects which have the same probabilities and outcomes can be valued differently by different individuals.

These characteristics of investor behavior affect how investors make decisions. EMH suggests that investors make rational decisions, which is in line with the expected utility theory. Following the prospect theory, one would say that investors are not rational in decision making. Even if certain outcomes should be valued the same according to expected utility theory, individuals value them differently. Another feature of investor behavior is pointed out by Shefrin and Statman (1985); their research points out that investors sell winning stocks too early and losing stocks too late. This suggests that investors are afraid to miss out on profits, so they sell winners as soon as a profit is made.

2.2.2 Market Characteristics

Investor behavior affects the market. Irrational behavior makes markets less efficient. Irrational behavior causes prices to no longer a reflect of the fundamental value, which gives rise to arbitrage opportunities. Investors can cause the market to overreact and underreact. Overreaction implies a too positive reaction of the market, because investors react extremely positive on news, while underreaction implies the opposite. After prices change in the market and the reaction is less or more than what it should be according to the fundamental value, one refers to over- and underreaction.

When news is brought to the market investors change their beliefs about the fundamental value. Pessimistic investors consider good news to be less good, while bad news is valued even worse in their mind. For optimistic investors the opposite is true, so good news will be even better and bad news will be less bad. This behavior causes arbitrageurs to take into account the risk of irrational behavior. For arbitrageurs this implies that overreaction of pessimistic investors cause them to lose money (Shleifer & Vishny, 1997). This risk is referred to as noise trader risk. Normally arbitrage refers to a situation in which a riskless profit is obtained. However, the irrational behavior causes a risky situation for arbitrageurs.

Other risks arbitrageurs face are model risk, fundamental risk and synchronized risk. Model risk arises from the risk that the valuation models of arbitrageurs are incorrect. The valuation models which determine the investment strategy conduct a fundamental analysis. There is a chance that these models are inaccurate. Fundamental risk refers to the risk that the fundamental value is wrong. This implies that due to irrational trades, the price moves away from fundamentals which causes wrong perceptions (Barberis & Thaler, 2003). Lastly, synchronized risk implies the contradictory actions of

(11)

8 investors. If a trend emerges due to irrational traders, arbitrageurs will trade in the opposite direction which causes a decrease of the trend. Therefore, arbitrageurs also affect each other’s decisions.

2.3 Momentum Effect

Inefficient markets are often the result of irrationality, which causes stock market anomalies. One of those anomalies are seasonal movements. The first seasonality in stock prices is shown empirically by Wachtel (1942). Investing strategies based on predictions of seasonal movements ignoring business cycles, have a high probability of success (Wachtel, 1942). Those seasonal movements should first be watched very closely before an investment strategy can be based on it.

The first evidence of momentum effects is shown by Jegadeesh and Titman (1993). Their sample consist of American stock data from 1965 until 1989. A trading strategy is created in which portfolios are based on stock returns over the past 3 to 12 months. Then the portfolios are hold for a time varying between 3 to 12 months. Therefore, there are 32 different trading strategies possible in which winners are hold and losers are either hold or sold. Strategies concerning the purchase of past winners and sale of past losers exhibit significant abnormal returns (Jegadeesh & Titman, 1993). Concluding that this would be the result of overreaction would be too short sighted. Besides, this evidence exploits the hypothesis that there is an overreaction to long-term prospects. These aspects of investor behavior can explain the momentum effect. However, it requires more information to conclude that the expectations of investors are biased in such a way that they result in momentum return trends.

Initially the work of Jegadeesh and Titman (1993) was welcomed with open arms, but then criticism prevailed. The results were either thought to show evidence of efficient markets or they were the result of data mining. In 2001, Jegadeesh and Titman came with new research supporting their previous work. This new research also provides evidence that stock-specific characteristics, like book-to-market ratios and market capitalization, are linked to momentum. Not only firm-specific characteristics, but also industry specific (Grinblatt & Moskowitz, 1999) and country specific factors (Chui, Titman & Wei, 2010) have a link with momentum.

Industry specific characteristics seem to be of high importance when looking at momentum investment strategies (Grinblatt & Moskowitz, 1999). Their research is based on U.S. stocks for the period 1963 to 1995. The distinction between industries is made by the SIC codes. They distinguish 20 different industries for which different portfolios are created. The high correlation of firms within an industry causes industries to be interesting for research. Investment strategies based on industry

(12)

9 momentum are proven to be highly profitable. Even when returns are adjusted for size, book-to-market and book-to-market effects there are significant results supporting the momentum strategies.

Next to industry characteristics, a research on momentum can be based on country specific characteristics. In 2010, Chui, Titman & Wei performed research on momentum profits linked to differences between countries. The effect of cultural differences on momentum returns are measured by the Hofstede (2001) individualism index. Individualism seems to have a positive link to momentum profits (Chui, Titman & Wei, 2010). This evidence, based on research on 41 countries worldwide, supports the belief that a country’s culture has an effect on the momentum of returns. So not only investor behavior, but also cultural differences affect momentum.

Furthermore, a distinction can be made by looking at worldwide markets, regions and local models. A global research based on the regions North America, Europe, Japan and Asia Pacific, finds evidence of decreasing momentum with decreasing firm size, except for Japan (Fama & French, 2012). Their dataset consists of stock data for 23 countries from 1989 until 2011. Besides worldwide data, the research also focuses on differences in size and value of stocks. Big firms have bigger momentums than small firms, though small stocks have larger value premiums. The local models were less successful when looking at size and momentum than the worldwide and regional models.

Momentum is closely related to reversal, where return momentums exhibit positive correlations, return reversals exhibit negative correlations. Both seasonalities are predictive. De Bondt and Thaler (1987) show that reversal patterns are consistent with overreaction. Reversals are more pronounced in losing stocks than winning stocks, which is an interesting feature of returns. Hence, not only momentum needs to be considered for the empirical part of this article, but also reversal.

2.4 Short Selling

short selling implies the sale of an asset without owning the asset (Foucault, Pagano & Röell, 2013). The seller borrows the asset from a third party and gives it back at a certain date. Short selling occurs when the seller believes the fundamental value of the asset is actually lower than it currently is. By selling the asset and giving it back later, which implies buying the asset again, the investor believes that the price will decline. Miller (1977) shows that short sale constrained firms which are also subject to divergence of opinion are overvalued. Firms being short sale constraint implies that it is costly for investors to find shares to borrow. For Miller’s theory to hold, firms will be overvalued when both short sale constraints and divergence of opinion, or in other words dispersion of beliefs, exist simultaneously.

(13)

10 This idea is further explored by Boehme, Danielsen and Sorescu (2006). Their research highlights the importance of both short sale constraints and dispersion of beliefs to be present in order to find overpricing. Not every company or industry is affected by short sale bans or constraints. Short sale constraints therefore need to be proxied. Different variables or methods can be used as a proxy, for example short stock rebate rates, relative short interest and option status. This is also true for dispersion of beliefs, which is a characteristic that is not just observable. Divergence of opinion can be proxied by IBES analyst forecast dispersion, stock’s volatility and turnover.

Earnings announcements can be used to reduce opinion differences among investors (Berkman et al, 2009). This gives another approach for looking at divergence of opinion. The research by Berkman et al (2009) finds that stocks with high opinion differences earn a significantly lower return at earnings announcements than stocks with low opinion differences. Besides, the results are in line with Miller (1977), in that stocks with high opinion differences and short-sale constraints experience a huge fall in the return after an earnings announcement.

More importantly, Daniel, Klos & Rottke (2017) investigate the effect of short sale constraints and optimism on returns. Instead of solely stating that the momentum effect is caused by a change in fundamentals, the research captures the change in optimism. The effect of lending supply, which is proxied by institutional ownership, is also a variable of interest in the research by Daniel, Klos and Rottke (2017). Their results conclude that positive shocks to optimism result in overpricing and thus momentum. Besides, their findings suggest that being short-sale constraint can cause prices to move away from fundamentals for a long period of time. This is unique, since it identifies bubbles for individual stocks.

2.5 Reg SHO pilot

The Regulation short sale pilot, as discussed in the introduction, was announced on June 23, 2003. The goal of this pilot was to see the effect of lifting the bid test and tick rule. Especially the effect these price restrictions have on market quality. The price restrictions are removed for a specific sample. If the price restrictions have no effect on the market quality, then the SEC would consider removing the price restrictions for all stocks. The SEC’s own research department tests the effect of the pilot. They concluded that the pilot only had a minor effect (US SEC, 2007). After removing price restrictions, the pilot stocks did not show an impact on market quality or liquidity. However, the SEC does not explicitly state if the restrictions can be removed.

The bid test and tick rule are regulations for short selling. The bid test implies that short sales can only be executed at a price equal to the previous bid price. The tick rule is similar to this. These

(14)

11 price restrictions are expected to affect market quality once they are lifted. Previous research already suggests that the bid test and tick rule are no good. After initiation, the tick rule has led to reduced price discovery, not only in markets with downward trends, but also in markets with upward trends (Alexander & Peterson, 1999). A slower price discovery is not good for the market. It implies that trades have prices which do not match the correct value, which in turn is harmful for traders.

Alexander and Peterson (2008) point out that removal of the price restrictions does not lead to a deterioration of market quality. Market quality is measured through liquidity, price efficiency and market volatility. They also focus on trade behavior. Removal of the restrictions gives traders more freedom to choose how quickly their orders are executed. Besides, the depth and order flow are reduced for stocks in the pilot compared to the control stocks. The distorting effect of the price restrictions on market quality are merely caused by the restrictions themselves (Diether, Lee & Werner, 2009). It would be a good and logical conclusion if the restrictions are removed permanently. The first research on the SEC’s Reg SHO pilot is mainly focused on the effect removing the price restrictions has on market quality. Afterwards, other research used the pilot to focus on different aspects like earnings announcements and short sale interest. A similar strategy is used in this research by using the Reg SHO pilot for a difference-in-difference analysis which is discussed in the next section.

(15)

12

3. Methodology

This section discusses the research framework used to obtain the results and the relationships that will be tested. The momentum strategy requires the use of returns from 2003 until 2009. One could either use prices to calculate the returns by hand or use a database which provides the holding period return. The methodology used in this research is based on the study of Jegadeesh and Titman (1993). The research in this article tests if stocks have an inefficient reaction before, during and after the Reg SHO pilot. The outline of this section is as follows. First, the outline of portfolio construction is stated. Afterwards, the use and implications of the Reg SHO pilot are discussed.

3.1 Portfolio construction

The momentum effect implies a correlation between past and future stock returns. Stocks which were winning in the past are still winning in the future and vice versa for losing stocks. This can be tested by creating portfolios of winning and losing stocks. One can choose to incorporate an X amount of stocks in the winning and losing portfolio or for example use the best and worst performing 10% of the sample. The latter is what Jegadeesh and Titman (1993) used in their research and what is also the strategy for portfolio construction in this research.

The relatively short time period causes the decision to create new portfolios each month. This does not imply that the research uses dynamic portfolios, in which the allocation of assets in the portfolio changes. It implies that due to the short time period used, more portfolios can be created which strengthens the research. Every month portfolios are created based on a 3 or 6 months formation period and a holding period of 3 or 6 months. Afterwards, 4 different trading strategies are possible with a different combination of formation and holding period. This research takes a long position in the winner portfolio and goes short in the losing portfolio. The portfolios are constructed based on historical returns. The following formula is used to obtain these returns:

𝑅𝑖 =

ln⁡(𝑃_𝑖,𝑡)

ln⁡(𝑃𝑖,𝑡−1) (5)

The return for each firm in the dataset is calculated following equation 5. The portfolio return is the average of all returns of the selected firms. This implies that each firm gets the same weight in the portfolio. When the portfolios are constructed, it is necessary to test if the market is efficient. If markets are efficient, returns will not significantly deviate from the market risk premium. If this is true then, by definition, momentum would not be able to exist. The market risk premium can be computed from the CAPM formula. The risk premium equals the market return minus the risk-free rate. If momentum exists, the portfolio returns would outperform the market.

(16)

13 This null hypothesis which follows this reasoning is presented in equation 6. If this hypothesis is rejected it implies that momentum exists. This hypothesis is tested by applying the Wilcoxon signed-rank test. The results of these tests are presented and discussed in section 5.

𝐻0: 𝑅𝑝− (𝑅𝑚− 𝑅𝑓) = 0 (6)

3.2 Use of Reg SHO

The Reg SHO pilot is exploited for this research on momentum. Three periods will be distinguished in this research; a pre-pilot period from January 2003 until March 2005, the pilot period from May 2005 until July 2007 and a post-pilot period from September 2007 until December 2009. April 2005 and August 2007 are not used, to prevent any biases which emerge from trades based on the pilot which is yet to come. Some investors and institutions might change their investment decisions due to the Reg SHO pilot. It could be that they find the pilot stocks now more interesting than the others. Excluding those months prevents the study to be affected by this.

The difference-in-difference methodology contributes in examining natural or randomized experiments. This research will use the difference-in-difference, diff-in-diff in short, to investigate the effect of the Reg SHO pilot. The regression used to test this looks like:

𝑦 = ⁡ 𝛽0+ 𝛽1(𝑇 ∗ 𝑃) + 𝛽2𝑃 + 𝛽3𝑇 + 𝜀 (7) This model shows the relationship between y, the excess returns, and the treatment, T, and time period, P. For a diff-in-diff to hold correctly also the interaction term treatment times time period,

T*P, is necessary. The estimates in this model thus show the effect of the stocks being treated or not

on the returns. This is shown by 𝛽1, which is referred to as the treatment effect. The effect of the time period is shown by 𝛽2. Lastly, 𝛽3 shows the effect of being treated. In a model this looks like:

𝛽3= (𝑦21− 𝑦11) − (𝑦22− 𝑦12) (8)

This research uses three time periods, a pretreatment period, a treatment period and a posttreatment period. The diff-in-diff regression needs to be augmented for that. There are now two time periods in the model, namely D for during treatment which is equal to 1 if the date falls in period 2, and P for post treatment which is equal to 1 if the date falls in period 3. Treatment is still indicated by capital letter T. The new model shows two interaction terms which can be seen below:

𝑦 = ⁡ 𝛽0+ 𝛽1(𝑇 ∗ 𝐷) + 𝛽2(𝑇 ∗ 𝑃) + 𝛽3𝑇 + 𝛽4𝐷 + 𝛽5𝑃 + 𝜀 (9) The treatment effect is thus equal to the interaction terms. The treatment effect during the pilot program is equal to 𝛽1 and the treatment effect after the pilot is equal to 𝛽2.

(17)

14

4. Data and descriptive statistics

This section discusses the data collection and descriptive statistics. The main dataset is constructed from CRSP and Compustat. Stock prices and returns are retrieved from CRSP and firm-specific data is retrieved from Compustat. Both databases are accessible through Wharton Research Data Services.

The Russell 3000 index is build based on market capitalization on May 28, 2004, May 31, 2005, May 30, 2006 and May 30, 2007. The Reg SHO pilot was announced in May 2004 and ended in 2007. The index created in this research is therefore constructed over the years from 2004 until 2007. The Russell 3000 index is created based on the rules of the Russell 3000 index. This implies that stocks with prices below $1 are excluded. American Depositary Receipts (ADRs), pink sheet and bulletin board stocks, closed-end mutual funds, foreign stocks, limited partnerships and royalty trusts are also excluded. Besides, the dataset keeps firms that are in the Russell 3000 index in all the years. This means that firms that are eliminated or added to the index in these years are not present in the final dataset. This file is merged with the list of pilot stocks. After merging, the file contains 634 out of the 968 pilot firms and 1,436 control firms. So, there are 2,070 firms part of this research. The final dataset contains 166,977 observations.

The SEC has created the pilot sample by sorting all Russell 3000 stocks on market capitalization. The sample is randomized by placing every third firm in the pilot group, starting at the second firm. So firm number 2, 5, 8 and so on are placed in the pilot sample. Investors trading in pilot firms do not have to pay attention to the price tests anymore. This makes it easier to short sell these stocks for investors and companies.

For the pilot to work in a proper manner, the pilot and control sample need to be similar. This implies that characteristics of both groups cannot show significant differences. Different measures are used to show the differences between the two groups. Measures of corporate investment, external financing and performance are constructed from Compustat variables. Capital Expenditures (CAPX) and Capital Expenditures plus Research and Development (CAPX R&D) are measures of corporate investment. External financing is measured by Equity Issues and Debt Issues. Performance can be tracked by Dividends and Past Profitability. All variables are scaled by Total assets which is Compustat item AT. Appendix I gives a broader overview of how the variables are constructed with the use of Compustat.

The descriptive statistics table is depicted on the next page. This table reports variable statistics for the pilot sample and control sample. From each variable the number of observations, mean, median and standard deviation are reported. Besides, the T-test which tests the difference

(18)

15 between pilot and control group and the difference itself is reported. Total assets is the only variable with a significant difference. The groups are randomized based on market capitalization that does not mean that the groups also have a similar proportion of big and small firms. This might cause the difference in total assets. Since this is only the case for total assets and this variable is not of significant importance in the methodology, is this not seen as a big problem.

The variable Total assets has a mean in the pilot group of 9,045 and the control group reports 23,181, both numbers are in millions of USD. The ratios and percentages presented in the table are similar. For example, the capital expenditures (CAPX) are 3.97 for the pilot and 4.21 for the control sample. The difference reported is the difference between the mean of both groups. The absolute difference goes from .02 to 8.08, excluding Total assets. All variables are scaled to Total assets, which is in millions of USD, which needs to be considered when the ratios are discussed.

Table 1 Summary Statistics

This table reports the summary statistics of the pilot sample and the control sample. The table shows the number of observations by N, the mean, the median and standard deviation of each variable. The difference in mean of the pilot and control group is reported as well as the t-statistic for the T-test if the variable in both samples differs significantly from each other. All variables are scaled to beginning-of-the-year total assets. Every variable becomes a percentage of total assets which makes them comparable. Note that total assets is denoted in millions of USD which needs to be taken into account when drawing conclusions from the percentages. For a definition of variables see Appendix I. *** denotes significance at the 1% level, ** denotes significance at the 5% level, * denotes significance at the 10% level.

Pilot Control

N Mean Median Std Dev N Mean Median Std Dev Diff. T-stat

Total assets 622 9,045 1,951 34,483 1,381 23,181 2,226 116,538 14135 2.97** Market-to-Book 517 222.49 160.19 188.93 1,138 230.57 157.18 504.64 8.08 0.35 CAPX 516 3.97 2.55 5.03 1,133 4.21 2.64 5.37 .23 0.83 CAPX R&D 516 7.02 4.56 8.88 1,133 6.64 4.71 7.40 -0.37 -0.90 Cash Flow 622 6.93 6.77 10.49 1,381 8.87 6.49 34.14 1.94 1.39 Leverage 622 37.00 33.80 32.20 1,381 37.93 35.75 48.46 0.93 0.44 Equity Issues 500 3.36 1.01 8.07 1,097 3.35 0.90 8.15 -0.02 -0.03 Debt Issues 500 10.55 1.15 27.68 1,089 10.03 0.92 37.68 -0.52 -0.27 Dividends 622 1.54 0.47 4.13 1,381 3.06 0.35 33.56 1.53 1.13 Cash Holdings 517 16.74 8.42 20.08 1,143 15.87 8.08 18.53 -0.87 -0.86 Past profitability 487 12.26 12.38 12.07 1,097 14.10 11.43 38.07 1.83 1.04

(19)

16

5. Results

This section states the results of the performed research. First, the results of the portfolio construction are stated. Second, the implication of the results from the difference-in-difference methodology are discussed. The next section describes some robustness checks.

5.1 Portfolios

The results are separated for each period. Table 2 shows the results for period 1, Table 3 for period 2 and Table 4 for period 3. The returns of the buy portfolio refer to a long position in winner stocks. The sell portfolio is a short position in loser stocks and the combined portfolio is a combination of the buy and sell portfolio. In the portfolio tables, H3 and H6 refer to a holding period of 3 and 6 months, while F3 and F6 refer to a formation period of 3 and 6 months. For the treated and control sample, there are therefore 4 possible portfolios; i.e. F3H3, F3H6, F6H3 and F6H6, with 3 different strategies; buy, sell and combined. To check if the returns outperform the market, the excess market return is subtracted from the returns and then a test checks if the returns are significantly different from zero. Also seen in equation 6. This is done by using the Wilcoxon signed-rank test.

The first period, from January 2003 until March 2005, shows that returns of the treated and control sample are quite alike. This is also what you would expect considering that the samples are constructed in a random way. The return of a formation period of 3 months and holding period of 3 months, F3H3, is 3.4% with a significance level of 5%. So, for F3H3, for both the treated and control sample, an average return of 3.4% is achieved, which is a significant outperformance of the market. Table 2. Portfolio Analysis Period 1

This table shows the Cumulative Abnormal Returns, in short CAR, with the standard deviation in parentheses. The formation period implies the months before portfolio formation and on which the portfolios are based. F3 is a formation of 3 months and F6 is a formation of 6 months. H3 and H6 refer to the holding period of the portfolio of respectively 3 and 6 months. F3H6 refers to a portfolio formation of 3 months which is then hold for 6 months.

Buy, Sell and Combined refer respectively to the winner, loser and a combination of winner and loser portfolio.

The stars show the result of the Wilcoxon signed-rank test, that tests if the CARs are different from 0. *** denotes significance at the 1% level, ** denotes significance at the 5% level, * denotes significance at the 10% level.

Period 1

Treated sample Control sample

H3 H6 H3 H6 Form at io n Per iod F3 Buy .034** (.064) .045** (.084) .034** (.070) .041* (.085) Sell -.021** (.037) -.007 (.044) -.025** (.045) -.015 (.047) Combined .013 (.044) .038 (.038) .009 (.054) .025 (.061) F6 Buy .033** (.055) .024 (.061) .024** (.048) .017 (.051) Sell -.008 (.036) .010 (.039) -.010 (.033) .001 (.030) Combined .024 (.059) .034 (.065) .013 (.047) .018 (.050)

(20)

17 All values in the table should be treated as percentages, so .045 of F3H6 from the treated sample implies a 4.5% average return. It seems that momentum does occur for winning stocks and most of them are also significant.

Losing stocks do not show momentum, but reversal. This is shown by the minus sign in the table. Only in the F6H6 portfolio losing stocks exhibit momentum. This could imply that losing stocks are subject to reversal in the short run, but show momentum in the medium-long run. The CARs for the sell portfolio are only significant for F3H3 for both samples. Section 4 shows that both samples are very similar, the results from Table 2 support this. They are not exactly the same, but they do not differ a lot from each other. Like for both samples, the combined F3H6 portfolio is the one with the highest CAR, 3.8% for the treated sample and 2.5% for the control sample.

The second period, from May 2005 until July 2007, during the Reg SHO pilot shows different results from the first period. These results are depicted in Table 3. The winner stocks are now showing reversal instead of momentum patterns. This is seen by the negative CARs for both samples. Why the return patterns change is unclear. What is even more interesting is that the loser stocks show reversal for the control sample, but momentum for the treated sample. This could imply that because the price tests are lifted, short selling affects the stocks negatively so that losing stocks keep losing in the future. Short selling activity helps to reveal the true value of a company.

Table 3. Portfolio Analysis Period 2

This table shows the Cumulative Abnormal Returns, in short CAR, with the standard deviation in parentheses. The formation period implies the months before portfolio formation and on which the portfolios are based. F3 is a formation of 3 months and F6 is a formation of 6 months. H3 and H6 refer to the holding period of the portfolio of respectively 3 and 6 months. F3H6 refers to a portfolio formation of 3 months which is then hold for 6 months.

Buy, Sell and Combined refer respectively to the winner, loser and a combination of winner and loser portfolio. The

stars show the result of the Wilcoxon signed-rank test, that tests if the CARs are different from 0. *** denotes significance at the 1% level, ** denotes significance at the 5% level, * denotes significance at the 10% level.

Period 2

H3 H6 H3 H6 Form at io n Per iod F3 Buy -.015** (.024) -.032*** (.028) -.005 (.023) -.0137 (.033) Sell .010** (.021) .018*** (.026) -.012 (.054) -.037** (.060) Combined -.005 (.021) -.014** (.016) -.017 (.049) -.052 (.059) F6 Buy -.017*** (.022) -.040*** (.028) -.013** (.022) -.024*** (.026) Sell .009* (.021) .015** (.027) -.016 (.045) -.028** (.048) Combined -.008* (.015) -.024*** (.015) -.029** (.039) -.052*** (.041)

(21)

18 An interesting feature of the results from period 2 is that the CARs of the F3H6 and F6H6 portfolios for both samples are significant. The highest returns also fall in this category, namely the 1.8% of F3H6 in the treated sample. The combined portfolios yield negative returns. If an investor would change its strategy timely, they should go short in the winner portfolio as well which would yield positive returns. All the returns are on an average basis. Investors therefore need to follow the strategy closely, because stepping out too early can result in losses. However, this is more the case for the first period than the second period. Since the second period already results in a loss.

The third period, from September 2007 until December 2009, is the period after the Reg SHO pilot. Most of the CARs in this period are not significantly different from zero. This violates the hypothesis from equation 6 and implies that the excess return is not different from zero. This period shows some puzzling results, depicted in Table 4. The winner stocks do not show momentum, but reversal. This was the same in period 2. For both samples winner stocks become losing in the near future. For losing stocks it depends on which sample you focus on. The losing stocks in the treated sample show reversal, while the same group in the control sample shows momentum. This could be the aftermath of the Reg SHO pilot, but it leaves some questions. The results are also quite unbelievable, if an investor would believe in reversal patterns and would invest in this in the F3H6 part, it would yield a return of 24.1%. This number is high, but in hindsight, it does work. For the control sample the highest return is achieved in F6H3. Namely 14.2%, this number is also high, but possible.

Table 4. Portfolio Analysis Period 3

This table shows the Cumulative Abnormal Returns, in short CAR, with the standard deviation in parentheses. The formation period implies the months before portfolio formation and on which the portfolios are based. F3 is a formation of 3 months and F6 is a formation of 6 months. H3 and H6 refer to the holding period of the portfolio of respectively 3 and 6 months. F3H6 refers to a portfolio formation of 3 months which is then hold for 6 months.

Buy, Sell and Combined refer respectively to the winner, loser and a combination of winner and loser portfolio. The

stars show the result of the Wilcoxon signed-rank test, that tests if the CARs are different from 0. *** denotes significance at the 1% level, ** denotes significance at the 5% level, * denotes significance at the 10% level.

Period 3

H3 H6 H3 H6 Form at io n Per iod F3 Buy -0.17 (.119) -.070 (.324) -.055 (.170) -.185** (.319) Sell -.020 (.488) -.171 (.523) .122 (.375) .243** (.552) Combined -.036 (.527) -.241*** (.627) .067 (.437) .059*** (.686) F6 Buy -.079 (.176) -.117 (.330) -.071** (.142) -.244*** (.316) Sell -.066 (.513) -.285 (.608) .214* (.465) .328 (.706) Combined -.145 (.546) -.402** (.669) .142 (.484) .084 (.825)

(22)

19

5.2 Difference-in-Difference

Previously, the results of portfolio creation are discussed. This part states the results of the difference-in-difference analysis which is explained in section 3. For each strategy; long position in winners, short position in losers and the combined portfolio, a difference-in-difference regression is used to investigate the impact of the pilot and the different periods therein. The regression used for this can be found in equation 9. Table 5 shows the results of this regression for the long position in winners, Table 6 shows the results of the short position in losers and Table 7 shows the results of the combined portfolio.

The long position in winners shows that there is a momentum effect, though it also displays reversal. The value of the constant differs from 1.7% to 4.1% which implies that in period 1 there is momentum even if the portfolio is treated. Treatment only has a small effect that differs from -.03% to .9%. During the pilot, the momentum effect changes to a reversal. This happens for both the treated and control sample. However, the treated sample has a slightly higher reversal, seen by T*D. The only significant effect is shown by Post, which is the period after the pilot has ended. After the pilot, the reversal is still there, from -9.5% to -26.1%, but the treated sample has a lower reversal now. T*P is positive, only for F6H3 reversal is shown. The total effect of being treated in the period after the pilot is equal to -1.64% (3.5% - 9.02% - .03% + 3.91%) for F3H3. For the control sample the total effect in the period after the pilot is equal to -5.52% (3.5% - 9.02%).

Table 5. Difference-in-difference long position winners

This table presents the results of the difference-in-difference of the Cumulative Abnormal Returns, in short CAR, of the winner portfolio as dependent variable: 𝑦 = ⁡ 𝛽0+ 𝛽1𝐷 + 𝛽2𝑃 + 𝛽3𝑇 + 𝛽4(𝑇 ∗ 𝐷) + 𝛽5(𝑇 ∗ 𝑃) + 𝜀

The table reports the CARs caused by each variable with the standard errors in parentheses. During is a dummy variable equal to 1 during the pilot years. Post is a dummy variable equal to 1 in the years after the pilot. Treatment equals 1 if the portfolio is from the pilot group and 0 for the control group. T*D, Treatment x During, and T*P,

Treatment x Post, are the interaction terms to reduce multicollinearity problems. F3H3, F3H6, F6H3 and F6H6 refer

to the different formation and holding periods of the portfolios. F3 and F6 refer to a formation period of respectively 3 and 6 months, while H3 and H6 refer to a holding period of respectively 3 and 6 months. So that F3H6 refers to a portfolio formation of 3 months which is then hold for 6 months. *** denotes significance at the 1% level, ** denotes significance at the 5% level, * denotes significance at the 10% level.

F3H3 F3H6 F6H3 F6H6 Constant .0350* (.0203) .0406 (.0449) .0237 (.0228) .0173 (.0485) During -.0399 (.0287) -.0544 (.0635) -.0367 (.0322) -.0412 (.0685) Post -.0902*** (.0284) -.225*** (.0627) -.0954*** (.0318) -.261*** (.0675) Treatment -.000390 (.0287) .00434 (.0635) .00889 (.0322) .00676 (.0685) T*D -.00923 (.0406) -.0223 (.0898) -.0132 (.0455) -.0228 (.0969) T*P .0391 (.0401) .111 (.0887) -.0162 (.0450) .120 (.0955) N 134 116 116 98 R-sq .103 .144 .164 .200

(23)

20 The treatment effect, equal to the interaction terms, shows a negative effect during the pilot and becomes positive after the pilot. During the pilot, the interaction term, measured by T*D, is negative from -2.28% to -.92%. After the pilot, the interaction term, measured by T*P, is mostly positive from 3.91% to 12.0%. For F6H3 it shows a negative effect of -1.62%. The results are not significant, but the treated firms show less seasonal movements, like momentum and reversal, than the control firms. This could imply that the treated firms are less sensitive to momentum, which is what you would expect from the theory and prior research.

The short position in losers, depicted in Table 6, shows a reversal effect which transforms to momentum. The constant factor differs from -2.5% to .05%. Treatment itself has a small positive effect on the return, differing from .22% to .97% This implies a decrease in the reversal effect. During the pilot, the control sample yields -3.87% to -1.2%, while the treated sample yields .9% to 1.8%. These findings imply that the pilot sample has smaller seasonal movements, but the reversal effect changes to a momentum effect during the pilot. The control sample exhibits the opposite and the returns are showing even higher reversals. After the pilot, the control sample yields 12.2% to 32.9%. The returns now shifted all the way to positive momentum returns. The treated sample yields -28.5% to 1.9%, which implies that the treated sample still shows reversal, but it changes more. The only significant variables are Post, which is the dummy variable for the period after the pilot and T*P, which is the interaction term. This shows a significant treatment effect after the pilot of -62.3% to -14.5%. The treatment effect during the pilot, T*D, is insignificant, but differs from 1.80% to 4.84%.

Table 6. Difference-in-difference short position losers

This table presents the results of the difference-in-difference of the Cumulative Abnormal Returns, in short CAR, of the loser portfolio as dependent variable: 𝑦 = ⁡ 𝛽0+ 𝛽1𝐷 + 𝛽2𝑃 + 𝛽3𝑇 + 𝛽4(𝑇 ∗ 𝐷) + 𝛽5(𝑇 ∗ 𝑃) + 𝜀

F3H3 F3H6 F6H3 F6H6 Constant -.0252 (.0548) -.0154 (.0731) -.0104 (.0664) .000564 (.0974) During .0132 (.0776) -.0233 (.103) -.00559 (.0938) -.0286 (.138) Post .147* (.0767) .259** (.102) .224** (.0927) .328** (.136) Treatment .00354 (.0776) .00808 (.103) .00219 (.0938) .00969 (.138) T*D .0180 (.110) .0484 (.146) .0230 (.133) .0338 (.195) T*P -.145 (.108) -.423*** (.144) -.282** (.131) -.623*** (.192) N 134 116 116 98 R-sq .042 .139 .094 .188

(24)

21 The combined portfolio of a long position in winners and a short position in losers gives a representation of the returns a normal momentum investment strategy would yield. There is a constant positive abnormal return from .9% to 2.5%. The treatment results in a more positive return, being treated results in an increase of .3% to 1.6% of the return. During the pilot, the control sample yields -5.2% to -1.7%. The treated sample yields -2.4% to -.5%. The pilot causes both samples to turn from a positive return to a negative one. However, the returns for the control sample are lower, thus more negative, than those of the treated sample. After the pilot, a similar change happens to the control sample. The control sample yields a return of 5.8% to 14.2% after the pilot, which implies that the returns have turned positive again. The treated sample yields a return of -40% to -3.6%, which is a change.

Table 7. Difference-in-difference combined portfolio

This table presents the results of the difference-in-difference of the Cumulative Abnormal Returns, in short CAR, of the combined portfolio as dependent variable: 𝑦 = ⁡ 𝛽0+ 𝛽1𝐷 + 𝛽2𝑃 + 𝛽3𝑇 + 𝛽4(𝑇 ∗ 𝐷) + 𝛽5(𝑇 ∗ 𝑃) + 𝜀

F3H3 F3H6 F6H3 F6H6 Constant .00974 (.0610) .0252 (.0892) .0133 (.0700) .0179 (.111) During -.0267 (.0862) -.0777 (.126) -.0423 (.0990) -.0698 (.157) Post .0570 (.0853) .0335 (.125) .129 (.0977) .0662 (.155) Treatment .00315 (.0862) .0124 (.126) .0111 (.0990) .0165 (.157) T*D .00879 (.122) .0261 (.178) .00983 (.140) .0110 (.222) T*P -.106 (.121) -.312* (.176) -.299** (.138) -.503** (.219) N 134 116 116 98 R-sq .013 .068 .077 .125

During the pilot, the treated sample turns to negative returns, which stay negative for the post pilot period. The treatment effect during the pilot, T*D, gives a positive effect of .88% to 2.61%. After the pilot, the treatment effect shifts to the negative side. It has a negative effect of -50.3% to -10.6%, which is significant at the 10% level. The different time periods seem to have a different effect on the treated and control sample. During the pilot, all three portfolios display a positive effect, which reverses after the pilot. All tables display a low R-squared. This is reasonable, because the difference-in-difference model cannot explain the variances in the CARs perfectly. There are other factors and variables which have an effect on the CARs.

(25)

22

6. Robustness checks

This section shows the results of the different robustness checks. Robustness checks are important to see if the results differ among subsamples, different variables or time periods. The first check shows how the results differ if another measure of return is used, namely the holding period return. This measure also incorporates dividend payouts, which is not included in the results section. The second check shows the effect of creating smaller portfolios. This implies that for the winner and loser sample not the bottom and top 10% is used for creating the portfolio, but the bottom and top 5%. The last check leaves out financial firms in the creation of portfolios. Financial firms are subject to regulations like capital requirements. Besides, between 2007 and 2009 there was a complete short sell ban for financial firms imposed by the SEC. Financial firms often have a much higher leverage than non-financial firms (Fama & French, 1992). The results for portfolio creation can be found in the appendices, the results for the difference-in-difference regressions are given in this section.

6.1 Holding period return

The results presented below are constructed with the use of holding period return instead of using the logarithmic returns. Appendix II presents the results of portfolio formation. The CARs found with the holding period return are much higher than those in the main results. In period 1, the results are highly significant, winner stocks show momentum, while loser stocks show reversal. In period 2, the results become less significant.

Table 8. Difference-in-difference long position winners

This table presents the results of the difference-in-difference of the Cumulative Abnormal Returns, in short CAR, of the winner portfolio as dependent variable: 𝑦 = ⁡ 𝛽0+ 𝛽1𝐷 + 𝛽2𝑃 + 𝛽3𝑇 + 𝛽4(𝑇 ∗ 𝐷) + 𝛽5(𝑇 ∗ 𝑃) + 𝜀

F3H3 F3H6 F6H3 F6H6 Constant .0949*** (.0201) .186*** (.0314) .0792*** (.0199) .146*** (.0279) During -.0696** (.0285) -.135*** (.0444) -.0537* (.0281) -.114*** (.0394) Post -.0589** (.0282) -.162*** (.0438) -.0726** (.0278) -.189*** (.0388) Treatment -.00551 (.0285) -.00767 (.0444) .000341 (.0281) -.00171 (.0394) T*D -.00402 (.0403) -.0155 (.0628) -.00432 (.0398) -.0163 (.0558) T*P .00770 (.0399) .00380 (.0620) -.00589 (.0393) .0134 (.0549) N 134 116 116 98 R-sq .099 .225 .126 .332

(26)

23 Momentum still exists for winners and reversal for losers, but the returns of the losers outweigh the winners which causes negative combined returns. Period 3 shows mostly insignificant results. There is still momentum for winning stocks and reversal for losing stocks. The diff-in-diff results for the holding period return are shown in Table 8-10. The long position in winners, depicted in Table 8, shows significant values for Constant, During and Post. The coefficients have a similar direction as in the main results, but they are now either smaller or bigger. For example, for the F3H3 portfolio after the pilot, the treated sample yields 3.8% (9.49% - 5.89% - .551% + .770%) and the control sample yields 3.6% (9.49% - 5.89%). The main results show negative results for these portfolios. The treatment effect, displayed by T*D and T*P, shows a negative effect during the pilot and a positive effect after the pilot which is similar to the main results. The CARs are much higher than for the initial returns, which causes the difference in the values of the regression results in table 8.

The short position in losers, depicted in Table 9, shows coefficients with similar signs as in the main results, but the coefficients for Post and Treatment for the F6H3 and F6H6 portfolio become negative. Besides, the results are less significant. During the pilot, the control sample yields 6.0% to -2.5% and the treated sample -4.7% to -2.3%. After the pilot, the control sample yields -27.3% to -6.1% and the treated sample -32.3% to -8.4%. The main results are different from these, during the pilot the treated sample shows momentum and not reversal, while after the pilot the control sample shows momentum and not reversal. The treatment effect is also of opposite direction compared to the main results presented in section 5.2.

Table 9. Difference-in-difference short position losers

This table presents the results of the difference-in-difference of the Cumulative Abnormal Returns, in short CAR, of the loser portfolio as dependent variable: 𝑦 = ⁡ 𝛽0+ 𝛽1𝐷 + 𝛽2𝑃 + 𝛽3𝑇 + 𝛽4(𝑇 ∗ 𝐷) + 𝛽5(𝑇 ∗ 𝑃) + 𝜀

F3H3 F3H6 F6H3 F6H6 Constant -.0679** (.0283) -.104* (.0532) -.0262 (.0384) -.0498 (.0718) During .0433 (.0401) .0437 (.0752) -.00279 (.0543) -.00338 (.102) Post .00705 (.0396) -.0783 (.0743) -.0657 (.0536) -.223** (.100) Treatment .00997 (.0401) .00835 (.0752) -.00622 (.0543) -.00861 (.102) T*D -.00811 (.0567) .00711 (.106) .0106 (.0768) .0149 (.144) T*P -.0329 (.0560) -.0601 (.105) -.0318 (.0758) -.0420 (.142) N 134 116 116 98 R-sq .029 .082 .060 .153

The effect of short selling on return momentums : an empirical analysis of the SEC’s Reg SHO pilot

MSc Finance, Quantitative Finance