Recent disposition and December effects in the United States of America

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Recent disposition and December effects in the United States of America

Master’s Thesis MSc. Finance, Final Version Date: 10-01-2019

H.H. DEBROT 1 University Of Groningen2 Faculty of Economics and Business

MSc. Finance Supervisor: J.H. Von Eije

Abstract

Investors are known to display a behavioral bias known as the “disposition effect” in which they tend to sell winning stocks (winners) too soon and keep losing stocks (losers) too long. Furthermore, several studies confirm that December is a special month in which investors generally act more rational as they tend to hold on to winners and sell losers. This paper studies what happens to the disposition effect and the December effect among individual tax-paying investors in the U.S. stock market for recent periods and uncovers if this changes during times of financial instability. Contrary to previous research, it also considers the effects for firms with large market shares. Results indicate that, in particular, firms with small market shares exhibit these effects. Overall, investors hold on to their losers throughout the year and sell them in December. Contrary to expectations, investors act similarly with small winners and also sell them in December. Big winners are, however, sold throughout the year. Furthermore, the disposition effect increases in times of financial instability for losers, suggesting that investors tend to act even less rational to losers during times of financial instability.

JEL Code Classification: G40, G41, and G01.

Keywords: behavioral finance, the disposition effect, December effects, the tax-loss-selling

hypothesis, the global financial crisis of 2007, financial instability.

Word count: 13,675 (*excluding appendices)

1_{Email address: h.h.debrot@student.rug.nl, Phone number: +3163035854, Student number: S3218570, Course:}

Master’s Thesis MSc. Finance, Course code: EBM866B20.

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1. Introduction

In the world of finance, there has been an ongoing debate as to whether investors should be seen as making rational decisions, or irrational decisions based on emotions. Modern-day finance has accepted that markets are flawed, but still assumes that investors behave rationally (Wärneryd, 2001). Behavioral finance, however, states that investors do not behave rationally as they are influenced by behavioral tendencies such as their emotional state, heuristics, limited discipline, social pressure, and self-deception (Wärneryd, 2001).

There are several reasons why it is important to understand how individual investors behave and if this changes in times of great volatility. Lakonishok and Smidt (1986) state that this knowledge would 1) give us a better understanding of how taxes influence stock prices and trading volumes, 2) might be taken into account when writing legislative proposals and policy plans concerning optimal revenue creation as well as decreasing the federal budget deficit, 3) allow us to understand investor behavior better, and 4) be of importance to investors who base their strategy on trading volume to understand if patterns are due to tax-motivated or non-tax-motivated reasons. Given this information, investors might be able to avoid behavioral biases that potentially lead to suboptimal investment strategies or, as long as they exist, might profit from this knowledge. Furthermore, this knowledge could serve as a guide to corporations to understand shareholder behavior and the influence this might have on shifts in the financial market.

Rational investors are expected to make predictions concerning tax income at the beginning of the year and apply tax planning throughout the year, which means that a rational investor should not exhibit abnormal trading behavior during any month of the year (Shefrin and Statman, 1985). Several studies, however, show that investors do not behave in such a manner, as they seem to exhibit abnormal behavior during the year (Dyl, 1977; Ferris, Haugen, and Makhija, 1988; Lakonishok and Smidt, 1986).

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3 December seems to be a special month of the year in which investors revert their behavior by deferring the sale of winners and by selling losers. One of the explanations for this behavior is the tax-loss-selling hypothesis (TLSH) that states that in December, investors that did not apply tax planning throughout the year (irrational investors according to Shefrin and Statman, 1985), only then think about their net tax and then lower it by selling losers and holding on to winners (Holt and Shelton, 1961; Holt and Shelton, 1962; Sprinkel and West, 1962). Kelly, Wu, and Chambers (2012) show that tax-paying investors that display irrational behavior throughout the year often make rational tax-related decisions in December. Another explanation for the behavior in December is “window dressing”, where professional investors want to improve their portfolio’s year- and quarter-end appearance by buying winners and selling losers (Haug and Hirschey, 2006). TLSH behavior has been demonstrated in several studies (Dyl, 1977; Ivković, Poterba, and Weisbenner, 2005; Brown, Ferguson, and Sherry, 2010). In addition, mixed, tax-motivated and non-tax motivated, effects are present (Shefrin and Statman, 1985; Lakonishok and Smidt, 1986; Badrinath and Lewellen, 1991; Odean, 1998; Brown, et al., 2006; Kelly, Wu, and Chambers, 2012; Firth, 2015).

While many studies only focus on the DE and the December effect, very little research examines these phenomena during times of financial instability and not one has focused on investor behavior in the U.S. stock market during the global financial crisis of 2007 (exceptions are presented in Appendix 1). How do investors react during times of financial instability? Do the same behavioral tendencies still appear in times where the entire market suffers losses? Will investors then consider taxes during the entire year or will they remain irrational and still wait until the end of the year to think about taxes? This paper investigates how the global financial crisis that began in 2007 (GFC2007) influenced U.S. stock market behavior.

The purpose of this paper is to assess investor behavior of individual tax-paying investors in the U.S. stock market for recent periods and to uncover if this changes during times of financial instability. The methodology by Dyl (1977), where stock prices are linked to trading volume, is applied. This paper examines investor behavior before, during, and after the GFC2007 to gain insight into investor behavior in times with and without financial instability.

This study differs from earlier studies in several aspects. First, it reviews investor behavior during times of financial instability in the U.S. stock market. Second, it is the only study that applies the methodology of Dyl (1977) to the period of the GFC2007. Third, the sample of 200 firms is three times bigger than the largest sample of comparable studies that also use stock data (Čekauskas and Liatukas , 2011; see Appendix 1). Finally, earlier studies only focus on stocks of firms with the smallest market share due to the assumption that these firms are more likely to be held by individual tax-paying investors. In this study, small and big market share stocks are included to see if they are treated similarly by investors, or not.

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2. Literature overview

In this section, investor behavior from a behavioral point of view is discussed first. Then, investor behavior from a rational point of view is discussed. Finally, a literature overview of empirical research is provided.

2.1 Investor behavior from a behavioral point of view

The DE is used to describe the irrational behavioral tendency of investors to prefer to realize gains and to be hesitant to realize losses. The DE is irrational behavior as it leads to suboptimal investment strategies; investors are better off if they do not give in to these behavioral tendencies. The following sections show why investors have these behavioral tendencies.

2.1.1 Prospect theory

One of the theories best explaining the DE is prospect theory. Before prospect theory was developed, expected utility theory was commonplace. Expected utility theory was developed to predict investor behavior under uncertainty. In utility theory, utility is a function of wealth; the higher your wealth, the higher your utility, and the lower your wealth, the lower your utility. One of the biggest downfalls of this theory is that the likelihood of an outcome is assumed to be known while usually, this is not the case (Ackert and Deaves, 2016).

This issue was resolved by Kahneman and Tversky (1979) who introduced prospect theory where the probabilities of outcomes are unknown. They show that when making decisions, human beings follow an “S”-shaped utility function. Compared to expected utility theory, prospect theory introduces three additional aspects: 1) the nature of a prospect is important, 2) people focus on a reference point rather than the amount of wealth, and 3) people have loss aversion (Ackert and Deaves, 2016). In Fig. 1 a typical prospect theory function is presented.

Figure 1: Investor’s utility function (Ferris, Haugen, and Makhija, 1986 p. 679)

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5 Risk-seeking and risk-averse behavior can be explained through Fig. 1 and by assuming that the revenues of realizing an investment at either a gain or a loss are kept rather than being reinvested immediately. Consider an investor being in the center point of the graph in Fig. 1, right after buying an investment; the investor can either experience a gain of G or a loss of –L, both equally likely. Ferris, Haugen, and Makhija (1986) show that because the graph is evenly shaped going from the center to either –L or G, the investor’s expected utility from holding on to the investment is similar to the utility obtained from realizing the investment and therefore the investor is indifferent between either holding on to the investment or realizing it. However, this indifference changes once the investor has experienced a gain or a loss. Now consider an investor whose investment has suffered a loss of –S. From this point on the investment can either increase in value to G-S or it can continue to decrease in value to -L-S. Due to the curvature of the utility curve in the loss-side of the graph, it is clear that the expected utility of holding on to the investment is higher than the utility obtained when realizing it at a loss. Thus, the investor is risk-seeking when its investment has suffered a loss and keeps holding on to it (Ferris, Haugen, and Makhija, 1986). The exact opposite is true for an investor whose investment has experienced a gain. Due to the curvature of the utility curve in the gain-side of the graph, it is clear that the expected utility of holding on to the investment is lower than the utility obtained when realizing it at a gain. Thus, the investor is risk-averse when its investment has increased in value and sells when a gain occurs (Ferris, Haugen, and Makhija, 1986).

Besides this risk-seeking and risk-averse behavior, prospect theory also states that people suffer from loss aversion. This means that, in general, people dislike losses, whether these are financial losses or non-financial losses. Ho and Vera-Muñoz (2001) show that loss aversion plays an important role in decision making, because even sophisticated investors, such as managers, want to increase the short-term value even though this means that the long-term value will suffer. Due to this behavioral phenomenon, investors tend to sell winners quickly, as they do not want to see a gain turn into a loss. It also causes investors to keep holding on to losers, as they do not want to admit to losses. This phenomenon is not a rational one, because momentum shows us that overall stocks that have been winners (losers) in the past six months tend to remain winning (losing) during the next six months (Barberis and Xiong, 2009).

In conclusion, prospect theory predicts investors to sell winners (too soon) and to hold on to losers (too long) However, it does not make this prediction for revenues that immediately are rolled over into another uncertain investment, because then a new reference point for a new stock is created. This is where mental accounting at the individual stock level comes into play.

2.1.2 Mental accounting

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6 When investors do not integrate their investment accounts, their behavior should be similar for closing an account and keeping the revenues of an investment, as it is for closing an account and rolling over the revenues into a new uncertain investment. This means that prospect theory also upholds when the revenues of realizing an investment at either a loss or a gain are rolled over into another uncertain gamble. Rolling over is like closing a mental account and opening a new one.

2.1.3 Regret aversion and pride-seeking behavior

Shefrin and Statman (1985) state that human beings also suffer from regret aversion. Regret occurs when one realizes that having made a different decision would have led to better results. When making a choice, people are able to imagine the regret they might feel by making a wrong decision. Regret aversion causes investors to hold on to losers as the investor believes that the price will increase somewhere in the future. Selling now at a loss and finding out that the price has risen, would cause the investor to feel regret. Furthermore, Shefrin and Statman (1985) state that investors also have pride-seeking behavior. This means that investors tend to want to realize their winners quickly (and often too soon) as this causes the satisfying feeling of pride. This shows us that investors will hold on to losers as they are regret averse and sell winners as they are pride-seekers.

O’Curry Fogel and Berry (2006) show that the DE primarily is related to regret aversion, as this leads investors to hold on to losers because the regret that is felt from realizing a loser that continues to lose is worse than that of selling a winner that continues to increase. Investors dislike realizing losses because this means that they have to admit to having made a mistake. Thaler (1980) shows that, in the short-term, investors prefer inaction over action, because taking action and making a bad decision (selling a loser that will start to increase) causes more regret than doing nothing (keeping a loser that continues to lose). Thus, inaction triggers the DE even more.

2.1.4 The disposition effect

Prospect theory, mental accounting, regret aversion, and pride-seeking behavior, as discussed in Sections 2.1.1, 2.1.2, and 2.1.3, all show that investors have a logical tendency to hold on to losers and sell winners. These theories are explanatory for investor behavior. Even though this behavior might have logical explanations, it is not rational, as it leads to suboptimal investment strategies which will be explained later in Section 2.2.1.

These behavioral tendencies all are reasons for the observed DE. For notational purposes and better comprehensibility, the DE is split up into two components: 1) a disposition effect for losers (DEL), as investors have a tendency to hold on to losers, and 2) a disposition effect for winners (DEW), as investors have a tendency to sell winners. The total effect is still referred to as the disposition effect (DE), however now there also is a distinction between DEL and DEW. The theories presented lead to the following two hypotheses belonging to the DE, namely:

DEL: Investors tend to hold on to losers DEW: Investors tend to sell winners

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2.2 Investor behavior from a rational point of view 2.2.1 Momentum

“Momentum” is defined as the speed at which a stock price moves and stands for the fact that, in general, stocks that have been winners (or losers) in the past six months tend to remain winning (or losing) during the next six months (Barberis and Xiong, 2009). This means that momentum might help investors make predictions about the trend the price is following. Given the fact that overall winners keep winning and losers keep losing and assuming momentum to continue, it is rational for investors to sell losers as the price is expected to drop even more and to keep holding on to winners as the price is expected to increase even more. Momentum shows that even though investor behavior as described by the DE might have logical explanations, it is irrational, as it leads to suboptimal investment strategies from a profit perspective.

2.2.2 The U.S. tax system and tax-loss-selling

To understand investor behavior even better from a rational and optimal investment point of view, it is important to understand the U.S. tax rules. The U.S. is unique in the way it recognizes gains and losses. Capital gains and losses are not recognized until they are realized (Hull, 2018). For non-corporate tax-payers, short-term gains on assets held less than one year are taxed at the same tax rate as ordinary income, whereas the long-term gains on assets held for more than one year are taxed at a maximum rate of 20% (Hull, 2018). Both long and short-term tax rates depend on an investor’s taxable income and usually, tax rates on short-term investment gains are larger than those on long-term investment gains. Capital losses are used to deduct from the tax on capital gains and may be carried forward to other years.

Other things being equal, investors prefer to have a minimum net tax. This means that each investor will prefer to minimize tax payments on gains and to maximize tax credit on losses. Based on the tax rules in the U.S., it is not difficult to understand that, from a tax-perspective, it is appealing for investors to defer the sale of winners so that capital gains are taxed on a low long-term tax rate, and to sell losers to obtain high tax benefits to offset the taxes being paid on winners.

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8 Shefrin and Statman (1985, p. 783) believe that “December tax-loss selling reflects a self-control strategy” rather than a rational strategy. They state that rational investors make predictions concerning tax income at the beginning of the year and apply tax planning throughout the year, which means that a rational investor would only sell additional losers in December to lower taxes if the taxable income is higher than expected. As rational investors apply tax planning throughout the year, it is not reasonable to assume that they will exhibit abnormal behavior or abnormal trading volumes during any month of the year. However, it is plausible to assume that those who did not apply tax planning throughout the year, irrational investors, want to lower their net tax by selling losers at the end of the year, as all investors want to lower their net tax. When income taxes need to be taken into account in December, their rational side and self-control force irrational investors to consider taxes. Meaning that in December irrational investors are expected to show different, more rational, behavior. These expectations are confirmed by Kelly, Wu, and Chambers (2012) whom state that tax-paying investors that show irrational behavior throughout the year often make rational tax-related decisions in December.

2.2.3 Turn-of-the-year effect

Tax-motivated selling has been used as an explanation for several irregularities such as the “turn-of-the-year effect” (also known as the “January effect”) that first was discovered in 1942 (Badrinath and Lewellen, 1991). Miller, et al. (1991) state that the turn-of-the-year effect entails that stocks that have a very low stock price in December usually perform abnormally high in January. The effect is most present for small caps. The link between the TLSH and the January effect is that investors sell their losers in December in order to obtain tax benefits to offset taxes being paid on winners. However, due to the extensive sale of these losers, they become underpriced. In response to the underpricing, investors start buying the underpriced stocks again in January, demand increases, and the “January effect” kicks in; the stocks that had a very low stock price in December usually perform abnormally high in January (Miller, et al., 1991). Experts state that the trend has slowly been disappearing, as by now investors are aware of this opportunity.

Besides the December tax-loss-selling explanation, “window dressing”, where professional investors want to improve their portfolio’s year- and quarter-end appearance by buying winners and selling losers, has also been given as an explanation to the turn-of-the-year and December effects (Haug and Hirschey, 2006).

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9 In a study of the effect that the 1986 tax reform3 had on the January effect Miller, et al. (1991), found that other reasons, besides tax-motivated selling, play an important role in the January effect and thus also in investor behavior in December. In January 1987, the percentage of long-term investment losses that can be deducted was increased to 100% up from only 50% before the tax reform. Based on this, Miller, et al. (1991) expected the sale of losers to be less than usual at the end of the year. The January effect was also expected to be lower than usual. Their prediction did not come out. If it had, it would provide evidence of tax-motivation as the driver of the TLSH. However, because the tax cut did not eliminate the turn-of-the-year effect, it means that investors either did not apply tax-reducing-strategies or that non-tax-motivated reasons were more predominant than tax-motivated reasons. Many other studies indicate that both, tax-related and non-tax-related, effects play a role in the TLSH phenomenon (Shefrin and Statman, 1985; Lakonishok and Smidt, 1986; Badrinath and Lewellen, 1991; Odean, 1998; Brown, et al., 2006; Kelly, Wu, and Chambers, 2012; Firth, 2015).

2.2.4 The December effect

Mental accounting, discussed in Section 2.2.1, shows that the DE cannot be explained from a rational perspective, as this behavior leads to suboptimal investment strategies. Phenomena such as the TLSH, window-dressing, and the turn-of-the-year effect, all show that at the end of the year (in December) investors might behave differently from what is usually predicted by the DE. Income taxes force irrational investors to listen to their rational side. From now on this behavior in December will be referred to as the December effect.

All in all, the DE predicts investors to sell winners (too soon) and to keep holding on to losers (too long). However, once forced to take income tax into consideration, in December, we expect to see the opposite behavior. Overall, non-tax-related motives dominate tax-related motives, except in December when self-control kicks in.

December effect of losers: Investors tend to sell losers in December December effect of winners: Investors tend to hold on to winners in December

The operationalized and technical hypotheses of the disposition effect will be presented later in Section 3.3 on p. 16.

3_{It should be noted that the tax-rules of the 1986 tax reform are no longer up to date with the current tax system and}

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2.3 Investor behavior during a financial crisis

The question remains as to how investors behave in times of financial instability. Do the DE and the December effect still appear in times where the entire market suffers losses? Will investors then consider taxes during the entire year or do they still wait until the end of the year?

The first signs of the GFC2007 started halfway 2007. In the U.S. the worst part of the GFC2007 occurred at the end of 2008 and the beginning of 2009. During the GFC2007, all major U.S. stock markets dropped significantly between December 31st, 2007 and December 31st, 2008 (see Table 1). The collapse of the financial system had (and likely still has) an immense impact on investor behavior and investment strategies.

Table 1: Equity value changes of the major U.S. stock market indices during the GFC2007

U.S. Stock Index 12/31/2007 12/31/2008 Difference

Dow 30 $13,264.82 $8,776.39 -33.84%

Nasdaq 100 $2,084.93 $1,211.65 -41.89%

Nasdaq $2,652.28 $1,577.03 -40.54%

S&P 500 $1,468.36 $903.25 -38.49%

Constantinides (1983) (see Section 2.2.2) states that tax-related selling especially is noticeable for stocks with medium to high stock price variance. This suggests that in a time of great volatility in the market, investor behavior will be different from normal times. Furthermore, Lin (2011) argues that during a period of crisis, the DE might diminish. Under the DEL, investors have the tendency to hold on to losers, however, during times of financial instability investors might be scared to obtain even bigger losses. Their fear of suffering even bigger losses could drive them into selling their losers; eliminating the DEL and decreasing the overall DE.

De Bondt (1993) states that in bull markets (upward trending) investors will be optimistic. The longer a market is in the bull state, the more investors believe that their winners have reached a peak before collapsing, the more they will sell their winners. Thus, during a bull market, the DEW is expected to increase, increasing the overall DE. Furthermore, Dyl (1977) claims that in a bull market the December effect is expected to be more significant as investors need to deal with a net tax that is higher than expected. To minimize their net tax, investors can minimize tax payments on gains by deferring the sale of winners to the next income tax year and to maximize tax credit on losses by selling losers before the end of the current tax year. These actions cause a stronger December effect for winners as well as for losers.

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11 Dacey and Zielonka (2008) review the DE when there is low volatility in the market, such as is the case in a bull market, and show that this stimulates a stronger DE. These results motivated them to repeat their study, but by focusing on the DE when there is high volatility in the market, such as is the case in a bear market. Dacey and Zielonka (2013) show that under high volatility, investors are more likely to sell winners (consistent with DEW), but are also more likely to sell losers (inconsistent with DEL). A few studies have been conducted to examine investor behavior during high volatility situations, such as a financial crisis.

Lin (2011) reviews the DE in the Chinese and Taiwanese stock markets during two periods of financial crisis and suggests that the DE is expected to disappear in times of crisis. Contrary to Lin’s (2011) expectations, the DE is shown to remain in both stock markets during the first financial crisis in 1997 and only seems to disappear in the Taiwanese stock market during the GFC2007. Lyn (2011) shows that periods of financial crisis do not significantly affect the DE, but that it is especially influenced by it being either a bull or a bear market, where the DE especially seems to be present (absent) in bull (bear) markets. This is in line with the predictions of De Bondt (1993) concerning the DE.

While focusing on the efficient market hypothesis (EHM), Čekauskas and Liatukas (2011) notice that DEL and DEW are present within the Estonian stock market. They find that this is irrational as momentum is at play; investments sold underperform investments bought. This means that investors have behavioral biases. Contrary to the findings of Lin (2011), Čekauskas and Liatukas note that the DE is even more present during the GFC2007.

Croonenbroeck and Matkovskyy (2014) analyze the demand for investment advice in the German stock market and find a decrease in demand for advice after the GFC2007. This might be explained through the link between the DE and stakeholder participation. In a bull market, they expect small individual investors to participate in the stock market, and that these investors will contribute to the DE as these investors are especially susceptible to behavioral biases. During a bear market, they expect less small investors to be able to participate in the stock market. In a bear market, they expect sophisticated institutional investors to contribute to the largest percentage of shareholder participants, thereby eliminating behavioral biases. Croonenbroeck and Matkovskyy (2014) show that the DEL and DEW are present before the GFC2007, however, in the years after the crisis they disappear. They explain this by suggesting that many small, individual investors might have removed themselves from the market after suffering tremendous losses.

Bellofatto, Winne, and D’Hondt (2014) analyze data from an online brokerage firm to review the DE over time and different groups of investors. They conclude that the DE is significantly lower during times when the market falls and that it is much more evident during times when the market rises. This is similar to the result of Lin (2011) who claims that in the Chinese and Taiwanese stock market, the DE is especially influenced by bull and bear market condition, where the DE especially seems to be present (absent) in bull (bear) markets.

While investors can be expected to behave differently during a financial market crisis, based on these diverging and contradicting insights, it is unclear how investors exactly will react.

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3. Data and methodology

In this section, at first, the data are discussed. Secondly, an analysis of the data is presented. Then, the methodology is presented. Finally, an overview of the technical hypotheses is given.

3.1 Data

In general, data can be collected from three types of sources: private transaction data, public market data, and survey data. Unfortunately, it was not possible to obtain private transaction data. Furthermore, the collection of survey data is a too time-consuming task. Therefore, this study uses public market data. According to Chang, Solomon, and Westerfield (2016), the DE is only noticeable in non-delegated stocks (meaning they are not managed by a professional) such as individual stocks. As this study is interested in individual investor behavior of non-professionals, only individual ordinary common stocks are focused on.

Tax-exempt investors often do not represent the group of individual investors and therefore should be excluded from the sample. To do so, Ferris, Haugen, and Makhija (1988) focus on firms with the smallest market share; they argue that these firms are mostly held by individual tax-paying investors, while larger firms are more likely to have bigger groups of tax-exempt investors. However, Barber, et al. (2007) state that this does not matter because even though some groups do not exert the DE bias, in general, the majority of investors does. To figure out which assumption is correct, this study focusses on the one-hundred firms with the smallest market share as well as the one-hundred firms with the biggest market share4_{. This allows us to see if investor behavior is} different between small and large firms, or if it would indeed be valid to pool them for further analysis. Firm size is based on the market capitalization of each firm in June 2009, which is half-way during the analyzed period of July 2000 until June 2018.

This study focusses on the common equity of firms listed on the NYSE and uses monthly data from the CRSP database from July 2000 until June 2018 (a total of eighteen years). Each equity value is compared to that of one year earlier. This means that eventually, a total of seventeen years of data is available for analysis, starting in July 2001 until June 2018. When looking at the initial sample, only 770 firms of the 3,811 firms in total survived during the entire analysis period. Given that a huge number of firms (2,986 of 3,811) did not survive the analysis period, only the survivors are included in the sample. This removes the impact that certain events, such as mergers, bankruptcy, and start-ups, have on the trading volume of the firm in question (Ferris, Haugen, and Makhija, 1988). There may be some survivorship bias, however, such bias may be small, because the focus is on investor behavior not on firm behavior. Only if investors are influenced by ex-ante knowledge of future firm survivorship, bias may occur.

4_{Even though a focus on two-hundred firms in total does not seem like a lot, there is a total of 43,200 data inputs}

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13 The total 770 companies that persisted during the entire analysis period account for the total market. Of these 770 firms, the smallest 100 and the biggest 100 are included in the sample.5 All firm and market data (PERMCO, share code, ticker, price, dividend cash amount, one month holding period return, cumulative factor to adjust the price, share volume, number of shares outstanding, and cumulative factor to adjust shares) are retrieved from the CRSP database.

Figure 2: The average rate of return of the entire market of 770 firms

The period of February 2008 until September 2009 is distinguished as the period of the GFC2007 as this is the period of the GFC2007 in which the entire market of 770 persisting firms is in a period of permanent negative average monthly returns (see Fig. 2).

3.2 Methodology

The use of public market data might be a disadvantage when having a microeconomic view, however, Dyl (1977) shows that it is possible to make predictions concerning individual investor behavior by using public data. In this research, the methodology of Dyl (1977) is applied.

3.2.1 Measuring stock gains and losses

At first, it is important to measure the percentage change that the price (the return) of each stock has experienced compared to a certain point in time.6_{This is a measure of the gain or loss} an investor has experienced by holding a certain stock during the past year.7

5_{Not more than 200 firms are included in the sample, as this would make the distinction between the smallest and}

biggest firms sample a lot less significant.

6_{This study compares the current price for each month to that of one year in the past.}

7_{Dyl (1977) also applies this method, but only focusses on investor behavior at the end of the tax year (in December).}

Ferris, Haugen, and Makhija (1988) show that one of the limitations of the methodology applied by Dyl (1977) is that it does not take into account the direction the price has gone during the entire period of a year. Therefore, this study compares each month, not only December, to its past price. This gives insight into the direction the price has gone during the entire period of a year.

-50% -40% -30% -20% -10% 0% 10% 20% 30% 12 /3 1/ 20 07 01 /3 1/ 20 08 02 /2 9/ 20 08 03 /3 1/ 20 08 04 /3 0/ 20 08 05 /3 0/ 20 08 06 /3 0/ 20 08 07 /3 1/ 20 08 08 /2 9/ 20 08 09 /3 0/ 20 08 10 /3 1/ 20 08 11 /2 8/ 20 08 12 /3 1/ 20 08 01 /3 0/ 20 09 02 /2 7/ 20 09 03 /3 1/ 20 09 04 /3 0/ 20 09 05 /2 9/ 20 09 06 /3 0/ 20 09 07 /3 1/ 20 09 08 /3 1/ 20 09 09 /3 0/ 20 09 10 /3 0/ 20 09

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14 The return each stock (i) has experienced in month (t) compared to one year ago (t-12) is calculated as follows:

𝑅_𝑖,𝑡 = (𝑃𝑖,𝑡− 𝑃𝑖,𝑡−12) + 𝐷𝑖,𝑡

𝑃_{𝑖,𝑡−12} (1) It is important to note that the price is adjusted for cash dividends, mergers, liquidations, stock dividends, and stock splits. Of course, it is not likely that each investor has held a stock for one year exactly in a certain month. However, this information does provide an indication of “the

likelihood that the owners of a given stock may possess unrealized portfolio gains and losses”

(Dyl, 1977, p. 167). It is more likely that a shareholder that held a share that increased (decreased) during the past year will have unrealized gains (losses) than a shareholder that held a share that decreased (increased) during the past year (Dyl, 1977).

3.2.2 Measuring abnormal monthly relative volume

To calculate the abnormal relative volume of each stock (i), it is first necessary to quantify a measure of the normal relative volume. One should keep in mind that a firm’s trading volume can be influenced by several internal and external factors, which should be adjusted for (Dyl, 1977). To be able to measure the abnormal relative volume several ratios should be calculated. The relative volume for each stock (i) in month (t) is calculated as follows:

𝑅𝑉_𝑖,𝑡 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠ℎ𝑎𝑟𝑒𝑠 𝑜𝑓 𝑠𝑡𝑜𝑐𝑘 𝑖 𝑡𝑟𝑎𝑑𝑒𝑑 𝑖𝑛 𝑚𝑜𝑛𝑡ℎ 𝑡

𝐴𝑣𝑔. 𝑚𝑜𝑛𝑡ℎ𝑙𝑦 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑠𝑡𝑜𝑐𝑘 𝑖 𝑖𝑛 𝑚𝑜𝑛𝑡ℎ 𝑡 − 1 𝑢𝑛𝑡𝑖𝑙 𝑡 − 12 (2) The relative volume for all stocks in the market8 in month (t) is calculated as follows:

𝑅𝑉_𝑚,𝑡 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠ℎ𝑎𝑟𝑒𝑠 𝑜𝑓 𝑎𝑙𝑙 𝑠𝑡𝑜𝑐𝑘𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑚𝑎𝑟𝑘𝑒𝑡 𝑡𝑟𝑎𝑑𝑒𝑑 𝑖𝑛 𝑚𝑜𝑛𝑡ℎ 𝑡

𝐴𝑣𝑔. 𝑚𝑜𝑛𝑡ℎ𝑙𝑦 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑎𝑙𝑙 𝑠𝑡𝑜𝑐𝑘𝑠 𝑖𝑛 𝑚𝑎𝑟𝑘𝑒𝑡 𝑖𝑛 𝑚𝑜𝑛𝑡ℎ 𝑡 − 1 𝑢𝑛𝑡𝑖𝑙 1 − 12 (3) In Eq. 2, the relative monthly volume of each stock (i) is calculated. Not only does this control for firm-specific characteristics by taking an average twelve-month volume, it also controls for firm size by normalizing the volume by the twelve-month average.

Both relative volume ratios (see Eq. 2 and 3) are applied in an OLS-regression to show the influence that market events have on the trading volume of individual stocks. It is especially important to do so as the sample includes times of great financial instability. The OLS-regression is as follows:

𝑅𝑉_𝑖.𝑡 = 𝛼_𝑖+ 𝛽_𝑖𝑅𝑉_𝑚,𝑡+ 𝜀_𝑖,𝑡 (4) Here, 𝜀𝑖𝑡 is a random error term with an expectation of zero. The regression formula is applied to

each stock and relates the expected relative volume of stock (i) in month (t) (the dependent variable) to the relative volume of all stocks in the market in month (t) (the independent variable). Given that there is no abnormal relative volume, the conditionally expected relative volume can be defined as follows:

𝐶𝐸𝑅𝑉𝑖,𝑡 = 𝐶𝐸𝑅𝑉(𝑅𝑉𝑖,𝑡|𝑅𝑉𝑚,𝑡) = 𝛼̂𝑖 + 𝛽̂𝑖𝑅𝑉𝑚,𝑡 (5)

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15 The difference between what is expected of stock (i) in month (t) (see Eq. 5) and the actual relative volume of stock (i) that occurred in month (t) (see Eq. 1) is the abnormal relative volume (ARV) and is calculated as follows:

𝐴𝑅𝑉_𝑖,𝑡 = 𝑅𝑉_𝑖,𝑡 − 𝐶𝐸𝑅𝑉_𝑖,𝑡 = 𝑅𝑉_𝑖,𝑡 − 𝛼̂_𝑖 − 𝛽̂_𝑖𝑅𝑉_𝑚,𝑡 (6)

When 𝐴𝑅𝑉_𝑖,𝑡 is positive (negative), the relative volume is higher (lower) than expected. 𝐴𝑅𝑉_𝑖,𝑡 (from Eq. 6) is interpreted as the trading of stock (i) in month (t) being x-per cent abnormally above or below the 12-month historical average of the entire market in a certain month. Then, the return data is grouped into four ranges9 according to the price change that occurred. The ranges are defined as follows: 𝑅𝑎𝑛𝑔𝑒 1: 𝑅_𝑖,𝑡 < −20% (7)

𝑅𝑎𝑛𝑔𝑒 2: − 20% ≤ 𝑅_𝑖,𝑡 < 0% (8)

𝑅𝑎𝑛𝑔𝑒 3: 0% < 𝑅𝑖,𝑡 ≤ 20% (9)

𝑅𝑎𝑛𝑔𝑒 4: 20% < 𝑅_𝑖,𝑡 (10) For ranges 1 (big loser) and 2 (small loser), there has been a decrease in closing price in the current month (t) when comparing to month (t-12). Range 1 (2) is the range with the biggest (smallest) price decrease. For ranges 3 (small winner) and 4 (big winner), there has been an increase in price when comparing to month (t-12). Range 3 (4) is the range with the smallest (biggest) price increase. The obtained information is used to review investor behavior during all months of the year. This data allows us to see if investor behavior is different between small and large firms, or if it would indeed be valid to pool them for further analysis. For an overview of the descriptive statistics of these different samples, see Table 2.

3.2.3 Robustness

As a robustness test, the definition of the periods “before” and “during” the GFC2007 are changed. In the initial analysis, the period “before” the GFC2007 is defined as July 2001 - January 2008 while the period “during” the GFC2007 is defined as February 2008 - September 2009. To test for robustness, the entire sample is split up into three types of markets (a bull, bear, or normal market) based on the average monthly return data of the entire market. This is similar to the methodology of Dyl (1977). The individual monthly firm return data, as calculated in Eq. 1, are used to calculate the monthly average return of the entire market and for further categorization.

Then, based on Pagan and Sossounov (2003), a bear (bull) market is categorized as one where the price has dropped (risen) by more than 20% during a given month. All other price changes are categorized as a normal market. This study compares the current price for each month to that of one year in the past and therefore also categorizes this monthly average return data into one of the three market types.

9_{Note that not one of the ranges includes the group with a zero-percentage change in return over the past year. This}

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16 The “before” the GFC2007 period is redefined as a normal market period and the “during” the GFC2007 period is redefined as a bear market period. The robustness test includes all periods where the market on average experienced a drop in the price of at least 20% instead of solely focusing on the set timeframe of the global financial crisis. It is important to do this as the results should make predictions about investor behavior in times of financial instability, which is not only during the GFC2007. As this study looks at times with and without financial instability, only the normal and bear markets are reviewed. The “after” the GFC2007 is not redefined as this might still be partially influenced by the GFC2007.10

3.3 Hypotheses

Tax considerations are expected not to be the only factor influencing investor behavior. Investor behavior is expected to be influenced by tax-related as well as non-tax-related reasons. Furthermore, during a crisis period, investor behavior is expected to be different. Based on the theories presented in Sections 2.1, 2.2, and 2.3 as well as the methodology, the following five operationalized and technical hypotheses are defined.

Hypothesis 1 and 2 concerning trading behavior from January to November11_: 𝐻1₁: 𝐴𝑅𝑉̅̅̅̅̅̅_{𝑙𝑜𝑠𝑒𝑟𝑠} < 0

𝐻1₂: 𝐴𝑅𝑉̅̅̅̅̅̅_{𝑤𝑖𝑛𝑛𝑒𝑟𝑠} > 0

Based on hypothesis 1 and 2, range 1 and 2 (losers) are expected to have a significant negative effect on the average ARV in January through November. Range 3 and 4 (winners) are expected to have a significant positive effect on the average ARV in January through November.

Hypothesis 3 and 4 concerning the trading behavior in December12: 𝐻1₃: 𝐴𝑅𝑉̅̅̅̅̅̅_{𝑙𝑜𝑠𝑒𝑟𝑠} > 0

𝐻1₄: 𝐴𝑅𝑉̅̅̅̅̅̅_{𝑤𝑖𝑛𝑛𝑒𝑟𝑠} < 0

Based on hypothesis 3 and 4, range 1 and 2 (losers) are expected to have a significant positive effect on the average ARV in December. Range 3 and 4 (winners) are expected to have a significant negative effect on the average ARV in December.

Hypothesis 5 concerning trading behavior during the GFC2007:

𝐻1₅ ∶ 𝑖𝑛𝑣𝑒𝑠𝑡𝑜𝑟 𝑏𝑒ℎ𝑎𝑣𝑖𝑜𝑟 𝑑𝑢𝑟𝑖𝑛𝑔 𝑡ℎ𝑒 𝐺𝐹𝐶2007 ≠ 𝑖𝑛𝑣𝑒𝑠𝑡𝑜𝑟 𝑏𝑒ℎ𝑎𝑣𝑖𝑜𝑟 𝑏𝑒𝑓𝑜𝑟𝑒 𝑎𝑛𝑑 𝑎𝑓𝑡𝑒𝑟 𝑡ℎ𝑒 𝐺𝐹𝐶2007

Here, the trading behavior of before and after the GFC2007 is compared to that of during the crisis. Based on the diverging and contradicting results of earlier conducted studies, investor behavior is expected to be different during the period of the GFC2007 from February 2008 until September 2009.

10_{This does not mean that the “after” the GFC2007 data is not used. All data are categorized into normal, bear, and}

bull market groups. However, the normal market data are compared to the “before” the GFC2007 data and the bear market data are compared to the “during” the GFC2007 period.

11_{Based on the DE: overall, investors tend to hold on to losers and tend to sell winners}

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17

3.4 Data analysis

The descriptive statistics of the sample of firms as well as the entire market is shown in Table 2. As expected, the descriptive statistics of the sample of firms with a small market share are much smaller than those of the sample of firms with a big market share. The descriptive statistics of the entire market lie in between both. As expected the sample of firms with a small market share shows most variance, whilst the sample of firms with a big market share shows the least variance. Again, the variance of the market data lies in between both.

Table 2: Descriptive statistics, from July 2000 through June 2018

Name No. of firms Mean trading volume Mean no. of shares outstanding A Mean market value Var. (Monthly ROR) B

Sample of firms with a small market share 100 96,953 57,550 $375,987 0.013662

Sample of firms with a big market share 100 3,251,138 1,798,177 $64,121,717 0.006247

Entire sample (biggest and smallest) 200 878,876 927,864 $32,248,852 0.009955

Market 770 771,828 415,319 $12,433,804 0.010256

A

Here the number of shares outstanding is adjusted based on a cumulative factor to adjust shares that accounts for four main distribution events: 1) spin-offs, 2) rights issues, 3) issuances and offers, and 4) stock splits.

B_{Variance is based on the monthly rate of return.}

Fig. 3 presents the average relative volume of the entire market (red) and that of the entire sample (blue). The sample behaves closely similar to the market and therefore represents the market very well. It can be noticed that especially during the time of the GFC2007 the average relative volume had high peaks. This suggests that during times of financial instability investors seem to react differently when it comes to trading than during times of financial stability. There indeed might be different trading behavior in periods of financial instability.

Figure 3: The average relative volume of the entire market compared to that of the sample from July 2001 until June 2018 based on a six-month interval

-0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 07 /3 1 /2 0 01 01 /3 1/ 20 02 07 /3 1 /2 0 02 01 /3 1 /2 0 03 07 /3 1 /2 0 03 01 /3 0 /2 0 04 07 /3 0 /2 0 04 01 /3 1 /2 0 05 07 /2 9 /2 0 05 01 /3 1/ 20 06 07 /3 1 /2 0 06 01 /3 1 /2 0 07 07 /3 1 /2 0 07 01 /3 1 /2 0 08 07 /3 1 /2 0 08 01 /3 0 /2 0 09 07 /3 1 /2 0 09 01 /2 9/ 20 10 07 /3 0 /2 0 10 01 /3 1 /2 0 11 07 /2 9 /2 0 11 01 /3 1 /2 0 12 07 /3 1 /2 0 12 01 /3 1 /2 0 13 07 /3 1/ 20 13 01 /3 1 /2 0 14 07 /3 1 /2 0 14 01 /3 0 /2 0 15 07 /3 1 /2 0 15 01 /2 9 /2 0 16 07 /2 9 /2 0 16 01 /3 1 /2 0 17 07 /3 1/ 20 17 01 /3 1 /2 0 18

Average Relative Volume of the Market and the Entire Sample

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4. Results

4.1 The entire sample versus firms with small and big market shares subsamples

Tables 3 and 4 show the different ranges, their average return, and the number of observations. Each range has two periods13: 1) January to November, and 2) December. Range 1 and 2 (losers) are expected to have a negative average ARV from January to November, as losers are then expected to be held on to due to risk-seeking behavior, regret aversion, and loss aversion. Range 3 and 4 (winners) are expected to have a positive average ARV from January to November, as winners are then expected to be sold due to risk-averse behavior, pride-seeking behavior, and loss aversion. Range 1 and 2 (losers) are expected to have a positive average ARV in December, as losers are then expected to be sold due to the tax benefits that lower the net tax rate, window-dressing, and the turn-of-the-year effect. Range 3 and 4 (winners) are expected to have a negative average ARV in December, as winners are then expected to be held on to, to defer taxable gains and thereby lowering the net tax rate and due to window-dressing. The green and bold (red) cells stand for when the average ARV is (is not) as expected. Insignificant cells are left blank.

Tables 3 and 414_{, show that the sample of firms with a big market share is different from} the sample of firms with a small market share. The average ARV data of the sample of firms with a small market share has greater volatility that of the sample of firms with a big market share (see Appendix 2). Ferris, Haugen, and Makhija (1988) suggest that when the goal is to observe the behavior of individual tax-paying investors, that it might be wise to exclude firms with a big market share, as these are mostly held by tax-exempt investors. Due to the visible difference in the volatility of trading behavior, one can assume that the sample of firms with a big market share includes more tax-exempt investors. By pooling the data of the samples (see Appendix 3), the results become less significant than when only using the sample of firms with a small market share (see Table 3). Tax-exempt investors often do not represent the group of individual investors and therefore should be excluded. The focus of this study is on the behavior of individual tax-paying investors, meaning that from now on only the sample of firms with a small market share of Table 3 is reviewed.

13_{Appendix 4 shows the results when splitting up each year in twelve periods of one month instead of two periods.}

14_{Note that even though the hypotheses presented in Section 3.3 are one-sided, that the t-values and p-values calculated}

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19 Table 3: Sample of firms with a small market share

Range 𝑹̅𝒊,𝑻A N 𝑨𝑹𝑽̅̅̅̅̅̅𝒋𝒂𝒏−𝒏𝒐𝒗B 𝑨𝑹𝑽̅̅̅̅̅̅𝒅𝒆𝒄B 1 -40.69% 3,119 -0.082** 0.210** t-value _(-20.823) C _(51.331) p-value _0.000C _0.000 2 -7.91% 5,783 -0.056** 0.350** t-value _(-22.296) _(88.806) p-value _0.000 _0.000 3 8.68% 6,489 -0.043** 0.045** t-value _(-16.312) _(18.696) p-value _0.000 _0.000 4 65.76% 4,993 0.120** 0.047** t-value _(27.214) _(15.729) p-value _0.000 _0.000

A_{This is the average rate of return of all data points in a certain range.}

B _{This is the average abnormal relative volume of a certain range in a certain time period (January to November or}

December).

C _{Sample sizes for subsample comparisons (t-values/p-values) differ from the reported total sample sizes (N).}

* Significant at a five per cent level ** Significant at a one per cent level

Table 4: Sample of firms with a big market share

Range 𝑹̅𝒊,𝑻A N 𝑨𝑹𝑽̅̅̅̅̅̅𝒋𝒂𝒏−𝒏𝒐𝒗B 𝑨𝑹𝑽̅̅̅̅̅̅𝒅𝒆𝒄B 1 -34.91% 2,368 0.005 0.098** t-value _(1.105) C _(21.520) p-value _0.269C _0.000 2 -8.44% 4,514 -0.003 0.038** t-value _(-1.182) _(8.883) p-value _0.237 _0.000 3 9.92% 7,304 -0.012** -0.022** t-value _(-4.832) _(-9.425) p-value _0.000 _0.000 4 41.18% 6,210 0.015** -0.037** t-value _(3.715) _(-13.744) p-value _0.000 _0.000

December).

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4.1.1 Big Losers

Table 3 shows that, in the sample of firms with a small market share, big losers (range 1) have a negative average ARV from January until November. Appendix 4 shows that this is true for all months except for in June and October. This result is significantly nonzero (P=0.000) and consistent with the first alternative hypothesis that investors overall tend to hold on to their big losers abnormally from January to November as trading is 8.2% below average. Furthermore, big losers have a positive average ARV in December. This result is significantly nonzero (P=0.000) and consistent with the third alternative hypothesis that investors tend to sell their big losers abnormally in December as trading is 21% above average.

4.1.2 Small Losers

Table 3 shows that, in the sample of firms with a small market share, small losers (range 2) have a negative average ARV from January to November. Appendix 4 shows that this is true for all months except for in June. This result is significantly nonzero (P=0.000) and consistent with the first alternative hypothesis that investors overall tend to hold on to their small losers abnormally from January to November as trading is 5.6% below average. Furthermore, small losers have a positive average ARV in December. This result is significantly nonzero (P=0.000) and consistent with the third alternative hypothesis that investors tend to sell their small losers abnormally in December as trading is 35% above average.

4.1.3 Small Winners

Table 3 shows that, for the sample of firms with a small market share, contrary to expectations, small winners (range 3) have a negative average ARV from January until November. This result is significantly nonzero (P < 0.01), but inconsistent with the second alternative hypothesis. Appendix 4 shows that for almost all months the results are significantly negative, except for in March and June, meaning that it does not have to do with lack of power of the test. Investors overall tend to hold their small winners abnormally from January to November as trading is 4.3% below average. Also in December, the results are contrary to expectations as small winners have a positive average ARV. This result is significantly nonzero (P < 0.01), but inconsistent with the fourth alternative hypothesis. Investors tend to sell their small winners abnormally in December as trading is 4.5% above average. Instead of deferring taxable gains, investors incur taxable gains by selling their small winners.

4.1.4 Big Winners

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4.2 Before, during, and after the global financial crisis of 2007

In this Section, the trading behavior of investors before, during, and after the GFC2007 is shown in Tables 5, 6, and 7.

4.2.1 Before the global financial crisis of 2007

The results in Table 5 are similar to those in Table 3, before splitting it up in before, during, and after crisis periods. Before the GFC2007 investors hold on to their losers throughout the year and sell them in December. The negative average ARV from January to November is significantly nonzero for small losers (P=0.010) and big losers (P= 0.000). These results are consistent with the first alternative hypothesis that investors tend to hold on to their losers abnormally from January to November. The positive average ARV in December is significantly nonzero for small losers (P=0.000) and losers (P=0.000). These results are consistent with the third alternative hypothesis that investors tend to sell their losers abnormally in December. Again, investors act to small winners as we would expect them to act to losers; holding on to them throughout the year, but selling them in December. The negative average ARV from January to November for small winners is significantly nonzero (P < 0.01), but is inconsistent with the second alternative hypothesis. The positive average ARV in December for small winners is significantly nonzero (P < 0.01), but is inconsistent with the fourth alternative hypothesis. Furthermore, throughout the entire year, investors sell their big winners. The positive average ARV from January to November is significantly nonzero (P=0.000) for big losers. This result is consistent with the second alternative hypothesis that overall investors sell their big winners abnormally from January to November. In December, they continue this behavior. The positive average ARV in December is significantly nonzero (P < 0.01), but contrary to the fourth alternative hypothesis.

Table 5: Sample of firms with a small market share before the GFC2007

Range 𝑹̅𝒊,𝑻A N 𝑨𝑹𝑽̅̅̅̅̅̅𝒋𝒂𝒏−𝒏𝒐𝒗B 𝑨𝑹𝑽̅̅̅̅̅̅𝒅𝒆𝒄B 1 -37.22% 1,037 -0.023* 0.135** t-value _(-2.566) C _(18.503) p-value _0.010 C _0.000 2 -7.46% 2,267 -0.029** 0.326** t-value _(-6.560) _(41.411) p-value _0.000 _0.000 3 8.04% 2,738 -0.023** 0.135** t-value _(-5.227) _(17.196) p-value _0.000 _0.000 4 56.24% 1,753 0.231** 0.134** t-value _(114.227) _(319.637) p-value _0.000 _0.000

December) before the GFC2007.

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4.2.2 During the global financial crisis of 2007

When reviewing the GFC2007 period in Table 6, most results are similar to the before the GFC2007 period. The only difference between the before and during the GFC2007 period is that the trading behavior of big winners in December has an expected negative average ARV. Thus, big winners are kept in December during the GFC2007. During the GFC2007 period, the negative average ARV in December is nonzero (P=0.000) and now in line with the fourth alternative hypothesis that investors tend to hold on to their big winners abnormally in December.

4.2.3 After the global financial crisis of 2007

When reviewing the after the GFC2007 period in Table 7, again most results are similar to the before and during the GFC2007 periods. The trading behavior of big losers has the expected negative average ARV similar to that of the before and during the GFC2007 periods. However, now this is insignificant. The trading behavior of big winners in December has an unexpected positive average ARV similar to that of the before the GFC2007 period. However, now this is insignificant. Note that when a group has a sign that is insignificant, this means that there is no abnormal selling or keeping behavior. This can be interpreted as investors behaving rationally, rather than irrationally selling (positive average ARV) or irrationally holding on to (negative average ARV) their investments.

Table 6: Sample of firms with a small market share during the GFC2007

Range 𝑹̅𝒊,𝑻A N 𝑨𝑹𝑽̅̅̅̅̅̅𝒋𝒂𝒏−𝒏𝒐𝒗B 𝑨𝑹𝑽̅̅̅̅̅̅𝒅𝒆𝒄B 1 -48.02% 1,226 -0.178** 0.416** t-value _(-25.165) C _(27.771) p-value _0.000 C _0.000 2 -9.76% 584 -0.130** 0.860** t-value _(-31.345) _(82.755) p-value _0.000 _0.000 3 6.20% 172 -0.073** 0.059** t-value _(-16.176) _(19.893) p-value _0.000 _0.000 4 60.88% 118 0.434** -0.109** t-value _(25.558) _(-78.467) p-value _0.000 _0.000

December) during the GFC2007.

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4.2.4 Comparing with the global financial crisis of 2007

Tables 8 compares the strength of the DE and the December effect between the before the crisis period and the crisis period. Table 9 compares the strength of the DE and the December effect between the after the crisis period and the crisis period. Both tables present the difference in average ARV for combined small and big losers and combined small and big winners during the two periods. The small and big ranges have been combined as the difference between small and big does not matter when analyzing whether the overall strengths of the DE and the December effect increase for either losers or winners during periods of financial instability. Furthermore, some of the subsamples, such as winners during the crisis, already are quite small when combining the ranges. Splitting these subsamples up in smaller groups would make testing, for some groups, impossible. It should be noted that the period from January to November represents the DE as here investors are expected to have the tendency to sell losers and hold on to winners. Furthermore, the December period represents the December effect as here investors are expected to have the tendency to sell losers and hold on to winners. For comprehensibility, the “difference coefficient” is adjusted in such a manner that whenever it is positive (negative), the effect is higher (lower) during the GFC2007. This means that when the average ARV is expected to be positive (negative) and it is more positive (negative) during the crisis, the difference coefficient is positive. For example, the average ARV for losers is expected to be negative for January to November. If it was -0.025 before the crisis and -0.075 during the crisis, then the difference coefficient is 0.05 because the DE is stronger during the crisis than before. Similarly, the average ARV for losers is expected to be positive in December. If it is 0.025 after the crisis and 0.075 during the crisis, then the difference coefficient also is 0.05 because the December effect is stronger during the crisis than after. The t-values and p-values are reported to show if the difference is significant.

Table 7: Sample of firms with a small market share after the GFC2007

Range 𝑹̅𝒊,𝑻A N 𝑨𝑹𝑽̅̅̅̅̅̅𝒋𝒂𝒏−𝒏𝒐𝒗B 𝑨𝑹𝑽̅̅̅̅̅̅𝒅𝒆𝒄B 1 -34.40% 856 -0.011 0.087** t-value _(-0.806) C _(13.974) p-value _0.420 C _0.000 2 -7.89% 2,932 -0.061** 0.348** t-value _(-13.900) _(50.688) p-value _0.000 _0.000 3 9.28% 3,579 -0.037** 0.088** t-value _(-9.820) _(21.116) p-value _0.000 _0.000 4 71.30% 3,122 0.044** 0.003 t-value _(7.785) _(0.725) p-value _0.000 _0.469

December) after the GFC2007.

(24)

24 Table 8: Comparing before the GFC2007 with during the GFC2007

Range 𝑹̅𝒊,𝑻A N 𝑫𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅𝒋𝒂𝒏−𝒏𝒐𝒗B 𝑫𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅𝒅𝒆𝒄B

All losers (range 1 + 2) -25.62% 5,114 0.134** 0.203

t-value _(8.990) C _(-1.814)

p-value _0.000 C _0.070

All winners (range 3 + 4) 32.84% 4,781 0.073 0.047

t-value _(-1.000) _(0.276)

p-value _0.317 _0.783

A_{This is the average rate of return of all data points in either all losing or all winning ranges.}

B _{This is the difference between the average abnormal relative volume before the GFC2007 and during the}

GFC2007 during a certain time period (January to November or December). In case it is positive, the effect (either DE or December effect) is larger during the GFC2007 and in case it is negative, it is smaller during the GFC2007.

Table 9: Comparing after the GFC2007 with during the GFC2007

Range 𝑹̅𝒊,𝑻A N 𝑫𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅𝒋𝒂𝒏−𝒏𝒐𝒗B 𝑫𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅𝒅𝒆𝒄B

All losers (range 1 + 2) -25.02% 5,598 0.112** 0.185

t-value (7.319) C _(-1.671)

p-value 0.000 C _0.096

All winners (range 3 + 4) 36.92% 6,991 0.133 0.052

t-value (-1.833) (0.309)

p-value 0.067 0.757

A_{This is the average rate of return of all data points in either all losing or all winning ranges.}

B _{This is the difference between the average abnormal relative volume during the GFC2007 and after the GFC2007}

during a certain time period (January to November or December). In case it is positive, the effect (either DE or December effect) is larger during the GFC2007 and in case it is negative, it is smaller during the GFC2007.

(25)

25 Based on the results in Tables 5, 6, and 7, the signs15 of the DE remain unchanged between the different periods. Furthermore, these tables show that the only signs that change are the DE sign for big losers and the December effect sign for big winners. Tables 8 and 9 show that only the DEL is significantly more present in the GFC2007 period compared to the before the GFC2007 (P=0.000) and after the GFC2007 periods (P=0.000). These results are consistent with the fifth alternative hypothesis. During times of financial instability, investors tend to hold on to losers even more actively from January to November compared to times of financial stability. Suggesting that during times of financial instability, investors tend to act even less rational when it comes to losers. All other measures also have a positive, but insignificant, sign. Meaning that the DEW and the December effect for losers as well as winners are not stronger during periods of financial instability. The results remain insignificant even when pooling the before and after the GFC2007 periods.

4.3 Robustness test

Table 5 defines the before the GFC2007 period as the period from July 2001 - January 2007. Table 10 shows the results when this period is defined as a normal market period where the price has dropped by 20% or less and increased by 20% or less. The results in both tables are identical, showing that the results are robust. Table 6 defines the GFC2007 period as the period from February 2008 - September 2009. Table 11 shows the results when this period is defined as a bear market period where the price has dropped by more than 20%. The result in both tables are identical, showing that the results are robust.

Table 10: Sample of firms with a small market share during a normal market

Range 𝑹̅𝒊,𝑻A N 𝑨𝑹𝑽 ̅̅̅̅̅̅_{𝒋𝒂𝒏−𝒏𝒐𝒗}B 𝑨𝑹𝑽 ̅̅̅̅̅̅_𝒅𝒆𝒄B 1 -37.64% 2,091 -0.057** 0.128** t-value _(-5.378) C _(18.968) p-value _0.000 C _0.000 2 -7.90% 4,485 -0.072** 0.289** t-value _(-16.776) _(40.127) p-value _0.000 _0.000 3 8.51% 4,724 -0.049** 0.041** t-value _(-13.747) _(10.910) p-value _0.000 _0.000 4 50.76% 2,586 0.167** 0.056** t-value _(20.977) _(10.494) p-value _0.000 _0.000

December) during a normal market.