Faculty of Economics and Business
THE EFFECT OF THE FINANCIAL CRISIS OF
2008 ON HERDING BEHAVIOR OF INVESTORS IN
THE UNITED STATES’
Bachelors’ Thesis
by
Bas van Kesteren
11021780
Thesis Supervisor: MSc Pascal Golec
April-June 2018
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Statement of originality
This document is written by Student Bas van Kesteren 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 ABSTRACT
This paper examines whether the financial crisis of 2008 had an impact on the degree of herding behavior on the United States’ financial markets. Specifically, we investigate the effect of extreme market returns, the direction of the market movement, and the financial crisis of 2008 on herding behavior. To measure the degree of herding behavior on the financial markets, the cross-sectional average dispersion method is used. By applying daily returns of all listed firms in the United States and the return of the S&P500, we conclude that herding behavior increased during the financial crisis of 2008. Furthermore, no evidence is found suggesting herding behavior to exist over the whole period. However, there is evidence that herding behavior is more likely to be present during declining markets compared to increasing markets. Moreover, proof is found suggesting herding behavior to occur more often during periods of extreme market stress.
4 TABLE OF CONTENTS
1. INTRODUCTION ...5
2. LITERATURE REVIEW ...7
2.1 Efficient market hypothesis compared to behavioral finance ...7
2.2 Herding behavior ...9
2.3 Previous research ... 11
3. METHODOLOGY ... 14
3.1 Measurements of herding behavior ... 14
3.2 Data ... 17
3.3 Testing for the presence of herding behavior ... 17
3.3.1 Herding behavior over the whole period ... 18
3.3.2 Herding behavior during extreme market movements ... 18
3.3.3 Herding behavior during up- and down-markets ... 18
3.3.4 Herding behavior during the financial crisis of 2008 ... 19
3.4 Heteroscedasticity and autocorrelation ... 20
4. RESULTS ... 21
4.1 Descriptive Statistics ... 21
4.2 Regression results main test... 22
4.3 Regression results extreme market movements ... 23
4.4 Regression results up- and down-markets ... 25
4.5 Regression results crisis ... 25
5. DISCUSSION ... 26
6. CONCLUSION... 28
5 1. INTRODUCTION
How does an investor react when they discover that the other investors made a decision that contradicts his private information? Will he stick to his own decision or is he going to follow the other investors?
The efficient market hypothesis states that the prices of securities will fully reflect all the available information to investors. The investment decisions of independent investors are based on the information available to them, this decision should not change as result of the decisions made by the other market participants (Fama, 1970). Most models in the field of economics and finance build upon the efficient market hypothesis and the rationality of investors. This results in a linear relationship between equity return dispersions and the market return (Bodie, Kane, & Marcus, 2014, pp. 350–352).
However, previous research concludes that because of the irrationality of some investors, the actual stock prices often contradict with the efficient market hypothesis (Lo, 2005; Malkiel, 2003). Behavioral finance attempts to combine psychology factors with the established financial theories, thereby trying to explain the irrationality of some investors (Bodie et al., 2014, pp. 362–363). One irrational decision often made by investors is acting as “herds”. Herding behavior is described as mimicking the investment decisions of other investors instead of following your own private analysis. Investors fear that their divergent belief will harm their reputation as good decision makers. (Scharfstein & Stein, 1990). On a market with herding behavior, a larger number of securities are needed to achieve the same level of diversification compared to a normal functioning market (Chang, Cheng, & Khorana, 1999).
Preceding research is very contradictive on the effect of the financial crisis, therefore, the main focus in this paper is to address the question whether the financial crisis of 2008 influenced the degree of herding behavior on the United States’ financial stock markets. Chiang & Zheng (2010), using weekly data of the firms listed on the New York Stock Exchange, found evidence suggesting the degree of herding behavior increased during the crisis. In contradiction, Lee (2017), using daily returns of all US industries, indicated that during the subprime crisis there was no proof of an increase in herding behavior. This paper uses daily data of all US listed firms and the S&P500, thereby using another approach than previous research to compare the degree of herding behavior before and after the crisis, to this degree during the crisis.
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In section two, a theoretical background regarding the efficient market hypothesis and herding behavior is presented, as well as a review of the preceding literature in the field of herding behavior. Section three provides a description of the used data, and addresses the specific research method used. Section four presents the results of the regression and section five discusses these results. Finally, section six concludes.
7 2. LITERATURE REVIEW
In order to fully comprehend the effects of the financial crisis of 2008 on the degree of herding behavior on the US financial markets, an extensive description of the essential theories and results of historical research are provided in this section. First a comparison of the efficient market hypothesis and behavioral finance is presented, as well as an explanation of herding behavior and its different forms and causes. Thereafter, an overview of relevant previous research in the field of herding behavior is presented.
2.1 Efficient market hypothesis compared to behavioral finance
Much of modern investment theory is based on the Efficient Market Hypothesis (EMH) (Lo, 2005). The EMH describes a market where investment decisions are based on the fully available information to the decision makers, such as investors and firms. As a result, prices will reflect the complete information set available. A market is considered to be efficient when the prices always reflect all the information (Fama, 1970). The EMH is built on the assumption that all market participants act rational, act in their own interest, and make their decisions by trading off costs and benefits (Lo, 2005).
There are three broad forms of the EMH. First, the weak form, which states that the information set contains only the history of the asset prices of the market. Second, the semi-strong form, in which the information set contains all the information that is publicly available. Third, the strong form, where the information set contains all possible information (Jensen, 1978). Jensen (1978, p. 4) states that the strong form of the EMH is an “extreme form which few people have ever treated as anything other than a logical completion of the set of possible hypotheses”.
Malkiel (2003) argues that some investors tend to act irrational. This causes pricing irregularities to exist and persist in the short run. Therefore, it is likely that the behavior of prices on the financial markets is not completely described by the EMH. It seems that lags exist in the adjustment process, which contradicts the belief that publicly available information is immediately priced in at the announcement (Basu, 1977). Furthermore, Lo (2005) argues that many departures from market rationality have been reported, in the form of behavioral biases. He describes EMH as the frictionless ideal; it would only hold when no market imperfections, such as the limits to the cognitive and reasoning abilities of investors, exist (Lo, 2005).
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Since the 1990s, the field of behavioral finance grew because the traditional models seemed to show many anomalies. Behavioral finance combines the field of finance with other social sciences, such as psychology and sociology; it studies the effect of psychology on finance. Describing markets as completely efficient cannot be regarded as an accurate description since financial markets do not always work well (Shiller, 2003). Ritter (2003) describes behavioral finance as the paradigm in which financial markets are described using models that are less based on expected utility theory and arbitrage assumptions. He argues that behavioral finance has two building blocks, namely cognitive psychology and the limits to arbitrage.
Cognitive psychology refers to the way people think. Psychologists reported some patterns of how people tend to behave. First of all heuristics, which are rules of thumb. These rules simplify decision making, however, they can causes biased decisions (Ritter, 2003). The next pattern is overconfidence. Investors tend to overestimate their abilities, it can diminish portfolio investments and can lead to firms making poor investment decisions (Bodie et al., 2014, p. 390; Ritter, 2003). Third is mental accounting, which refers to separating decisions which should be combined. For example, investors holding two investment accounts, of which one contains substantial more risk than the other account (Bodie et al., 2014, pp. 391–392; Ritter, 2003). Framing is the fourth pattern and refers to the fact that decisions can be influenced by the way choices are described (Bodie et al., 2014, p. 391). Fifth is representativeness, which relates to investors putting too much weight on recent experience, instead of looking at longer-term averages (Ritter, 2003). The sixth pattern is conservatism; investors seem to be slow in adjusting beliefs when changes occur, “They anchor on the ways things have normally been” (Ritter, 2003, p. 432). Last is the disposition effect, which is described as the incentive to sell assets that are in-the-money and hold on to assets out-of-the-money (Weber & Camerer, 1998).
The biases described above would not matter if arbitrageurs could exploit these mistakes. However, several limits exist on making profits from mispricing (Bodie et al., 2014, p. 394). Fundamental risk refers to the uncertainty regarding the time needed for prices to go back to intrinsic value. As John Maynard Keynes described: “Markets can remain irrational longer than you can remain solvent” (Bodie et al., 2014, p. 394). Another limit to arbitrage are the implementation costs. Specifically, short-selling comes with costs which can limit the profits of arbitrage. The last limitation is the model risk; there is uncertainty whether the apparent arbitrage opportunity is indeed such a profitable opportunity (Bodie et al., 2014, p. 395).
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As described above, nowadays EMH is the main assumption of the finance- and investment theories. However, it is questionable whether EMH really holds. Behavioral finance is a growing field since the EMH does not have an answer to many anomalies. Behavioral finance describes the irrational behavior of investors and the limits to arbitrage: it provides a more accurate description of the financial markets than EMH currently does. However, neither EMH nor behavioral finance provides the perfect description of the financial markets (Barberis & Thaler, 2003).
2.2 Herding behavior
There are many situations in which our decisions are influenced by the decisions other people made. Whether it is the decision about how many children to have, choosing a restaurant to go to, or voting during elections, it is likely that your decision is influenced by the behavior of others (Banerjee, 1992). This type of behavior is known as herding behavior.
Herding behavior has the possibility of explaining many phenomena in the field of finance, such as excess volatility and momentum (Nofsinger & Sias, 1999). It is described as the situation in which an investor copies the behavior of another investor, even though their private information might suggest a different action (Banerjee, 1992). Chiang & Zheng (2010) discuss that herding behavior causes trades on the financial markets to become correlated and to co-move. It is considered to be rational behavior for less informed investors, since obtaining their own information is too costly for them (Chiang & Zheng, 2010). Devenow & Welch (1996) explain that mass groups of investors buying one and the same stock, could also be due to simultaneous exposure to new information. Therefore, it is superior to relate herding to a population disposed to consistently erroneous decision-making (Devenow & Welch, 1996). Herding behavior can cause asset prices to conflict with their economic fundamentals; assets are not correctly priced in (Chiang & Zheng, 2010).
Herding behavior is in contradiction with the EMH (Caparrelli, D’Arcangelis, & Cassuto, 2004). While the EMH states that investors should buy a stock when it is undervalued and sell a stock when it is overvalued, investors participating in herding behavior neglect this statement and just follow the rest of the market participants. For this reason, herding behavior describes an inefficient market situation in which investors follow other investors to feel more secure (Caparrelli et al., 2004).
A distinction is made between intentional- and spurious herding. If investors are affected by the investment decisions of other investors, they may start copying a decision that
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is wrong for all of them: such a situation is called intentional herding (Sharma & Bikhchandani, 2000). When market participants make the same decisions, facing a comparable decision-making problem and an equal information set, this is called spurious herding. While spurious herding is considered to be an efficient outcome, intentional herding is not efficient. It is important, but also difficult to distinguish between these two forms of herding (Sharma & Bikhchandani, 2000).
Another distinction is made between irrational- and rational herding. According to Devenow & Welch (1996), irrational herding can be described from a psychologist point of view. It is explained as investors neglecting their own rational analysis and beliefs, and instead imitate the actions of other investors on the financial markets. Christie & Huang (1995), argue that one possible explanation for irrational herding is the presence of financial distress. Financial distress leads to uncertainty on the capital markets and it is likely that market participants start looking for ways to make them feel less uncertain (Caparrelli et al., 2004). For that reason, investors are more likely to suppress their own rational analysis and beliefs and instead follow the market consensus to make them feel more certain about their decisions (Christie & Huang, 1995). Rational herding is comparable to intentional herding, and it is described as the intention of an individual to copy the actions of the other market participants (Sharma & Bikhchandani, 2000).
There are three potential reasons for rational herding. The first reason is asymmetric information, second is the concern for reputation, and third is the compensation structure of investment managers (Sharma & Bikhchandani, 2000).
Sharma & Bikhchandani (2000) describe information-based herding as a situation in which all investors face similar investment decisions and there is uncertainty about the quality of the available information. As a result, each individual has its own private assessment on the quality of the information. Since an investor can observe the decisions of all the other market participants, he can make inferences about the private information the other possesses. The setting described above can lead to herding behavior under investors (Sharma & Bikhchandani, 2000).
Concern for reputation is a result of the uncertainty a manager has about his skills and/or abilities. If an investment manager is unconfident with his skills, conformity with other managers might cover up the uncertainty on the investors ability of managing the portfolio (Sharma & Bikhchandani, 2000). Suppose a market with only two investors. On this market, a herding equilibrium exists. In this equilibrium, the first investor will follow his own signal, whether this signal is informative or noise is unknown to the second investor. The second
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investor will follow the decision of the first investor regardless of the signal he received: he is uncertain about his abilities and avoids taking a decision different than that of the first investor and risk being fired. In the case that the common decision turns out to be incorrect, it is described as an unfortunate situation rather than a lack of skill of the manager (Sharma & Bikhchandani, 2000).
The final reason for rational herding is the compensation structure of investment managers. Suppose the compensation for an investment manager is based on his results compared to the results of other managers. Such a reward plan is likely to cause herding, since copying the decisions of the other managers would ensure that his individual results do not fall short compared to the results of the other managers (Sharma & Bikhchandani, 2000).
As explained above, there are several distinctions in herding behavior. First a distinction between intentional herding and spurious herding. While it is important to distinguish between these two forms, it is often considered to be difficult (Sharma & Bikhchandani, 2000). Furthermore, we consider irrational herding to be different from rational herding. Herding behavior contradicts with the EMH, it describes an inefficient market in which investors follow the herd to make them feel secure (Caparrelli et al., 2004).
2.3 Previous research
The section above described the theoretical background of the contradicting efficient market hypothesis and behavioral finance, as well as the background regarding herding behavior. This section provides the most significant results of the empirical research that have been conducted so far.
First, research showed that the characteristics of emerging markets are positively correlated with the likelihood of the presence of herding behavior on those markets (Economou, Kostakis, & Philippas, 2011). Economou et al. (2011) described that underdeveloped financial markets, exposure to volatile international capital, and thin trading are all potential reasons for this increased likelihood. Sharma & Bikhchandani (2001) add that weak reporting requirements, lower accounting standards, and costly information acquisition can potentially increase the degree of herding behavior on the financial markets. This view is supported by the research done by Chang et al. (2000). In their research on herding behavior on the financial markets of the US, Hong Kong, Japan, South Korea, and Taiwan, they only found evidence on the presence of herding behavior for South Korea and Taiwan: the two emerging countries in their sample. They explain that incomplete information disclosure in the
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emerging markets might be the reason for their findings. In addition, Lao & Singh (2011) found evidence on the presence of herding behavior on the Chinese and Indian stock markets. They supported the work by Sharma & Bikhchandani (2000) since these two markets are considered to be inefficient for the reasons described by Economou et al. (2011).
Next, some authors argue that the market capitalization of firms has an effect on the degree of herding behavior. However, this effect differs per observed country. Sharma & Bikhchandani (2000) presented evidence of relatively more herding behavior in stocks of small companies compared to stocks of larger companies. They argue that because there is less information available on small companies, investors are more likely to act according to the actions of the other market participants (Lakonishok, Shleifer, & Vishny, 1992; Sharma & Bikhchandani, 2000). Zhou & Lai (2009) performed research on the financial markets of Hong Kong. They divided the stocks on the financial markets into three subgroups: small-cap, mid-cap, and large-cap. Their results suggest an inverse relationship between the market capitalization of the stock and the degree of herding behavior, thereby supporting the theory of Sharma & Bikhchandani (2000). Conversely, the results of the research performed by Lao & Singh (2011) contradict the conclusion of Sharma & Bikhchandani (2000). They report that there is no herding behavior in small-cap stocks on the financial markets of India. They explain that this is the result of the higher associated risk with these stocks, resulting in an aversion of investors towards small-cap stocks. Therefore, individual investors rarely hold these stocks. The conclusions of Zhou & Lai (2009) and Lao & Singh (2011) support the statement that the effect of market capitalization on herding behavior differs across countries.
Third, there are significant results suggesting an effect of the direction of the market movement on the degree of herding behavior on the financial markets. Lao & Singh (2011) and Lee (2017) pointed out that degree of herding behavior increased during periods of negative price movements on the financial markets of the US and China, while there is relatively little evidence of herding behavior when these markets were in an upswing. The opposite holds for India; market participants are more likely to herd during periods of positive price movements on those financial markets (Lao & Singh, 2011). These conflicting results support the conclusion of Chiang, Mason, Nelling, & Tan (2008) that the degree of herding behavior is asymmetric during different market returns on the markets of Asia. Therefore, the degree of herding behavior during different market movements is likely to vary per country observed.
Moreover, Demirer, Kutan, & Chen (2010) suggest that during times of extreme market movements, herding behavior is more likely to exist. They explain that this is the result of investors being triggered to follow the market consensus during such periods. Caparrelli et al.
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(2004) performed research on the Italian stock markets, thereby using the method described by Christie & Huang (1995) and Chang et al. (2000). They found that herding is indeed more present during extreme market conditions. Lao & Singh (2011) investigated this hypothesis for the financial markets of India and China. They describe that due to psychological reasons, herding behavior is more likely to occur during extreme market conditions. To investigate whether this statement holds for the market of India and China, they compared the degree of herding behavior during normal market conditions to this degree during times of extreme conditions. To distinguish between normal- and extreme market returns, a cut-off of 10%, 5%, and 1% of the lower- and upper tails are used. They conclude that at a significance level of 1%, herding is more severe during extreme up- or down movements on the markets of India and China. One possible reason for this result is the fact that inexperienced market participants are easily misled by, for exampe, the media (Lao & Singh, 2011).
At last, Lee (2017), using weekly returns of the firms that were listed on the New York Stock Exchange (NYSE), found no evidence on the presence of herding behavior during the subprime crisis of 2008 in the United States. However, using daily industry- and market indices, the research by Chiang & Zheng (2010) provided evidence of herding behavior during the crisis of 2008. This conflicting view provides the opportunity to further investigate the effect of such a crisis on the degree of herding behavior by using another approach than Lee (2017) and Chiang & Zheng (2010).
14 3. METHODOLOGY
This paper reviews the relationship between herding behavior and the sign of the market return, the presence of the financial crisis of 2008 and extreme market movements for the US financial markets. This section starts with an explanation of return dispersion and the method that is used to measure the degree of herding behavior. Thereafter it describes the data that is used, and finally the statistical tests that are used to answer the research questions.
3.1 Measurements of herding behavior
When herding behavior is present on the financial markets, as described above, investors neglect their private information and instead follow the market consensus. As a result, the returns on individual securities are likely to follow the market return closely. Christie & Huang (1995) defined equity dispersions as the difference between the return on individual assets and the return on the equally-weighted market portfolio. Herding behavior and rational asset pricing models offer a conflicting view on the relationship between dispersions and extreme market movements. Whereas rational asset pricing models predict dispersions to be positively correlated with extreme market movements, the theorem of herding behavior describe that dispersions instead decrease (Christie & Huang, 1995). Previous research presented two methods for measuring the dispersions on a financial market. First the method of Christie & Huang (1995) is presented, and thereafter the method of Chang et al. (2000).
Christie & Huang (1995) described the cross-sectional standard deviation (CSSD) of individual returns with respect to the market return. It is measured using the following formulae:
𝐶𝑆𝑆𝐷$ = '
∑1 (𝑟+,$− 𝑟.,$)0 +23
𝑁 − 1 (1)
, where 𝑟+,$ is the return of firm i at time t, 𝑟.,$ is the cross-sectional average return on the market portfolio at time t, and N is the amount of firms in the market portfolio. CSSD is expected to be low when herding is present, however, it should be noted that low dispersions do not necessarily imply herding, it could be due to other reasons such as the lack of new information during trading intervals (Christie & Huang, 1995). The difference between the predictions of rational asset pricing models and herding behavior are most observed during
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periods of large price movements. Therefore, after calculating the CSSD, it is regressed against a constant and two dummy variables. These dummy variables indicate whether the market returns are located in the extreme lower- or upper tail of the distribution of market returns.
𝐶𝑆𝑆𝐷$ = 𝛼 + 𝛽3𝐷$9+ 𝛽
0𝐷$: + 𝜀$ (2)
, where 𝐷$9 (𝐷
$:) equals 1 when the market return is located in the 1% or 5% of the lower
(upper) tail of the market returns on time t, and is equal to zero otherwise. The constant 𝛼 accounts for the regions that are not covered by the two dummy variables. Because each individual asset differs in its sensitivity to the market, rational asset pricing models predict equity dispersions to increase during extreme market movements. In contradiction, when herding behavior is present during extreme market movements, this would lead to a reduced level of dispersion during those periods. This reduction would be reflected in a negative, statistically significant, coefficient for the two dummy variables (Christie & Huang, 1995). Since measuring herding using the CSSD can be relatively sensitive to outliers, Chang et al. (2000) suggest using the cross-sectional absolute dispersion (CSAD) instead of the CSSD. First the relationship between the CSAD and the market return in rational asset pricing models is explained. The capital asset pricing model is an example of a rational asset pricing model, and is expressed in the following formulae:
𝐸$(𝑟+) = 𝑟>+ 𝛽+∗ 𝐸$@𝑟.− 𝑟>A (3)
, where 𝐸$(𝑟+) is the expectation of the return at time t of the individual stock i, 𝑟> is considered to be the risk-free interest rate, 𝛽+ is the systematic risk measure of asset i, and 𝐸$(𝑟.− 𝑟>) is the expectation of the excess return of the market at time t. The systematic risk of the equally-weighted market portfolio is computed using the following formulae:
𝛽. = 1 𝑁C 𝛽+
1
+23
(4)
The absolute value of the dispersion of the return on one individual asset i from the equally-weighted market return at time t, can be expressed as:
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𝐴𝐷+,$= |𝛽+− 𝛽.| ∗ 𝐸$@𝑟.− 𝑟>A (5)
Consequently, we define the expected CSAD of all stock returns at time t as:
𝐸$(𝐶𝑆𝐴𝐷) = 1 𝑁C|𝛽+− 𝛽.| ∗ 𝐸$@𝑟.− 𝑟>A 1 +23 (6)
Therefore, the first- and second derivative become respectively:
𝑑𝐸$(𝐶𝑆𝐴𝐷) 𝑑𝐸$(𝑟.) = 1 𝑁C|𝛽+ − 𝛽.| > 0 1 +23 , (7) 𝑑0𝐸 $(𝐶𝑆𝐴𝐷) 𝑑𝐸$(𝑟.)0 = 0. (8)
These derivatives indicate that the CAPM-model predicts the relationship between the return on the equally-weighted market portfolio and the equity dispersions to be linearly increasing (Chang et al., 2000).
As shown, rational asset pricing models predict the relationship between equity dispersion and market returns to be linear and positive (Lao & Singh, 2011). Chang et al. (2000) argue that if market participants follow the market consensus during periods of extreme market movements, this relation will no longer hold; it results in a non-linearly increasing or decreasing relationship. Therefore, their research included an additional parameter in the regression equation to account for the possibility of a non-linear relationship. This results in the following regression equation:
𝐶𝑆𝐴𝐷$ = 𝛼 + 𝛾3P𝑟.,$P + 𝛾0@𝑟.,$A0+ 𝜀$ (9)
, where 𝑟.,$ is the daily return of the market portfolio at time t. If investors are following the
market consensus during periods of large price movements, the CSAD would decrease. As a result, the relationship between the CSAD and the market return becomes non-linearly decreasing, and this will be captured in a negative, statistically significant, 𝛾0 coefficient in the
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In this paper, the CSAD is calculated using the formulae proposed by Philippas, Economou, Babalos, & Kostakis (2013):
𝐶𝑆𝐴𝐷$ =∑1+23P𝑟+,$− 𝑟.,$P
𝑁 (10)
, where 𝑟+,$ is the return on the individual stock at time t, 𝑟.,$ is the market return at time t, and N is the amount of firms in the market portfolio. This is the most commonly used measure for dispersion in previous studies since it is less sensitive to outliers compared to the CSSD, and likewise, more powerful at indicating herding behavior (Philippas et al., 2013). The research done in this paper will be based on the regression equation above and on subtests derived from this equation.
3.2 Data
This research covers the period from January 2005 up until December 2011. This time frame raises the possibility to investigate the degree of herding behavior over a significant dataset. This period is relevant since it includes many extreme market movements, as well as the financial crisis of 2008. The dataset consists of the daily stock returns for all US listed companies and the daily return on the S&P500 index, and is obtained from the Center for Research in Securities Prices (CRSP) using the Wharton Research Data Services database. This way, since we consider the S&P500 return to be the best representative for economic development in the United States, the return on the S&P500 is used as the return on the market portfolio (𝑟.,$), and the daily returns of all companies reflect the individual stock returns (𝑟+,$). In this research, a total of 1763 daily CSADs, calculated using the individual returns of the companies and the index, were analyzed using the regression equations described in the next paragraphs.
3.3 Testing for the presence of herding behavior
This section describes the four statistical tests that are used in order to give an answer on the research question. First a main test over the whole period is considered, and thereafter some subtests are performed. The subtests will follow the approach described by Philippas et al. (2013), these alternative tests are adopted to test for the effects of the financial crisis of 2008, extreme market movements, and the direction of the market. For the tests described in the next
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paragraphs, as stated above, a negative and statistically significant 𝛾0 coefficient is considered to be an indication for the presence of herding behavior on the financial market (Chang et al., 2000).
3.3.1 Herding behavior over the whole period
For the main test of herding behavior on the US financial markets, the basic model proposed by Chang et al. (2000) as described in the previous section is used:
𝐶𝑆𝐴𝐷$ = 𝛼 + 𝛾3P𝑟.,$P + 𝛾0@𝑟.,$A0+ 𝜀$ (11)
, where 𝑟.,$ is the return on the market portfolio at time t.
Hypothesis 1. In the presence of herding we expect 𝛾0 < 0.
3.3.2 Herding behavior during extreme market movements
As described above, previous research has suggested that herding behavior is likely to be more present during periods of extreme market movements. To test whether this holds for the US financial markets, the following regression is implied on the data:
𝐶𝑆𝐴𝐷$= 𝛼 + 𝛾3P𝑟.,$P + 𝛾0𝐷ST$P𝑟 .,$P + 𝛾U@𝑟.,$A 0 + 𝛾VP𝑟.,$P𝐷ST$@𝑅 .,$A 0 + 𝜀$ (11)
, where 𝐷ST$ is a dummy variable that takes the value of one if the market return on that day is
located in the extreme lower (upper) tail of the distribution, and zero otherwise. In this research a cut-off point of 1%, 5%, and 10%, of the lower- and upper tail of the distribution, are used to differentiate between normal market times and periods of extreme up- and down movements. 𝑟.,$ is the return on the market portfolio at time t.
Hypothesis 2. In the presence of herding behavior we expect 𝛾U < 0, and 𝛾V < 𝛾U if these effects are more likely to occur during days with extreme market returns.
3.3.3 Herding behavior during up- and down-markets
As discussed in section 2, previous studies argued that the reaction of herding behavior on up- and down-markets is different across countries. To test whether herding behavior is more
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present during up- or down-markets on the US financial markets, the following regression is implied: 𝐶𝑆𝐴𝐷$ = 𝛼 + 𝛾3P𝑟.,$P + 𝛾0𝐷XP𝑟.,$P + 𝛾U@𝑟.,$A 0 + 𝛾VP𝑟.,$P𝐷X@𝑅.,$A 0 + 𝜀$ (12)
, where 𝐷X is a dummy variable that is equal to one on days with negative market returns and
zero on days with positive market returns, and 𝑟.,$ is the return on the market portfolio at time t. If herding behavior is more present during declining markets we would expect the cross-sectional average dispersion to decrease during those days.
Hypothesis 3. In the presence of herding behavior we expect 𝛾U < 0, and 𝛾V < 𝛾U if these effects are more likely to occur on days with negative market returns.
3.3.4 Herding behavior during the financial crisis of 2008
Finally, the effect of the financial crisis of 2008 on the degree of herding behavior is reviewed. As discussed, previous empirical research reasoned that the presence of a crisis is likely to increase herding because of the increase in uncertainty. For this research, the crisis period is defined as 06/01/2007 – 03/31/2009, thereby following the time-line presented by Guillén (2009). To test whether the financial crisis of 2008 caused the degree of herding behavior to increase, the following regression is implied:
𝐶𝑆𝐴𝐷$ = 𝛼 + 𝛾3P𝑟.,$P + 𝛾0𝐷YZP𝑟 .,$P + 𝛾U@𝑟.,$A 0 + 𝛾V𝐷YZ@𝑟 .,$A 0 + 𝜀$ (13)
, where 𝐷YZ is a dummy variable that is equal to one on the days during the crisis and zero
otherwise, and 𝑟.,$ is the return on the market portfolio at time t. If herding behavior is more present during a financial crisis, we would expect a decrease in the cross-sectional average dispersion for those days.
Hypothesis 4. In the presence of herding behavior we expect 𝛾U < 0, and 𝛾V < 𝛾U if this
20 3.4 Heteroscedasticity and autocorrelation
Heteroscedasticity refers to a situation in which the error terms in the regression are correlated to the value of the independent variables. Heteroscedasticity causes biased estimations for the standard errors of the coefficients, therefore, heteroscedasticity-robust standard errors should be used whenever heteroscedasticity is present in the data (Stock & Watson, 2015, pp. 204– 207). To test whether heteroscedasticity is present, we use the White test described by White (1980) for all regressions.
When the value of the dependent variable, CSAD, is correlated with its value in the next period, the data is called auto-correlated (Stock & Watson, 2015, pp. 574–575). To test whether autocorrelation is present, we use a Breusch-Godfrey test. This test measures whether the residuals of a regression are correlated across time (Breusch, 1978; Godfrey, 1978).
Since autocorrelation and heteroscedasticity were present in all of the regressions, we make use of Newey-West standard deviations for all regressions (Stock & Watson, 2015, pp. 647– 652). The number of lagged terms is determined using the formulae proposed by Schwert (2002). The tests for heteroscedasticity and autocorrelation, as well as the determination of the number of lagged terms for the Newey-West regressions, are included in the appendix.
21 4. RESULTS
This section starts with an overview of the descriptive statistics regarding the dataset proposed in the previous section. Subsequently it discusses the results of the regressions that were explained above. First the regression results over the whole period are discussed, second the results for extreme market returns, thereafter the results for different market movements, and finally the results for the period of the financial crisis.
4.1 Descriptive Statistics
Table 1 provides the descriptive statistics of the CSAD and the market return 𝑟.. It reports that the skewness of the market return is negative, this implies that there are slightly more days with a negative market return, than days with a positive market return in the dataset. Besides, the kurtosis for both variables is large. This statistic indicates that there are heavy tails in the distributions of the two variables. The range of the market return is approximately 20%, the size of this range is not outstanding since the financial crisis of 2008 is included in the sample. The minimum of the market return equals -9.035% and corresponds to 10/15/2008, this was during the financial crisis in the US. Both the CSAD and the market return are considered to be approximately normal distributed based on the Central Limit Theorem (Keller, 2012, p. 306).
Table 1: Descriptive statistics of CSAD and market return
CSAD Market return
Number of observations 1,763 1,763 Mean 0.0199481 0.0001276 Median 0.0170257 0.000818 Standard deviation 0.0085711 0.0145945 Minimum 0.0108447 -0.09035 Maximum 0.0831012 0.1158 Skewness 2.659816 -0.0430049 Kurtosis 12.31884 12.20014
Note: This table reports descriptive statistics for the cross-sectional average dispersion (CSAD) and the market return for the period 01/01/2005 – 12/31/2011. The S&P500 return is taken as the market return.
22 4.2 Regression results main test
Table 2 shows a summary of the results for the main regression which covers the whole sample period of 01/01/2005 – 12/31/2011, as explained in section 3.3.1. The positive coefficients of 𝛾3 and 𝛾0 relate to a financial market where the cross-sectional average dispersion tends to increase as markets are decreasing or increasing.
Table 2: Regression results whole period
𝐶𝑆𝐴𝐷$ = 𝛼 + 𝛾3P𝑟.,$P + 𝛾0(𝑟.,$)0 + 𝜀 $ 𝛼 𝛾3 𝛾0 Adjusted 𝑅0 0.0150665*** (0.004) 0.4977186*** (0.0780) 1.139226 (0.9975) 0.5405
Note: Newey-West standard deviation is between parentheses. (*) Significant at 5% sided, (**) significant at 1% two-sided, (***) significant at 0.1%. Sample size consists of the period 01/01/2005 – 12/31/2011, resulting in 1,763 daily observations.
Figure 1 plots the relationship between the return on the equally-weighted market return and the CSAD. This figure illustrates the linear relationship between the market return and the CSAD, thereby it supports the results of the regression over the whole period.
23
4.3 Regression results extreme market movements
Table 3 and 4 show the regression results for the extreme down- and the extreme up market respectively.
In table 3 the estimates for the coefficients of the regression during extreme down-markets are reported. For the 1% cut-off point of the lower tail, we see that 𝛾U is positive and insignificant. Furthermore, 𝛾V is negative and significant at the 5%-level one-sided. At the 5% cut-off point, 𝛾U is positive and insignificant. Moreover, 𝛾V is negative and significant at a
significance level of 5% one-sided. Finally, for the 10% cut-off point the regression reports a positive value for 𝛾U, and a negative value for 𝛾V. However, both estimates are insignificant.
Table 3: Regression results extreme down-markets
𝐶𝑆𝐴𝐷$= 𝛼 + 𝛾3P𝑟.,$P + 𝛾0𝐷ST$P𝑟 .,$P + 𝛾U(𝑟.,$)0+ 𝛾V𝐷ST$(𝑟.,$)0+ 𝜀$ Lower tail 1% 𝛼 𝛾3 𝛾0 𝛾U 𝛾V Adjusted 𝑅0 0.0150951*** (0.0004) 0.4822868*** (0.0849) 0.0500414 (0.0875) 1.967984 (1.2186) -2.318808* (1.0315) 0.5446 Lower tail 5% 𝛼 𝛾3 𝛾0 𝛾U 𝛾V Adjusted 𝑅0 0.0149276*** (0.0004) 0.5176514*** (0.0889) -0.0345374 (0.0435) 1.671112 (1.2631) -1.241781 (0.6814) 0.5461 Lower tail 10% 𝛼 𝛾3 𝛾0 𝛾U 𝛾V Adjusted 𝑅0 0.01482*** (0.0004) 0.550617*** (0.0938) -0.0811088* (0.0408) 1.293593 (1.2719) -0.6110883 (0.6946) 0.5481
Note: Newey-West standard deviation is between parentheses. (*) Significant at 5% two-sided, (**) significant at 1% two-sided, (***) significant at 0.1%. Sample size consists of the period 01/01/2005 – 12/31/2011, resulting in 1,763 daily observations.
Table 4 presents the estimates for the coefficients of the regression during extreme up markets. For the 1% cut-off point of the upper tail, it follows that 𝛾U is positive and 𝛾V is negative, both estimates are insignificant. At the 5% cut-off point, 𝛾U is positive while 𝛾V is negative.
24
However, both estimates are not significant. Finally, for the 10% cut-off point the regression reports a positive and statistically insignificant value for the coefficient of 𝛾U, and a negative insignificant estimate for 𝛾V.
Table 4: Regression results extreme up markets
𝐶𝑆𝐴𝐷$ = 𝛼 + 𝛾3P𝑟.,$P + 𝛾0𝐷ST$P𝑟 .,$P + 𝛾U(𝑟.,$)0 + 𝛾V𝐷ST$(𝑟.,$)0+ 𝜀$ Upper tail 1% 𝛼 𝛾3 𝛾0 𝛾U 𝛾V Adjusted 𝑅0 0.0151098*** (0.0004) 0.4970468*** (0.0805) 0.2510395* (0.1043) 0.6073495 (1.1770) -1.768609 (1.1874) 0.5462 Upper tail 5% 𝛼 𝛾3 𝛾0 𝛾U 𝛾V Adjusted 𝑅0 0.0153383*** (0.0004) 0.4434734*** (0.0731) 0.1982462*** (0.0510) 0.9555967 (1.0386) -0.934899 (0.6296) 0.5539 Upper tail 10% 𝛼 𝛾3 𝛾0 𝛾U 𝛾V Adjusted 𝑅0 0.0152563*** (0.0004) 0.4478715*** (0.0804) 0.1313894*** (0.0348) 0.9001603 (1.1130) -0.088878 (0.5257) 0.5507
Note: Newey-West standard deviation is between parentheses. (*) Significant at 5% two-sided, (**) significant at 1% two-sided, (***) significant at 0.1%. Sample size consists of the period 01/01/2005 – 12/31/2011, resulting in 1,763 daily observations.
25 4.4 Regression results up- and down-markets
Table 5 shows the estimates of the regression coefficients for equation 12. It reports a positive estimate for the coefficient 𝛾U, however, this value is not significant. In addition, it displays a negative value for 𝛾V, which is significantly smaller than zero at the 5% level. Moreover, testing
whether 𝛾V < 𝛾U results in a p-value of 0.0040. Therefore, the estimate for 𝛾V is significantly smaller than the estimate for 𝛾U.
Table 5: Regression results asymmetric herding
𝐶𝑆𝐴𝐷$ = 𝛼 + 𝛾3P𝑟.,$P + 𝛾0𝐷XP𝑟 .,$P + 𝛾U(𝑟.,$)0 + 𝛾V𝐷X(𝑟.,$)0 + 𝜀$ 𝛼 𝛾3 𝛾0 𝛾U 𝛾V Adjusted 𝑅0 0.0149635*** (0.0002) 0.5475193*** (0.0289) -0.0652096 (0.0334) 1.305795 (0.4572) -0.8799026 (0.6651) 0.5479
Note: Newey-West standard deviation is between parentheses. (*) Significant at 5% two-sided, (**) significant at 1% two-sided, (***) significant at 0.1%. Sample size consists of the period 01/01/2005 – 12/31/2011, resulting in 1,763 daily observations.
4.5 Regression results crisis
Table 6 reports the estimates for the regression coefficients of equation 13. It shows a positive estimate for the coefficient 𝛾U, this value is significantly higher than zero at a significance level of 1%. Furthermore, it reports a negative value for the coefficient of 𝛾V which is significantly lower than zero at the 1% level. Besides, testing whether 𝛾V < 𝛾U results in a p-value of 0.000.
Therefore, the estimate for 𝛾V is significantly smaller than the estimate for 𝛾U.
Table 6: Regression results crisis
𝐶𝑆𝐴𝐷$= 𝛼 + 𝛾3P𝑟.,$P + 𝛾0𝐷YZP𝑟 .,$P + 𝛾U(𝑟.,$)0 + 𝛾V𝐷YZ(𝑟.,$)0+ 𝜀$ 𝛼 𝛾3 𝛾0 𝛾U 𝛾V Adjusted 𝑅0 0.0158329*** (0.0004) 0.2038379* (0.0934) 0.5071288*** (0.1362) 5.899651** (1.9876) -7.458771** (2.3897) 0.5945
Note: Newey-West standard deviation is between parentheses. (*) Significant at 5%, (**) significant at 1%, (***) significant at 0.1%. Sample size consists of the period 01/01/2005 – 12/31/2011, resulting in 1,763 daily observations.
26 5. DISCUSSION
Before attempting to answer the research question, this section briefly discusses the results that were presented in the previous section and reviews whether the results are in line with previous research.
First, looking at the results for the regression over the complete time-period we observe a significant and positive value for the coefficient 𝛾3, and an insignificant value for the coefficient 𝛾0. Therefore, this regression shows no evidence of herding behavior on the US financial markets over the whole period of 01/01/2005 – 12/31/2011. Moreover, the results are in line with the rational asset pricing models which predict a positive linear relationship and thus only a positive, significant, value for 𝛾3. Considering the characteristics of emerging markets as described by Economou et al. (2011) and Sharma & Bikhchandani (2001), and the fact that the financial markets of the US do not match these descriptions, we assume the financial markets of the United States to be advanced. Taking into consideration that there is no proof in favor of herding behavior and that the US stock markets are advanced, the results of this regression are in line with the research of Chang et al. (2000): it supports the belief that herding behavior is less likely to be present on advanced stock markets.
Second, looking at the results for the regression regarding extreme down-markets, we observe that the coefficient 𝛾V is significantly negative for the 1% and 5% lower tails, and that
this coefficient is always smaller than the coefficient 𝛾U. These results relate to a financial market where herding behavior occurs more often during periods of extreme down-markets. The regression results for the periods of extreme up markets show that the estimates of 𝛾V are insignificant at all of the proposed cut-off points. Because of this insignificance, we can state that herding behavior does not occur more often during extreme up markets. The observations of these regressions support the statement described by Demirer et al. (2010) partly; herding behavior is indeed more likely to be present during extreme down-markets, however, this is not the case for extreme up-markets.
Third, the belief that herding behavior is more likely to be present during declining financial markets is discussed. Looking at the results, we can observe that the coefficient of 𝛾V is significantly negative and smaller than the positive estimate for 𝛾U. Testing whether 𝛾V is
significantly smaller than 𝛾U results in accepting the alternative hypothesis stating that 𝛾V is smaller than 𝛾U. So, while there is no significant evidence of herding behavior during the periods of increasing stock prices on the financial markets, there is proof of herding when
27
markets are declining. These results are in line with the research done by Lao & Singh (2011) and Lee (2017), and contribute to the belief that herding behavior increases during declining financial markets.
Finally, we review what happens to the degree of herding behavior on the financial markets of the US during the financial crisis of 2008. Looking at the results for the final regression, we observe a highly positive and significant value for 𝛾U, which is the coefficient for the days before and after the crisis. This indicates that before and after the financial crisis no herding behavior was observed. Moreover, the regression shows significant evidence against herding behavior for those days. For the days during the crisis a highly negative and significant value for 𝛾V is observed. This indicates that during the financial crisis of 2008 herding behavior was present on the markets, and that investors were likely to suppress their own beliefs and instead follow the market consensus. Combining these results, we can state that herding behavior increased during the financial crisis of 2008 on the US stock markets.
However, these results should be interpreted with caution. First, as discussed by Greenwood & Sosner (2007) and Wurgler (2010), the secular increase in index investing might cause an increase in comovement between the returns of the stocks included in these indexes. Furthermore, the developments on the financial markets raise the possibility of investors observing the same information simultaneously and therefore increase the correlation between prices and returns of assets on the financial markets (Veldkamp, 2006). For these reasons it is unclear whether the comovement of returns we have measured during the financial crisis of 2008 are indeed due to herding behavior on the financial markets.
28 6. CONCLUSION
This study examined whether market participants on the US stock markets are likely to participate in herding behavior. Furthermore it assesses whether this type of behavior is more present during extreme market returns, whether there is a difference between up- and down-markets, and whether the financial crisis of 2008 influenced this behavior.
In this paper the cross-sectional average dispersion, as described by Chang et al. (2000), is used to measure the degree of herding behavior of investors on the financial markets. When dispersion is measured using the CSAD, rational asset pricing models predict the relationship between dispersion and the market return to be positive and linear. Herding behavior would imply that investors neglect their own analysis and instead follow the market consensus, this behavior implies the relation between market return and dispersion to be non-linearly decreasing instead of linear. Therefore we used the non-linear regression equations explained by Philippas et al. (2013) in combination with other sub regressions to test whether herding behavior is present on the financial markets of the US.
The empirical results of this research show that over the whole period of January 2005 up until December 2011 no herding behavior is detected on the stock markets of the US. Investigating whether herding behavior is more present during increasing- or decreasing markets, revealed proof of herding behavior occurring more often during declining markets. Moreover, the results showed evidence of herding behavior being more likely to occur during extreme down movements on the markets. For the financial crisis of 2008 we find significant proof that herding behavior of investors increased during the crisis, compared to the days before and after the crisis.
This paper provided additional research on the presence of herding behavior on the US stock markets. However, as discussed, it is unclear whether the comovement during the crisis is indeed due to herding behavior, or that it is caused by other factors. Future research could use weekly and monthly data to assess whether herding behavior is a short-lived phenomenon or that it persists over time. Additionally, by distinguishing between small- and large cap stocks, future research could assess whether herding behavior depends on the size of the firm. Finally, to get a better understanding of herding behavior, future research could analyze the possible causes for the presence of herding behavior and the implications on the functioning of the financial markets.
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33 APPENDIX
HETEROSCEDASTICITY
The White test, as explained by White (1980), tests whether the residuals of the original regression are correlated to the dependent variables in the regression. An auxiliary regression is used with the squared residuals of the regression as dependent variables, the independent variables consist of a constant, all original independent variables and their squares and cross-terms. Suppose there are two independent variables in the original regression, then this would result in the following auxiliary regression:
𝑒+0 = 𝛼
]+ 𝛼3𝑋1+ + 𝛼0𝑋1+0+ 𝛼U𝑋2+ + 𝛼V𝑋2+0+ 𝛼_𝑋1+𝑋2+ + 𝑣+ (𝐴. 1)
, where 𝑒+0 are the squared residuals of the original regression, 𝛼
] is a constant, and 𝑋1, 𝑋2 are
the independent variables from the original regression. When testing for heteroscedasticity, the test statistic (TS) is the following formulae:
𝑇𝑆 = 𝑛𝑅0 ~ 𝜒
e>0 (𝐴. 2)
, where n is the amount of observations, 𝑅0 is the r-squared of the auxiliary regression, and df
equals the amount of independent variables in the auxiliary regression minus 1. The null hypothesis for this test is homoscedasticity, and therefore, homoscedasticity is rejected when the value of the test-statistic is larger than the critical value of 𝜒e>0 at the preferred significance
level (Stock & Watson, 2015, pp. 204–207; White, 1980). The test statistics and their p-values are displayed in table A.1.
34 Table A. 1: Results White-test
Heteroscedasticity test Observed nR0
Regression for whole period 44.38***
Regression for extreme down-markets, lower-tail 1% 45.32***
Regression for extreme down-markets, lower-tail 5% 44.82***
Regression for extreme down-markets, lower-tail 10% 43.34***
Regression for extreme up-markets, upper-tail 1% 40.15***
Regression for extreme up-markets, upper-tail 5% 37.61***
Regression for extreme up-markets, upper-tail 10% 40.28***
Regression for difference up- and down-markets 44.34***
Regression for influence of crisis 110.10***
Note: (*) Significant at 5%, (**) significant at 1%, (***) significant at 0.1%.
According to the White-test, homoscedasticity can be rejected at a significance level of 0.1% for all regressions. Thus, heteroscedasticity is present.
AUTOCORRELATION
Autocorrelation can be tested using the method described by (Breusch, 1978) and (Godfrey, 1978). It tests whether there exists correlation between the residuals of the regression. In order to so, an auxiliary regression is used. The value of residuals are regressed on the original independent variables and the lagged residual terms, thereby, the optimal amount of lagged terms is determined by using the formulae of Schwert (2002):
𝑡ij$ = 12 ∗ k 𝑛 100l
3 V
(𝐴. 3)
, where n equals the number of observations. This would result in the following auxiliary regression:
35
, where 𝑒+ is the residual at time i, all 𝑋+’s are the independent variables of the original regression, and 𝑒+q$rst is the residual at 𝑡ij$ periods ago. When testing for autocorrelation, the test statistic (TS) is the following formulae:
𝑇𝑆 = @𝑛 − 𝑡ij$A𝑅0 ~ 𝜒
e>0 (𝐴. 5)
, where n is the amount of observations, 𝑡ij$ is the amount of included lagged terms, 𝑅0 is the
r-squared of the auxiliary regression, and df equals 𝑡ij$. The null hypothesis for this test is 𝜌3 = 𝜌0 = ⋯ = 𝜌$rst = 0, this would imply that there exists no autocorrelation. No autocorrelation is rejected when the test-statistic is larger than the critical value of 𝜒e>0 at the
preferred significance level (Breusch, 1978; Godfrey, 1978; Stock & Watson, 2015, pp. 574– 575). The test statistics and their p-values are displayed in table A.2.
Table A. 2: Results Breusch-Godfrey test
Autocorrelation test Observed
Regression for whole period 1,287.916***
Regression for extreme down-markets, lower-tail 1% 1,304.509***
Regression for extreme down-markets, lower-tail 5% 1,317.871***
Regression for extreme down-markets, lower-tail 10% 1,323.502***
Regression for extreme up-markets, upper-tail 1% 1,305.797***
Regression for extreme up-markets, upper-tail 5% 1,326.467***
Regression for extreme up-markets, upper-tail 10% 1,327.800***
Regression for difference up- and down-markets 1,325.453***
Regression for influence of crisis 1,140.208***
Note: The number of included lagged terms equals 25. (*) Significant at 5%, (**) significant at 1%, (***) significant at 0.1%.
According to the Breusch-Godfrey test, no autocorrelation can be rejected at a significance level of 0.1% for all regressions. Thus, autocorrelation is present.
Since both heteroscedasticity and autocorrelation are present, we use the Newey-West variance estimator for the standard errors of the regression parameters (Stock & Watson, 2015, p. 651).
