Is the Dutch stock market prone to overconfident trading behavior?

Is the Dutch stock market prone to overconfident

trading behavior?

Hans Blom S2049686

Faculty of Economics & Business University of Groningen

Thesis MSc. Finance Supervisor: E. Karmaziene*

January 2017 Abstract

2 TABLE OF CONTENTS

1. INTRODUCTION 3

2. RELATED RESEARCH 6

2.1 COMBINING PAST LITERATURE 6

2.2 SHARE OWNERSHIP 8 2.3 LITERATURE REVIEW 8 2.4 FIRST HYPOTHESIS 9 2.5 SECOND HYPOTHESIS 9 2.6 THIRD HYPOTHESIS 10 3. METHODOLOGY 11 4. DATA 12 4.1 SAMPLE 12 4.2 OPERATIONAL VARIABLES 13

4.3 STATISTICAL TESTS FOR HYPOTHESIS TESTING 16

5. RESULTS 16

5.1 OVERCONFIDENT TRADING BEHAVIOR ON MARKET LEVEL 17

5.2 OVERCONFIDENCE IN DIFFERENT MARKET STATES 18

5.3 COMPARING THE THREE DUTCH STOCK INDICES 21

5.4 ROBUSTNESS CHECKS 23

5.4.1 GRANGER CAUSALITY TEST 23

5.4.2 IMPULSE RESPONSE FUNCTION 24

5.4.3 DETRENDED TURNOVER 24

5.4.4 LARGER TIME FRAME 25

5.4.5 VAR MODEL WITHOUT CCI 25

6. DISCUSSION AND CONCLUDING REMARKS 26

7. REFERENCES 28

8. APPENDICES 30

3 1. Introduction

Stock markets have been part of the economy for decades. In fact, the Dutch stock market is known to be one of the oldest stock markets in the world. However, little work has been done so far to study overconfident trading behavior on the Dutch stock market. The overconfidence model of Gervais and Odean (2001) predicts that positive returns on the market are followed by aggressive trading behavior of investors who hope to accumulate wealth quickly. Overconfident investors wrongly relate stock returns, which are earned on a market wide level, to their trading abilities (Statman, Thorley and Vorkink, 2006). Generally, investors hold long positions in equity markets, thus most investors profit from market increases. The Dutch stock market shows the same association to long positions, where short positions only count for less than 2% on a market wide level (Shortsell, 2017). However, this paper contains no consistent evidence that high market returns lead to high trading volumes in the subsequent months when controlled for market volatility, dispersion and the Consumer Confidence Index (CCI, hereafter).

Overconfidence is a cognitive bias and it might be difficult to prove its existence looking at it from an aggregate market perspective. However, the papers of Statman et al. (2006) and Metwally and Darwish (2015) take the same approach by looking at trading volume responses on high market returns on the US stock market and the Egyptian stock market, respectively. Both papers come up with similar conclusions about excessive trading volumes in the months after high returns. If overconfident trading behavior is a systematic cognitive bias from which most investors suffer, it must be possible to detect such behavior on an aggregate market level (Liu, Chuang, Huang and Chen, 2016).

4 Statman et al. (2006), and Metwally and Darwish (2015) who explain this delay by overconfident trading behavior. On an aggregate market level, I find a slightly positive and significant response of trading volumes on the third lagged market return with a coefficient of 0.06. According to the sample, current trading volumes are thus influenced by past market returns of three months before. The positive association is, however, not strong enough to relate this trading response to overconfident trading behavior.

Little literature is known about the overconfidence bias on the Dutch stock market, which consists in this paper of the stock indices Amsterdam Exchange Index (AEX, hereafter), the Amsterdam Midcap Index (AMX, hereafter) and the Amsterdam Small Cap Index (AScX, hereafter). Much research has been conducted in the United States on household level as well as on aggregate market level. However, traders on the Dutch stock market differ significantly from traders on the US market. On the Dutch Stock Market, individual investors are considered to be conservative, with large investments in institutions such as pension funds and insurance companies, and participate in an individualistic culture (Donkers and Van Soest, 1999). Firms which have been listed for decades on the AEX are for example AEGON, AKZO Nobel and ASML Holding. The outstanding shares of these firms are held by institutional investors for ratios of 83%, 92% and 84.2%, respectively. On the contrary, firms such as Walt Disney, Coca-Cola and Wal-Mart which are listed at the US Dow Jones Index have an institutional ownership of 57.81%, 63.81% and 28.87%, respectively. Chuang and Susmel (2011) find evidence that individual investors are more prone to overconfident trading behavior compared to institutional investors.

Concluding, a big difference between households in the Netherlands and the United States is the fraction of equity held in relation to their total financial assets. Over the years there has been a shift allocating the Dutch households’ financial assets to pension funds. The allocation in equity dropped from 14% in 2005 to 8.1% in 2015 whereas the allocation in pension funds rose from 43% to 60% in that same period (OECD, 2016). Pension funds in the Netherlands are known to have around 30% of their asset allocation invested in equities (Moss, 2017). On the contrary, for households in the United States the allocation to equity remained stable around 35% as well as the allocation to pension funds around 30% in the period 2005 to 2015 (OECD, 2016).

5 larger reaction henceforth in trading volume the months after. This is in line with the overconfidence hypothesis. In this paper, smaller capitalization stocks indeed experience higher returns in the Netherlands. These stocks also show more evidence that current trading volumes are influenced by past returns. The AScX shows trading volumes coefficients of 0.07 and 0.04 on the first and third lagged market return, whereas the AMX shows turnover coefficients of 0.11 and 0.08 on the first and fourth lagged market return. The AEX shows no significant results. However, this doesn’t prove that the market is prone to be overconfident. The coefficients are of a very small magnitude and there has to be a positive association on the second lagged market return as well. For comparison, the paper of Statman et al. (2006) provides turnover coefficients on the first and second lagged market returns of 0.82 and 0.43, respectively.

Lastly, I do not find evidence of more overconfident trading behavior in periods of low volatility compared to highly volatile periods. Chuang and Susmel (2011) prove that investors on the Taiwanese stock market trade more actively after market gains in low-volatility market states than in high-low-volatility market states, which is applicable for individual investors as well as institutional investors. Metwally and Darwish (2015) also state in their paper that the Egyptian stock market is more prone to be overconfident in upward trending periods than downward, volatile periods. In order to explore this relationship, I split the sample based on market volatility. The first period ranges from March 2005 to November 2007 and is little volatile. The second period is a highly volatile period ranging from November 2007 to December 2011. The third period starts in December 2011, ends in October 2016 and is known as little volatile. Only the second period shows a turnover coefficient of 0.35 on the second lagged market return. This means that there is a delay of one month before investors react on market returns. The delay cannot be explained by overconfident trading behavior since there is no significant result on the first lag, the previous month.

6 2. Related research and hypotheses

In this section I compare this paper to and briefly discuss my contributions in light of the related literature. While there is literature known about overconfident trading behavior in countries as the US, Taiwan and Egypt, no research has been conducted yet for overconfident trading behavior on the Dutch stock market. Table 1 gives an overview of the most important articles which are relevant to this paper. Most studies are focused on an individual investors’ level. Statman et al. (2006), Metwally and Darwish (2015), and Liu et al. (2016) conduct their research about the overconfidence theory on an aggregate market level for the US stock market, Taiwanese stock market and the Egyptian stock market, respectively. Their empirical findings are central in this paper.

2.1 Combining previous literature

This paper combines the research designs of Statman et al. (2006), and Metwally and Darwish (2015). Besides from monthly observations on the aggregate market, I split the sample in small, medium and large capitalization stocks on the one hand, and make a distinction in volatile periods and less volatile periods on the other hand. The reason to divide the sample based on market capitalization, is based on findings of the research of Statman et al. (2006). They investigate monthly trading data of the US stock market in the period 1962 to 2002 and find evidence for overconfident trading behavior on market level as well as on individual stock level. There is no other rational or behavioral explanation for excessive trading volumes in the months after high market returns. Investors are overconfident and mistakenly attribute the high market returns to their own skills which lead to high trading volumes afterwards. By splitting the sample in large, medium and small capitalization stocks, Statman et al. (2006) find evidence that small capitalization stocks are more prone to overconfident trading behavior than the larger stocks. The impact of retail investors, who own a higher proportion of smaller capitalization stocks, is larger in this category and explains the differences in the level of overconfidence among stocks.

7

Table 1. Literature review

Author, year and country Variables/proxy for overconfidence Sample Results

Daniel et al. 1998 A theory of securities market under- Model based on different theories Overconfident investors overestimate private information signals and underestimate (US) and overreactions based on investor from past literature. publicly available information.

overconfidence and self-attribution

Odean, 1998 Determination whether buying and Trades from 1987 - 1993 in 10.000 Overconfident investors may trade even when their expected gains through (US) selling securities outperform trading accounts provided by a nationwide trading are not enough to offset trading costs. In fact, even excluding trading costs

costs discount brokerage house. out of the sample, these investors experience lower returns when trading. Barber & Odean, 2000 Explanation for difference in turnover, 78,000 households at a large discount Households that trade the most earn the lowest returns compared to the market. (US) gross return and net return brokerage firm over a six-year period This is in line with the overconfidence bias: investors attribute returns to their own

ending in January 1997. skills, which make them trade excessively.

Gervais & Odean, 2001 The patterns in trading volume, Multi-period market model with Average levels of overconfidence are greatest for traders who have been trading (US) expected profits, price volatility resulting three different traders for a short time. With more experience, the trader comes to better recognize

from overconfidence is analyzed his own ability.

Barber & Odean, 2002 Overconfidence can explain the increase 1607 investors who switched from When investors go online, they trade more actively and more speculatively, (US) in trading and reduction in performance phone-based to online trading from resulting in a worse performance than the market. This is augmented by

1992 to 1995. self-attribution bias and the illusions of knowledge and control.

Glaser & Weber, 2003 Questionnaire about miscalibration, A sample of approximately 3000 Investors who think that they are above average in terms of investment skills (Germany) better than average effect, illusion of individual investors with online broker or past performance trade more.

control and unrealistic optimism. accounts between 1997 and 2001.

Statman et. al, 2006 Market trading volume responses on Monthly observations of turnover and Market trading volumes and individual trading volumes are positively related (US) returns as a overconfidence model return for the US stock market from to lagged market returns. Overconfident overestimate their abilities

is tested. 1962 to 2002. what explains high observed trading volumes.

Bailey et. Al, 2011 An investors' propensity to trade 6-year panel of trades and monthly Factor analysis suggests that biased investors often conform to stereotypes such (US) frequently, but unsuccessfully. portfolio positions of individual investors as overconfident. Behaviorally biased investors typically make poor decisions

at a major US discount broker. about trading frequency, for example, resulting in poor performance.

Metwally & Darwish, Market turnover ratios are used as The Egyptian Stock Market from 2002 The research finds a significant impact of past market return on current turnover 2015 (Egypt) proxies for overconfidence to 2012 using monthly observations of Market states are found to be strongly affecting the trading activity, especially

in different market states. stocks, returns and trading volumes. in an upward trending market.

Daniel & Hirshleifer Arguments that trading volumes are Reviewing two sets of empirical findings Overconfidence seems likely to be a key factor in financial decision-making. 2015 (US) excessive and the evidence that seemingly at odds with rational agent It provides a natural explanation for why investors who process the same public

stock returns are predictable. asset-pricing theories. information end up disagreeing so much.

Liu et al., 2016 Association of current trading volumes Weekly trading turnover and stock Consistent evidence that individual investors are more prone to overconfident trading (Taiwan) and past market returns, relating the returns from 2001 to 2014. behavior than institutional investors in upward market states, less volatile markets,

8 According to Daniel, Hirshleifer and Subrahmanyam (1998), overconfidence is on average greater in the period after positive market returns.

2.2 Share ownership

This paper further differs from previous literature because of the participants on the Dutch stock market compared to other countries as the US, Taiwan and Egypt. Individual investors are more prone to overconfident trading behavior than institutional investors. The Dutch stock market is known to be dominated by institutional investors. In Egypt, most of the controlling shareholders are individuals, families or influential institutions (Azzam, 2010). In Taiwan, most participants on the Taiwan Stock Exchange are individual investors, although institutional investors have become gradually more active over time (Liu et al., 2016). On the US stock market the same trend is observed as in Taiwan, but the proportion of individual investors is still significantly larger than in the Netherlands. Liu et al. (2016), and Chuang and Susmel (2011) compare the trading activity of individual versus institutional investors subsequent to market gains on the Taiwan Stock Exchange. They find that market gains make individual investors trade more actively in subsequent periods during up-state markets than institutional investors. Both papers provide extensive evidence that individual investors show more overconfident trading behavior than institutional investors.

2.3 Literature review overconfidence, trading volume and performance

9 2.4 Hypothesis 1

As behavior on stock markets is the same as aggregating the behavior of all investors, the overconfidence bias of individual investors will accordingly influence the behavioral of the overall stock market in return (Metwally and Darwish, 2015). The Dutch stock market is known to be small, but well sophisticated and with a lot of trading. Just as earlier findings in the US, Taiwan and Egypt I expect that the Dutch stock market also shows evidence of overconfident trading behavior, although I expect a smaller effect because of the domination of institutional investors on the market. They are less influenced by short-term movements than individual investors. Based on the previous discussion, the first hypothesis is:

H1: Investors are overconfident and, therefore, the current trading activity is positively related to past market returns on the Dutch stock market.

The outcomes of this paper may also contradict the findings of Statman et al. (2006), Chuang and Susmel (2011) and Metwally and Darwish (2015). According to Chuang and Susmel (2011), the Taiwanese stock market shows evidence that individual investors trade with more overconfidence than institutional investors. Liu et al. (2016) come up with the same findings. They also find evidence that individual investors are more prone to overconfident trading behavior than institutional investors when the market is in an upward state and less volatile.

2.5 Hypothesis 2

Past literature (Metwally and Darwish, 2015; Liu et al. 2016; Chuang and Susmel, 2011) provides evidence that the level of overconfidence differs in different market states. In general, investors hold long positions in the stock market, thus profit when there are market wide positive returns. Overconfident investors will wrongly relate the market returns to their trading abilities. Upward trending markets are followed by overreactions under the assumption that investors are more prone to be overconfident then (Cooper, Gutierrez Jr and Hameed, 2004). Metwally and Darwish (2015) find evidence on the Egyptian stock market that the market is indeed more prone to be overconfident in upward, calm market states than downward, volatile periods. Highly volatile periods are often equal to periods of negative market returns. Lower volatile periods on average experience higher returns and occur when the economy is upward trending. Investors are expected to become more overconfident during these times. A period consists of multiple months based on market volatility.

10 H2: Investors’ overconfidence is higher in low-volatility periods than in periods which are volatile and so trading activity is affected in subsequent periods.

In line with the expectations regarding the first hypothesis, I expect the difference between the periods to be smaller than in the papers of Metwally and Darwish (2015) and Liu et al. (2016) because of the larger proportion of individual investors on the Egyptian and Taiwanese stock market, respectively. The Dutch stock market, on the contrary, is known to be dominated by institutional investors. Individual investors are usually seen as amateurish and less experienced investors, whereas institutional investors are seen as professional, more experienced investors and are less influenced by short term market movements (Liu et al. 2016).

2.6 Hypothesis 3

Lastly, earlier research in this field has found interesting evidence among stocks with different market capitalizations. Statman et al. (2006) makes such a distinction on the NYSE (New York Stock Exchange) and divide the sample in large capitalization stocks, medium capitalization stocks and small capitalization stocks. This distinction in terms of market capitalization per stock has already been made on the Dutch stock market since the stock market is divided in the stock indices AEX, AMX and AScX, ranked on market capitalization. They find that overconfidence trading is more pronounced for smaller capitalization stocks and appears to be declining over time. A further explanation is given by Gompers and Metrick (2001). They find evidence that size regularities may be related to the impact of retail investors, who hold relatively more smaller capitalization stocks. The third and last hypothesis is based on the previous discussion:

H3: Small-capitalization stocks are more prone to overconfident trading behavior than medium-capitalization stocks and large-capitalization stocks.

11 3. Methodology

The main objective is to relate returns to trading volumes in the periods afterwards, which can be explained as overconfident trading behavior in the case of significant and excessive trading volume responses. To elaborate on this relationship, I test whether past market turnover is also correlated with market return. If that is the case, the results are biased and show that return and turnover are auto correlated. Turnover and trading volumes are used interchangeably in the remainder of this paper.

The most accurate method for exploring the relationship between market return and turnover is a vector autoregressive model (VAR, hereafter), a time-series analysis. This model is also used in the papers of Statman et al. (2006), and Metwally and Darwish (2015). In a VAR there is more than one dependent variable, which makes the model a hybrid between simultaneous equations models and univariate time series models (Brooks, 2014). This is a convenient feature for this research since the relationships of both return and turnover can be observed towards each other and towards independent variables, which influence the movements of return and turnover.

To evaluate the turnover response on monthly returns earned by the total market, I estimate the following monthly time-series regression:

( 𝑚𝑡𝑢𝑟𝑛𝑡 𝑚𝑟𝑒𝑡𝑡 ) = ( 𝛼 𝑚𝑡𝑢𝑟𝑛𝑡𝛼 𝑚𝑟𝑒𝑡𝑡 ) + ∑ 𝐴𝑘 (𝑚𝑡𝑢𝑟𝑛𝑡_𝑘𝑚𝑟𝑒𝑡𝑡_𝑘 ) 10 𝑘=10 + ∑ 𝐵𝑙 ({ 𝑚𝑣𝑜𝑙 𝑚𝑑𝑖𝑠𝑝 𝑐𝑐𝑖 ) + ( 𝜖 𝑚𝑡𝑢𝑟𝑛𝑡 𝜖 𝑚𝑟𝑒𝑡𝑡 ) 0 𝑙=0 , (1)

where _{𝑚𝑡𝑢𝑟𝑛𝑡} = the monthly aggregated market turnover, _{𝑚𝑟𝑒𝑡𝑡} = the monthly market return, 𝑘 = the number of monthly lags for market return and turnover, _{𝐴𝑘 (}𝑚𝑡𝑢𝑟𝑛𝑡_𝑘

𝑚𝑟𝑒𝑡𝑡_𝑘 ) = the regression coefficient for lagged monthly market return and turnover, 𝑙 = the number of monthly lags for market volatility, dispersion and CCI, _{𝐵𝑙 ({}

𝑚𝑣𝑜𝑙 𝑚𝑑𝑖𝑠𝑝

𝑐𝑐𝑖

) = the regression

coefficients for contemporaneous market volatility, dispersion and CCI, _{𝜖 𝑚𝑡𝑢𝑟𝑛𝑡} = the market turnover residual, and _{𝜖 𝑚𝑟𝑒𝑡𝑡} = the market return residual. The variables are aggregated on a value weighted basis rather than an equal weighted basis.

12 Within a VAR the number of lags must be estimated. I set the number of monthly lags at 10. The determination of this lag length is stated in Appendix 1. Past theories about overconfidence are not clear in setting a time frame for the association between returns and turnover. However, just as Statman et al. (2006) I set the lag length at 10, which in this analysis is based on the Akaike Information Criteria (AIC). When selecting a model which consist of a large sample size, the AIC model is the best fit model (Lutkepohl, 1991). Current values of return and turnover are compared towards each other looking back up to 10 months. If, for instance, current turnover shows positive and significant results on the last five lagged market returns, this means that markets returns of the last five months consistently influence current turnover. This proves that investors keep on trading more because of past returns, which may be due to overconfident trading behavior.

4. Data 4.1 Sample

The primary data set for this paper is information from Euronext, which is a European stock exchange seated in different European cities. Amsterdam is one of them. The website of Euronext provides monthly statistics about companies listed on the AEX, AMX and AScX. Having its origin in 1602, the Amsterdam Stock Exchange is considered the oldest securities market in the world for dealing in printed stocks and bonds (Braudel, 1983). The AEX index was initiated in 1983, followed by the introduction of the AMX index in 1995 and concluded by the AScX in 2005. All three indices are composed of 25 companies each, ranked in terms of market capitalization. The composition of each index is subject to changes as de-listings, initial public offerings and transfers to one of the other indices.

13 the total stock index. For convenience, in this paper the weight of each stock on the indices are estimated on a value-weighted basis and thus slightly differ from the real weightings. However, this does not influence the general results. Appendix 2 presents evidence that value-weighted calculations of returns are very close to return calculations which use real weightings.

Table 2 provides descriptive statistics about the full period of the Dutch stock market. The variables in the table are explained in the next section.

4.2 Operational variables

Market return is the monthly return of each index which can be calculated by comparing the closing price of the index with the closing price of the previous month. The percentage change is the index return of that month. The indices are adjusted for stock-splits and dividends. I measure the aggregated market return as

𝑚𝑟𝑒𝑡𝑡 = (𝑅𝐴𝐸𝑋𝑊𝐴𝐸𝑋) + (𝑅𝐴𝑀𝑋𝑊𝐴𝑀𝑋) + (𝑅𝐴𝑆𝑐𝑋𝑊𝐴𝑆𝑐𝑋) , (2) where 𝑅 is the monthly return for each index, and 𝑊 is the weight of each index relative to the accumulated market capitalizations of all 75 stocks per month. The average monthly market return for the full sample is 0.29%. The biggest loss is found in October 2008, where the market lost 19.48% of its value in one month, because of the global financial crisis.

Market turnover for each month is determined following the method of Lo and Wang (2000) who estimate trading activity per stock as

turnover= 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠ℎ𝑎𝑟𝑒𝑠 𝑡𝑟𝑎𝑑𝑒𝑑

𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠ℎ𝑎𝑟𝑒𝑠 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 (3) The eventual monthly market turnover is calculated by multiplying each firms’ turnover ratio

by their relative market capitalization compared to the total market capitalization. This is conducted in the same way as the value-weighted calculation in equation (2). The average

Table 2. Descriptive statistics market full period March 2005 - October 2016

Monthly Mean Median Maximum Minimum Standard Number of

14 aggregated monthly market turnover in is 9.02%. The month in which the most trading took place is also October 2008, when the market turnover estimated 20.77%.

An overview about market returns and market turnover per index over the full period is given in figure 1 and figure 2. Although the findings on an aggregate market level are central in this paper, figure 1 shows that the monthly returns of the three indices follow a similar pattern, whereas figure 2 shows that the small capitalization index, the AScX, has considerable lower raw turnover ratios than the two larger stock indices.

The first control variable is market volatility. The survey of Karpoff (1987) conducts research on the contemporaneous relationship between trading volumes and volatility, and proves how volatility is related to trading volumes. The most common way to determine volatility for stock indices is to use the standard deviation of closing prices. Instead of monthly observations, daily observations are used for estimations. Statman et al. (2006) also follow this approach to determine monthly volatility on an aggregate market level. Again, the value-weighted calculation of equation (2) is used to determine monthly market volatility. The average monthly market volatility is 2.06%. The most volatile month is, again, October 2008 with 11.12%.

Dispersion is the second control variable. This is equal to the monthly cross-sectional standard deviation of returns for each stock related to the return on the market. The proportion of idiosyncratic risk in stocks is related to dispersion. Dispersion controls for possible trading activities which can be related to the rebalancing of portfolios. Big differences between returns of individual stocks, for instance, could cause investors to trade stocks in order to hold equal portfolio weights (Statman et al. 2006). For each stock, I estimate dispersion as

15 Figure 1. Dutch stock indices compared 03/2005 to 10/2016. The basis of each index is set at 1000. The graph shows that the AScX beats the other indices, although the indices follow a similar pattern.

Figure 2. Monthly turnover per stock index over the full period. The AEX and AMX show consistently higher trading volumes than the AScX. The turnover peak is observed during the financial crisis, which started in November 2007.

0 500 1000 1500 2000

ASCX AMX AEX

0 0,05 0,1 0,15 0,2 0,25

16 The third and last control variable is the Consumer Confidence Index (CCI). This index is based on households’ planned spending related to their economic situation, both currently and expectations for the nearby future (OECD, 2016). It can be a good estimate about the level of confidence a consumer has about the economic state. The basic level is 100 and is focused on the Netherlands in the period subject to the research. Levels above 100 means that consumers have more confidence in the economy in contrast to levels below 100 where consumers are less confident.

4.3 Statistical tests for hypothesis testing

I test whether the variables are stationary and provide the results in Appendix 3. To examine the statistical significance of the coefficients for hypothesis tests, it is essential that all of the components of the VAR are stationary (Brooks, 2014). If the residuals prove to be non-stationary, this could lead to bias in the results. A useful way to test this for a VAR is by using an AR roots table on the lag structure. Since the modulus of each index at each lag is below one, all roots are inside the unit circle and the system is stationary.

Another test which I conduct is to test for autocorrelation in the residuals. The Autocorrelation LM test is a convenient method, which is stated in Appendix 4. The market shows significant results within the five percent rejection region at the first two lags, so a VAR(2) model would not be sufficient to capture all the dynamics. Choosing a VAR(10) model is sufficient, because the test shows insignificant results from lag 3 on. There is no serial correlation.

In Appendix 5 the results of testing for heteroskedasticity are provided. If the errors of the variables do not have a constant variance, it means that the variance changes with one explanatory variable or changes over time. Estimating a VAR model with the presence of heteroskedasticity could lead to inappropriate standard errors and observed inferences misleading (Brooks, 2014). The market indicates a probability value of 0.0777, which is outside the five percent rejection region. This means that standard errors are homoscedastic and have a constant variance. The data is unbiased and can be used for hypothesis tests.

5. Results

17 large market capitalization stocks, medium market capitalization stocks and small market capitalization stocks. Lastly, several robustness checks are conducted.

5.1 Overconfident trading behavior on market level

The method which is applicable to this paper is a Vector Auto Regression (VAR). The data of the Dutch stock market determines that the lags for the endogenous variables market return and market turnover is set at ten, which means that the regression looks back up to ten months to look for any correlation between market turnover and return within this period. The exogenous variables, which consist of a constant, market volatility, dispersion and the CCI are only regressed on contemporaneous values of market return and turnover. Table 3 shows the VAR estimations for the Dutch stock market during the full period, starting in March 2005, ending in October 2016. The columns are equal to the independent variables, whereas the rows are equal to the dependent variables. Calculations of the probability values in table 3 are provided in Appendix 6.

The most important association to observe in table 3 is the association between market turnover and lagged market return over multiple periods. Significant positive outcomes over multiple periods means that the investors on the market consistently trade more after gaining from market returns. This could be explained by overconfident trading behavior. The Dutch stock market doesn’t provide significant proof of this relationship in the first two lags, but indicates a significant result in the third lag measured by a probability value of 0.046 and a relating coefficient of 0.064.The positive coefficient of 0.062 in the second lag shows a probability value of 0.057 and thus falls just outside the five percent rejection region. The fifth lagged market return shows a coefficient of 0.073 on a probability value of 0.02. Investors on the market are on average responding to market returns after three and five months by trading slightly more. This doesn’t seem to give proof for overconfident behavior.

18 Table 3. Market VAR Estimation full period 2005 – 2016

Returns are aggregated to the market level on a value-weighted basis, as well as the other variables market turnover, volatility, dispersion and CCI. **, and * indicate significance at the 1, and 5 percent levels, respectively (two-tailed).

Lagged Market Turnover

mturn(t-1) mturn(t-2) mturn(t-3) mturn(t-4) mturn(t-5) mturn(t-6) mturn(t-7) mturn(t-8) mturn(t-9) mturn(t-10) mturn Coefficient 0.277 0.111 0.122 -0.106 0.304 0.170 0.090 0.103 -0.019 -0.202 Standard error 0.089 0.091 0.092 0.093 0.093 0.095 0.094 0.093 0.094 0.092 P-value 0.002** 0.229 0.191 0.259 0.002** 0.076 0.344 0.272 0.844 0.406 mret Coefficient 0.345 0.162 0.145 -0.110 -0.270 -0.083 -0.173 -0.637 0.548 -0.113 Standard error 0.235 0.242 0.245 0.246 0.247 0.251 0.250 0.246 0.249 0.243 P-value 0.145 0.503 0.553 0.655 0.276 0.742 0.489 0.011* 0.023* 0.220

Lagged Market Return

mret(t-1) mret(t-2) mret(t-3) mret(t-4) mret(t-5) mret(t-6) mret(t-7) mret(t-8) mret(t-9) mret(t-10) mturn Coefficient 0.048 0.062 0.064 0.039 0.073 0.016 0.027 0.044 0.008 0.037 Standard error 0.035 0.032 0.032 0.033 0.031 0.032 0.031 0.031 0.032 0.031 P-value 0.171 0.057 0.046* 0.232 0.020* 0.606 0.381 0.157 0.791 0.238 mret Coefficient -0.024 -0.057 0.042 -0.023 -0.133 -0.027 -0.188 -0.049 -0.037 -0.157 Standard error 0.091 0.086 0.084 0.086 0.082 0.084 0.082 0.082 0.084 0.082 P-value 0.795 0.508 0.623 0.789 0.108 0.745 0.025* 0.554 0.656 0.060 Exogenous Variables

19 Table 3 shows that market turnover is highly significantly auto correlated on the first lag with a probability of 0.002. The coefficient equals 0.277. The market return dependent variable shows few statistically significant coefficients, which is generally consistent with weak-form market efficiency, according to Statman et al. (2006). The only market return prediction anomaly is a positive and significant autocorrelation at the seventh lagged market return with a coefficient of -0.188 and a probability value of 0.025. This result is presumably because of a couple of coincidental high market returns with seven months in between. The returns are considered to be outliers in the sample. For instance, the market crash of

September 2008 (-19.38%) was followed by a market gain in April 2009 of 11.34%.

In line with the findings of Karpoff (1987) about trading volumes, the relation of market turnover to contemporaneous volatility is large and positive for the Dutch stock market seeing the coefficient of 0.798 and a highly significant probability value of 0.00. Volatile periods often show periods of high trading volumes. Although not being predictive in this model, table 3 shows that contemporaneous market volatility is negatively related to market returns. The market shows highly significant associations with a coefficient of -2.912 and a relating probability value of 0.00. Market return is positively related to contemporaneous dispersion looking at the coefficient of the market, which is 0.554. The corresponding probability value of 0.011 is significant. My findings about market volatility, dispersion and market return as a dependent variable seem to be in line with the findings of Statman et al. (2006). The CCI does not have consistent and significant correlations with market return and turnover.

5.2 Overconfidence in different market states

20 Table 4. Market VAR Estimations periods split in volatility

Average monthly volatility for the first, second and third period are 1.51%, 2.82% and 1.74%, respectively. Average monthly return for the first, second and third period are 1.30%, -0.95% and 0.77%, respectively. **, and * indicate significance at 1, and 5 percent levels.

Panel A: First period March 2005 - October 2007

Lagged Market Turnover

mturn(t-1) mturn(t-2) mturn(t-3) mturn(t-4) mturn Coefficient 0.480 0.105 0.043 0.503

P-value 0.052 0.657 0.874 0.121 mret Coefficient -0.115 0.103 -0.427 -0.341

P-value 0.733 0.757 0.277 0.437

Lagged Market Return

mret(t-1) mret(t-2) mret(t-3) mret(t-4) mturn Coefficient 0.066 0.282 -0.170 0.038

P-value 0.712 0.077 0.216 0.774 mret Coefficient -0.446 -0.319 -0.064 -0.108

P-value 0.086 0.152 0.738 0.570

Panel B: Second period November 2007 - November 2011

Lagged Market Turnover

mturn(t-1) mturn(t-2) mturn(t-3) mturn(t-4) mturn Coefficient 0.214 0.069 0.010 -0.015

P-value 0.176 0.649 0.945 0.914 mret Coefficient 0.268 0.199 0.511 -0.321

P-value 0.600 0.690 0.280 0.473

Lagged Market Return

mret(t-1) mret(t-2) mret(t-3) mret(t-4) mturn Coefficient -0.023 0.122 -0.004 0.014

P-value 0.667 0.027* 0.940 0.797 mret Coefficient -0.009 -0.173 0.219 -0.169

P-value 0.957 0.322 0.244 0.355

Panel C: Third period December 2011 - October 2016

Lagged Market Turnover

mturn(t-1) mturn(t-2) mturn(t-3) mturn(t-4) mturn Coefficient 0.087 -0.068 0.112 -0.230

P-value 0.542 0.628 0.423 0.106 mret Coefficient 0.773 -0.342 0.505 0.106 P-value 0.251 0.603 0.440 0.872

Lagged Market Return

mret(t-1) mret(t-2) mret(t-3) mret(t-4) mturn Coefficient 0.015 -0.012 0.027 0.052

P-value 0.645 0.733 0.393 0.106 mret Coefficient -0.137 -0.241 -0.034 -0.069

21 be tested, I set the lag length at four. This has been determined by the data of the first period, which is the shortest one. Evidence of this lag length is provided in Appendix 7.

In table 4 the results are stated of the three different periods. The comparison between the three periods doesn’t show many significant results between market turnover and market return. The only significant result can be observed in the crisis period where the coefficient of 0.122 in the second lagged market return has an influence on current market turnover. Although this is the relation I am interested in regarding this paper, it doesn’t back overconfident trading behavior. In that case, at least the first lagged market return also must show a significant positive coefficient.

Furthermore, I expected this result in the first and third period. This is not in line with any evidence of overconfident behavior on the markets and with the second hypothesis. H2: Market states affect investors’ overconfidence and so trading activity is affected in subsequent periods. Because of these results, the second hypothesis cannot be proved.

5.3 Comparing the three Dutch stock indices

The last hypothesis to be tested is to compare large capitalization stocks with medium capitalization stocks and small capitalization stocks. The determination of which stocks belong to which category is already done on the Dutch stock market since the market is divided in three indices, based on market capitalization. The observations of tables 3 and 4 already indicate that there is not much support of overconfident trading behavior on the market regarding the full sample and the sub-periods divided in volatility. However, the impact of each index on the eventual market index differs drastically. On average the market index is composed of the AEX, AMX and AScX with relative stakes in of 90%, 8% and 2%, respectively. Table 5 indicates the coefficients of the association of the return of each index in relation to the turnover on each index. Because of the high stake of the AEX in the eventual market index determination, it is not surprising that the results in panel A of table 5 are almost identical to the results in table 3. The AMX and AScX in panels B and C show significantly different results. The only similarity among the three stock indices is that turnover of each index is auto correlated in the first lag, which means that trading volumes of one month ago on average have a positive coefficient of 0.259, 0.233 and 0.396 on current trading volumes for the AEX, AMX, and AScX, respectively.

22 Table 5. Indices separated VAR Estimation full period 2005 - 2016

Index returns and turnover are determined on a value-weighted basis. **, and * indicate significance at the 1, and 5 percent level.

Panel A: AEX-index

Lagged Market Turnover

mturn(t-1) mturn(t-2) mturn(t-3) mturn(t-4) mturn(t-5) mturn(t-6) mturn(t-7) mturn(t-8) mturn(t-9) mturn(t-10) mturn Coefficient 0.259 0.099 0.113 -0.118 0.308 0.151 0.090 0.084 -0.010 -0.119

P-value 0.004** 0.272 0.219 0.203 0.001* 0.107 0.334 0.358 0.914 0.181

mret Coefficient 0.353 0.157 0.088 -0.155 -0.257 -0.051 -0.176 -0.552 0.611 -0.142

P-value 0.133 0.514 0.719 0.530 0.300 0.836 0.476 0.025* 0.014* 0.548

Lagged Market Return

mret(t-1) mret(t-2) mret(t-3) mret(t-4) mret(t-5) mret(t-6) mret(t-7) mret(t-8) mret(t-9) mret(t-10)

mturn Coefficient 0.029 0.056 0.048 0.023 0.062 0.005 0.020 0.023 0.002 0.023

P-value 0.409 0.092 0.145 0.500 0.052 0.872 0.532 0.460 0.958 0.464

mret Coefficient -0.018 -0.045 0.037 -0.016 -0.119 -0.007 -0.172 -0.023 -0.021 -0.141

P-value 0.851 0.607 0.670 0.854 0.160 0.936 0.042* 0.787 0.803 0.093

Panel B: AMX-index

Lagged Market Turnover

mturn(t-1) mturn(t-2) mturn(t-3) mturn(t-4) mturn(t-5) mturn(t-6) mturn(t-7) mturn(t-8) mturn(t-9) mturn(t-10) mturn Coefficient 0.233 0.113 0.196 0.013 0.167 0.076 -0.043 -0.066 -0.092 -0.107

P-value 0.009** 0.209 0.031* 0.886 0.076 0.411 0.644 0.461 0.331 0.261

mret Coefficient -0.017 -0.428 0.176 0.161 0.263 0.011 0.328 -0.544 0.120 -0.194

P-value 0.929 0.026* 0.354 0.405 0.184 0.955 0.095 0.005** 0.549 0.336

Lagged Market Return

mret(t-1) mret(t-2) mret(t-3) mret(t-4) mret(t-5) mret(t-6) mret(t-7) mret(t-8) mret(t-9) mret(t-10) mturn Coefficient 0.111 0.019 0.036 0.082 0.046 -0.017 -0.050 0.027 -0.045 0.085

P-value 0.009** 0.645 0.333 0.037* 0.247 0.664 0.205 0.496 0.246 0.026*

mret Coefficient 0.070 -0.108 0.231 -0.066 -0.032 -0.132 -0.113 -0.044 0.013 -0.148

P-value 0.433 0.207 0.004** 0.426 0.708 0.108 0.177 0.592 0.877 0.068

Panel C: ASCX-index

Lagged Market Turnover

mturn(t-1) mturn(t-2) mturn(t-3) mturn(t-4) mturn(t-5) mturn(t-6) mturn(t-7) mturn(t-8) mturn(t-9) mturn(t-10) mturn Coefficient 0.396 0.127 0.122 0.018 0.027 0.060 -0.008 0.087 0.125 -0.089

P-value 0.000** 0.211 0.227 0.855 0.788 0.551 0.939 0.390 0.223 0.355

mret Coefficient 0.813 0.073 -0.544 0.230 0.021 0.284 -0.538 -0.696 0.768 -1.007

P-value 0.055 0.872 0.231 0.612 0.964 0.535 0.243 0.130 0.099 0.022*

Lagged Market Return

mret(t-1) mret(t-2) mret(t-3) mret(t-4) mret(t-5) mret(t-6) mret(t-7) mret(t-8) mret(t-9) mret(t-10)

mturn Coefficient 0.066 -0.012 0.042 0.011 0.011 0.000 0.002 0.010 0.012 0.001

P-value 0.000** 0.536 0.025* 0.562 0.557 0.981 0.934 0.600 0.520 0.969

mret Coefficient 0.161 0.010 0.099 0.064 -0.143 -0.140 -0.034 0.009 0.108 0.049

23 this positive association does not exist anymore in the second lag. Since former overconfidence theories such as Statman et al. (2006) state that returns must influence trading volumes over multiple periods, overconfident trading behavior cannot be proved. For comparison, the paper of Statman et al. (2006) found significant coefficients of 0.819 in the first lag and 0.433 in the second lag. Apart from the length, also the magnitude of the coefficient differs drastically from their research.

The smallest stock index, the AScX, shows similar results. On the first lagged market return it provides a highly significant coefficient of 0.066. The second lag has no statistically significant coefficient, whereas the third lagged market return has a significant coefficient of 0.042 on current turnover. Although the effect of past market returns of up to three months is statistically proved, it does not show support for overconfident trading behavior. In that case at least the second lag should also show a positive and significant association of return to turnover. These findings do not provide enough evidence for overconfident trading on the market, but it does show that trades on the AScX are more subject to past returns than the AMX and the AEX. Trading volumes of smaller capitalization stocks are thus more influenced by past returns than large capitalization stocks. H3: Small-capitalization stocks are more affected by overconfidence than medium-capitalization stocks and large-capitalization stocks

The third and last hypothesis cannot be proved since there is too little evidence for overconfident trading behavior.

5.4 Robustness checks

In this section, several robustness checks are conducted which consist of a Granger Causality test, a Impulse Response Function, detrending trading volumes in a VAR model and, a larger time frame for several stocks and the exclusion of the CCI in a VAR model.

5.4.1 Granger Causality test

24 The first result of Appendix 8 shows that the hypothesis is rejected that market return does not Granger cause market turnover with a highly significant probability of 0.0005. I conclude from this result that current trading volumes have a correlation with past returns. There is no evidence of overconfident trading behavior because of this result, but the test does show that trades on the market are influenced by past returns. Seeking for Granger causality of market turnover towards returns gives no significant result. The hypothesis that market turnover does not Granger cause market return is not rejected on any significance level for the market since the probability is 0.0764 and falls outside the five percent rejection region. It cannot be proved that current market return is correlated with past turnover.

5.4.2 Impulse Response Function

Another method which is applied in the papers of Statman et al. (2006) and Metwally and Darwish (2015) is the Impulse Response Function. This method does not provide evidence either on overconfident trading behavior on the Dutch stock market. All the coefficient estimates of the VAR model are being used to explore the effect of a shock of the one variable to the other variable and vice versa. The impact of a residual shock is traced that is one sample standard deviation from zero and shows the effects over multiple periods. The descriptive statistics in table 2 provide an average market return of 0.29% and a standard deviation of 5.09%. This method thus shows what the long-term effect is of a market return shock of 5.38%. The results are indicated in Appendix 9. As can be observed, the response of a market return shock of 5.38% leads to an increase in market turnover of 0.18% in the first lag, has its peak in the sixth lag of 0.45% and after 12 months remains slightly positive till the end of 24 months. To put these numbers in perspective, the paper of Statman et al. (2006) shows a turnover response in the first month of almost 9%, remains positive up to six months and accumulates to a total of 30% in this period. My test accumulates to 1.8% in six months. This association is very small and it does not provide enough evidence that these higher trading volumes are due to overconfident trading behavior on the market.

5.4.3 Detrended turnover

25 turnover for trends. Detrended turnover is the monthly difference between turnover and its trend. I use this variable instead of the raw turnover ratio and implement this in a newly estimated VAR model on the market in the full period. The results are provided in Appendix 10. It does not lead to different outcomes. There is not a single significant coefficient of lagged market return to detrended market turnover. Detrending trading volumes neither proves the existence of overconfident trading behavior on the Dutch stock market.

5.4.4 Larger time frame

For this robustness check I use data of seven firms which have been listed on the AEX since the initiation of the index in February 1986. These firms are Aegon, Ahold-Delhaize, Akzo Nobel, Heineken, Philips Electronic, Unilever and Royal Dutch Shell. I aggregated return, turnover, volatility and dispersion again on a value-weighted basis and estimate this in a VAR model with 10 lags in the period March 1986 to December 2002. The findings are stated in Appendix 11. Only in the second lagged market return there is a positive significant coefficient of 0.056 observable on current turnover. After two months, there is thus a small response of market turnover on market return. Since this association is not present in the first lag, there is no evidence of overconfident trading behavior in subsequent months after a positive return.

5.4.5 VAR model without CCI

As a last robustness check I exclude the CCI from the VAR(10) model on an aggregate market level, as is conducted in table 3. The results are identical to table 3 and are provided in Appendix 12. In the VAR models of Statman et al. (2006), and Metwally and Darwish (2015) the CCI is also not included. Only the fifth lagged market return on market turnover shows a significant coefficient of 0.07. In contrary to the initial VAR(10) estimate in table 3, the third lagged market return on turnover does not show a significant association in Appendix 12. The probability value of 0.052 falls just outside the five percent rejection region. The effect is little, but the CCI has some influence on the VAR model. However, this does not change the general view. The association between lagged market returns and turnover are too weak to prove the existence of overconfident trading behavior.

26 6. Discussion and concluding remarks

Using the returns and trading volumes of each firm which is listed on one of the three Dutch stock market indices and aggregating this on a market level, does not give significant results to prove overconfident trading behavior over a period for almost 12 years ending in October 2016. Overconfidence is often used as an explanation of excessive trading volumes observed in stock markets following market gains (Liu et al., 2016). Behavioral finance theory suggests that investors’ overconfident trading is more pronounced during bull markets and up-market states (Chuang and Susmel, 2011). In my analysis, I find no evidence which backs this theory. However, it is observed that current trading volumes are influenced by past positive returns for at least one month. A possible explanation for this positive trading volume response is that positive market earnings are followed by reinvestments in the market, which seems to be logical. The effect is stronger for the small capitalization stock index AScX and the medium capitalization stock index AMX. This effect could be caused by the impact of retail level investors, who hold relatively more smaller capitalization stocks in their portfolios. In the research of Statman et al. (2006), the same effect is observed.

Furthermore, the Dutch stock market is known to be dominated by institutional investors, who are generally less influenced by short term market movements and hold stocks over the long term. Evidence of past literature about overconfidence on stock markets in the US, Taiwan and Egypt might not be good proxies since the US and Taiwan have a larger proportion of individual investors who trade on the market. Liu et al. (2016) find evidence that individual investors are more prone to overconfident trading behavior than institutional investors. The Egyptian stock market efficiency is weak, according to Metwally and Darwish (2015) as market anomalies tend to be more dominant in emerging markets. The results of this paper, along with the differences compared to previous literature, would suggest that the Dutch stock market is indeed efficient and investors behave rationally.

Concluding remarks

27 Odean (2000), portfolios of households are compared in which they find evidence that the high trading volume responses after market returns are indeed because of overconfidence. For further research I suggest to take a similar approach as Barber and Odean (2000) by gathering data about portfolios of investors and rank the portfolios on levels of trading activity. Comparing the portfolios on trading activity and returns could show evidence of overconfident trading behavior and a worse performance than the market. A further option is to compare portfolios of individual investors to institutional investors.

28 7. References

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30 8. Appendix

Appendix 1. VAR Lag Order Selection Criteria Market full period

Various information criteria are used for determining the optimal lag length of a VAR model. In this case, the Schwarz information criterion shows an optimal lag length of one, the Hannan-Quinn information criterion a lag length of five, whereas both the Final prediction error and the Akaike information criterion select a lag length of ten as optimal. The likelihood ratio (LR) is the least desirable since the LR test assumes that errors in the equation are normally distributed. Information criteria require no such normality assumptions concerning the distribution of errors. Since a VAR model uses OLS (Ordinary Least Squares), testing for normality is not an issue. Estimating a VAR(10) model is the most appropriate lag length because 10 lagged periods meet the requirements of all information criteria.

Endogenous variables: MARKET_RETURN MARKET_TURNOVER

Exogenous variables: C MARKET_VOLATILITY DISPERSION CCI

Lag LogL LR FPE AIC SC HQ

0 523.71 NA 0.00 -8.06 -7.88 -7.99 1 566.98 82.48 0.00 -8.67 -8.404160* -8.56 2 576.60 18.04 0.00 -8.76 -8.40 -8.61 3 581.06 8.21 0.00 -8.77 -8.32 -8.59 4 583.98 5.29 0.00 -8.75 -8.21 -8.53 5 597.37 23.86 0.00 -8.90 -8.27 -8.642915* 6 600.69 5.81 0.00 -8.89 -8.17 -8.60 7 606.27 9.585011* 0.00 -8.91 -8.11 -8.58 8 608.95 4.53 0.00 -8.89 -8.00 -8.53 9 614.13 8.58 0.00 -8.91 -7.93 -8.51 10 618.67 7.37 4.64e-07* -8.916647* -7.85 -8.48 11 619.22 0.88 0.00 -8.86 -7.70 -8.39 12 623.76 7.10 0.00 -8.87 -7.62 -8.36

31 Appendix 2. Value-weighted returns compared to real index returns

Variables which are aggregated to a market level are returns, turnover, volatility, dispersion and CCI. In this paper value-weighted calculations are used to determine index levels and market levels. The weight per stock depends on its market capitalization, which is explained in equation (1). Comparing this to real weightings per index, which are adjusted for dividends, does not show large differences in the table below. The general outcomes about market variables do not differ significantly when using value-weighted returns instead of real index returns.

Year

Real weights return (%) Value-weighted return (%) 2005 1.95 1.91 2006 1.25 1.37 2007 0.34 0.82 2008 -5.56 -4.23 2009 2.93 3.49 2010 0.69 0.98 2011 -1.06 -0.64 2012 0.85 1.09 2013 1.40 1.44 2014 0.48 0.78 2015 0.52 0.61 2016 0.20 0.59 Average 0.33 0.68

Appendix 3. Unit root test to prove a stationary system

Since the modulus on each lag is below one, the system is stationary and the data can be used for unbiased results. Modulus Lag 1 0.935817 Lag 2 0.924629 Lag 3 0.906805 Lag 4 0.847652 Lag 5 0.844505 Lag 6 0.841684 Lag 7 0.821036 Lag 8 0.802685 Lag 9 0.780173 Lag 10 0.757715

32 Appendix 4. VAR Residual Autocorrelation LM test

The two first lags both reject the null hypothesis of no serial correlation on a five percent level. The third lag does not reject the null hypothesis since the probability value of 0.094 falls outside the five percent rejection region. From the third lag on, the null hypothesis is not rejected, thus choosing a VAR(10) model is sufficient to avoid autocorrelation.

LM-Stat Probability Lag 1 10.818 0.029 Lag 2 15.885 0.003 Lag 3 7.934 0.094 Lag 4 4.163 0.384 Lag 5 7.347 0.119 Lag 6 3.201 0.525 Lag 7 1.142 0.888 Lag 8 4.595 0.332 Lag 9 1.383 0.847 Lag 10 2.074 0.722

Null Hypothesis: no serial correlation at lag order h Probabilities from chi-square with 4 degrees of freedom

Appendix 5. VAR Residual Heteroskedasticity White Test: No Cross Terms (only levels and squares)

Testing the variables on heteroskedasticity is the last method which must be conducted in order to use OLS for regression estimates. The residuals do not reject the null hypothesis on a five percent region that the residuals are homoscedastic with a probability value of 0.078.

Joint test

Chi-square 162.2315

degrees of freedom 138

Probability 0.078

Individual components:

Dependent R-squared F(46,83) Prob. Chi-sq(46) Prob.

res1*res1 0.516 1.922 0.005 67.058 0.023

res2*res2 0.340 0.931 0.598 44.255 0.546

res2*res1 0.418 1.297 0.151 54.360 0.186

33 Appendix 6. Calculations T-test

To calculate probability values for each coefficient in a VAR model, I use a statistical method which differs per lag and sample size. Parameters are estimated as

𝑔 + 𝑘 (𝑔2) , (5) where 𝑔 = the number of equations, one for each of 𝑔 variables, and 𝑘 = the number of lags. There are

two equations in the VAR model in this paper. One equation for market return and one equation for market turnover. The number of parameters for lag 9 is, for example 2 + 9 (22_{), which equals 38.} Degrees of freedom are determined by subtracting parameters from the number of observations in the sample. The sample size of the full period is 140. However, since I estimate a VAR(10) model, the adjusted number of observations is 130. The probability value can be determined afterwards by making use of a two-tailed test table. The degrees of freedom are known as well as the two-tailed T-statistic per coefficient. The table below is used for the calculation of lagged market return coefficients on turnover in table 3.

Parameters Degrees of T-statistic P-value

Freedom (two-tailed) Lag 1 6 124 [ 1.37611] 0.171 Lag 2 10 120 [ 1.92548] 0.057 Lag 3 14 116 [ 2.01240] 0.046* Lag 4 18 112 [ 1.20074] 0.232 Lag 5 22 108 [ 2.36827] 0.020* Lag 6 26 104 [ 0.51694] 0.606 Lag 7 30 100 [ 0.87987] 0.381 Lag 8 34 96 [ 1.42691] 0.157 Lag 9 38 92 [ 0.26575] 0.791 Lag 10 42 88 [ 1.18929] 0.238

Appendix 7. VAR Lag Order Selection Criteria sub periods

The optimal lag length for the results in table 4 is a VAR(4). Using a lag length of ten for small samples would rapidly use degrees of freedom and lead to high standard errors on the coefficients. As is stated in the table below a lag length of four is the most optimal for the final prediction error, the Akaike information criterion and the Hannan-Quinn information criterion.

Endogenous variables: MARKET_RETURN MARKET_TURNOVER

Exogenous variables: C MARKET_VOLATILITY DISPERSION CCI

Lag LogL LR FPE AIC SC HQ

0 125,61 NA* 0,00 -9,05 -8.659859* -8,94 1 129,57 6,09 0,00 -9,04 -8,46 -8,88 2 134,06 6,22 0,00 -9,08 -8,31 -8,86 3 137,65 4,42 0,00 -9,05 -8,08 -8,77 4 146,02 9,02 3.34e-07* -9.386508* -8,23 -9.052090* 5 147,23 1,11 0,00 -9,17 -7,82 -8,78 6 151,34 3,16 0,00 -9,18 -7,63 -8,73

34 Appendix 8. Granger Causality Test

Estimates of the VAR(10) model in table 3 are used to explore whether market return ‘Granger causes’ market turnover and whether market turnover ‘Granger causes’ market return. **, and * indicate significance at the 1, and 5 percent level.

Market return does not Granger cause market turnover 0.0005** Market turnover does not Granger cause market return 0,0764

Appendix 9. Impulse Response Function

Shocks of one standard deviation away from zero are estimated on market return and market turnover to explore what the responses of the two variables are in the next months while using the same VAR(10) estimates of table 3.

-.02 -.01 .00 .01 .02 .03 .04 .05 1 2 3 4 5 6 7 8 9 10

Response of MARKET_RETURN to MARKET_RETURN

-.02 -.01 .00 .01 .02 .03 .04 .05 1 2 3 4 5 6 7 8 9 10

Response of MARKET_RETURN to MARKET_TURNOVER

-.005 .000 .005 .010 .015 .020 1 2 3 4 5 6 7 8 9 10

Response of MARKET_TURNOVER to MARKET_RETURN

-.005 .000 .005 .010 .015 .020 1 2 3 4 5 6 7 8 9 10

Response of MARKET_TURNOVER to MARKET_TURNOVER

35 Appendix 10. Market VAR detrended turnover full period 2005 – 2016

Appendix 11. VAR of 7 AEX stocks March 1986 – December 2002

Lagged Market Turnover

mturn(t-1) mturn(t-2) mturn(t-3) mturn(t-4) mturn(t-5) mturn(t-6) mturn(t-7) mturn(t-8) mturn(t-9) mturn(t-10) mturn Coefficient 0.497 0.028 0.075 0.005 -0.009 0.131 -0.050 0.010 0.123 -0.023 Standard error 0.074 0.084 0.085 0.084 0.085 0.084 0.085 0.085 0.087 0.074 P-value 0.000** 0.743 0.375 0.949 0.915 0.123 0.555 0.906 0.157 0.758 mret Coefficient 0.666 -0.238 0.122 -0.121 -0.094 0.232 -0.148 0.406 -0.530 -0.144 Standard error 0.241 0.274 0.274 0.273 0.275 0.273 0.276 0.275 0.281 0.239 P-value 0.006** 0.386 0.658 0.659 0.732 0.398 0.593 0.142 0.061 0.549

Lagged Market Return

mret(t-1) mret(t-2) mret(t-3) mret(t-4) mret(t-5) mret(t-6) mret(t-7) mret(t-8) mret(t-9) mret(t-10) mturn Coefficient -0.020 0.056 0.004 0.046 0.012 -0.018 0.016 -0.001 0.025 -0.015 Standard error 0.025 0.023 0.024 0.025 0.025 0.025 0.025 0.025 0.025 0.025 P-value 0.429 0.017* 0.863 0.064 0.621 0.470 0.540 0.982 0.322 0.540 mret Coefficient -0.006 -0.012 -0.021 -0.021 -0.032 0.009 -0.087 0.053 0.155 -0.054 Standard error 0.082 0.076 0.078 0.080 0.080 0.080 0.082 0.083 0.082 0.080 P-value 0.938 0.869 0.787 0.788 0.690 0.908 0.292 0.523 0.061 0.501

Lagged Market Turnover

mturn(t-1) mturn(t-2) mturn(t-3) mturn(t-4) mturn(t-5) mturn(t-6) mturn(t-7) mturn(t-8) mturn(t-9) mturn(t-10) mturn Coefficient 0.117 -0.016 0.009 -0.191 0.177 0.053 -0.001 0.026 -0.085 -0.191 Standard error 0.084 0.085 0.085 0.085 0.088 0.089 0.086 0.085 0.086 0.086 P-value 0.166 0.851 0.914 0.025* 0.045* 0.547 0.992 0.756 0.328 0.028* mret Coefficient 0.274 0.109 0.099 -0.159 -0.324 -0.113 -0.184 -0.648 0.532 -0.233 Standard error 0.253 0.254 0.255 0.254 0.262 0.264 0.258 0.254 0.257 0.258 P-value 0.279 0.668 0.697 0.530 0.217 0.670 0.477 0.012* 0.04* 0.368

Lagged Market Return

36 Appendix 12. Market VAR excluding CCI full period 2005 – 2016

The Consumer Confidence Index (CCI) is removed from the VAR(10) model. **, and * indicate significance at the 1, and 5 percent level.

Lagged Market Turnover

mturn(t-1) mturn(t-2) mturn(t-3) mturn(t-4) mturn(t-5) mturn(t-6) mturn(t-7) mturn(t-8) mturn(t-9) mturn(t-10) mturn Coefficient 0.288 0.120 0.130 -0.102 0.302 0.158 0.080 0.090 -0.036 -0.133

P-value 0.002** 0.194 0.164 0.278 0.002** 0.098 0.398 0.336 0.703 0.146 mret Coefficient 0.308 0.131 0.117 -0.123 -0.264 -0.043 -0.140 -0.592 0.608 -0.133

P-value 0.196 0.592 0.635 0.621 0.292 0.863 0.578 0.019* 0.017* 0.583

Lagged Market Return

mret(t-1) mret(t-2) mret(t-3) mret(t-4) mret(t-5) mret(t-6) mret(t-7) mret(t-8) mret(t-9) mret(t-10) mturn Coefficient 0.044 0.060 0.063 0.039 0.072 0.013 0.022 0.039 0.003 0.033

P-value 0.204 0.067 0.052 0.240 0.023* 0.680 0.474 0.216 0.920 0.288

mret Coefficient -0.012 -0.049 0.047 -0.021 -0.128 -0.016 -0.170 -0.028 -0.019 -0.144