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Effects of MiFID II on stock price formation

On January 3, 2018 MiFID II regulations came into effect. This paper compares properties of European stocks for 2017 and 2018. The introduced tick size regime impacted the microstructure in accordance with existing literature on tick size changes. Remarkably, the modification of the microstructure also impacted volatility and transacted volume. Furthermore, it is shown that closing auction volumes increased heavily since MiFID II, leading to higher absolute returns in the auctions. Before MiFID II, high closing auction returns reverted overnight, but after MiFID II this reversion disappeared, showing that closing prices became more efficient.


Introduction
At the outset of the year 2018, the new regulations for European financial markets, called the Markets in Financial Instruments Directive II (MiFID II), came into force. MiFID II is the successor of the original MiFID 1 regulations and is introduced in order to create fairer, safer, more efficient and more transparant markets. In this article the effects of MiFID II on the price formation of stocks belonging to the STOXX Europe 600 index 2 (hereafter referred to as the STOXX600), are examined. As there is a lot of data available pre-and post-MiFID II, this creates an opportunity to test the effects of these regulatory interventions on market microstructure and price formation. An important part of the new regulations is a new tick size regime aimed at creating a level playfield between different trading venues in Europe. 3 The tick size refers to the smallest possible price increment when trading an asset. During the last decade, exchanges have reduced their tick sizes in order to create tighter bid-ask spreads and improve their market share. However, since a few years it is recognized that this has had a negative effect on the quality of the market. That is why with MiFID II a new tick size regime was introduced, setting a minimum tick size for every traded instrument on every exchange in Europe, taking into account the price and liquidity of the instrument. Another important part of the MiFID II regulations is the limitation of the volume that is allowed to be traded in the so-called dark pools, i.e. private exchanges in which liquidity is not visible a priori. These dark pools give traders the opportunity to conduct (possibly large) trades without revealing their intentions before the transaction is completed. In order to protect the transparency of the market, part of the MiFID II regulations deals with limiting trading in dark pools: the so called double volume cap (DVC) limits the amount of volume that is allowed to be traded in dark pools. Only 8% of the total transacted volume (over all trading venues) in a stock is allowed to be carried out in dark pools, and only 4% of the total transacted volume is allowed to be carried out in a single dark pool. 4 A third part of MiFID II that has effects on trading and market microstructure is the so called 'best execution' rule, which mandates intermediaries to obtain the best possible price when executing a client's order. 5 A similar rule already existed in the previous MiFID regulations, but the obligation to prove fulfillment has become much more urgent, possibly changing the way orders are executed.
The first part of this article is devoted to the effects of the new tick size regime. There already exists a large body of literature on the effects of changes in tick size, most of it based on the change to decimal pricing in the US in 2001 (see e.g. Bessembinder (2003); Chakravarty et al. (2004Chakravarty et al. ( , 2005 and many others), but also on other moments in time and other exchanges (see e.g. Anderson and Peng (2014); Bacidore (1997); Ronen and Weaver (2001)). See Verousis et al. (2018) for a very recent and exhaustive review of the literature on tick sizes. Most of the existing literature on this subject is relatively old (before the rise of high frequency trading) and/or based on level-1 data (i.e. only trade-and best bid/ask-data). This study confirms that existing results still hold in today's financial markets: an increase (decrease) in tick size has a negative (positive) effect on liquidity, but a positive (negative) effect on the stability of the market. This study is the first (to the best knowledge of the authors) independent large scale examination of the effects of the new tick size regime, which is highly relevant to both market practitioners and the academic world. An early assessment of the effects of the tick size regime was done by the French financial market regulator, the Autorité Des Marchés Financiers (AMF, 2018). Their analysis covers a period of two months, December 2017 (before MiFID II came into force) and January 2018 (after MiFID II came into force), investigating more than 500 stocks traded on Euronext Paris. They find that the new tick size regime has had the desired effect. More particularly, they find that market depth increased and that the noise in the order book reduced after a tick size increase, leading to a more stable market. We confirm this positive effect of a tick size increase on the stability of the market, however we also observe the opposite effect for stocks of which the tick size decreased. This adverse effect was not detected by the AMF, as their sample of French mid-and large-cap stocks did not contain stocks of which the tick size decreased. Finally, we find that a decrease in tick size leads to a decrease in volatility and an increase in tick size leads to higher (lower) transacted volumes, which is at odds with the findings of the AMF that the new tick size regime did not disrupt volatility and transacted volumes.
The second part of this article focuses on the closing auction. In today's financial markets most securities are traded in continuous double auctions. However, to determine a daily closing price, a closing auction is conducted for most securities. In these closing auctions orders are collected for a while without giving rise to trades immediately, after which a closing price is determined and every possible transaction is made against this price. 6 We show in section 3 that since the introduction of MiFID II an increasing part of the daily transacted volume is transacted in the closing auction, meaning that understanding the auction gets more important. However, the literature on the auction is fairly scarce compared to the enormous (both empirical and theoretical) literature on continuous trad-ing. Recent theoretical contributions are by Muni Toke (2015) and Derksen et al. (2020), while the empirical literature mainly focuses on the effects of call auction mechanisms on price formation and the difference with continuous trading (see e.g. Hillion and Suominen (2004); Kandel et al. (2012); Pagano and Schwartz (2003), among others). We contribute to the literature on closing auctions by assessing price formation in closing auctions. We show that, along with the increase in volumes, the average absolute return in the closing auction and the number of auctions with a high 7 absolute return increased, as well as the deviation of the indication price 8 relative to the closing price. In 2017 a high absolute return in the closing auction was followed by a correction the next day, but in 2018 this mean reversion on the next trading day has vanished, implying that price formation in closing auctions has become more efficient. We show that higher volumes lead to lower mean reversion and thus a higher efficiency, however a total disappearance of mean reversion can not be merely explained by the increase in transacted volume. This suggests that informed investors are attracted to the closing auctions on the main exchanges since the introduction of MiFID II. To check if this does not have a global cause, we do the same analysis for constituents of the S&P500, outside the purview of MiFID II. 9 We show that for these stocks closing prices are inefficient in both 2017 and 2018, supporting the claim that the disappearance of mean reversion is caused by MiFID II. We show that the new tick size regime did not cause this effect and we find no evidence that the DVC rule has caused volume to move from dark pools to the regular exchanges (in line with Johann et al. (2019)), which leaves the best execution rule as a possible explanation.
The remainder of this article is organized as follows. In section 2 the effects of the new tick size regime are examined. In section 3 price formation in the closing auction is investigated. Finally, in section 4 the results are summarized and concluding remarks are made. In appendix A information on the different closing auction mechanisms can be found and in appendix B we study the effects of dark pool suspensions caused by the DVC rule. 7 Say higher than 30 basis points. 8 During the auction an indicative price is published continuously, indicating the price which would be the closing price if the auction would end immediately, see appendix A for more information.
9 The S&P500 consists of the 500 largest listed US companies.

The new tick size regime
In this section the effects of the change in tick sizes on several quantities of interest are investigated. First the data is summarized and the method is explained, then the effects of the new tick size regime on the quantities are examined.

Data and method
In order to examine the effects of the new tick size regime, two years (2017 and 2018, before and after the new regulations) of one minute-interval order book data (5 levels deep on both sides) and transaction data is obtained for all constituents of the STOXX600 index. The stocks are first divided into three groups, based on the market capitalization of the stock, which leads to 200 small-cap stocks, 200 mid-cap stocks and 200 large-cap stocks. Stocks that were not in the STOXX600 index for one of the years are excluded, as well as stocks that switched from one market cap category to another during the considered period. To examine the effects of the new tick size regime, the stocks are divided into groups based on the way their tick size is affected by this new regime: a group of which the tick size increased (ts↑), a group of which the tick size decreased (ts↓) and a group of which the tick size remained unchanged (ts↔). The last group acts as a control group for the other two groups. Because tick sizes can (as well in the old as in the new tick size regime) also change during a calendar year due to changes in the stock price, the groups have the following definitions.
• ts↑: every stock whose average tick size over 2018 is a factor 10 1.5 higher than its average tick size over 2017. This group contains 179 stocks, of which 64 small-caps, 68 mid-caps and 47 large-caps.
• ts↓: every stock whose average tick size over 2017 is a factor 1.5 higher than its average tick size over 2018. This group contains 144 stocks, of which 42 small-caps, 43 mid-caps and 59 large-caps.
• ts↔: all other stocks. This group contains 220 stocks, of which 80 small-caps, 70 mid-caps and 70 large-caps.
10 All the results discussed in this article are robust with respect to a reasonable choice of the factor 1.5.
In table 1 the average tick size change and the average market capitalization of the groups is shown. In this section a couple of quantities is considered in order to asses  the influence of the MiFID II tick size regime. Every quantity is computed as a per day average for every stock, after which it is averaged over the year to find the average per stock per year. Then the percentual change in the value of the quantity in 2018 (after the introduction of the MiFID II tick size regime) relative to the value of the quantity in 2017 (before the introduction of MiFID II) is computed for every stock and this is also averaged over the different groups. This is the level on which statistical significance is assessed: a standard t-test and a Wilcoxon signed rank test 11 are conducted to test the null-hypothesis that the mean percentual change of the considered group (ts↑ or ts↓) equals the mean percentual change of the control group (ts↔) versus the alternative hypothesis that the mean percentual changes of the both groups differ.

Effects on liquidity
There exists a large empirical literature on the relation between tick size and liquidity. Generally, the focus is on the bid-ask spread (defined as the difference between the lowest ask price and the highest bid price) and market depth (the volume that is accumulated in the order book). The literature unanimously shows that a higher (lower) minimum tick size leads to a higher (lower) bid-ask spread and higher (lower) volumes at the best bid and ask (see e.g. Alampieski and Lepone (2009) , among others). We confirm these findings with our results in tables 2 and 3, where it is shown how the relative bid-ask spread (relative to the mid-price, averaged over the year and the particular group) and the volume that is accumulated at the best bid and best ask prices (for 1, 3 and 5 levels deep) changed after the introduction of the new tick size regime. Complementing the existing literature, the results in table 3 show that the positive relationship between tick size and the volumes in the order book, does also exist on levels deeper in the order book. To take both the bid-ask spread  and market depth into account at the same time, we look at the spread-at-x, which is defined as the relative (to the mid-price) difference between the average price you pay if you want to buy shares for a total amount of x EUR and the average price you obtain if you want to sell shares for a total amount of x EUR. In fact, this measures the cost of conducting a large market order. In table 4 the effects of the new tick size regime on the spread-at-x (for x = 10.000, 20.000, 50.000 and 100.000) are summarized. It is seen from table 4 that for stocks of which the tick size increased (decreased), the spread-at-x also increased (decreased) significantly. It is concluded that an increase in tick size has a negative effect on liquidity, while a decrease in tick size impacts liquidity positively.

Effects on volatility and transacted volume
The existing literature about the influence of changes in tick size on volatility (as defined below) suggests that a higher (lower) tick size leads to a higher (lower) volatility (see e.g. Hau (2006); Ke et al. (2004)). However the AMF (2018) finds that the new tick size regime does not affect volatility. Here, per stock, per trading day, the volatility is measured as the square root of the sum of squared one-minute returns. Table 5 shows the average volatility of the different groups for the both years and the average percentual increase,  Table 3: How the total volume at the n best bid and ask prices (for n = 1, 3, 5) changed in 2018 compared to 2017, due to the new minimum tick size regime.
* significantly different from the average increase in the control group 'ts↔' of the same column(p < 0.001, t-test). + significantly different from the average increase of the control group 'ts↔' of the same column(p < 0.001, Wilcoxon test).
showing that the group that was subject to a decrease in tick size has a significantly lower increase in volatility (p-values< 0.05 for both tests). Hence, it is observed that volatility is negatively affected by a decrease in tick size (in line with Hau (2006); Ke et al. (2004)). This contradicts the findings of the AMF (2018) that the new tick size regime does not impact volatility. This can be explained by the observation that their sample of French stocks only contains mid-and large-cap stocks of which the tick size increased or remained unchanged, none of the French large-cap or mid-cap stocks had a tick size decrease.
In table 6 the average intra-day transacted volumes in millions of euros are shown, together with the average increase in intra-day transacted volume from 2017 to 2018. The results in the table suggest that an increase (decrease) of the minimum tick size has a positive (negative) effect on the intra-day transacted volume (only significant for largecap stocks). In the literature little is known about the relationship between tick size and transacted volumes, Ahn et al. (1996Ahn et al. ( , 2007 do not find evidence of effects of tick size reduction on transacted volumes and the AMF (2018) finds that transacted volumes are not impacted by the new tick size regime. Because the observed differences are only significant for large-cap stocks, a possible explanation of this observation is that the higher    (2018)) show that a higher tick size is more attractive for HFT-strategies, as it implies a higher bid-ask spread. This possibly caused a shift of HFT activity towards stocks with a high tick size in the new regime. In table 7 the transacted volume in the closing auction is displayed. For the closing auction volumes we see the same effect as for intra-day volumes: higher tick sizes lead to higher volumes, however this is not statistically significant in most cases. More interestingly, the transacted volumes in the closing auction increased for all stocks in 2018 relative to 2017, regardless of the change in tick size. The reason for this observed effect and its consequences are investigated in more depth in section 3.

Effects on microstructure and price formation
In this subsection the effects of the new tick size regime on the micro scale are examined.
To create a more stable market microstructure (which is one of the goals of MiFID II), a lower number of bid-ask price changes and a lower number of (small) trades, combined with a higher trade size are desired. In table 8 the average number of daily changes of the best bid-or ask-price is shown for the different groups. For small-, mid-and large-cap stocks an increase (decrease) in tick size has a negative (positive) effect on the number of best bid-ask price changes. This relationship is easily explained: the tick size acts as a lower bound on the bid-ask spread, hence less spread crossings are possible in a regime with a higher tick size. Another important metric to measure the activity in the market, is the number of intra-day trades. In   with a decrease in tick size (cf. also subsection 2.3). It just means that the average size of trades increases with an increase of the minimum tick size, as we can see from the results in table 10, which shows the average trade size in euros for the different groups. It is concluded that an increase (decrease) in tick size has a positive (negative) effect on the stability of the market.

Impact of the new tick size regime
In this section the effects of the new tick size regime on several important quantities were studied. To summarize, it was shown that an increase (decrease) in tick size has a negative (positive) impact on liquidity, which confirms that results in the early literature still hold in today's financial markets. Remarkably, it was shown that the new tick size   regime also impacted the volatility and transacted volume of mid-and large-cap stocks, as a decrease in tick size leads for these stocks to a decrease in volatility and an increase (decrease) in tick size leads to higher (lower) transacted volumes. This in contrast to results from the French market authority (AMF, 2018), who reported that the new tick size regime did not influence volatility and transacted volume for French stocks. Finally, it was shown that that an increase in tick size leads to a more stable market (in line with AMF (2018)), but a decrease in tick size disturbs the market microstructure (not observed by the AMF). The differences can be explained by the observation that the sample of French stocks of the AMF only contains mid-and large-cap stocks of which the tick size increased or remained unchanged, no mid-and large-cap stocks of which the tick size decreased, while those are present in Europe in equal amount.

The Closing Auction
We already mentioned in the previous section that transacted volumes in the closing auctions on the main exchanges have significantly increased since the introduction of MiFID II, but that this is not caused by the new tick size regime. In this section we will have a closer look at the closing auction and how price formation of closing prices has changed after the introduction of MiFID II.

Data and method
We take the same set of stocks as in the previous section, again splitting them in small-, mid-and large-cap stocks. For these stocks, we obtain intra-day transaction data and closing auction data. It is known that price formation in closing auctions is highly influenced by calendar effects. Firstly, transacted volume in closing auctions is significantly higher on the third friday of the month, when options expire and indices are reweighted. Also, transacted volume in closing auctions is higher on the last trading day of the month, when investors have to publish their results and MSCI indices are reweighted. See table  11 for an illustration of these effects. For those reasons, we exclude third fridays and last trading days of the month from our analysis, such that our analysis only takes normal market conditions into account. Several quantities will then be computed, averaged for every stock, for 2017 and 2018 separately. To test if these average quantities per stock significantly differ between 2017 and 2018, we will conduct a t-test for paired samples. Furthermore, to check if reported phenomena are related to MiFID II or to more global issues, we will investigate the same for 250 randomly selected constituents of the S&P 500 index.

Transacted volumes
Since the introduction of MiFID II, an increasingly larger part of the day's total transacted volume gets transacted in the closing auction. In  the intra-day transacted volume increased for small-and mid-cap stocks, and decreased slightly for large-cap stocks, but these results are not significant. More interestingly, it is shown that transacted volumes in the closing auction have significantly increased (by around 25%) for small-, mid-and large-cap stocks. These two effects together lead to a significant increase in the fraction of total volume that is transacted in the closing auction. In figure 1 it is illustrated that this increase in importance of the closing auction relative to intra-day trading, already started in 2017, but was amplified after the introduction of MiFID II (the vertical black line in the figure). It is thus likely that some of the changes that came with MiFID II have caused market participants to prefer trading in the closing auction over alternatives. In particular there are two parts of MiFID II that seem reasonable causes of this shift towards the closing auction: the restriction on dark pools and the best execution rule. Firstly, the restrictions on dark pools could have caused a shift from dark pools to the main exchanges. As trading in the closing auction is far more similar to dark pool trading than continuous trading, a reasonable explanation of the observed effect would be that volume is moved from dark pools into closing auctions, but not into intra-day trading, thereby increasing the importance of the closing auction. However, our analysis in appendix B shows that there is no evidence that this is the case. Hence, the best execution rule of MiFID II seems a better candidate to explain the observed shift towards closing auctions. Under this rule, intermediaries are obliged to execute a client's orders against the best possible price. However, during the closing auction there is no price which is traded upon, so it is unclear what the best price is. As it is impossible for market participants to determine the best price, they might refrain from trading (on other venues) during the closing auction and instead wait to trade on the close. Whatever the exact reason of the observed shift towards closing auctions, in the next subsections we investigate its consequences for price formation in the closing auction.

Closing auction returns
In the previous subsections we saw that transacted volumes in the closing auction significantly increased in 2018 as compared to 2017. Now one wonders what kind of effects this has on the formation of the closing price. To address this question, we first examine the returns in the closing auction. We define the closing auction return R CA t on day t by where X CA t denotes the auction's closing price on day t andX t is the volume weighted average price (VWAP) over the last five minutes of continuous trading. In table 13 the absolute values of the closing auction returns (averaged per stock over all trading days of the particular year, and over all stocks in the same market cap group) are shown. We observe that in 2018 the absolute closing auction returns have significantly increased compared to 2017. Furthermore, in table 14 the frequency of high return auctions with an absolute return above 10 or 30 bps is displayed. It is observed that the frequency of auctions with an absolute return above 10 bps has slightly increased in 2018 compared to 2017, but this is not significant. Interestingly, the number of auctions with an absolute return above 30 bps has significantly increased in 2018 compared to 2017.

Price formation in the closing auction
In this subsection we will have a closer look at the price formation process during the auction. As can be read in more detail in appendix A, on Euronext the closing auction starts at 5:30 pm and ends at a random time between 5:35:00 pm and 5:35:30 pm. During this process an indication price (representing the price that would be determined if the auction would stop at that time) is displayed continuously. We obtain indication price data for all stocks belonging to the STOXX600 index that are traded on Euronext. In figure 2 the evolution of the absolute deviation of the indication price relative to the eventual closing price during the auction is showed, averaged over all large-cap stocks traded on Euronext and over all days in the four quarters of 2017 and 2018. Strikingly, since the introduction of MiFID II in 2018, the average difference between the indication price and the closing price has increased strongly. For example, in 2017, one minute before the end of the closing auction, the average absolute deviation of the indication price relative to the closing price is around 35 bps, while this increased to around 60 bps in 2018. These observations are in line with the observation in the previous subsection that the absolute returns made in the closing auction have increased: in 2018 the price walks further away during the closing auction from the last mid-price. Theoretically, this can be linked to the increase in transacted volumes in the closing auction, as follows.
If one thinks of the closing auction as a random walk in transaction time, the increase in volumes in 2018 just means that the duration of the closing auction (in transaction time) has increased, allowing the random walker to walk away further from the last midprice, which is also illustrated by the indication price that deviates more from the closing price. Although the devations of the indication price with respect to the closing price  have increased, the shapes of the above graphs, which resemble the behaviour of the convergence of the indication price over the 5 minutes, did not change. The first minute of the auction exhibits a lot of noisy price changes, because of large market orders that are sent in early and are able to set the indication price artificially high or low (for this reason the first part of the auction is not shown in figure 2). Then a large part of the convergence takes place from roughly 5:31:45 until 5:32:45, after which convergence slows down until the last minute, when convergence accelerates again. This pattern is roughly the same in 2017 and 2018. This observation is confirmed in figure 3, where it is shown how the indicated transacted volume evolves as a fraction of the eventual transacted closing auction volume. In accordance with the convergence of price deviation, a large part of the volume is already submitted in the first two minutes of the auction, after which a two minute period of relative low activity starts, approximately the last 10% of the volume is submitted in the last 30 seconds of the auction. This pattern did not change in 2018 compared to 2017, as is seen from figure 3. To summarize, it is found that absolute deviation between the indicative price and the eventual closing price has increased, in line with the higher returns and volumes. However, the way the price converges and the way the arrival of orders is distributed over the duration of the auction did not change.

Efficiency of the price formation process
From the observations that the returns made in the closing auction and the deviation of the indication price with respect to the closing price increased in 2018 compared to 2017, one could at first sight naively conclude that price formation in closing auctions has become less efficient. Indeed, a higher indication price deviation and higher returns could mean more noise in the closing prices and hence a less efficient price formation process. However, if the higher returns were generally in the right direction (that is, towards the 'efficient price'), it would actually mean that price formation in closing auctions became more efficient. In order to decide which of the two is the case, we look at the mean reversion the day after an auction with a high absolute return (higher than 10 bps or 30 bps). 12 If the next day a correction takes place, this is a sign that the closing price was not efficient. If not, it seems that the closing auction return was not noisy, but instead was a move in the correct direction. To make this rigorous, we define the overnight return R t,t+1 from day t to day t + 1 by where as before X CA t denotes the closing price on day t andX t+1 is the VWAP over the last five minutes of continuous trading on day t + 1. Note that this is the return made from the closing price on day t to the last five minutes of continuous trading before the closing auction on day t + 1. We explicitly do not take the closing price of day t + 1 as endpoint, because then possible noise of the next closing auction is also taken into account. 13 Having defined the auction return and the overnight return, we estimate the following simple linear regression model, for all days t with an absolute auction return |R CA t | above 10 or 30 bps. The quantity of interest is the coefficient b, which measures if overnight mean reversion takes place: if b is significantly below zero, it means that the returns made in the closing auction are (partially) reverted the next trading day. If b is not significantly different from zero, it means that there is no linear correlation between the closing auction return and the following overnight return. In table 15 the estimated values of b are displayed, over 2017 and 2018, for small-, mid-and large-cap stocks. The results make clear that over 2017 closing auction returns and following overnight returns were significantly negatively correlated, meaning that large absolute returns in the closing auction were partially corrected the next day. However, this effect completely vanished in 2018, as it is seen that the mean reversion coefficient b is not significantly different from zero for small-, mid-and large-caps, meaning there is no consistent mean reversion after a high return in the closing auction in 2018. It is thus concluded that closing prices have become efficient in 2018, while they where significantly inefficient in 2017.   (3), changed in 2018 compared to 2017, for auction with absolute returns higher than 10 bps or 30 bps.

Mean reversion coefficient
* The mean reversion coefficient b is significantly different from 0 on the 0.01-level.

The influence of the extra volume
In the previous subsections we showed that along with the increased volumes in 2018, the returns in the closing auctions have increased, while the mean reversion on the next day vanished, showing that closing prices have become more efficient. Usually higher transacted volumes are associated with more efficient price formation, so maybe the efficient closing prices in 2018 can be merely explained by the increase in transacted volume. Theoretically, assuming a normal distribution, we would expect the standard deviation of closing auction returns to scale as 1/ √ N with the transacted volume N in the auction. This square root scaling is also supported by the call auction models by Muni Toke (2015) and Derksen et al. (2020). An average increase in closing auction volume of around 25% (cf. table 12) should then lead to a reduction of noise by a factor 1/ √ 1.25 ≈ 0.89, however a total disappearance of closing price inefficiency can not be explained in this way. Empirically, if the vanishing of the price inefficiency is caused by the increase in transacted volume, one would expect to see no mean reversion for the days in 2017 with high closing auction volumes and existence of mean reversion for the days in 2018 with low closing auction volumes. If that would be the case, it would mean nothing is changed in the nature of the volume in 2018 compared to 2017. To investigate if this is the case, we take for every stock only the 25% of the days with the highest closing auction volume or the 25% with the lowest closing auction volume and check how that affects the mean reversion coefficient. In fact, this comes down to estimation of the following linear regression model, where 1 Qi , i = 1, 4 denotes if a day is in the lowest (Q1) or highest (Q4) quartile of closing auction volumes for the particular stock. The coefficients of interest are again the parameters b i , i = 1, 2, 3. Now b 1 denotes the mean reversion coefficient for days with median volumes (i.e. all days that fall in the second and third quartile of closing auction volumes for the particular stock). Furthermore, b 2 denotes the additional mean reversion that is observed for days with low volumes (first quartile), meaning that the mean reversion coefficient for these days is given by b 1 + b 2 . Similarly, b 1 + b 3 is the mean reversion coefficient for days with high volumes (fourth quartile). In table 16 the results of this regression are summarized. The reported values are the mean reversion coefficients for the three groups, i.e. b 1 + b 2 for Q1, b 1 for Q2,3 and b 1 + b 3 for Q4. It is seen from table 16 that there exists some relationship between volume and efficiency: in 2017 the high (low) volume days have less (more) overnight mean reversion, although the differences are not all statistically significant. For example, for large-cap stocks, the mean reversion coefficient equals −0.367 for median volume days and −0.095 (implying less mean reversion, but still some reversion) for high volume days, and this difference is significant on the 0.05-level. For low volume days the mean reversion coefficient becomes −0.497, but is not significantly different from the value for median volume days. Importantly, it is seen that the mean reversion coefficient is (except for small-cap stocks) still below 0 for the high volume days in 2017. This in contrast to the results for 2018 in table 16: there is no significant mean reversion after a high auction return for any of the groups (Q1, Q2,3 or Q4). This implies that the vanishing of the mean reversion in 2018 can not be fully explained by the increase in transacted volumes, because there would still be mean reversion for days in Q1 in that case. 14 To summarize, it turns out there exists some relationship between volume and efficiency (higher volumes lead to more efficient prices in 2017), but it is not enough to account for the observed differences between 2017 and 2018. From this we conclude that the extra volume that has come to the closing auctions on main exchanges seems to be of a different nature: the market participants responsible for this extra volume are better informed, leading to more efficient prices.  Table 16: How the mean reversion coefficient of the model in equation (4), changed in 2018 compared to 2017. The mean reversion coefficient b 1 is the value reported under Q2,3, the value reported under Q4 is b 1 + b 3 and the value under Q1 is b 1 + b 2 , as b 2 and b 3 give the difference in mean reversion coefficient between Q2,3 and Q1, Q4 respectively.
* The mean reversion coefficient (b 1 for Q2,3, b 1 + b 2 for Q1, b 1 + b 3 for Q4) is significantly different from 0 on the 0.05-level. + The mean reversion coefficient b 1 + b i , i = 2, 3 is significantly different from the mean reversion coefficient b 1 belonging to the Q2,3 group in the same year and market cap, on the 0.05-level.
If the higher transacted volumes in the closing auctions are indeed caused by the arrival of better informed market participants, one would expect that the increase in transacted volumes is mainly caused by an increase in limit order volume, not market order volume. 15 To check if this is indeed the case, we obtain data on market order volume in the closing auctions, for all stocks belonging to the STOXX600 index, as well as closing auction transaction data. This gives, for every stock i and every day t, the transacted volume T V i,t and the executed market order volume M O i,t (all measured in euros, i.e. volume times closing price in euros). We denote the executed limit order volume by LO i,t and note that as every transaction has a buyer and a seller. This gives us the executed limit order volume LO i,t for every stock i and day t. All quantities are averaged over all stocks to obtain average values for every day. Moving averages of these values are shown in figure  4. From this figure we conclude that the increase in auction volume is indeed mainly driven by an increase in limit order volume. This is consistent with the finding that closing prices have become more efficient and with the observation that this is caused by better informed investors moving to the closing auctions on the main exchanges. 6 month moving average, auction volume 6 month moving average, market order volume 6 month moving average, limit order volume Figure 4: How the transacted volume (in euros) and the executed marketand limit-order volumes (in euros) increased since the introduction of MiFID II (the solid black line denotes the introduction of MiFID II). Market and limit order volumes are divided by two such that market order volume plus executed limit order volume equals transacted volume. Clearly, the increase in auction volume is mainly driven by an increase in executed limit order volume 3.7 MiFID II or other factors: checking the S&P500 In the previous subsections we showed that since the introduction of MiFID II mean reversion after high closing auction returns has disappeared, implying that the closing price has become more efficient. Now, one wonders if this is really due to MiFID II regulations, or that it is caused by other factors. Although it is remarkable that all of this happened suddenly after the introduction of MiFID II (cf. also figure 1), it is not totally clear at this point that MiFID II really has something to do with it. That is why in this subsection we check our results for stocks outside Europe (i.e. outside of MiFID II influence). For this we obtain closing auction data of 250 randomly selected stocks belonging to the S&P500, for the years 2017 and 2018 and repeat some of the research we did in the previous subsections. To start with, in table 17 the average transacted volume in closing auctions is shown, as well as the average absolute return made in the closing auctions, where the closing auction return is again defined as in equation (1). Clearly, we see a significant increase in the closing auction's transacted volume and along with this increase in volume, a similarly sized increase in the average absolute returns. This is very comparable with the results on European stocks in the previous subsections.
Although the average increases are a lot higher for American stocks, the pattern is the same: volume in the closing auction increased in 2018 compared to 2017. This is part of a global trend of increasing auction volumes that is caused by the increase in passive investing and ETF trading, as is shown recently by Bogousslavsky and Muravyev (2019  of equation (3), but now for American stocks. In table 18 the resulting mean reversion coefficients are shown. Clearly, the mean reversion coefficients are for American stocks in 2017 far more negative than for European stocks in 2017. This can have several reasons. Firstly, the closing auctions are in the USA less important in terms of fraction of the total transacted volume (for S&P500 stocks around 7% of total transacted volume is transacted in the closing auction, while this is around 30% for European stocks). Secondly, this can be explained by the differences in the auction mechanisms. As can be read in appendix A, on NASDAQ/NYSE it is harder to act on new information than on Euronext, making closing prices possibly more efficient on Euronext (this reasoning is supported by the results of Comerton-Forde and Rydge (2006), who find that price formation is enhanced when more information is released). What is more interesting about the results in table 18, is that the mean reversion coefficient for American stocks is in 2018 still significantly negative. For closing auctions with an absolute average return larger than 30 bps, it is even more negative than in 2017. It is thus observed that closing prices in the USA are in 2018 still far from efficient. This allows us to conclude that there is not a global reason for the observation that European stock's closing prices suddenly have become efficient after the introduction of MiFID II.   (3), changed in 2018 compared to 2017, for S&P500 stocks.
* The mean coefficient b is significant on the 0.05-level. ** The mean reversion coefficient b is significant on the 0.01-level.

The impact of MiFID II on closing auctions
In this section price formation in closing auctions was examined. To summarize, it was shown that the fraction of the total transacted volume that is traded in the closing auction, did increase strongly over the past years, and this increase was amplified since the introduction of MiFID II. It was also shown that this increase was mainly driven by an increase in limit order volume. Along with this increase in transacted volumes in the closing auctions, the returns in the closing auctions increased, as well as the deviation between the published indicative price and the eventual closing price. In 2017 a high return in the auction was consistently followed by a correction the next day, while this mean reversion vanished in 2018, after the introduction of MiFID II. It was shown that higher volumes can explain a lower mean reversion, but that the increased transacted volumes can not account for the complete disappearance of mean reversion, implying that informed investors are attracted to the closing auctions on the main exchanges after the introduction of MiFID II, consistent with the observed increase in limit order volumes in the closing auctions. To check if this is not caused by other factors than MiFID II, we conducted the same analysis for stocks belonging to the S&P500 index. For these stocks high auction returns are in 2018 still followed by a mean reversion the next day, supporting the claim that MiFID II rules caused closing prices to become more efficient. It is nevertheless unclear which exact rules did trigger this move of informed investors towards the closing auction. We showed in appendix B that there is no significant evidence that the suspension of dark pool trading has moved volume towards the main exchanges (in agreement with recent work by Johann et al. (2019)) and the new order flow is also not caused by the new tick size regime. Possibly, it is caused by the best execution rule, which mandates intermediaries to obtain the best possible price when executing a client's order. During the closing auction there are no transactions, so it is unclear what the best price is, possibly forcing market participants to wait and trade on the close.
However, to point out the exact rule that caused the move of informed investors towards the closing auction, one would need to have data separating different market participants, to investigate what type of traders represent the new order flow in closing auctions.

Conclusions
In this article, the effects of MiFID II on trading the constituents of the STOXX Europe 600 index are examined by comparing the years 2017 and 2018. It is found that the new tick size regime that was part of MiFID II has lead to the results that could have been expected based on the existing literature on tick size changes. Most importantly, it was shown that an increase (decrease) in tick size has a negative (positive) impact on liquidity and a positive (negative) effect on the stability of the market. Remarkably, volatility and transacted volumes were also impacted by the new tick size regime: higher (lower) tick sizes lead to higher (lower) transacted volumes and lower tick sizes lead to lower volatility. While the consequences of the new tick size regime could largely have been expected, we also found other consequences of MiFID II that were probably less anticipated. It was shown that since MiFID II transacted volumes in the closing auctions have significantly increased and that this increase was mainly driven by an increase in limit order volume. Along with this increase, closing prices have become more efficient, suggesting that the new regulations have attracted informed investors towards the closing auction on the main exchanges. We did not find evidence that this was caused by the introduced limits on dark pool trading or by the new tick size regime, leaving open for further research which exact part of the MiFID II regulations triggered these observations. with equal transactable volume, the price that is closest to the last automated trade is taken. After the closing price is set and the order book is cleared (where market orders are ranked based on time-priority and have priority over limit orders, which are then ranked based on price-time priority), a phase of Trading-At-Last starts, which basically means that orders can be entered for execution at the closing price and for that price only.

NASDAQ 17
On NASDAQ, orders for the closing auction can be entered the whole day, until the start of the auction at 3:55 pm. Two types of orders can be entered all day, market-on-close (MOC) orders and limit-on-close orders (LOC). MOC orders are executed against the closing price, whatever that price is, LOC orders are entered with a limit and are only executed if the closing price is equal or better than the limit price. At 3:55 pm NASDAQ starts to display the net order imbalance information. Between 3:55 pm and 3:58 pm it is not allowed to cancel or modify pending orders anymore, but participants can still enter LOC orders (as long as they are not more aggresive than the reference price at 3:55 PM, otherwise they are capped on this reference price). Hence, the possibility to act on released imbalance information is fairly limited. Then after 3:58, until the closing of the market at 4:00 pm, only imbalance orders (IO) can be entered, which are orders that can only be entered against the order imbalance. That is, when there are more (less) buyers than sellers up to 3:58, it is only possible to add sell (buy) orders after 3:58, in order to balance the order book. At 4:00 pm the closing price is determined by the system. The system determines the price that maximizes the transacted volume. If this does not give a single closing price, the system determines the price that minimizes the order imbalance. If this still does not lead to a single price, the system takes the price that is closest to the NASDAQ inside bid-ask midpoint. For execution, MOC orders have priority over LOC orders. First, MOC orders are executed with time priority, then (if still possible) LOC orders are executed with price-time priority.

NYSE 18
The NYSE closing auction is very similar to the one on NASDAQ. However, on NYSE there are floor brokers that have priority, adding extra complexity to the system. On NYSE, MOC and LOC orders can be entered the whole trading day until 3:45 pm (changed to 3:50 pm in 2019), after this time only orders on the contra side of the imbalance can be entered and modification or cancellation of orders is not possible anymore. This is also the time that order imbalance information dissemination starts. The biggest difference with NASDAQ is the existence of so-called D-quotes, which can only be used by floor brokers and are not subject to the above mentioned rules: they can be entered, modified and cancelled until 3:59:25 pm, regardless of their side of the order imbalance. Also, they are hidden from the imbalance information until 3:55 pm. At 4:00 pm, the closing price is determined in a similar way as on NASDAQ.

B Dark Pool Suspensions
As already mentioned in the introduction of this paper, an important part of MiFID II is the DVC mechanism which allows only 4% of a stock's yearly transacted volume to be transacted in a single dark pool, and only 8% in all dark pools together. When these limits are violated for a particular stock, this stock gets suspended, meaning that this stock can not be traded in a dark pool anymore for a certain period of time. The European Securities and Markets Authority (ESMA) published the first suspensions on March 3, 2018. The list of suspended stocks can be used to test whether volume moved from dark pools to the regular exchanges for this suspended stocks. We split the stocks in the STOXX600 index in 2 groups: a group consisting of suspended stocks and a group consisting of stocks that are not suspended. The second group acts as a control group for the first group. In table 19 the change in transacted volume on the main exchanges from before March 3, 2018 to after this date is shown for the two groups, again separated for small-, mid-and large-cap stocks. If volume was moved from dark pools to the main exchanges after the suspensions, one would expect an increase in transacted volumes on the main exchanges for the suspended stocks, significantly higher than the increase in transacted volumes for the not suspended stocks. However, the results in  Table 19: How the transacted volume in closing auctions and intra-day changed after the first DVC-suspensions, for suspended and not suspended stocks. None of the increases for the suspended stocks is significantly higher than the increases for the not suspended stocks, all p-values> 0.15.
table 19 show that this is not the case. Although volumes in the closing auction did increase significantly, this is also the case for not suspended stocks, and the increase is not significantly higher for suspended stocks (all p-values > 0.15). Clearly, volumes also did not move into continuous trading on the main exchanges. For small-and mid-cap stocks, the intra-day transacted volumes increased, but again not significantly more for suspended stocks. For large-cap stocks the intra-day transacted volumes even slightly decreased for suspended stocks. We conclude that the DVC regulations did not lead to the desired result: there is no evidence that significant volume did move from dark pools to the main exchanges after suspensions of stocks. This is in line with results by Johann et al. (2019), who also find that little volume from dark pools returned to the main exchanges after MiFID II. Instead, volumes moved to systems more similar to dark pools, such as periodic auction mechanisms and systematic internalisers (the definition of which is given by MiFID II, Article 4, which states "systematic internaliser means an investment firm which, on an organised, frequent systematic and substantial basis, deals on own account when executing client orders outside a regulated market, an MTF or an OTF without operating a multilateral system ").