Market Fragmentation, Mini Flash Crashes and Liquidity

Market fragmentation, mini ﬂash crashes and liquidity

Ester F´elez-Vi˜nas∗ Stockholm Business School

January 12, 2017

Abstract This study analyzes the impact of market fragmentation on liquidity with a focus on episodes of mini flash crashes (defined as large price changes that are reversed within seconds). I find that in normal market conditions, market fragmentation improves liquidity as measured by quoted spreads and depth at best prices. When focusing on episodes of mini flash crashes, the results show that market fragmentation reduces the number of mini flash crashes and speeds up their recovery. Furthermore, market fragmentation is not a source of market instability. Liquidity shocks are mostly less harmful in fragmented, but interrelated markets than in concentrated markets.

∗Contact: [email protected]

1 1 Introduction

Stock markets have evolved from local concentrated exchanges to fragmented structures that are comprised by traditional regulated exchanges and alternative trading platforms such as Multilateral Trading Facilities (MTFs). Market fragmentation is the consequence of the implementation of recent regulations aiming to enhance fair competition in financial markets.1 Despite the raise in market fragmentation, its effects on market quality and especially, on market stability, are unclear. Regulatory authorities are concerned that market fragmentation is a source of market instability and that it is behind recent episodes of liquidity dry-ups. To my knowledge, this paper is the first to analyze the impact of market fragmentation on liquidity in the presence of mini flash crashes, which are defined as large price changes that are reversed within seconds. First, I evaluate the effect that market fragmentation has on liquidity in normal market conditions. In a concentrated market, all liquidity is located in one venue, which facilitates finding a counterparty and speeds up execution time (Mendelson, 1987). In fragmented markets, liquidity is scattered across trading venues, which constrains order matching. In line with this, my first hypothesis is that market fragmentation deteriorates liquidity. On the other hand, fragmentation enables competition, which potentially leads to reduced trading costs (Foucault and Menkveld, 2008), and accommodates traders with distinct needs (Harris, 1993). Accordingly, I develop an alternative hypothesis stating that market fragmentation does not deteriorate liquidity. Further, I investigate the impact of market fragmentation on liquidity when stocks experience liquidity shocks in the form of mini flash crashes. The con- centration of liquidity provides markets with a greater ability to absorb trades without causing large price impacts. Under market fragmentation, individual markets have thinner books making it more likely to experience sudden price changes (Madhavan, 2012). Thus, I formulate an hypothesis stating that market fragmentation is detrimental for market stability. In particular, I measure market stability as changes experienced in market liquidity in the occurrence of mini flash crashes. However, if fragmented markets are perfectly interrelated, their consolidated ability to absorb trades should not be lower than than in concentrated markets. This leads to an alternative hypothesis stating that market fragmentation is not detrimental for market stability. Following Degryse et al. (2015), I evaluate my hypotheses for both the local and the consolidated order book. The first is the order book of the local regulated exchange. The latter is constructed by aggregating the individual order books of the different trading venues under consideration (i.e., local regulated exchange and MTFs), and it mirrors the liquidity that is available to traders with access to several venues. Not all traders have access to the different 1In the European Union, the implementation of the Markets in Financial Instruments Directive (MiFID) in 2007 boosted market fragmentation. In 2005, the Regulation-National Market System (Reg-NMS) led to the proliferation of alternative trading systems in the US.

2 venues, nor do all allocate resources to continuously monitor them. Depending on whether traders operate locally or at several trading venues, they are exposed differently to the effects of market fragmentation. Furthermore, the direction of the effect is not straightforward. For the local regulated exchange, the reduction in market share due to competition may harm its ability to absorb trades, causing a negative impact on liquidity when there is a liquidity shock. On the other hand, competition reduces transaction costs, which incentivises trading and should equip the market with greater depth and ability to absorb shocks. For the consolidated order book, if fragmented markets are interrelated, traders with access to all venues should not encounter greater liquidity impacts when a stock experiences a liquidity shock than without fragmentation. However, if markets are not perfectly interrelated, liquidity shocks may be amplified due to a significant reduction in the participation of liquidity providers (Cespa and Vives, 2016). The empirical setting for this study is the Spanish stock market. Following the implementation of a new regulation (Title V), and the lift of short-selling bans, the Spanish stock market started to fragment on February 1st 2013. That is, about five years later than its EU counterparts. This unique event provides a quasi-natural experiment setup for examining the effects of fragmentation. I use as benchmark the Italian stock market, whose level of fragmentation re- mained constant throughout the sample period (November 2012 - April 2013) and who, by the end of the sample period, presented similar fragmentation levels to the ones of the Spanish stock market (≈ 20%). The analysis is conducted by means of an event study approach. It relies on the estimation of a difference-in- differences regression to determine the impact of market fragmentation on liquidity in normal market conditions, and a difference-in-difference-in-differences regression to evaluate the impact of fragmentation on market stability. In this way, I control for different types of endogeneity problems, making the analysis more robust. In particular, this study focuses on the impact of lit market fragmentation. Lit venues such as regulated exchanges and MTFs, are characterised by displaying their limit order books to market participants. In contrast, dark markets (e.g., dark pools) only display information on executed trades. The lack of order book information provided by dark markets, hinders the possibility to study the effects of dark fragmentation on market stability. The results mainly support the hypothesis stating that market fragmentation does not deteriorate liquidity in normal market conditions. In fact, the results show that liquidity improves after the fragmentation event. The relative quoted spread of the treatment group falls significantly relative to the one of the control group both at the local regulated exchange and for the consolidated order book. The decrease in trading costs boosted by competition incentivises trading, which translates into a significantly lower fall in depth at best prices than the one experienced by the control group. This is more evident for the consolidated order book, where the difference between the treatment and control group is higher than in the local exchange. Depth at the local regulated exchange deteriorates for small stocks. The migration of liquidity to MTFs leads to significantly

3 thinner books for the less liquid stocks of the sample. For these stocks, market fragmentation harms traders that only trade locally. Further, the results support the hypothesis stating that market fragmentation does not deteriorate market stability since it does not aggravate liquidity shocks. First, I find evidence of a decrease in the number of mini flash crashes after the fragmentation event both at the local regulated exchange and for the consolidated order book. Moreover, after fragmentation, the time it takes for prices to recover after a crash decreases notably. Further, I find that when measuring liquidity by quoted spreads, market fragmentation makes liquidity shocks less harmful. When turning to depth at best prices, in most cases there is no significant evidence that fragmentation contributes to a greater liquidity deterioration relative to a scenario of concentrated markets. This is not the case for the consolidated order book of small stocks, whose depth significantly deteriorates. The migration of liquidity of the less liquid stocks makes them more vulnerable to liquidity shocks if markets are not perfectly interrelated. This deterioration especially occurs at the newly entrant MTFs. MTFs have thinner books relative to the dominant local exchange, and are less able to absorb liquidity shocks on their own. This study adds to the literature analysing the impact of market fragmentation on liquidity. Previous literature has empirically analysed the link between these two variables under normal market conditions. Consistently with the results presented in this study, Foucault and Menkveld (2008) find that after the entry of a new MTF at the Dutch equity market, consolidated depth increases and so does depth at the local regulated exchange. The reason is found in the decrease in trading costs, which incentivises trading at the local exchange. In contrast, Degryse et al. (2015) show that while lit market fragmentation improves quoted spreads and depth at the consolidated order book, it deteriorates depth at the local regulated exchange. O’Hara and Ye (2011) find that market fragmentation is not detrimental for liquidity as measured by effective spreads. The authors argue that although markets are spatially fragmented they are in essence interrelated. Also, and in contrast to this study, O’Hara and Ye (2011) find that small stocks benefit the most from market fragmentation. My main contribution to the literature on fragmentation is through the study of the relation between market fragmentation and market stability, where market stability is measured as changes experienced in market liquidity in the presence of mini flash crashes. So far the literature on market fragmentation has focused on normal market conditions. However, after the Flash Crash of May 6, 2010 and other recent episodes of sharp mini flash crashes at individual stocks,2 regulatory authorities have expressed their concern that market fragmentation may be aggravating liquidity shocks (SEC, 2010). Golub et al. (2012) is one of the few papers empirically studying the impact of mini flash crashes on liquidity. The authors find that mini flash crashes have a negative impact on the

2For more information on recent episodes of mini ﬂash crashes see Bowley (2010b), Kamin- ska (2010) and Bowley (2010a)

4 quoted spreads of the consolidated order book. They claim that market fragmentation is behind the occurrence of mini flash crashes. However, they do not test it empirically nor do they explain it by means of a theoretical model. My results show that not only does market fragmentation lead to a lower number of mini flash crashes and to a faster recovery, but that, especially for large stocks, fragmentation mitigates liquidity dry-ups during mini flash crashes. Market fragmentation has increased significantly in the recent years (Gen- tile and Fioravanti, 2011; Gomber et al., 2013) and so has the number of mini flash events (Cespa and Vives, 2016). Yet, the results presented in this study show that market fragmentation improves liquidity and that it does not aggravate liquidity shocks. These results should be relevant for regulators that are evaluating the desirability of market fragmentation in the development of new regulatory policies.

2 Theoretical Framework

Previous theoretical work disagrees on whether market liquidity is greater in concentrated or in fragmented markets. An argument in favour of concentrated markets is the fact that ”liquidity begets liquidity”. As noted by Pagano (1989), Chowdhry and Nanda (1991) and Harris (1993) traders are attracted to each other and, in equilibrium, they shift towards the most liquid market. Mendelson (1987) also argues that ﬁnding a counterparty trader is eas- ier in a concentrated marketplace since all liquidity is located in one venue, which speeds up order execution. Market fragmentation hinders order matching and it reduces the possibility to execute orders fast at the best possible price. This in turn discourages trading, further reducing market liquidity. Har- ris (1993), O’Hara and Ye (2011) and Upson and Van Ness (2016) also note that market fragmentation may lead to the violation of the time priority rule across markets. In this scenario, traders are disincentivised to submit limit orders, prompting thinner books and lower market liquidity. This discussion leads to the ﬁrst empirical hypothesis: H1.A: Market fragmentation deteriorates liquidity On the other hand, market fragmentation enables exchange competition. As noted by Foucault and Menkveld (2008), competition reduces transaction costs, which makes trading cheaper. This incentivises trading and enhances market liquidity. Moreover, a concentrated marketplace can not satisfy the needs of all traders. Harris (1993) points out that market fragmentation makes possible to accommodate traders with distinct types of trading needs. This fosters trading from market participants that would be in disadvantage in a concentrated market, leading to an increase in market liquidity. Based on these arguments, I develop an alternative hypothesis: H1.B: Market fragmentation does not deteriorate liquidity

5 In a completely concentrated marketplace, all market participants trade in the same venue, providing it with high liquidity and with the ability to absorb trades without causing large price impacts. When liquidity is scattered across trading venues, the individual liquidity at each venue is lower. However, as pointed out by Harris (1993), if information flows between markets and traders have access to the different venues, market fragmentation does not imply lower market quality. In this case, prices in each venue are efficiently determined according to the aggregated demand and supply of liquidity rather than on the liquidity of the isolated fragments. Moreover, since traders have access to different venues, they can send and split their orders across them to execute as many orders as possible at best prices. In this scenario of fragmented, but interrelated markets, fragmentation does not necessarily lead to larger price impacts than in a concentrated market. Accordingly, I formulate the following empirical hypothesis: H2.A: Market fragmentation does not deteriorate market stability Madhavan (2012) argues that in fragmented markets, prices are more likely to experience large price impacts. That is because although markets are interrelated, the linkages between markets are imperfect, leading to de facto thinner books. Indeed, Menkveld and Yueshen (2015), who study the cause of the Flash Crash of May 6, 2010, attribute the illiquidity of the Flash Crash to a broken cross-market arbitrage. In his theoretical study, Van Kervel (2015) shows that High Frequency Traders (HFTs) have incentives to duplicate orders in fragmented markets. Once the order is executed in one market, they cancel the orders submitted in the others. The aggregated liquidity in fragmented, but interrelated, markets is lower than what it seems a priori and could lead to large price impacts after the occurrence of liquidity shocks. This discussion leads to the alternative hypothesis: H2.B: Market fragmentation deteriorates market stability

3 Regulatory Framework

After MiFID, financial markets in the European Union started to fragment. The directive was meant to be applied to all EU countries with the aim to harmonise regulation and foster competition. However, the regulatory framework of the Spanish financial market hindered its full application. As a consequence, Bolsa y Mercados Españoles(BME) or, the Spanish Stock Exchange, continued to operate as an effective monopoly up until 2013 (Stafford, 2013; Bakie, 2013). Figure 1 depicts a schematic timeline with the main events and regulations that contributed to the late fragmentation of the Spanish equity market. [Insert Figure 1 Here] Until February 2013, MTFs had a small presence in the Spanish market with

6 an average aggregate market share below 3% between 2009 and 2012.3 In 2011, a reform known as Title V, was introduced in the Spanish legislation with the aim to facilitate trading at MTFs. Before Title V was implemented, when a trade took place in a MTF, its clearing house had to submit the order to a local broker to proceed with the registration to Iberclar.4 This had to be done through BME, who provided an identiﬁcation number that was sent to Iberclar for the registration of the trade.5 The MTF ended up re-registering the trades and paying three layers of fees in the process: the broker, the settlement agent and BME, which at the same time was its competitor. After the implementation of Title V, trades taking place at MTFs can be submitted by the clearing house to Iberclar directly through a settlement agent. However, MTFs did not experience the expected increase in market share immediately after the reform. Several factors might have contributed to this situation. First, as pointed out by Degryse et al. (2015), MTFs may need some time to gain investors reliance and attract trading activity. Second, due to the unstable economic situation, shortly after the reform Spain introduced a ban on the short- selling of equities which lasted until February 2012. A second ban was launched from July 2012 to January 2013. Third, despite the reform, there still existed diﬀerences regarding the settlement window and fees for MTFs and BME, which impeded full competition (Grant, 2011; Love, 2011). In an attempt to attract trading activity, in October 2011 Chi-X launched a 3-month rebate on market making and clearing fees when trading Spain’s top 6 stocks. Although Chi-X’s market share increased, it did so marginally. Concurring with the end of the second short-selling ban, BATS Chi-X launched a strong rebate for executions in all IBEX35 securities. The market fragmented shortly after and it reached close levels (≈ 20%) to the ones in similar EU countries such as Italy (Figure 2), which also implemented short selling bans in 2011 and 2012. Nowadays, the Spanish equity market has reached comparable fragmentation levels (≈ 40%) to those of the most fragmented equity markets in Europe (see Figure 3). It would not be accurate to assert that the lift of the short-selling ban on its own was what triggered the market fragmentation of Spanish stocks. It was rather a combination of events that led to the fragmentation of its market. [Insert Figure 2 Here] [Insert Figure 3 Here]

3Information on market share has been retrieved from BATS Chi-X Europe: http://www. batstrading.co.uk/market_data/venue/batschixeurope/ 4Iberclar is the central security depository in Spain. 5BME is the owner of Iberclar.

7 4 Empirical Setting

4.1 Data and Sample

I access tick-by-tick data on trades and quotes, time-stamped at a millisecond frequency, from the Thomson Reuters Tick History (TRTH) database, which is maintained by the Securities Industry Research Centre of Asia-Pacific (SIRCA). The trades dataset contains information on prices and trade size. I use this information to calculate volume fragmentation. The quotes dataset contains information on prices and depth at the best bid and ask quotes. I gather two types of quote datasets: The first contains information on visible limit orders submitted at the local exchange of the Spanish and Italian stock markets (BME and Borsa Italiana (BI), respectively). The second is a global consolidated order book of the different trading venues operating in each of the two markets. This dataset includes information on the venue responsible of the quote updates in the consolidated order book. I use the first dataset to investigate the impact of market fragmentation on the liquidity of the local regulated exchange, and whether market fragmentation deteriorates local liquidity in the presence of mini flash crashes. The second dataset is used to evaluate the effects of fragmentation in the consolidated order book. My sample comprises the Spanish IBEX35 (treatment group) and the Italian FTSE MIB (control group) index constituents. Only stocks that remain listed at the index during the entire sample period are retained. I also remove stocks that do not trade in the four venues where IBEX35 and FTSE MIB constituent stocks trade (BME or BI for the local exchanges and Chi-X, BATS and Turquoise (TQ) as the main MTFs). As in Degryse et al. (2015), for the MTFs, I only use quote data coinciding with the trading session at the local regulated exchanges. In total, 30 out of 35 IBEX35 stocks and 39 out of 40 FTSE MIB stocks are included in the sample. The sample period spans from November 2012 to April 2013. That is, three months before and three months after the event of February 1st 2013 that triggered the fragmentation of the Spanish equity market. Spanish Equity Market The Spanish stock market is the 5th largest equity market in Europe based on the market capitalization of its listed domestic companies.6 BME, is the local and dominant exchange in Spain. Since 2001, BME is constituted as a holding company grouping the country’s four regional exchanges (Madrid, Barcelona, Bilbao and Valencia). At BME, all trading takes place through the Spanish Stock Market Interconnection System (SIBE), which is an electronic platform that communicates the four regional exchanges. SIBE ensures a unique point of liquidity and a single price and order book per stock. Orders in SIBE are matched following a strict price-time priority rule. That is, limit orders with

6Information retrieved from: http://www.indexmundi.com/facts/indicators/CM.MKT. LCAP.CD/rankings/europe

8 the highest bid and lowest ask have priority over orders deeper in the book. At a certain price, orders are executed according to the time they are entered into the system. BME is an electronic limit order market with continuous trading from 9:00 to 17:30 on weekdays. Opening and closing call auctions take place in the market in order to determine prices at the beginning and end of the trading session. The opening call auction takes place from 8:30 to 9:00 and the closing call auction runs from 17:30 to 17:35. Apart from BME, mainly three MTFs trade Spanish equities: Chi-X, BATS and Turquoise. Table 1:Panel A reports information on the average market share of the venues and MTFs trading Spanish equities. The market share at each venue is computed as the ratio between the daily volume executed at the individual venue and the total daily volume executed in all venues. During the period of study, BME had an average market share between 95% and 85% of the volume traded in IBEX35 stocks. Its main competitors were Chi-X (with an average market share between 4 and 10%), Turquoise (0% to 3%) and BATS (0.6% to 1.2%). Table 1 and Figure 3, show a tendency of MTFs to capture market share from the local exchange. [Insert Table 1 Here] The last column in Table 1 reports information on the average market fragmentation of the stocks. During the sample period, the fragmentation of the Spanish equity market increased from an average 8% for the three months before the fragmentation event, to an average 23% after the event date. As in Degryse et al. (2015) and Upson and Van Ness (2016), the per-stock daily fragmentation is computed as

V X 2 F ragmentationi,t = 1 − HHIi,t = MSv,i,t (1) v=1 where i indicates the stock, t the day and v the venue (BME or BI for the local exchanges and Chi-X, BATS and Turquoise for the MTFs); MS is the market share of a certain venue and HHI corresponds to the Herﬁndhahl-Hirschman Index. Italian Equity Market The Italian equity market is used as control group due to its similarities with the Spanish stock market. On a qualitative level, the economic crisis of 2008 aﬀected the two markets in a similar way, the two markets initiated short-selling bans as a response to the crisis, and the two equity markets are of similar size. On a microstructure level, BME and BI are designed as limit order markets with similar trading hours and mechanisms to open and close trading. Since 2007, BI is part of the London Stock Exchange group (LSE). At the time of study, BI’s continuous trading session ranged from 09:00 to 17:25 on weekdays. An opening call auction was scheduled from 08:00 to 09:00 and a

9 closing call auction from 17:25 to 17:30.7 As BME, BI is an electronic limit order book where orders are matched following a price-time priority rule during the continuous trading session. Chi-X, BATS and Turquoise are the main competitors of BI. Table 1:Panel B provides information on the average market share of the venues trading Italian equities and on the average market fragmentation of the stocks. The venues operating at the Italian equity market present a stable market share during the sample period. BI presents a constant average market share of 73%. Turquoise experiences a signiﬁcant increase in market share in the second half of the sample period. However, rather than taking market share from BI, it mostly takes it from Chi-X and BATS. This explains why the fragmentation of the Italian equity market remains rather constant throughout the sample period. Note that up until July 2013, the level of fragmentation of the Italian stock market only increases by 3%.

4.2 Mini Flash Crashes

As main contribution, I investigate the effect that market fragmentation has on liquidity under the presence of mini flash crashes. I define a mini flash crash as a sudden and sharp price change that is reversed within a few seconds. In this paper, for a change in price to be categorised as a mini flash crash it has to comply with three requirements: It has to occur within a maximum of 2 seconds, the change in price within this two seconds has to be of at least 0.8%, and the recovery of the crash has to take place within a maximum of 300 seconds. Moreover, the recovery has to be of at least 90% of the price that was quoted before the initiation of the mini flash crash. The first two requirements are in accordance with the definition of mini flash crash provided by Nanex (2010) and Golub et al. (2012). I added as a third requirement a restriction on the recovery time after the detection of a mini flash crash. The reasoning is to avoid capturing changes in price that are due to fundamental volatility rather than a momentary liquidity dry-up. A 300 second recovery limit is long enough to ensure the order book has time to be re-filled with new orders (especially for the less active stocks of the sample) but short enough to ensure that the change in price is not driven by fundamental volatility. Figure 4 shows an example of a mini flash crash for the Abertis (ABE.MC) stock on April 10, 2013 at BME. The fall from top (12:38:31.187) to bottom (12:38:31:230) occurs within 43 milliseconds. The fall is of around 0.8% and it takes about 7 milliseconds for the price to bounce back to the midpoint that was quoted before the mini flash crash.

7Since November 2015 the continuous trading session has been extended until 17:30 and the closing call auction takes place from 17:30 to 17:35. Technical details presented here are retrieved from: http://www.borsaitaliana.it/homepage/nuovi-orari.en.htm and http: //www.indexmundi.com/facts/indicators/CM.MKT.LCAP.CD/rankings/europe

10 [Insert Figure 4 Here] Rather than identifying mini flash crashes by considering changes in prices of concurrent trades, I use the order book midpoint as reference price. By construction, mini flash crashes have to lead to changes in order book prices since they are liquidity shocks associated to a liquidity dry-up. However, abrupt changes in the reported trading prices may be due, for instance, to the execution of derivatives contracts, leaving book prices unaffected. To ensure that the change in price is due to a liquidity shock, I identify mini flash crashes on the basis of changes in the midpoint. Tables 2 and 3 provide summary statistics of the mini flash crashes detected at the local and consolidated order books for the treatment and control groups. In both order books, market fragmentation leads to a decrease in the number of flash crashes for the Spanish stock market. The Italian stock market experiences an increase in the number of mini flash crashes in the second half of the sample period. However, the decrease in the Spanish market is considerably greater than the increase in the Italian market. Additionally, the recovery time after the occurrence of a mini flash crash also decreases after the fragmentation event. For the consolidated order book, the median recovery time for the IBEX35 stocks falls from 8 to 2 seconds. Although to a lesser extent, market fragmentation is also associated to a decrease in the median percentage price change experienced within a crash. Note that the recovery time and percentage price change are lower at the local regulated exchange than at the consolidated order book. This may signal that the different venues are not perfectly interrelated, which could explain why the local, and still dominant, exchange recovers faster after a crash. [Insert Table 2 Here] [Insert Table 3 Here]

5 Methodology

The late fragmentation of the Spanish stock market relative to its EU counterparts, provides a quasi-natural experiment setup for examining the eﬀects of market fragmentation. In this section I present the regressions and measures of market liquidity that I use to conduct the study.

5.1 Diﬀerence-in-Diﬀerences Analysis

I employ a Difference-in-Differences (DD) regression model to evaluate the impact of market fragmentation on liquidity in normal market conditions. By using this approach, I control for permanent differences in liquidity between the control and treatment group that are unrelated to market fragmentation.

11 To assess the impact that market fragmentation has on liquidity I set up the following regression model:

Yi,t = α + β1P osti,t + β2T reatmenti,t + β3P osti,t · T reatmenti,t + i,t (2) where i indicates stocks and t trading days; Y is a liquidity variable (described in Section 5.3); P osti,t is a dummy variable that equals 1 from the fragmentation st st date onwards (February 1 to April 31 2013); and T reatmenti,t is a dummy variable that takes value 1 for stocks belonging to the treatment group. The parameter of interest, β3 captures the eﬀect that market fragmentation has on the liquidity of the treatment group relative to the control group.

5.2 Difference-in-Difference-in-Differences Analysis

By means of a Difference-in-Difference-in-Differences (DDD) estimation approach, I investigate the effect that market fragmentation has on liquidity when stocks experience liquidity shocks in the form of mini flash crashes. By following a DDD estimation procedure, it is taken care of two additional trends that could otherwise bias the outcome: changes in liquidity between the control and treatment group that are unrelated to the fragmentation event, and changes in liquidity that are unrelated to mini flash crashes. To conduct the event study, I set up the following regression model:

Yi,t = α + β1P osti,t + β2T reatmenti,t + β3F lashEventi,t

+ δ1P osti,t · T reatmenti,t + δ2P osti,t · F lashEventi,t (3) + δ3T reatmenti,t · F lashEventi,t

+ λ1P osti,t · T reatmenti,t · F lashEventi,t + i,t where F lashEventi,t is a dummy variable that equals 1 for the ten seconds after the detection of a mini flash crash and 0 for the thirty seconds before. I choose a post-event window of ten seconds because I intend to capture whether market fragmentation worsens the immediate impact of a liquidity shock. As shown in Table 3, the median recovery time after a flash crash is below ten seconds and as little as 0.2 and 2 seconds for the local and consolidated order books of the Spanish stock market. Choosing a wider window may average out the results.8 The choice of a pre-event window of 30 seconds is to average out price changes that are part of the mini flash crash but that occur immediately before its detection. The parameter of interest, λ1 captures the effect that market fragmentation has on the liquidity of the treatment group in the presence of mini flash crashes. 8For robustness, I have also computed the regression with a post event window of 20 seconds. The results are similar to those obtained with a window of 10 seconds.

12 5.3 Liquidity Measures

I evaluate order book liquidity by means of two measures: Relative Quoted Spread (Spread) and Depth at Best Prices (Depth). Rather than taking snapshots of the order book every certain amount of time, the two liquidity measures are computed each time the best quotes of the order books are updated. The reason lays behind the definition of a mini flash crash, which is restricted to take place within a maximum of 2 seconds (2000 milliseconds). To avoid omitting mini flash crashes, I use all order updates in their detection. Since, in some cases, the recovery of the crash may take place in a matter of a few milliseconds, considering all quote updates is more accurate to detect changes in book liquidity levels. I define Spread as

AskP ricei,τ − BidP ricei,τ Spreadi,τ = (4) Midpointi,τ where i indicates the stock and τ the time of the order book update; AskP ricei,τ and BidP ricei,τ refer to the best bid and ask quotes of the order book. Midpointi,τ is deﬁned as the average of the best bid and ask prices. Depth is computed as

AskSize AskP rice + BidSize BidP rice Depth = i,τ i,τ i,τ i,τ (5) i,τ 2 where BidSizei,τ and AskSizei,τ is the volume resting at the best bid and ask quotes, respectively. Once the liquidity measures are calculated for each quote update, I compute a time weighted average of the measures. This takes into account the amount of time a quote remains unchanged, giving more weight in the average to quotes staying longer in the order book. In this way, for the DD analysis I obtain one observation per day and stock for each of the two liquidity measures. For the DDD model, I get one observation per mini ﬂash crash and event window. That is, for each mini ﬂash crash and liquidity measure, the time weighted liquidity is computed for the thirty seconds before the crash and for the ten seconds after.

6 Impact of Market Fragmentation

In this section I present the results of the DD and DDD analysis for the local and consolidated order books and relate them to the empirical hypotheses introduced in Section 2.

13 6.1 Does Market Fragmentation Deteriorate Market Liq- uidity?

I start by investigating hypothesis H1, which is concerned with the impact of market fragmentation on liquidity in normal market conditions and is evaluated by means of the DD regression model. Tables 4 and 5 show the DD coefficient estimates and standard errors for the local and consolidated order books, respectively. In all cases, the standard errors have been double clustered by stock and day. The tables depict the results when fitting all stocks into the regression independently of their size, and when subsetting the regression according to stock size.9 The reason for splitting the sample is that previous literature has found that the effects of market fragmentation on liquidity diverge for stocks of different sizes (see O’Hara and Ye (2011)). [Insert Table 4 Here] [Insert Table 5 Here]

The coefficient of the parameter of interest P osti,t · T reatmenti,t is negative and significant for the Spread measure in both, the local and the consolidated order book for all size groups. According to the coefficient estimates, when considering all stocks together, the relative quoted spread of the treatment group falls from 15 basis points to 12 after the fragmentation event in the local exchange, and from 13 to 11 in the consolidated order book. The spread of the control group does not experience significant changes. Small and medium stocks are the ones experiencing a greater fall in spreads, although the spread of large stocks also decreases significantly from 7 to 5 basis points in the consolidated order book and from 7 to 6 in the local. This result is in line with hypothesis H1.B. Market fragmentation does not only not deteriorate liquidity measured by quoted spreads, but it improves it for all stocks independently of their size. Order book Depth appears to be lower in the second half of the sample both for the treatment and control group. However, market fragmentation has a positive effect in the treatment group since Depth falls relatively less in the treatment than in the control group in both the local and the consolidated order book. Yet, it is only medium and large stocks that benefit from relatively more depth. Although marginally, Depth for small stocks significantly deteriorates at the local exchange. At the consolidated order book, Depth does not significantly improve neither deteriorate for small stocks. Overall, the results show a strong support for hypothesis H1.B. They are consistent with Foucault and Menkveld (2008) and O’Hara and Ye (2011), who note that market fragmentation reduces transaction costs. Consistent with increased competition, the reduction in transaction costs occurs both in the local exchange and in the consolidated order book. The decrease in trading costs incentivises trading. This, together with the fact that market fragmentation makes possible

9The stock size is based on the weighted contribution of each individual stock to the index.

14 to accommodate heterogeneous traders (Harris, 1993), potentially explains the improvement in book depth at best prices. These results show that all traders beneﬁt from market fragmentation, independently of whether they have access to several trading venues or are constrained to trade locally.

6.2 Does Market Fragmentation Deteriorate Market Sta- bility?

I now turn to investigate hypothesis H2, which is concerned with the impact of market fragmentation on market stability. The hypothesis is evaluated by means of a DDD regression model. Tables 6 and 7 show the results of the regression for the local and the consolidated order book, respectively. Both tables depict the results when splitting the regression according to stock size. However, since there is a low number of mini flash crashes detected for large stocks, I include medium and large stocks in the same size category. [Insert Table 6 Here] [Insert Table 7 Here] According to the coefficient estimates, market fragmentation makes mini flash crashes less harmful for liquidity when measured in terms of Spread. That is significantly the case for small and medium/large stocks at the local exchange and for medium/large stocks at the consolidated order book. After market fragmentation, and in the occurrence of a liquidity shock, the Spread of small stocks in the treatment group deteriorates 7 basis points less than before fragmentation and, on average, it deteriorates 1 basis point less relative to the control group. The same interpretation applies for medium/large stocks, who also experience a relative improvement of Spread compared to a scenario without market fragmentation. In most cases, after the occurrence of a mini flash crash, market fragmentation does not significantly deteriorate Depth more than in a scenario of concentrated markets. The exception is the consolidated order book of small stocks, where Depth after the occurrence of a liquidity shock is significantly lower after fragmentation than before it. The regression results, taken together with the decrease in the number of mini flash crashes detected after market fragmentation and their lower recovery time, mostly support hypothesis H2.A. Consistent with increased competition, market fragmentation leads to a reduction in transaction costs and increased market liquidity. Moreover, as pointed out by Harris (1993), if markets are interrelated, information and trading activity flows between markets and fragmentation does not lead to greater price impacts than in a concentrated market. However, that is not the case for the consolidated order book of small stocks. For these stocks, market fragmentation leads to significantly lower depth. This supports hypothesis H2.B and the argument of Madhavan (2012), who claims

15 that the linkages between markets are imperfect. Small stocks are especially vulnerable due to their per se lower liquidity levels. With market fragmentation liquidity is scattered, leading to thinner books at each individual venue. If intermarket linkages are imperfect, in the occurrence of a liquidity shock the local and dominant exchange is the one with greater ability to absorb the shock. MTFs, who have thinner books especially for the less traded stocks, are more likely to experience a signiﬁcant deterioration in their Depth levels.

7 Conclusion

This paper uses a quasi-natural experiment setup, based on the fragmentation of the Spanish stock market, to empirically examine the effects of market fragmentation on liquidity with a focus on episodes of market instability. To my knowledge, this paper is the first to analyze the impact of market fragmentation on liquidity in the presence of mini flash crashes. After the Flash Crash of May 6, 2010 and the occurrence of recent episodes of sharp liquidity dry-ups at a stock level, regulatory authorities have raised concerns that market fragmentation may be a source of market instability and may aggravate liquidity shocks. Given the rising tendency of markets to fragment, understanding the impact that fragmentation has on market stability is increasingly relevant for regulators and policy-makers. This study shows that market fragmentation does not deteriorate liquidity in normal market conditions. Indeed, increased competition associated to market fragmentation reduces quoted spreads significantly, making trading cheaper independently of stock size. The lower transaction costs incentivises trading, leading to greater book depth at best prices both at the local and the consolidated order book. However, only medium and large stocks benefit from greater depth at the local exchange. The migration of liquidity to MTFs significantly deteriorates depth for the smaller stocks of the sample. I also find that market fragmentation makes mini flash crashes less harmful for liquidity as measured in terms of quoted spreads, and that it does not deteriorate depth significantly with the exception of small stocks for the consolidated order book. The overall effect of market fragmentation on liquidity and market stability is positive and both, traders only operating at the local exchange such as retail traders, and those that have access to several venues, are better-off with market fragmentation. I caution, however, that this empirical study has limitations and its results are preliminary. For instance, the definition of mini flash crash given by Nanex (2010) is subjective. In a future version I plan to base the detection of mini flash crashes on stock-price characteristics rather than using a fix 0.8% price change for all stocks. I also intend to add proper controls into the regressions to ensure the robustness of the results. This is especially relevant since determining the effects of fragmentation on liquidity is complicated due to endogeneity issues. Conducting the study by means of cross-sectional regressions and the use of

16 instrumental variables could enhance the validity of the results and help to get rid of problems related to imperfect benchmarks.

References

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18 Figures

Figure 1: Main Events and Regulations

Figure 1 depicts a timeline with the main event and regulations that aﬀected the Spanish equity market between 2011 and 2013.

1st Short 2nd Short Title V Selling Ban Selling Ban Fragmentation

May 2011 August 2011 February 2012 July 2012 February 2013

19 Figure 2: Evolution of Market Fragmentation (August 2012 - August 2013)

Figure 2 shows the evolution of the average market fragmentation experienced by the constituent stocks of the main Spanish and Italian indices (IBEX and MIB, respectively) between August 2012 - August 2013. The purple vertical line indicates the day of the fragmentation event (February 1st 2013). The daily fragmentation of the sample stocks is computed as: PV 2 F ragmentationi,t = 1 - v=1 MSv,i,t, where i indicates the stock, t the day and v the venue (BME or BI for the local exchanges and Chi-X, BATS and Turquoise for the MTFs); MSi,t is the stock-day market share of a certain venue. For each day, the average market fragmentation is computed to obtain the observations in Figure 2.

IBEX − Treatment 40

MIB − Control 30 20 Market Fragmentation (%) Fragmentation Market 10 0

Sep Nov Jan Mar May Jul Date

20 Figure 3: Marketshare Evolution of the Spanish, Italian and German Stock Markets

Figure 3 shows snapshots of the market share of the main venues and MTFs for the IBEX35, FTSE MIB and DAX stocks from January 2010 until De- cember 2016. Spanish Stock Market

January 2010 January 2013 December 2016

Italian Stock Market

January 2010 January 2013 December 2016

German Stock Market

January 2010 January 2013 December 2016

Information on market share has been retrieved from BATS Chi-X Europe http://www. batstrading.co.uk/market_data/venue/batschixeurope/ 21 Figure 4: Mini Flash Crash for Abertis - April 10, 2013

Figure 4 depicts a mini ﬂash crash occurring on April 10, 2013 at the local Spanish exchange (BME) for the stock of the ﬁrm Abertis.

22 Tables

Table 1: Market Share and Market Fragmentation of Trading Venues

Table 1 shows the average market share of the main venues trading IBEX35 and FTSE MIB stocks (BME or BI for the local exchanges, Chi-X, Turquoise (TQ) and BATS for the MTFs). The last column depicts the average fragmentation of the stocks constituting the indices. The information is provided for the entire sample period (November 2012 - April 2013), for the period before the fragmentation event (November 2012 - January 2013) and for the period after the fragmentation event (February 2013 - April 2013). The table also depicts the average market share and average fragmentation up until three months after the end of the sample period (July 2013) to reﬂect the fragmentation tendency of the stocks. The market share at each venue is computed as the ratio between the daily volume executed at each individual venue and the total daily volume executed in all venues. The fragmentation PV 2 of the sample stocks is computed as: F ragmentationi,t = 1 - v=1 MSv,i,t, where i indicates the stock, t the day and v the venue (BME or BI for the local exchanges and Chi-X, BATS and Turquoise for the MTFs), MSi,t is the stock-day market share of a certain venue. For each period, the average market fragmentation of the individual stocks is computed. The values are presented in percentage form. Panel A: Spanish Stock Market - IBEX35 BME Chi-X TQ BATS Fragmentation November 2012 - April 2013 90 7 2 1 16 November 2012 - January 2013 95 4 0 1 8 February 2013 - April 2013 85 10 3 1 23 July 2013 82 13 3 2 29 Panel B: Italian Stock Market - FTSE MIB BI Chi-X TQ BATS Fragmentation November 2012 - April 2013 73 19 4 4 33 November 2012 - January 2013 74 21 1 4 31 February 2013 - April 2013 73 17 7 3 34 July 2013 73 17 6 4 34

23 Table 2: Number of Mini Flash Crashes

Table 2 shows summary statistics of the number of mini ﬂash crashes found in the sample. The information is provided for both, the local regulated exchange (BME or BI) and for the consolidated order book (BME or BI together with Chi-X, BATS and Turquoise). The table gives information on the total number of crashes, together with the number of up and down crashes.

Panel A: Local Regulated Exchange Spanish Stock Market Italian Stock Market Total Up Down Total Up Down Entire period 2105 1065 1040 947 495 452 Before fragmentation 1179 599 580 375 195 180 After fragmentation 926 466 460 572 300 272

Panel B: Consolidated Order Book Entire period 1556 737 819 1538 694 844 Before fragmentation 883 411 472 697 317 380 After fragmentation 673 326 347 841 377 464

24 Table 3: Characteristics of Mini Flash Crashes

Table 3 shows information on the recovery time and percentage price change of the mini ﬂash crashes that have been detected in the sample. The information is provided for both, the local regulated exchange (BME or BI) and the consolidated order book (BME or BI together with Chi-X, BATS and Turquoise).

Panel A: Local Regulated Exchange Spanish Stock Market Italian Stock Market Mean Median Mean Median Recovery Time (seconds) Entire period 23 0.3 20 1 Before fragmentation 27 0.7 13 0.5 After fragmentation 17 0.2 25 1.2 Percentage Price Change Entire period 1.10 0.98 1.10 0.96 Before fragmentation 1.11 0.98 1.07 0.96 After fragmentation 1.08 0.97 1.12 0.98

Panel B: Consolidated Order Book Recovery Time (seconds) Entire period 33 4 31 5 Before fragmentation 41 8 28 4 After fragmentation 24 2 34 7 Percentage Price Change Entire period 1.14 0.97 1.43 1.02 Before fragmentation 1.14 0.98 1.36 1.01 After fragmentation 1.14 0.95 1.50 1.02

25 Table 4: Diﬀerence-in-Diﬀerences Analysis for the Local Regulated Exchange

Table 4 evaluates the impact of the fragmentation of the Spanish stock market on the liquidity of the local regulated exchange (BME). Reported results correspond to a balanced panel difference-in-differences regression of i stocks and t days: Yi,t = α + β1T reatmenti,t + β2P osti,t + β3P osti,tT reatmenti,t + i,t. The regression is computed for two different dependent variables that capture two different dimensions of liquidity. Spread is the ratio between the quoted spread (Best Ask Price - Best Bid Price) and the midpoint. Depth is the average of the volume (in Euros) found at the best bid and ask prices. T reatmenti,t is a dummy variable that takes value 1 if the observation belongs to the treatment group (IBEX35 as a representative of the Spanish stock market) and 0 if it belongs to the control group (FTSE MIB as a representative st of the Italian stock market). P osti,t is a dummy variable that takes value 1 for the post-event window (February 1 2013 th st st to April 30 2013) and 0 for the pre-event window (November 1 2012 to January 31 2013). P osti,tT reatmenti,t is the parameter of interest. It captures the effect of the event for the treatment group relative to the control group. Standard errors are corrected by double clustering on stock and day (numbers in brackets). ***, ** and * indicate the statistical significance at 1%, 5% and 10% level, respectively.

All Stocks Small Stocks Medium Stocks Large Stocks Spread Depth Spread Depth Spread Depth Spread Depth Intercept 1.27E-03*** 73860*** 1.44E-03*** 36446*** 9.74E-04*** 77849*** 8.90E-04*** 246268*** (5.79E-05) (12818) (6.17E-05) (3543) (4.40E-05) (7417) (9.07E-05) (42590)

T reatmenti,t 1.97E-04* -41366*** 3.75E-04*** -9144 4.13E-04*** -47646*** -2.09E-04* -194072*** (1.24E-04) (13400) (1.45E-04) (7343) (1.35E-04) (8208) (1.13E-04) (43082)

P osti,t 2.08E-05 -8471*** -5.95E-06 1427 7.10E-05*** -13196*** 6.40E-05*** -47475*** (2.66E-05) (3146) (3.78E-05) (1946) (2.29E-05) (1999) (9.95E-06) (13040)

P osti,t · T reatmenti,t -2.98E-04*** 4109 -3.22E-04*** -3434* -3.92E-04*** 7897*** -1.48E-04*** 37735*** (3.82E-05) (3022) (6.01E-05) (1950) (4.61E-05) (2135) (2.18E-05) (12651) AdjR2 0.04 0.10 0.09 0.04 0.21 0.57 0.33 0.62 Table 5: Diﬀerence-in-Diﬀerences Analysis for the Consolidated Order Book

Table 5 evaluates the impact of the fragmentation of the Spanish stock market on the liquidity of the consolidated order book (local venue (BME) together with MTFs (Chi-X, Turquoise and BATS)). Reported results correspond to a balanced panel difference-in-differences regression of i stocks and t days: Yi,t = α+β1T reatmenti,t+β2P osti,t+β3P osti,tT reatmenti,t+i,t. The regression is computed for two different dependent variables that capture two different dimensions of liquidity. Spread is the ratio between the quoted spread (Best Ask Price - Best Bid Price) and the midpoint. Depth is the average of the volume (in Euros) found at the best bid and ask prices. T reatmenti,t is a dummy variable that takes value 1 if the observation belongs to the treatment group (IBEX35 as a representative of the Spanish stock market) and 0 if it belongs to the control group (FTSE MIB as a representative of the Italian stock market). P osti,t is a dummy variable that takes value 1 for the post-event window (February 1st 2013 to April 30th 2013) and 0 for the pre-event window (November 1st 2012 to st January 31 2013). P osti,tT reatmenti,t is the parameter of interest. It captures the effect of the event for the treatment group relative to the control group. Standard errors are corrected by double clustering on stock and day (numbers in brackets). ***, ** and * indicate the statistical significance at 1%, 5% and 10% level, respectively.

All Stocks Small Stocks Medium Stocks Large Stocks Spread Depth Spread Depth Spread Depth Spread Depth Intercept 1.19E-03*** 101851 *** 1.34E-03*** 43447*** 8.99E-04*** 117491*** 8.77E-04*** 354037*** (5.47E-05) (18756) (5.94E-05) (4913) (4.51E-05) (13006) (6.31E-05) (56931)

T reatmenti,t 1.51E-04 -71822*** 3.82E-04*** -20556*** 3.28E-04*** -88842*** -2.28E-04*** -302063*** (1.20E-04) (19189) (1.48E-04) (8513) (1.20E-04) (13526) (8.83E-05) (57293)

P osti,t 2.44E-05 -13215 *** 1.43E-05 232 4.43E-05* -23494*** 4.56E-05*** -59256*** (2.74E-05) (3558) (3.87E-05) (2545) (2.44E-05) (2486) (1.28E-05) (11268)

P osti,t · T reatmenti,t -3.12E-04*** 12948*** -3.56E-04*** 1192 -3.67E-04*** 22028*** -1.79E-04*** 56937*** (3.63E-05) (3468) (5.92E-05) (2620) (4.15E-05) (2382) (1.83E-05) (10678) AdjR2 0.03 0.13 0.06 0.11 0.20 0.60 0.38 0.67 Table 6: Difference-in-Difference-in-Differences Analysis for the Local Regulated Exchange

Table 6 evaluates the impact of the fragmentation of the Spanish stock market on the liquidity of the local regulated exchange in the presence of mini flash crashes. Reported results correspond to a difference-in-difference-in-differences regression of i stocks and t days: Yi,t = α + β1T reatmenti,t + β2P osti,t + β3F lashEventi,t + γ1P osti,tT reatmenti,t + γ2P osti,tF lashEventi,t + γ3T reatmenti,tF lashEventi,t + λ1P osti,tT reatmenti,tF lashEventi,t + i,t. The regression is computed for two different dependent variables. Spread is the ratio between the quoted spread (Best Ask Price - Best Bid Price) and the midpoint. Depth is the average of the volume (in Euros) found at the best bid and ask prices. T reatmenti,t is a dummy variable that takes value 1 if the observation belongs to the treatment group (IBEX35 for the Spanish stock market) and 0 if it belongs to the control group (FTSE MIB for the Italian stock market). P osti,t is a dummy variable that takes value 1 for the post-event window (February 1st 2013 to April 30th 2013) and 0 for the pre-event window (November st st 1 2012 to January 31 2013). F lashEventi,t is a dummy that takes value 1 after the detection of a mini flash crash. P osti,tT reatmenti,tF lashEventi,t is the parameter of interest. It captures the effect of the fragmentation event in the presence of mini flash crashes for the treatment group relative to the control group. Standard errors are corrected by double clustering on stock and day (numbers in brackets). ***, ** and * indicate the statistical significance at 1%, 5% and 10% level, respectively. Small Stocks Medium/Large Stocks Spread Depth Spread Depth Intercept 2.18E-03*** 40381* 1.16E-03*** 48374*** (1.17E-04) (21854) (1.06E-04) (7108) T reatmenti,t 8.35E-04*** -19093 1.06E-04*** -28791 (2.09E-04) (23300) (2.15E-04) (7122) P osti,t 5.12E-05 -17280 3.77E-04*** -8817 (1.55E-04) (20842) (7.85E-05) (8932) F lashEventi,t 1.79E-03*** -21684 5.46E-04*** -6067 (1.65E-04) (19143) (7.69E-05) (4108) P osti,t · T reatmenti,t -6.12E-04*** 21563 -7.89E-04*** 8551 (1.98E-04) (21539) (1.91E-04) (8833) T reatmenti,t · F lashEventi,t 7.78E-04** 17645 2.96E-03*** 4570 (3.86E-04) (19830) (2.26E-04) (3789) P osti,t · T reatmenti,t -6.31E-04*** 21230 4.11E-04* 2412 (1.20E-04) (18978) (2.53E-04) (3543) P osti,t · T reatmenti,t · F lashEventi,t 5.03E-04* -23968 -1.11E-03*** -4291 (3.06E-04) (19433) (3.78E-04) (3255) AdjR2 0.2 0.01 0.33 0.2 Table 7: Difference-in-Difference-in-Differences Analysis for the Consolidated Order Book

Table 7 evaluates the impact of the fragmentation of the Spanish stock market on the liquidity of the consolidated order book in the presence of mini flash crashes. Reported results correspond to a difference-in-difference-in-differences regression of i stocks and t days: Yi,t = α + β1T reatmenti,t + β2P osti,t + β3F lashEventi,t + γ1P osti,tT reatmenti,t + γ2P osti,tF lashEventi,t + γ3T reatmenti,tF lashEventi,t + λ1P osti,tT reatmenti,tF lashEventi,t + i,t. The regression is computed for two different dependent variables. Spread is the ratio between the quoted spread (Best Ask Price - Best Bid Price) and the midpoint. Depth is the average of the volume (in Euros) found at the best bid and ask prices. T reatmenti,t is a dummy variable that takes value 1 if the observation belongs to the treatment group (IBEX35 for the Spanish stock market) and 0 if it belongs to the control group (FTSE MIB for the Italian stock market). P osti,t is a dummy variable that takes value 1 for the post-event window (February 1st 2013 to April 30th 2013) and 0 for the pre-event window (November st st 1 2012 to January 31 2013). F lashEventi,t is a dummy that takes value 1 after the detection of a mini flash crash. P osti,tT reatmenti,tF lashEventi,t is the parameter of interest. It captures the effect of the fragmentation event in the presence of mini flash crashes for the treatment group relative to the control group. Standard errors are corrected by double clustering on stock and day (numbers in brackets). ***, ** and * indicate the statistical significance at 1%, 5% and 10% level, respectively. Small Stocks Medium/Large Stocks Spread Depth Spread Depth Intercept 2.40E-03*** 27227*** 1.07E-03*** 82046*** (4.16E-04) (5500) (1.05E-04) (22533) T reatmenti,t 7.44E-04 -6341 7.01E-04*** -64078*** (4.94E-04) (10068) (1.96E-04) (23081) P osti,t 2.58E-03* 67 4.12E-04*** -31751* (1.40E-03) (3101) (1.40E-04) (18863) F lashEventi,t 9.17E-04*** -8837*** 1.67E-04 -4313 (3.19E-04) (3559) (1.13E-04) (19224) P osti,t · T reatmenti,t -3.13E-03** -808 -8.26E-04** 36992** (1.45E-03) (4338) (2.84E-04) (19222) T reatmenti,t · F lashEventi,t 1.59E-03*** 6100* 3.28E-03*** -529 (5.68E-04) (3777) (4.41E-04) (19440) P osti,t · T reatmenti,t 8.60E-04 6376** 1.16E-02* -1348 (1.05E-03) (2739) (6.73E-03) (15706) P osti,t · T reatmenti,t · F lashEventi,t -1.64E-03 -10127** -1.29E-02** -5376 (1.22E-03) (4020) (6.78E-03) (16007) AdjR2 0.02 0.02 0.33 0.35