Volatility and dark trading: Evidence from the Covid-19 pandemic

We study the effect(s) of volatility on the share of trading in dark pools by exploiting the exogenous shock of the Covid-19 pandemic on financial markets and regulatory restrictions on dark trading. We find that high levels of volatility in lit exchanges is linked to an economically significant loss of market share by dark pools to lit exchanges. In line with the theory, the loss appears to be driven by informed traders’ migration from lit to dark markets during high volatility periods. The market quality implications of the trading dynamics are mixed: while it tempers liquidity decline in the lit market, it exacerbates the loss of informational efficiency.


Introduction
The evolution of the share of informed and uninformed trading activity across lit and dark venues underpins the debate about the market quality effects of trading in dark pools (see Hendershott & Mendelson, 2000;Menkveld et al., 2017;Zhu, 2014). Indeed, the less-than-adequate understanding of this phenomenon in an empirical sense may be driving the mixed evidence on the impact of dark trading on market quality characteristics. For example, Buti et al. (2011) find no supporting evidence that dark trading harms market liquidity. Based on their analysis of FTSE data, Ibikunle et al. (2021a) and Brugler (2015) show that dark trading leads to improved liquidity in the aggregate and primary (lit) exchanges respectively. However, Nimalendran and Ray (2014) investigate trading data from one of the 32 US dark venues and find that dark trading is associated with increased price impact on quoting exchanges. This is consistent with the findings of Degryse et al. (2015), who use data from the Dutch market to show that dark trading has a detrimental effect on market liquidity. The increasingly popular view that the effects of dark trading on market quality characteristics are non-linear makes this question even more complex (see Comerton-Forde & Putniņš, 2015;Ibikunle et al. 2021a).
investors other than the day trader. As pointed out by Van Kervel and Menkveld (2019), the impact of change in market structure on the market quality debate should also focus on end-user costs. Chordia and Miao (2020) further note that one of the unexplored areas in the market microstructure literature is the role of technological changes in market quality at low (non-intraday) frequencies.
Second, the Covid-19 pandemic is a high impact threat. It created not only an urgency beyond the scope of the shocks employed in Menkveld et al. (2017), but also generated what may well in time be regarded as a once-in-a-generation panic, an element that is lacking in the shocks used in Menkveld et al. (2017). A shock may create urgency that motivates traders to move their trading activities from dark to lit venues; however, a shock that induces panic is likely to force some traders to stop trading altogether (see as an example, Choe et al., 1999). This suggests that traders may have also delayed their trading in dark venues during the Covid-19 shock. 3 Therefore, the venue market share dynamics may be different in our setting compared to the fundamentals-related shocks used in Menkveld et al. (2017).

Institutional background
The enactment of the Markets in Financial Instruments Directive (MiFID) in November 2007 introduced alternative high-tech trading venues known as multilateral trading platforms (MTFs). MTFs operate as intermediaries facilitating the exchange of financial instruments between several market participants. Concurrently, under MiFID, pre-trade and post-trade transparency requirements are imposed on all trading venues in order to reduce potential adverse selection costs linked to market fragmentation. However, MiFID also offers pre-trade transparency waivers for certain types of orders. These pre-trade transparency waivers include: (1) reference price waivers (RPW); (2) negotiated trade waivers (NTW); (3) large-in-scale (LIS); and (4) order management facilities (OMF). RPW applies to trading systems that match trading at the midpoint current bid and ask price. NTW allows two parties to formalise negotiated transactions. LIS offers block traders the right to hide their trading intention when the transaction size is larger than the prevailing normal market size. OMF allows orders to be held by exchanges in an order management facility pending disclosure.
Since the implementation of MiFID, trades in dark pools operated by MTFs have mainly benefited from RPW and LIS. Pre-trade opacity and midpoint execution help fund managers to conceal their trading intention and reduce transaction costs. However, European regulators, concerned about the potential negative influence of dark liquidity on the price discovery process, enacted a second iteration of MiFID, the so-called MiFID II, and the Market in Financial Instruments Regulation (MiFIR), published in June 2014. One important goal of MiFID II and MiFIR is to secure a high level of market transparency and fairness. As a result, the double volume cap (DVC) was introduced to curb dark trading and force more trades to be executed on lit venues. The DVC dictates that the venue and aggregate market trading limits for each instrument are 4% and 8% respectively. If the DVC is triggered in an instrument, then dark trading in that instrument will subsequently be suspended for six months. The DVC is calculated for each affected instrument on a daily rolling basis and relates to average daily trading volume over the preceding 12-month period. According to the first DVC-related data published in March 2018 by the European Securities and Markets Authority (ESMA), a total of 744 and 643 instruments breached at least one of the caps in January and February 2018 respectively, and they were therefore subjected to six-month trading suspensions from 12 th March 2018. As of September 2018, six months after the implementation of the DVC, more than 1200 instruments, mainly equities, were under dark trading suspensions. The affected instruments corresponded to about 35% of the most liquid European stocks. For our sample period, spanning 24th January to 24 th March 2020, ESMA data shows that 62 instruments' 4 (55 of which are European stocks) are under DVC dark trading suspensions; their suspensions were from 14 th November 2019 until 13 th May 2020.
It is worth noting that an enforcement of the DVC in a stock does not entirely preclude some form of dark trading in the stock. Large block trades in such stocks are still allowed in dark pools if the trade sizes are large enough to qualify for the LIS waiver. The LIS wavier threshold is based on the average daily volume (ADV) for each instrument. For small-cap stocks with an ADV of less than €50,000, the LIS waiver threshold is €15,000, and for large-cap stocks with ADVs greater than €100 million, the LIS waiver threshold can be up to €650,000. In any case, market data shows that the dark trading volume recorded once the DVC is enforced for a stock is zero to negligible.

Hypothesis development
The literature on the role of volatility in venues' share of trading is an emerging but promising stream (see, as an example, Degryse et al., 2021). However, studies in this stream mainly focus on establishing a linear association between volatility and venue market share. Contrastingly, the two leading theoretical models in the dark trading literature - Zhu (2014) and Menkveld et al. (2017) predict non-linear effects of volatility on the evolution of dark market share. The hypotheses we test in this study are inspired by the theoretical predictions outlined in Zhu (2014) and Menkveld et al. (2017). Volatility in financial markets is driven by either information or noise (see Brogaard et al., 2014), and this implies that any shocks on volatility will arise from (permanent) information or (temporary) price pressures, i.e. noise. Classical information-based trading models, such as Kyle (1985), and more recent ones, such as Foucault et al. (2017), show that shocks on both the information and noise components of price discovery generate trading needs that induce investors to adjust their trading positions as market conditions evolve. Thus, consistent with the well-established positive association between volatility and trading volume (see Karpoff, 1987), volatility shocks raise investors' opportunity cost of not trading. Zhu (2014) shows that when volatility is high, informed traders move to trade in dark markets to avoid the accompanying higher trading costs (wider spreads) in lit markets. This move may reduce the adverse selection risk in lit markets, thus making them more attractive to uninformed traders. This should also increase the aggregate trading volume in lit markets. However, this process has ambiguous effects on trading volume in dark markets. On the one hand, informed traders' migration to dark pools increases adverse selection risk there, and hence reduces the uninformed trading volume in dark pools. On the other hand, as suggested in Menkveld et al. (2017), informed traders can interpret information-driven price volatility differently, thus may increase trading volume by generating "two-sided" markets. Due to this ambiguous relationship, in Zhu (2014), trading volume can increase slightly or decrease in dark pools when volatility attains sufficiently high levels in lit markets. Thus, our first set of hypotheses are as follows: Hypothesis 1a. Positive volatility shocks (i.e., changes from sufficiently low to sufficiently high volatility state) are linked to increases in the trading volume in lit markets.
Hypothesis 1b. The evolution of trading volume in dark venues is linked to positive volatility shocks. The cross-migration of informed and uninformed traders in the presence of sufficiently high volatility has important implications for how positive volatility shocks affect dark venues' market share (i.e., the fraction of trading occurring in dark venues). Zhu (2014) predicts that even if heterogeneous expectations of informed traders increases the trading volume in dark markets, this increase is offset by uninformed traders' migration from dark to lit markets. The pecking order theory proposed in Menkveld et al. (2017) also suggests that while lit markets have a higher trading cost following volatility shocks, the opportunity cost of not trading is higher than this trading cost and, therefore, most traders move from dark to lit markets to as they may not be able to trade in dark markets due to a high non-execution risk. This suggests that, during periods of sufficiently high volatility shocks, the increase in lit venues' trading volume will be higher than any increase in trading in dark venues; thus, we hypothesise that: Hypothesis 2. Dark venues' market share decreases following positive volatility shocks. Zhu (2014) and Menkveld et al. (2017) identify two related channels that could explain traders' venue selection. Menkveld et al. (2017) show that investors' need for immediacy drives their venue selection. This is consistent with the anecdotal evidence presented in some media coverage of the phenomenon in the wake of the Covid-19 pandemic 5 ; therefore, this channel provides a potential explanation for the hypothesised effects of volatility on dark venues' market share evolution (see Hypothesis 2). Another channel is proposed by Zhu (2014), who predicts that adverse selection/information risk (which is proxied by volatility in his model) is a key driver of the venue selection decisions made by traders (see also Ibikunle et al. 2021a). These two channels are inter-related, as investors' demand for immediacy is also driven by information. Therefore, we view both channels as one, which we call the adverse selection channel.
The adverse selection channel suggests that informed traders stay on the lit exchange under "normal" market conditions; these "normal" condition means a sufficiently low volatility state and narrow lit exchange bid-ask spread. This is because in these conditions exchange spread is not wide, and thus the cost of non-execution risk is higher than a potential price-improvement benefit in a dark pool. However, when there is a sufficiently high level of volatility in financial markets, informed traders start to move to dark pools to avoid wider lit exchange spreads. This implies that a sufficiently high volatility state in lit markets is linked with an increase in adverse selection costs in dark pools. This increase in adverse selection costs forces uninformed/liquidity traders to migrate to lit venues. If this cross-migration holds, we should expect that: Hypothesis 3. Positive volatility shocks induce a reduction in informed trading activity in lit venues and thus are linked to an impairment of informational efficiency.
Our second hypothesis suggests that dark market share declines and lit market share increases during high volatility states, while Hypothesis 3 implies that the reduction in dark venues' market share is linked to informed traders moving from lit to dark markets. The implication of both events should be attendant reductions in adverse selection risk and trading costs in lit markets. This is also in line with Bayona et al. (2017), who show that, for stocks experiencing high price volatility, the existence of dark pools may motivate informed traders to shift trading in them to dark pools, which in turn reduces the bid-ask spread in lit markets. Therefore, we hypothesise that: Hypothesis 4. Positive volatility shocks in lit exchanges are linked with a reduction in adverse selection risk and, thus, an improvement in liquidity in lit markets.

Sample selection
To directly investigate trader-level migration between venues, one requires a dataset, which provides trader identification (ID). Since datasets such as this are not commonplace, we employ an empirical framework that presents an aggregate view of trading volume dynamics among venues. This approach is feasible with the more accessible ultra-high frequency times and sales datasets. Our empirical approach is a DiD-type framework consistent with the one deployed by Goldin and Rouse (2000). The main difference between this approach and the standard DiD modelling framework is that both the treatment and control groups are shocked in our specification; by contrast, in the standard DiD framework, only the treatment group is shocked. Our main model is further discussed in Section 5.2.
Our treatment group includes stocks that trade on both dark and lit venues, while the control group of stocks are restricted from trading on dark venues during our sample period. The dark trading restriction is due to the imposition of a dark trading cap under the MiFID II provisions. We first identify a group of stocks with restricted dark trading privileges during a period corresponding to one month before and after the start of the Covid-19 shock in European financial markets. Baker et al. (2020) show that the Covid-19-induced unusually high levels of volatility in global markets started on 24 th February 2020, when the virus started to spread quickly in the US and Europe. 6 Gormsen and Koijen (2020) also document that the volatility increased sharply in European markets around 20 th February 2020. Hence, we select a sample period spanning 24th January to 24 th March 2020. 7 We then identify the 55 European equities serving dark trading suspensions between 14 th November 2019 and 13 th May 2020 -a period that covers our sample periodas the stocks in our control group. Next, we match every stock in the control group with a stock with dark trading privileges using the method described in Shkilko and Sokolov (2020). We compute the matching error for price, size and volume. Then, the 55 stocks with the corresponding lower matching errors for each of the 55 stocks in the control group are included in the treatment group; hence, our total sample size equals 110 European stocks. 8 The method works well because our key microstructure metrics do not differ economically and statistically between groups prior to the emergence of the Covid-19 shock (see Table 2).
The shock is characterised in Fig. 1, which shows the impact of the Covid-19 pandemic on volatility in the 110 stocks in our sample. The volatility proxy is the daily cross-sectional average, Volatility i,d , defined in Section 4.2 and Table 1. Consistent with Baker et al. (2020), there is a substantial increase in volatility from 24 th February 2020. Volatility i,d more than doubles between 24th February and 24 th March 2020 in comparison to the month before (the difference is also statistically significant, as shown in Table 3), which implies that our sample period can indeed capture the impact of the Covid-19 shock on European markets. We further test the validity of our selected event date in Section 6 by using Markov regime-switching modelling.

Data sources and variable construction
For every stock in the treatment and control groups, we obtain ultra-high-frequency intraday trading data from the Refinitiv Tick History (RTH) database. We collect data from the main venues where our selected stocks are traded: (1) the main market where stocks are listed (for example, London Stock Exchange (LSE) for the UK stocks, Xetra for the German stocks, etc.); (2) Cboe Europe, which hosts the most liquid pan-European limit order books and dark pools, including BXE and CXE; and (3) Turquoise, hosting one of the most liquid dark pools in Europe, Turquoise Plato (formerly Turquoise Midpoint Dark). Cboe Europe provides market data showing daily trading volume for various European markets, providing daily trading activity data for each venue across Europe. 9 Based on this, the venues included in our dataset account for a daily minimum of 93% of the currency trading value for the stocks in our sample; hence, our data is representative of the stocks in the sample. The dataset contains standard transaction-level variables such as date, exchange time, transaction price, volume, bid price, ask price, bid size and ask size. Using the obtained dataset, we compute daily estimates of trading activity, liquidity, order imbalance, HFT and volatility.
We proxy venue choice at an aggregate level by using dark market share and trading volume in lit and dark marketsthe three variables embody aggregate trader venue selection. LitVolume i,d and DarkVolume i,d are the number of shares traded in the selected lit and dark venues for stock i on day d (selected main venues are discussed above). The dark market share, DMS i,d , is computed as DarkVolume i,d divided by the total trading volume (LitVolume i,d + DarkVolume i,d ) for stock i on day d. Within our framework, we aim to control for general market dynamics by including several relevant variables. We measure liquidity using relative quoted spread (Rspread i,d ) and depth (Depth i,d ). Rspread i,d is the relative quoted spread for stock i on day d and it is computed as a time-weighted average of the difference between ask and bid prices divided by the mid-price (mid-price is the average of ask and bid prices) corresponding to each transaction. Rspread i,d encapsulates the cost of trading and the level of illiquidity in stock i; hence, the larger the measure, the less liquid is stock i. Depth i,d is the top-of-book depth and it is computed as the natural logarithm of the sum of the best bid and ask sizes corresponding to each transaction for stock i on day d. Depth i,d captures the volume of shares available for trading at stock i's best ask and bid prices; hence, larger values suggest the market's ability to absorb large orders with relatively less price impact, and this is also an indication of the level of liquidity in stock i. Volatility i,d is a proxy for volatility and computed as the standard deviation of hourly mid-price returns for stock i on day d (see Malceniece et al., 2019). OIB i,d is the order imbalance metric described in Chordia et al. (2008), computed as the absolute value of the buyer-initiated volume minus the seller-initiated volume divided by the total volume stock i on day d. OIB i,d captures buying and selling pressure and could therefore be indicative of trading on private information (see Chordia et al., 2002). HFT i,d is the proxy for high-frequency trading (HFT) and computed as the number of messages divided by the number of transactions for stock i on day d (see Malceniece et al., 2019). As pointed out by Hasbrouck and Saar (2013), the majority of quote messages are generated by 6 Although Baker et al.'s (2020) analysis is based on the US financial markets, and we focus on European markets, the volatility trend is consistent, as shown in Fig. 1 and the statistical test of the difference in volatility between the pre-event and event periods presented in Table 3. Furthermore, in Section 6, we use the Markov switching model to show that our selected date is valid. 7 In Section 6, we employ an additional methodological framework to check the reliability of our selected sample period and the robustness of our results. 8 Appendix A contains a detailed list of all the stocks used in the study. 9 https://www.cboe.com/europe/equities/market_share/market/venue/ #dm=tbpcan&dr=5day&mt=1&ms=0&hc=1&f=0&ID=e6bf20a14833c25152c7&V=a09b8bfe7037e768a9c5.
high-frequency traders. However, using the number of messages alone is not valid as it may also pick up the overall impact of trading volume (see Hendershott et al., 2011). Therefore, we normalise the number of messages with the number of traders. Frag i,d is a proxy for market fragmentation for stock i on day d, computed using the Herfindhal-Hirschman Index. We define Frag i,d as one divided by the sum of the squared market shares based on the daily number of shares traded. Size i,d is the market capitalisation for stock i on day d, computed as the number of outstanding shares multiplied by daily closing price. Size i,d is obtained from Refinitiv Eikon. Table 1 provides an overview of the different variables used in this paper. Table 2 provides descriptive statistics for the 110 stocks, the 55 treated and 55 control stocks in the sample. Panel A reports the summary statistics for the pre-event period (from 24 th January 2020 to 23 rd February 2020), whilst Panel B presents the summary statistics for the event period (from 24 th February 2020 to 24 th March 2020). 10 In both panels, we provide statistics for the treatment and control groups of stocks separately and compute the statistical differences in our model variables in order to observe the differences in market dynamics for these groups; standard errors of the mean estimates are used for statistical inferences.

Descriptive statistics
Panel A shows that the stock-day averages of none of the variables between the two stock groups, except for DarkVolume i,d and DMS i,d , are statistically different from each other during the pre-event period. This underscores the relevance of our matching procedure and provides evidence that the two groups have similar market microstructure characteristics/dynamics prior to the Covid-19 shock. There are some important points to note when comparing the evolution of variables during the event period. Firstly, as evident in Panel B, the average values of all variables (except Frag i,d ) change significantly during the event period, which indicates that market conditions are different after the onset of the Covid-19 shock. For example, the average LitVolume i,d increases 2.5 (2.2) times for the treated (control) group, and the average DarkVolume i,d increases 2.06 (2.17) times for the treated (control) group. Moreover, Rspread i,d widens by more than 40% for both groups, indicating liquidity constraints. Secondly, while the average LitVolume i,d of the control group is marginally higher than the average LitVolume i,d of the treatment group prior to the event, a significant switch occurs following the onset of the Covid-19 shock with the treatment group's average LitVolume i,d suddenly outstripping that of the control group by 14% (=(3.28-2.88)/2.88). This is consistent with our argument that the Covid-19 shock contributes to the market dynamics of stocks traded simultaneously on both dark and lit venues. The observed 16% (=(2.1%-2.5%)/2.5%) decline in DMS i,d for the treatment group of stocks suggests that some traders move to lit venues during the Covid-19 shock. However, these traders could have also just exited the market altogether (we test whether this holds in the next section). Linked to the previous point, thirdly, we also observe (in Panel B) statistically and economically significant differences between the treatment and control groups' estimated variable values in the event period, evidencing the variation in the impact of the Covid-19 shock on the two groups of stocks' characteristics. The findings presented in Table 2 raise an interesting question about why the Covid-19-induced high levels of volatility affects stocks differently. We argue that this phenomenon is linked to traders being able to select dark and lit venues as trading destinations when trading regular sizes in some stocks and while being unable to trade some stocks at dark venues. This is because when we This table contains the pre-event (Panel A) and event (Panel B) periods' stock-day mean and standard deviation estimates for variables using data for 55 European stocks that could be traded at both lit and dark venues, i.e. treated stocks, and for 55 European stocks with dark venue restrictions, i.e. control stocks. The final column presents the t-statistics of two-sample t-tests of differences between the treatment group and the control group's variables. For the definitions and calculations of variables, see Table 1. The sample period is from 24th January to 24 th March 2020. The event start date is 24 th February 2020, when the Covid-19-induced shock is judged to have commenced in global financial markets (see Baker et al., 2020;Gormsen & Koijen, 2020). *, ** and *** correspond to statistical significance at the 0.10, 0.05 and 0.01 levels respectively.

Fig. 1. The evolution of volatility
The figure plots the day-by-day evolution of the cross-sectional average of Volatility i,d for 110 European stocks employed in the study. Volatility i,d is computed as the standard deviation of hourly mid-price returns for stock i on day d. The sample period covers 24th January to 24 th March 2020. The vertical bar indicates 24 th February 2020, when the Covid-19-induced shock is judged to have commenced in global financial markets (see Baker et al., 2020;Gormsen & Koijen, 2020).
compare the general market conditions (dark trading, liquidity, volatility, order-book dynamics and HFT activities) of the treatment and control groups during the pre-event period, only DMS i,d and DarkVolume i,d differ significantly (see Panel A of Table 2). The significant (both economically and statistically) difference in these variables is expected as the control group's stocks have been suspended from dark trading, whilst the treatment group's stocks are available for trading in dark pools. Thus, being able to migrate trading across venues appears to be a strong indicator of the differences between the control and treatment groups' market determinants during the event period. In the next section, we formally test the above arguments.

Volatility shocks and lit/dark trading volume
Our first set of hypotheses suggest trading volume in lit markets increases following positive volatility shocks. However, the association between dark trading volume and positive volatility shocks is ambiguous. To test these hypotheses, we follow Degryse et al. (2021) and use the following panel system of simultaneous equations 11 where Event i,d is a dummy variable that equals one for the days between 24th February and 24 th March 2020 inclusive and zero where LitVolume i,d and DarkVolume i,d are trading volume in lit and dark markets respectively, α i is a stock and ϑ m is an industry fixed effects, Event i,d is a dummy equalling 1 from 24th February to 24 th March 2020 and 0 from 24th January to 23 rd February 2020. For the definitions and calculations of variables, see Table 1. The sample period is from 24th January to 24 th March 2020. The sample includes 55 European stocks that could be traded at both lit and dark venues, i.e. treated stocks. Standard errors are robust to heteroscedasticity and autocorrelation. *, ** and *** correspond to statistical significance at the 0.10, 0.05 and 0.01 levels respectively. 11 We are grateful to an anonymous reviewer for suggesting this analysis.
otherwise. α i and ϑ m are stock and industry fixed effects respectively. We do not include time fixed effects as Event i,d only has timevariation. Standard errors are robust to heteroscedasticity and autocorrelation. 12 All other variables are as defined in Section 4.2 and Table 1. Table 3 reports the estimation results for Equation (1). Consistent with Hypothesis 1a, we find a positive and statistically significant association between Event i,d and LitVolume i,d . The positive relationship between Event i,d and LitVolume i,d relationship suggests that, in line with the predictions and empirical findings of Menkveld et al. (2017), traders increase their trading activity in more transparent markets following positive volatility shocks to adjust their positions. Specifically, as trading conditions become more challenging, as encapsulated by increased price volatility, we observe that traders appears to crave urgency at the expense of a focus on cost, which trading in less transparent venues would normally offer. The implication here is that traders then prioritise trading in high-cost and high-immediacy venues (e.g., lit markets) over low-cost and low-immediacy venues (e.g., dark pools). In our analysis, we find that the economic magnitude of this shift in trading is economically significant. After controlling for important market determinants, trading volume in lit markets increases by 44% (=0.59/1.33) during the Covid-19-induced period of high volatility. With respect to the impact of positive volatility shocks on dark trading volume, the results show that Event i,d is positive and statistically significantly (at the 5% level) related to DarkVolume i,d . This, consistent with Menkveld et al. (2017), demonstrates that while uninformed trading in dark pools may reduce due to the arrival of informed traders in them during periods of high volatility, the arriving informed trading volumes due to informed traders' attempts to evade the widening bid-ask spread in the lit market (as in Zhu, 2014) may compensate for the loss of uninformed trading volume. Furthermore, since informed traders interpret information differently from uninformed traders, their orders may avoid being crowded on one side of the market. We also note the economic meaningfulness of the increase in dark trading volumes during the sufficiently high volatility period: DarkVolume i,d increases by about 52% (=17.78/34.73).
It is important to note that the Covid-19-pandemic is a comprehensive economic shock that impacts the whole financial system, including financial markets. This implies that the results we present here may be explained by many other factors. We conjecture that this is not an important concern for these set of results for the following reasons. First, we control for most of the important market quality determinants (including market capitalisation) that drive trading volume dynamics. Second, given that there is heterogeneity in the effects of Covid-19 on economic dynamics across various industries, we include industry fixed effects in our model. Moreover, statistically, Volatility i,d is not significantly related to LitVolume i,d and DarkVolume i,d in the model. To rule out the possibility that our results are driven by alternative factors, we estimate the same model without Event i,d and find that once Event i,d is not controlled for, only the Volatility i,d coefficient becomes statistically significant. This underscores the validity of the Covid-19-induced volatility as a natural experiment to test the association between volatility shock and venues' shares of aggregate trading activity.

Volatility shocks and dark market share
Our second hypothesis suggests that volatility shocks are negatively related to dark market share. Given that we employ the Covid-19 pandemic as an exogenous shock on volatility, we expect that dark market share reduces significantly during the Covid-19 period. We test this by first conducting a univariate analysis, and then estimating a multivariate regression model. For the univariate analysis, we compute the evolution of dark market share during our sample period, and then test the null hypothesis that there is no difference between dark pool share during the pre-event and the Covid-19 shock periods. It is important to note that, similar to the volatility-dark volume analysis, this part of the investigation is strictly based on the treatment group of stocks because the control group of stocks are under dark trading suspensions during the sample period. Fig. 2 and Table 4 present the evolution of average daily dark trading volume and dark market share during pre-event and event periods. Although the average daily dark trading volume in the treated stocks doubles during the event period (increments in dark volume are also observed in Menkveld et al., 2017), this is only reflective of the overall increase in trading activity driven by the market response to the Covid-19 pandemic (see Fig. 3 and Table 3). Indeed, dark market share declines from 2.50% to 2.10% (about 16%), which implies that the magnitude of the increase in trading activity is higher in the lit venue (the difference between the pre-event and event periods is statistically significant at the 0.01 level for both dark volume and dark market share). This is consistent with the predictions of Zhu (2014) and Menkveld et al. (2017). Nevertheless, the insights are based on a univariate analysis and should be supported by more robust analysis. We achieve this by estimating the following model (all variables are as previously defined):  Zhu (2014) and Menkveld et al. (2017), this indicates a decline in DMS i,d following the onset of the positive volatility shock in European markets. One interpretation of this result is that the need for an urgent execution of orders appears to trump the need for low cost and low immediacy execution as price volatility heightens (as in Menkveld et al., 2017). Another is that, as predicted by Zhu (2014), the volatility-driven widening of the bid-ask spread in the lit market leads to a migration of informed traders to dark pools, which in turn may incentivise uninformed traders to shift their trading to the lit market in order to avoid being adversely selected by the arriving informed traders. The result in this section is also consistent with the univariate analysis we present in Table 4 and shows that the decline is still statistically significant after controlling for important market dynamics/variables. The economic significance of the decrease, as estimated with the 12 Please note that standard errors are robust to heteroscedasticity and autocorrelation in all models estimated in the paper. multivariate analysis, is even bigger than estimated using the univariate analysis. While in the univariate analysis we find a 16% (0.40/2.50) reduction in dark market share, it is about 49% (1.23/2.50) in the multivariate analysisabout half of the dark trading share of the market is lost during periods of market stress. Another important point to note is that, statistically, Volatility i,d is not significantly related to DMS i,d after including Event i,d in the model. By contrast, all other variables keep their significance even after controlling for Event i,d . This again shows that the Covid-19-induced volatility is a valid natural experiment to test the association between volatility and the distribution of the share of trading between dark and lit venues.
The insights offered by Fig. 2 and Tables 4 and 5 allow us to speculate that a fraction of dark market share moves to lit venues during sufficiently high volatility periods. However, the decrease in dark market share reported in this section could potentially be explained by two mechanisms: (1) traders using dark pools move to lit venues during shocks (see Menkveld et al., 2017;Zhu, 2014); and (2) these traders delay their trading activity, in which case they are not migrating to lit venues (the possibility of delay is alluded to by Zhu, 2014). We employ a DiD-type framework, as proposed by Goldin and Rouse (2000), to formally test which of these mechanisms explain our earlier finding (a similar empirical design is also used by Blank, 1991).
We demonstrate in Section 3.3 and Table 2 that the two groups of treated and control stocks we employ in this paper have very similar market microstructure dynamics prior to the onset of the Covid-19 pandemic. The two groups' liquidity, volatility, order-book dynamics and HFT levels do not significantly differ from each other before the event. The only observable microstructure-related difference between these groups is the availability of dark trading privileges for the treatment group of stocks, with the control group of stocks restricted from dark trading because they had previously breached the DVC under MiFID II provisions. Therefore, it is logical to expect that any difference between the impact of the Covid-19 shock on treatment and control groups' market activities is linked to differences in dark trading privileges for both groups of stocks. In order to test whether this expectation holds, in the spirit of Goldin and Rouse (2000), we estimate the following model where the dependent variable is lit volume, LitVolume i,d : where Treated i,d is a dummy equalling one for the treatment group of stocks and zero for the stocks in the control group. α i and ϑ m are stock and industry fixed effects, and all other variables are as previously defined. As noted above, in contrast to a standard DiD model, in our empirical design, both the treatment and control groups are allowed to be affected by the shock, and thus the key interaction variable (Event i,d * Treated i,d ) encapsulates the different impact of Covid-19 on these two groups' LitVolume i,d dynamics. This

Fig. 2. The evolution of dark pool trading
The figure plots the day-by-day evolution of the dark volume and dark market share for 55 European stocks that could be traded at both lit and dark venues. Dark market share is computed as the dark trading volume for a given day divided by the total trading volume on the same day. The sample period covers 24th January to 24 th March 2020. The vertical bar indicates 24 th February 2020, when the Covid-19-induced shock is judged to have commenced in global financial markets (see Baker et al., 2020;Gormsen & Koijen, 2020). This table presents average daily dark trading volume and dark market share for the treatment group and volatility for the whole sample during preevent and event periods, along with t-statistics of the two-sample t-tests of differences between pre-event and event periods' dark volume statistics. The sample period is from 24th January to 24 th March 2020. The event start date is 24 th February 2020, when the Covid-19-induced shock is judged to have commenced in global financial markets (see Baker et al., 2020;Gormsen & Koijen, 2020). *, ** and *** correspond to statistical significance at the 0.10, 0.05 and 0.01 levels respectively.
identification allows us to infer whether the reduction in dark market share during Covid-19 (see Table 5) arises because of traders migrating to lit venues or because they delay their trading. If traders delay their trading in dark pools because of the Covid-19 shock, then the impact of Covid-19 should be the same for both the treatment and control groups' lit volume. This suggests that the coefficient of Event i,d * Treated i,d would not be statistically significant because dark market availability is the only observable microstructure difference between the control and treatment groups' market dynamics during the pre-event period (see Table 2), and that difference should evaporate if traders using dark pools delay their trading. However, if traders who are active in dark pools before the event move to lit venues, then the coefficient of Event i,d * Treated i,d would be positive and statistically significant because it captures the excess lit market trading activity impact of traders with access to both lit and dark venues, and it could then be argued that they are, in aggregate, shifting at least a significant proportion of their trading from dark to lit venues. This would be consistent with the pecking order hypothesis advanced by Menkveld et al. (2017) and the predicted effects of sufficiently high volatility in lit markets on dark market share (see Zhu, 2014). Before estimating Equation (3), it is useful to conduct some univariate analysis designed to guide our thinking on what to expect from the model estimation. Panel A of Fig. 3 presents the evolution of total trading volume, whilst Panel B presents the evolution of the treatment and control groups' volumes separately; note that this is the evolution of the day-by-day total volume for all stocks. As is evident in Panel A, the total daily trading volume increases during the event period. This is not unusual as investors are expected to increase their trading activity during this period in an attempt to exploit information or hedge risks, i.e. the event creates an urgent demand for immediacy (see Menkveld et al., 2017). Panel B of Fig. 3 offers us a more nuanced view of the impact of the Covid-19 crisis on the trading activity of investors with respect to the treatment and control groups of stocks. The control group's volume is slightly higher than the treatment group's volume before the event (the difference is not statistically significant). However, the situation changes drastically following the onset of the Covid-19 shock and the treatment group's volume rises above that of the control group (see Table 6 for more details). Another important point to note in Panel B is the correlation between the evolution of the control and treatment groups' volume during the pre-event period. It is noted that LitVolume i,d for the two groups has parallel trends in the absence of an event. This implies that the parallel trend assumptionwhich is vital for the empirical relevance of a DiD-type frameworkholds. Indeed, the break in the evolution of volume between the two groups is underscored by the differences in their level of volume increase

Fig. 3. The evolution of trading volume
The figure presents the day-by-day evolution of lit volumefor 110 European stocks. Panel A presents the day-by-day evolution of lit volume for the full sample (both the 55 stocks that could be traded at both lit and dark venues, i.e. treated stocks, and the 55 stocks with dark venue restrictions, i.e. control stocks), while Panel B shows the day-by-day evolution of lit volume for the control and treatment groups separately. The sample period covers 24th January to 24 th March 2020. The vertical bar indicates 24 th February 2020, when the Covid-19-induced shock is judged to have commenced in global financial markets (see Baker et al., 2020;Gormsen & Koijen, 2020).
after 24 th February 2020. Table 6 shows that while the control group's average daily lit volume increases by about 112% between 24th February and 24 th March 2020, this increase is about 130% for the treatment group, which indicates that the magnitude of increase is about 18% higher for the treatment group. This reflects a significant economic impact of the Covid-19 pandemic and is consistent with our main argument regarding the move of traders from dark to lit venues. It is also consistent with estimates in Table 5 indicating significant falls in dark trading market share for our sample of stocks between 24th February and 24 th March 2020.
We now shift our attention to the outcome of the estimation of Equation (3), as reported in Table 7. There are some important points to note here. Firstly, Event i,d is statistically significantly (at the 0.05 level) and positively related to LitVolume i,t , implying that there is indeed a significant increase in lit volume during the Covid-19 period, as compared to the prior month. Economically, this suggests that the number of shares traded daily during the event period increases by about 0.94 million or, on average, 71% (= 0.94/1.33) for the 110 stocks in our sample. 13 This is a significant economic effect and shows that the pandemic crisis has an unmistakable impact on trading in financial markets. Secondly, and most importantly, the interaction coefficient (γ 3 ) suggests that the Covid-19 shock is linked with average daily increases of about 480,000 shares for each of the treated stocks when compared to the control group of stocks; the coefficient is statistically significant at a 0.01 level. The economic significance of this relative increase in lit trading activity is obvious. The average LitVolume i,d for the control group of stocks is about 2 million shares during our sample period. Thus, the magnitude of increases in trading volume is about 24% (=0.48/2.00) higher for the treatment group compared to the control group. This is indeed a significant change in economic terms, and it offers compelling evidence that, although traders increase their lit venue trading activity for all stocks during the Covid-19-induced sufficiently high volatility period, they do so on a larger scale for stocks with trading privileges in both lit and dark venues. This result is consistent with Menkveld et al. (2017) and Zhu (2014), as well as our Hypothesis 2 that traders migrate in aggregate from dark to lit venues during sufficiently high volatility periods and this reduces dark market share. Thus, the reduction in dark market share reported in Table 5 is linked to traders moving their trading to lit venues rather than delaying it.  This table contains the pre-event and event average daily volume estimates for 55 European stocks that could be traded at both lit and dark venues, i.e. treated stocks, and for 55 European stocks with dark venue restrictions, i.e. control stocks. The estimates are reported separately for the treatment and control groups, along with t-statistics of the two-sample t-tests of differences between preevent and event periods' average daily volumes. The sample period is from 24th January to 24 th March 2020. The event start date is 24 th February 2020, when the Covid-19-induced shock is judged to have commenced in global financial markets (see Baker et al., 2020;Gormsen & Koijen, 2020). *** corresponds to statistical significance at the 0.01 level.  is stock and ϑ m is industry fixed effects, Event i,d is a dummy equalling 1 from 24th February to 24 th March 2020 and 0 from 24th January to 23 rd February 2020. Treated i,d is a dummy, which equals 1 for the treatment group of stocks and 0 for the control group of stocks. For the definitions and calculations of variables, see Table 1. The sample period is from 24th January to 24 th March 2020. Standard errors are robust to heteroscedasticity and autocorrelation. *, ** and *** correspond to statistical significance at the 0.10, 0.05 and 0.01 levels respectively.

Volatility shocks, informed trading and informational efficiency dynamics
Hypothesis 3 proposes a channel explaining dark market share dynamics during various volatility states (i.e., sufficiently low versus sufficiently high volatility states). The hypothesis conjectures that informed traders, in aggregate, move from lit to dark markets when there is sufficiently high volatility in financial markets. A testable implication of this prediction is that adverse selection risk and informational efficiency should decrease in lit markets following positive volatility shocks. We test this prediction by using the DiD approach developed in the previous section. If indeed this channel explains our findings, in comparison to the control group of stocks, we should expect to see reduced adverse selection risk in the lit market for the treatment group of stocks following the onset of the Covid-19 volatility shock, because only the latter group has relatively unfettered access to dark pools.
We proxy adverse selection risk and informed trading activity by using the adverse selection component metric, ASC i,d , developed by Lin et al. (1995), 14 which proxies the risk faced by liquidity suppliers when trading with informed traders in financial markets. Essentially, this is a cost levied by liquidity suppliers, such as market makers, in order to account for the risk of trading with traders holding more relevant information than them (see Glosten & Milgrom, 1985).
Panel A of Fig. 4 presents the evolution of the treatment and control groups' ASC i,d estimates during the sample period. ASC i,d increases for both groups during the event period, indicating that informed traders are more active during that period. This is expected as Rspread i,d also increases for both groups during the event period. Thus, an increase in ASC i,d is not very informative by itself. To investigate whether adverse selection cost increases or not, we need to compute the percentage of Rspread i,d driven by adverse selection cost and compare its values before and after the onset of the Covid-19 shock. Thus, we obtain the weighted adverse selection cost component of Rspread i,d , ASW i,d , by dividing ASC i,d by Rspread i,d and then multiplying the outcome by 100. The estimates reported in Panel B of Table 8 show that, for the treatment group, the average ASW i,d is 21% (=(13.14/61.14)*100) in the pre-event period, reducing to 19% (=(16.81/87.95)*100) during the Covid-19 shock period. For the control group, the average ASW i,d is 25% (=(15.69/ 61.39)*100) during the pre-event period, increasing to 37% (=(35.22/94.25)*100) during the Covid-19 shock period. Thus, while the control group's adverse selection cost increases by 12%, the treatment group's adverse selection cost declines by about 2%. This clearly shows that the Covid-19 crisis does not appear to have the same impact on the adverse selection costs of the two stock groups.
The above finding is further underscored by the evolution of the difference between control and treatment groups' ASC i,d , shown in Panel B of Fig. 4. It is evident that the difference is relatively stable and close to zero before the event. However, it increases and becomes more unstable after the event, which may be an indication of both a reduction in the proportion of information-driven trading activity in the treated stocks and the magnitude of the ASC i,d increases for the control group of stocks during the Covid-19-induced sufficiently high volatility period. The difference is also found to be statistically significant when we use the standard error of the mean difference for statistical inference, as shown in Panel A of Table 8. The estimates presented suggest that the difference between the control and treatment groups' ASC i,d prior to the Covid-19 crisis is 2.55 bps and not statistically significant. However, the difference increases to 18.41 bps and becomes statistically significant at the 0.01 level following the onset of the crisis. The same results hold for ASW i,d (see Panel B). While we do not have trader-level data on informed and uninformed traders, the reduction of ASW i,d in the treatment group compared to the control group may be interpreted as, in the aggregate, informed trading activity in the treatment group of stocks being significantly transferred to dark pools during the Covid-19 shock, which would be in line with Zhu (2014). To formally test the argument in a multivariate framework, we estimate the following model (all variables are as previously defined): Table 9 reports the estimation results for Equation (4). Event i,d 's coefficient is positive and (weakly) statistically significantly (at the 0.10 level), which implies that overall ASW i,d increases during the event period. 15 However, the interaction coefficient (γ 3 ) is negative and statistically significant (at the 0.05 level), implying that the treatment group's ASW i,d reduces over the same period when we compare it with the control group's ASW i,d . The magnitude of the association is also economically meaningful. The ASW i,d of the treatment group reduces by 2.25% during the event period when we compare it with the control group. The economic significance of this estimate is put into some perspective when we consider that the stock-day average ASW i,d is about 29% for the control group in our sample period. The implication here is that, on average, the level of adverse selection in stocks with dark trading privileges declines by about 7.76% (=2.25%/29%) during the period of the Covid-19-induced market turmoil in comparison with stocks without this privilege. This is consistent with the adverse selection channel argument and the results presented in Fig. 4 and Table 8. Therefore, this suggests that, in the aggregate and as predicted by Zhu (2014), a non-negligible proportion of informed trading activity is shifted to dark pools during periods of market turmoil, such as the one driven by the Covid-19 pandemic. It could be argued that informed traders stop trading, and therefore the reduction in ASW i,d of the treatment group is related to this. However, if this is the case, we should expect to see the same effects in the control group. Given the consistency of microstructure properties in the pre-event period for both groups of stocks, it is implausible that a factor other than the opportunity to trade in a relatively unrestricted manner in dark pools is driving the differential in the evolution of ASW i,d during the Covid-19-induced sufficiently high volatility. Furthermore, established market microstructure thinking on informed trader properties strongly suggests that informed traders do not exit the market when they 14 For robustness, we estimate the adverse selection component of the spread by using Stoll (1989) approach and we obtain qualitatively similar results. 15 As reported in Table 8, this positive relationship is driven by the control group.

Fig. 4. Adverse selection component
Panel A presents the day-by-day evolution of the cross-sectional average of ASC i,d for 55 European stocks that could be traded at both lit and dark venues, i.e. treated stocks, and for 55 European stocks with dark venue restrictions, i.e. control stocks. Panel B shows the evolution of the difference between the control group's ASC i,d and the treatment group's ASC i,d . ASC i,d is the adverse selection component of relative spread Rspread i,d for stock i on day d and is computed using the method developed by Lin et al. (1995). The sample period covers 24th January to 24 th March 2020. The vertical bar indicates 24 th February 2020, when the Covid-19-induced shock is judged to have commenced in global financial markets (see Baker et al., 2020;Gormsen & Koijen, 2020).  Baker et al., 2020;Gormsen & Koijen, 2020). *, ** and *** correspond to statistical significance at the 0.10, 0.05 and 0.01 levels respectively. hold actionable information. Indeed, it is the nature of the informed trader not to exit markets when holding actionable information, especially during a period where the market conditions are evolving quicklyinformation during this period is likely to be short-lived. Thus, our framework allows us to interpret the obtained result as a non-negligible aggregate shifting of informed trading activity from lit to dark venues. To further test the robustness of the results reported in Table 8, we investigate the evolution of informational efficiency in lit markets during the volatile trading period. The concept is straightforward. Given that informed traders move from lit to dark markets during sufficiently high volatility periods, we expect to see stock prices becoming less informationally efficient in lit venues during these periods. To test this argument, we estimate the following model: where Corr i,d , the proxy for informational efficiency, is computed as the absolute value of first-order return autocorrelation for each stock i on day d and is expressed in basis points (bps). It is computed by first estimating 30-s returns within each stock-day (ret i,t,d ), where t = 30 s, and then computing Corr i,d as We employ the absolute value of the correlation  Lin et al. (1995). α i is stock and ϑ m is industry fixed effects . Event i,d is a dummy equal to 1 from 24th February to 24th March 2020 and 0 from 24th January to 23rd February 2020, Treated i,d is a dummy equalling 1 for the treatment group of stocks and 0 for the control group of stocks. For the definitions and calculations of variables, see Table 1. The sample period is from 24th January to 24th March 2020. Standard errors are robust to heteroscedasticity and autocorrelation. *, ** and *** correspond to statistical significance at the 0.10, 0.05 and 0.01 levels respectively. coefficient as it captures both the under-and over-reaction of returns to information, with smaller values indicating greater efficiency. This measure is based on the theory that if stock prices follow a random walk and are fully efficient, then the prices should be unpredictable and Corr i,d should be zero. Thus, a larger value of Corr i,d implies greater inefficiency. The empirical relevance of this metric is underscored by its wide use in the literature (see as examples, Hendershott & Jones, 2005;Comerton-Forde & Putniņš, 2015). All other variables are as previously defined. Table 10 shows the estimated coefficients for Equation (5). The interaction variable, Event i,d * Treated i,d , is positively related to Corr i,d ; the relationship is (weakly) statistically significant at the 0.10 level. The implication of the positive coefficient estimate is that the treatment group's informational efficiency deteriorates as compared to the control group's informational efficiency. The change in informational efficiency is also economically meaningful. The average Corr i,d for the control group is 1082 bps, which suggests that the treatment group's informational efficiency deteriorates by about 3.1% (=33.17/1082) because of the Covid-19 pandemic market turmoil, in comparison to that of the control group. This finding is consistent with Hypothesis 3, suggesting a significant aggregate migration of informed trading activity from lit venues to dark pools.
We note that the Covid-19 shock not only impacts financial markets through the channel we propose aboveinformed traders' migration from lit to dark marketsbut the pandemic is also implicated in shocks to price levels and margin calls, as well as fiscal policy interventions etc. However, in this study, we primarily focus on this channel because it has a very clear theoretical basis in the literature (see Menkveld et al., 2017;Zhu, 2014) and it is arguably a vector for the other Covid-19-related developments as they imply informational risk. Therefore, the evidence presented in this section should be interpreted with some caution. We do not claim that the channel proposed in this study is the only channel explaining the impact of the Covid-19 shock on the evolution of the share of trading in dark venues. Nevertheless, theory suggests it is a significant driver of trading activity in dark pools. The fact that ASW i,d declines and Corr i,d increases in our treated group of stocks relative to the control group of stocks may also not necessarily be due to traders' migration between lit and dark venues. This is because we investigate the volatility shock on ASW i,d and Corr i,d in lit venues only. As already acknowledged, it is also possible, although improbable given that they are assumed to be rational actors, that informed traders exit the markets, and hence we observe this process. Thus, while our DiD-based approach allows us to downplay the suggestion that informed traders exiting is the main explanation, these results should still be interpreted with caution.

Volatility shocks, dark trading and lit market liquidity
The empirical findings reported so far suggest that, overall, traders shift significant portions of their trading from dark to lit venues when there are positive volatility shocks. While reporting on these dynamics is of academic and arguably practical interest, the bottomline should ultimately be what they mean for market quality (Zhu, 2014 also alluded to this). Therefore, in the next hypothesis, we examine the liquidity implications of the significant loss of market share by dark pools to lit venues during the Covid-19 pandemic. We estimate the following models with liquidity metrics on the left-hand side (all variables are as previously defined).
Table 11 reports the estimation results for Equations (6) and (7). The interaction variable's coefficient, γ 3 , is negative (positive) and statistically significant (at the 0.05 level), suggesting that the treatment group's Rspead i,d (Depth i,d ) decreases (increases) during the Covid-19 shock period as compared to the control group's Rspead i,d (Depth i,d ). This implies that the treatment group's liquidity improves over the same period as compared with the control group's liquidity, or at a minimum it suffers less from the liquidity shock comparatively, and this is linked to the loss of market share by dark pools to lit venues. Thus, the results are in line with Hypothesis 4 and are what we should expect to find if informed traders significantly shift their trading to dark venues following the onset of the Covid-19-induced market volatility (see Zhu, 2014). The reduction in informed trading activity in the lit market will lead to a reduction in adverse selection risk for liquidity traders and a subsequent narrowing of the spread. Depth will also deepen as more liquidity traders migrate to the lit market, either in search of immediacy (see Menkveld et al., 2017) or to avoid the increasingly precarious dark venues now harbouring informed traders (see Zhu, 2014). The magnitude of the impacts is also economically meaningful. On average, the Rspead i,d (Depth i,d ) estimates of stocks with dark trading privileges narrow (increase) by about 9.83% = 7.96/81 (2.14% = 0.30/14) during the event period as compared with the control group. 16 Comprehensively, the positive influence of access to dark trading for the treatment group of stocks as documented is consistent with the findings of the emerging dark trading literature. For example, Ibikunle et al. (2021b) show that stocks subject to removal of dark trading privileges suffer a deterioration in liquidity compared to those that are not, and that this has implications for informational efficiency. As implied by our results, their findings emphasise the potential for dark pools to encourage market quality-enhancing inter-venue competition and how this can enhance economic welfare, such as by reducing transaction costs (see Oriol et al., 2018).

Robustness analysis based on the Markov switching model
The results thus far are consistent with our expectations, and hence confirm our hypothesis that there is a significant link between positive volatility shocks and the share of trading in lit and dark venues. As noted, the main challenge in studying the effects of volatility shocks on dark market share and trading activity is endogeneity. To address this issue, in this study, we employ the Covid-19induced change in volatility as a natural experiment to build a DiD framework since the Covid-19 pandemic is exogenous to financial markets (see Danielsson et al., 2020). However, the uncertainty surrounding the start (event) date of the exogenous volatility shock event is a potential limitation of this study. Although, in line with the relevant literature, we select 24 th February 2020 as our event date (see Baker et al., 2020), Fig. 1 appears to show that volatility increases gradually from the selected event date. Moreover, it is likely there are cross-sectional variations in the event date. Hence, in this section, we employ an alternative approach based on the Markov switching model (MSM) to address these limitations. 17 The existing literature suggests that the association between volatility and dark market share is not linear and depends on an where Corr i,d is first-order return autocorrelations for each stock i on day d at 30 s frequencies. α i is stock and ϑ m is industry fixed effects, Event i,d is a dummy equalling 1 from 24th February to 24th March 2020 and 0 from 24th January to 23rd February 2020, Treated i,d is a dummy equalling 1 for the treatment group of stocks and 0 for the control group of stocks. For the definitions and calculations of variables, see Table 1. The sample period is from 24th January to 24 th March 2020. Standard errors are robust to heteroscedasticity and autocorrelation. *, ** and *** correspond to statistical significance at the 0.10, 0.05 and 0.01 levels respectively.
unspecified volatility threshold (see Zhu, 2014), and since MSM is an ideal methodological approach for modelling non-linear associations with unknown threshold levels, it is well-suited to our empirical needs. Furthermore, the comprehensive nature of the instability linked to the Covid-19 pandemic shock in financial markets implies that it has an impact on many market microstructure factors. Although we address this by controlling for the known potential complicating factors in the DiD framework, employing MSM allows us to further isolate the effects of volatility on share of trading in lit and dark venues. The MSM we estimate is as follows: where DV i,d corresponds to one of three measures for share of trading in trading venues: LitVolume i,d , DarkVolume i,d , or DMS i,d . All other variables are as previously defined. As seen in Equation (8), we are estimating the same model in both states (s i,d ). Therefore, any changes in the estimated coefficients reflect the changes in associations between various market quality determinants and venues' share of trading during two different states. Table 12 presents the estimation results of MSM. One of the important properties of MSM is that the states are hidden and not directly observed. Therefore, based on the change in relationships between dependent and independent variables, we can economically interpret the states defined in the model. Given that our main interest is the effects of volatility states on venues share of trading, we mainly discuss the DV i,d -Volatility i,d association. The results are twofold. First, the effects of Volatility i,d on LitVolume i,d (DarkVolume i,d ) are about 3.5 (5) times higher (lower) during the second state (s i,d = 2). Second, while the relationship between where Rspread i,d is the relative quoted spread for stock i on day d, α i is stock and ϑ m is industry fixed effects, Event i,d is a dummy equalling 1 from 24th February to 24th March 2020 and 0 from 24 January to 23 February 2020, Treated i,d is a dummy equalling 1 for the treatment group of stocks and 0 for the control group of stocks. For the definitions and calculations of variables, see Table 1. The sample period is from 24th January to 24th March 2020. Standard errors are robust to heteroscedasticity and autocorrelation. *, ** and *** correspond to statistical significance at the 0.10, 0.05 and 0.01 levels respectively.
Volatility i,d and DMS i,d is positive and statistically significant (at the 0.05 level of statistical significance) during the first state, it becomes negative and statistically significant at the 0.01 level in the second state. Interestingly, across all our indepdendent variables, we see this clear dynamic in Volatility i,d only. These results are consistent with our main results. More importantly, they suggest that our second state is a sufficiently high volatility state. Inferring from the predictions of Zhu (2014) and Menkveld et al. (2017), we expect that the effects of volatility on trading volume in lit (dark) markets is higher (lower) when there is sufficiently high volatility in financial markets. Thus, the impact of volatility on dark market share is expected to be negative during sufficiently high volatility periods and the fact that the Volatility i,d -DMS i,d association is negative in the second state implies that the second state is a sufficiently high volatility state. To further test this interpretation, we estimate the smoother probabilities of the second state. If indeed the second state is a sufficiently high volatility state, then the probability of being in the second state should be high during the Covid-19-induced sufficiently high volatility period (post-24th February 2020). This analysis can also allow us to check the validity of our selected event date. We expect to see an increase in the probability of being in the second state starting from our event date. Fig. 5 depicts the day-by-day evolution of the cross-sectional average of Volatility i,d and the probabilities of being in the second state estimated using the MSM. It is important to note that our data is panel data, and hence we follow Agudze et al. (2021) and estimate the probabilities as the average of the smoothed probabilities of all firms. There are two important observations in the figure. First, the probability of being in the second state is significantly higher during our event period. Second, the probability of being in the second state starts to increase gradually from our selected event date (24 th February 2020). The average probability of being in the second state is 50.72% on this date, while it is 4.10% on the last trading day (21 st February 2020) before that date. Overall, the estimated results of MSM suggest that while trading volume in lit and dark venues increases during high volatility periods, dark market share declines during these periods. The results also underscore the validity of the event date selected for our DiD framework.

Conclusion
The share of transactions executed in dark pools has increased significantly in recent years. Therefore, investigating the factors contributing to venues share of trading is an important endeavour, especially given the market quality implications of traders choosing to trade in venues with varying degrees of transparency. In this study, we exploit the sufficiently high volatility shocks induced by the Covid-19 pandemic in early 2020 as an exogenous event to test the effects of volatility on venues share of trading dynamics as it relates to dark and lit venues.
We show that, in line with the theoretical literature (see Menkveld et al., 2017;Zhu, 2014), the Covid-19-linked high levels of volatility shock is related to an economically significant loss of market share from dark pools to lit exchanges. The market quality implications of this loss, although mixed, are economically meaningful and statistically significant. While stocks with dark trading privileges experience significantly less adverse liquidity shocks, i.e., wider spreads, when compared with stocks under dark trading restrictions during the Covid-19 period, the impact of loss of informational efficiency on their prices is worse in comparison to the  Table 1. The sample period is from 24th January to 24th March 2020. The sample includes 55 European stocks that could be traded at both lit and dark venues, i.e. treated stocks. Standard errors are robust to heteroscedasticity and autocorrelation. *, ** and *** correspond to statistical significance at the 0.10, 0.05 and 0.01 levels respectively.