Order routing decisions for a fragmented market: A review

Mishra, Suchismita; Zhao, Le Article Order routing decisions for a fragmented market: A review Journal of Risk and Financial Management Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Mishra, Suchismita; Zhao, Le (2021) : Order routing decisions for a fragmented market: A review, Journal of Risk and Financial Management, ISSN 1911-8074, MDPI, Basel, Vol. 14, Iss. 11, pp. 1-32, https://doi.org/10.3390/jrfm14110556 This Version is available at: https://hdl.handle.net/10419/258659 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Journal of Risk and Financial Management Review Order Routing Decisions for a Fragmented Market: A Review Suchismita Mishra * and Le Zhao *   Citation: Mishra, Suchismita, and Le Zhao. 2021. Order Routing Decisions for a Fragmented Market: A Review. Journal of Risk and Financial Management 14: 556. https:// doi.org/10.3390/jrfm14110556 Academic Editor: Thanasis Stengos Received: 30 September 2021 Accepted: 11 November 2021 Published: 17 November 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Department of Finance, College of Business, Florida International University, Miami, FL 33199, USA *Correspondence: [email protected] (S.M.); [email protected] (L.Z.) Abstract: This paper reviews the up-to-date theoretical, empirical, and experimental literature related to the trading venue choice in the context of the fragmented equity markets. We provide a brief background on the history of trading fragmentation in the equity market and its determinants. We discuss the direct and indirect impacts of the market fragmentation on market quality in various dimensions, including liquidity, volatility, and price efficiency. Next, we identify possible determinants and channels from theoretical and empirical studies that could explain order routing decisions and present the possible directions for future research. Finally, we discuss the major regulatory reforms in the U.S. equity market on routing venue decisions. This topic is relevant in current times when phenomena such as “GameStop Frenzy” have drawn significant attention to commission-free trading venues. Keywords: market structure; fragmentation; market quality; trading volume; order routing decision 1. Introduction The evolution of the United States stock exchange started in 1790 with the birth of the Philadelphia stock exchange. After more than 200 years of the evolutionary process, equity trading in the U.S. is currently dispersed across 16 national exchanges, more than thirty alternative trading systems, and numerous broker-dealers and wholesalers (SEC 2021). The market has never had such fragmentation before, and traders nowadays have many options in choosing venue to execute their orders. Each trading venue competes against the other in terms of fee structure and trading protocols. Moreover, strong trading volume growth, technology innovation, and policy initiatives intensify the competition among exchanges. An exchange must adopt ever more advanced trading technology or update pricing models and trading rules to attract more market share. Ultimately, market fragmentation 1 has increased. By merging with and acquiring regional exchanges, three groups, namely the New York Stock Exchange (NYSE) group, Nasdaq group, and the CBOE Global market, together dominate the trading volume in the U.S. equity market. Meanwhile, the competition is explicitly enforced by the US Regulation National Market System (Reg-NMS) regulatory policy that allows new trading venues. Newly launched exchanges, such as the Investor Exchange in 2016, Members Exchange (MEMX), Miami International Securities Pearl Exchange (MIAX), and Long-Term Stock Exchange (LTSE) in 2020, foster diversity through innovation in pricing features. Market fragmentation impacts the investor and market as well. On the one hand, intensified competition lowers transaction fees and ultimately benefits market participants. On the other hand, varying levels of venue transparency and the heterogeneity in transaction speeds change information asymmetry among investors, thus raising adverse selection concerns. Especially, the recent increase in retail trading gamification phenomena such as “Game Stop” has drawn significant attention to commission-free trading brokers and the payment for order flow (PFOF) practice by market makers in off-exchanges. Therefore, examining the routing order decision is extremely relevant in the current time and is worth exploring. J. Risk Financial Manag. 2021,14, 556. https://doi.org/10.3390/jrfm14110556 https://www.mdpi.com/journal/jrfm J. Risk Financial Manag. 2021,14, 556 2 of 32 In this paper, we concentrate on the portion of the microstructure literature that addresses order flow fragmentation, specifically, order routing decisions 2 . We provide an up-to-date survey of the main theoretical developments and empirical studies of the determinants of venue routing choice. We also identify several promising directions for future research. The routing decision is directly affected by the market design, which decides the venue’s pricing structure, levels of transparency, and execution quality. We document the changes in the studies from examining features of call vs. continuous markets to limit order vs. hybrid market. Remarkably, studies such as Venkataraman (2001) and Brogaard et al. (2021) highlight the role of human intermediates and show that floor trading service by humans is irreplaceable because of their expertise. The experience that floortraders have allows them to deal with highly complex issues related to liquidity provision situations more efficiently than an algorithm. Therefore, human floor trading service ultimately improves market quality by narrowing the spreads and decreasing pricing errors. Moreover, the routing venue decision involves the trade-offs among transaction cost, execution risk, and adverse selection risk. In fact, types of traders matter as well in terms of the trade-off. Informed traders are concerned more with the trade-off between cost and execution risk as they already have the profitable private information, while uninformed traders focus more on the trade-off between the cost and adverse selection risk. Meanwhile, the routing venue decision is also influenced by technology. The nano-second response speed allows high-frequency traders to quickly react to new information and send orders across venues to harvest the information arbitrage profit. At the same time, exchanges must continually invest in low-latency technology, including co-location, to attract order flow. In the end, we discuss the major regulatory reforms in the U.S. equity market that impact the market trading environment and the routing venue decision. Overall, the routing venue decision shapes the direction of the exchanges’ evolution and the policy attention, and the changes in the exchanges’ design and policy reforms again alter the routing venue decision. The rest of the survey is organized as follows. Section 2discusses the development of U.S. trading venues and the consequences of increased fragmentation and venue competition. Section 3describes the possible determinants and channels that could explain the order routing choice. Section 4reviews the impact of policy reforms on the routing decision, and Section 5concludes. 2. Market Fragmentation This section briefly shows the evolution of U.S. equity exchanges and discusses the related theoretical and empirical literature that focus on the impact of market fragmentation and venue competition. First, we show that the development of the U.S. trading venues results in a highly fragmented market. Next, we review related studies on market fragmentation and show that fragmented market changes venue competition and market quality such as liquidity and volatility. 2.1. The Evolution of U.S. Equity Trading Venues The modern U.S. equity market has been evolving from floor trading by brokers who read the ticker tape and bid on offer to purely electric trading coded into computer algorithms. Table 1presents the timeline in the evolution of U.S. equity national exchanges. Notably, the electronic communications network (ECN) was developed in the 1990s to allow direct-matched trading between buyer and seller without an intermediary. The big ECNs, such as Archipelago and Instinet, started gaining popularity as alternative trading systems. J. Risk Financial Manag. 2021,14, 556 3 of 32 Table 1. Timeline of the evolution for U.S. equity national exchanges. Year Timeline 1790 Philadelphia Stock Exchange founded (PHLX) 1817 New York Stock and Exchange Board (NYSE) was officially founded 1835 Boston Stock Exchange (BEX) founded 1882 San Francisco Stock Exchange founded Chicago Stock Exchange (CHX) founded 1885 Cincinnati Stock Exchange founded (renamed as National Stock Exchange in 2003) 1899 Los Angeles Oil Exchange founded 1924 The New York Curb Market created (renamed as New York Cub Exchange in 1929, and renamed as American Stock Exchange in 1953) 1956 Pacific Coast Stock Exchange was created by the merge of San Francisco Stock Exchange and Los Angeles Oil Exchange (rename as Pacific Stock Exchange in 1973) 1971 Nasdaq founded 1996 Archipelago created 2005 Bats Global Markets (BATS) founded Archipelago purchased Pacific Stock Exchange (PCX) 2006 Archipelago was acquired by NYSE and the exchange renamed as NYSE Arca 2007 Boston Stock Exchange (BSE) was acquired by Nasdaq and renamed as Nasdaq OMX BX Philadelphia Stock Exchange (PHLX) was acquired by Nasdaq and renamed as Nasdaq PHLX 2008 American Stock Exchange (AMEX) was acquired by NYSE and renamed as NYSE American BATS launched BZX exchange 2010 Direct Edge launched EDGA and EDGX exchanges BATS launched BYX Exchange 2014 BATS merged with Direct Edge 2016 Cboe acquired Bats Global Markets Investors Exchange launched 2017 National Stock Exchange (NSX) was acquired by NYSE and renamed as NYSE National 2018 Chicago Stock Exchange (CHX) was acquired by NYSE and renamed as NYSE Chicago 2020 Members Exchange (MEMX) launched MIAX Peral’s Exchange (MIAX) launched Long-term Stock Exchange (LTSE) launched Market participants benefit from the evolution of the technology. First, the stock trading process became much easier with the proliferation of the internet and personal computer. Second, the reduction in the brokerage commission due to enhanced competition also incentivized traders to participate in the equities market. Figure 1shows the changes in total equities trading volume (in a million shares) in the U.S. market from 2011 to 2021. The average trading volume in the U.S. equities market increased by half, from 160 billion shares per month in 2011 to 250 billion shares per month in 2021. J. Risk Financial Manag. 2021,14, 556 4 of 32 J. Risk Financial Manag. 2021, 14, x FOR PEER REVIEW 4 of 34 Figure 1. Change in trading volume in 2011 vs. 2021. This figure plots the average number of shares executed in the overall market per month in 2011 and 2021. The data was taken from the CBOE’s U.S. Equities Market Volume Summary (https://www.cboe.com/us/equities/market_share, accessed date: 20 August 2021). Moreover, equity trading volume steadily increased by greater participation from retail investors induced by zero brokerage commissions and the widely adopted “working from home” policy under the Coronavirus disease (COVID-19) pandemic. In consequence, the market makers in off-exchange such as Citadel and Virtu gained significant volume share. Figure 2 depicts the change in the market share from 2011 to 2021 in the U.S. equity market. Combined with the increased trading volume shown in Figure 1, it is clearly implicit that the volume in the U.S. equity market has significantly increased in the past ten years, while the markets also have become highly fragmented. Moreover, Figure 2 suggests two trends in terms of fragmentation: first, the competition among exchanges intensified as the number of securities exchanges increased from 13 to 16 within ten years. The merger and acquisition activity has blown in the past ten years, as many regional exchanges such as Boston Stock Exchange (BEX) and Chicago Exchange (CHX) were acquired by the big national exchange groups. In addition, other new independent exchanges, such as the Investors Exchange, MIAX Pearl exchange and Members exchanges, and the Long-Term Stock Exchange, were launched in recent years to increase the competition. Second, the off-exchange trading gained a significant proportion (increased from 30.28% to 44.24%), while the volume share for traditional primary exchanges steadily decreased during the past two years. For example, the market share for NYSE and NASDAQ dropped 3.64% and 2.35%, respectively. Figure 1. Change in trading volume in 2011 vs. 2021. This figure plots the average number of shares executed in the overall market per month in 2011 and 2021. The data was taken from the CBOE’s U.S. Equities Market Volume Summary (https://www.cboe.com/us/equities/market_share, accessed date: 20 August 2021). Moreover, equity trading volume steadily increased by greater participation from retail investors induced by zero brokerage commissions and the widely adopted “working from home” policy under the Coronavirus disease (COVID-19) pandemic. In consequence, the market makers in off-exchange such as Citadel and Virtu gained significant volume share. Figure 2depicts the change in the market share from 2011 to 2021 in the U.S. equity market. Combined with the increased trading volume shown in Figure 1, it is clearly implicit that the volume in the U.S. equity market has significantly increased in the past ten years, while the markets also have become highly fragmented. Moreover, Figure 2suggests two trends in terms of fragmentation: first, the competition among exchanges intensified as the number of securities exchanges increased from 13 to 16 within ten years. The merger and acquisition activity has blown in the past ten years, as many regional exchanges such as Boston Stock Exchange (BEX) and Chicago Exchange (CHX) were acquired by the big national exchange groups. In addition, other new independent exchanges, such as the Investors Exchange, MIAX Pearl exchange and Members exchanges, and the Long-Term Stock Exchange, were launched in recent years to increase the competition. Second, the off-exchange trading gained a significant proportion (increased from 30.28% to 44.24%), while the volume share for traditional primary exchanges steadily decreased during the past two years. For example, the market share for NYSE and NASDAQ dropped 3.64% and 2.35%, respectively. J. Risk Financial Manag. 2021,14, 556 5 of 32 J. Risk Financial Manag. 2021, 14, x FOR PEER REVIEW 5 of 34 Figure 2. The average market share by venue in 2011 vs. 2021. This figure presents the changes in the market share by venue in 2011 (panel a) vs. 2021 (panel b). The market share is calculated as the volume executed on a particular market venue divided by the total volume on all venues. The volume data by the exchange is obtained from the CBOE’s U.S. Equities Market Volume Summary (https://www.cboe.com/us/equities/market_share, accessed date: 20 August 2021). 2.2. The Conequences of the Market Fragmentation The equilibrium in the early theoretical market microstructure studies does not incorporate the multiple venue consideration. Early theoretical studies, such as the multimarkets strategic trading model by Chowdhry and Nanda (1991) and the limit order auction markets model by Glosten (1994), assume that the liquidity supply is competitive. Therefore, combined with the order matching system and large tick size, these models imply that a fragmented market should not affect the quotes. However, many empirical studies in the same period disagreed with the theoretical suggestions. For instance, Easley et al. (1996) and Hasbrouck (1995) observe that different markets obtain significant differences in information contents of order flow, hence arguing that the market fragmentation impacts market quality. Still, the theoretical predictions and empirical findings on market fragmentation are mixed. The conclusions about fragmentation on market quality are diverse and differ according to the factors considered. The directive consequence of market fragmentation is the intensified competition across trading venues. Several studies suggest that the competition that raised from the fragmentation can improve the market quality by reducing fees, promoting innovation, and hence improving quality (Chao et al. 2017). For example, Macey and O’Hara (1997) suggest that the multi-venues environment allows traders to have a chance to compare the execution quality under each venue, and ultimately the trader could achieve the best execution. Biais et al. (2000) theoretically examine competition among liquidity suppliers and limit order trading in a decentralized market. Their model assumes that market makers are risk-neutral, and the model predicts that the trading volume increases under a high decentralized market. Furthermore, Buti et al. (2017) analyze competition between a limit Figure 2. The average market share by venue in 2011 vs. 2021. This figure presents the changes in the market share by venue in 2011 (panel a ) vs. 2021 (panel b ). The market share is calculated as the volume executed on a particular market venue divided by the total volume on all venues. The volume data by the exchange is obtained from the CBOE’s U.S. Equities Market Volume Summary (https://www.cboe.com/us/equities/market_share, accessed date: 20 August 2021). 2.2. The Conequences of the Market Fragmentation The equilibrium in the early theoretical market microstructure studies does not incorporate the multiple venue consideration. Early theoretical studies, such as the multimarkets strategic trading model by Chowdhry and Nanda (1991) and the limit order auction markets model by Glosten (1994), assume that the liquidity supply is competitive. Therefore, combined with the order matching system and large tick size, these models imply that a fragmented market should not affect the quotes. However, many empirical studies in the same period disagreed with the theoretical suggestions. For instance, Easley et al. (1996) and Hasbrouck (1995) observe that different markets obtain significant differences in information contents of order flow, hence arguing that the market fragmentation impacts market quality. Still, the theoretical predictions and empirical findings on market fragmentation are mixed. The conclusions about fragmentation on market quality are diverse and differ according to the factors considered. The directive consequence of market fragmentation is the intensified competition across trading venues. Several studies suggest that the competition that raised from the fragmentation can improve the market quality by reducing fees, promoting innovation, and hence improving quality (Chao et al. 2017). For example, Macey and O’Hara (1997) suggest that the multi-venues environment allows traders to have a chance to compare the execution quality under each venue, and ultimately the trader could achieve the best execution. Biais et al. (2000) theoretically examine competition among liquidity suppliers and limit order trading in a decentralized market. Their model assumes that market makers are risk-neutral, and the model predicts that the trading volume increases under a high J. Risk Financial Manag. 2021,14, 556 6 of 32 decentralized market. Furthermore, Buti et al. (2017) analyze competition between a limit order book and a dark pool. Their model implies that the introduction of a dark pool increases trading volume. Overall, both Biais et al. (2000) and Buti et al. (2017) predict that the fragmentation could increase overall market volume. Nevertheless, there is still an ongoing debate on whether market fragmentation improves or harms liquidity. The supporters who discuss the impact of fragmentation on liquidity mainly focus on the competition perspective, given that the fragmented market increase the competition, hence it could push the exchanges to lower their fee, thus promote the liquidity (see the theorical prediction by Colliard and Foucault (2012); Pagnotta and Philippon (2018), and empirical supports by Boehmer and Boehmer (2003); De Fontnouvelle et al. (2003); Nguyen et al. (2007); O’Hara and Ye (2011); Menkveld (2013); He et al. (2015); Foucault and Menkveld (2008)). Conversely, the negative view of the impact of fragmentation on liquidity stresses the information asymmetry perspective. A fragmented market increases adverse selection, hence harms liquidity. The theories were developed by Chowdhry and Nanda (1991) and Dennert (1993) and supported empirical studies can be found in Bessembinder and Kaufman (1997b); Amihud et al. (2003); Hendershott and Jones (2005); and Bennett and Wei (2006). For instance, recent theoretical work by Baldauf and Mollner (2021) examines the market relegation effects by allowing exchanges to adjust the trading fees in responding to competition and adverse selection, and their empirical tests in the Australian market support theoretical predictions that fragmentation increases the arbitrage opportunities, hence increases adverse selection. In addition, a theoretical model by Yin (2005) postulates that increased search costs due to fragmentation decrease competition among liquidity providers and harm liquidity and price discovery. Alongside the two contradictory views above, several studies argue that the relationship between fragmentation and liquidity should be U-shaped. Degryse et al. (2015) suggest that market fragmentation improves the liquidity in lit-exchanges while harming liquidity in off-exchanges 3 .Gresse (2017) empirically tests whether positive or negative effects dominate the fragmentation on liquidity. The results show the spreads substantially decrease in both lit fragmentation and dark trading venues after the implementation of MiFID in Europe 4 , suggesting the benefits from market competition outweigh the negative effect from information asymmetry. Wittwer (2021) studies the welfare effects of connecting the disconnected markets and the model predicts that market fragmentation decreases market depth. Chen and Duffie (2021) extend Wittwer’s model by increasing the number of exchanges in the equilibrium. Chen and Duffie (2021) confirm Wittwer’s (2021) prediction and further show that market fragmentation also alters trader’s strategy to submit a more aggressive order, hence increasing allocative efficiency. Ultimately, overall price informativeness increases. To sum up, there are exhaustive discussions about the impact of fragmentation on liquidity. However, as suggested by Barardehi et al. (2019), traditional liquidity measures may underestimate the liquidity provision under the current fast-trading environment. Therefore, to better estimate trading cost and understanding the impact of the liquidity under the fragmented market, it is still worthy to compare the liquidity among litand off-exchanges by using the new liquidity measures, such as the average per-dollar price impacts of fixed-dollar volume that was proposed by Barardehi et al. (2019). Alongside liquidity, market volatility by fragmentation is another important dimension that is worth emphasizing. Prices under fragmented markets are more disposed to order imbalances, while increase transitory volatility. The Biais (1993) model conducts theoretical research comparing centralized and fragmented markets and provides two predictions: first, the fragmented markets should increase stock price volatility since the information is fragmented. Second, the spread should be less volatile in fragmented market. Easley et al. (1996) and Bessembinder and Kaufman (1997a) assume heterogeneous information in the model and show that trading fragmentation leads to information fragmentation, which in turn results in higher volatility and wider spreads. Ultimately, both of the works suggest that fragmentation leads to cream-skimming effects and harms J. Risk Financial Manag. 2021,14, 556 7 of 32 markets. In empirical tests, Madhavan (2012) examines the Flash Crash and finds that more fragmented stocks had a more significant negative impact during the Flash Crash in 2010. By contrast, Boneva et al. (2016) empirically tests the effect of fragmentation on volatility for the London Stock Exchange and finds that fragmentation lowers overall volatility. In addition, Boneva et al. (2016) further separates the overall fragmentation into dark trading and visible fragmentation and suggests that the effects of dark trading and visible fragmentation on market quality are different. For further discussion towards venue competition under a fragmented trading environment, readers may refer to a literature survey by Gomber et al. (2017), who review the literature that focus on examining the economic arguments and motivations underlying market fragmentation. 3. The Determinants of the Trading Venue Choice This section reviews a body of theoretical and empirical studies about possible determinants of the trading venue choice. This overview emphasizes that the trader’s routing choice is influenced by many factors other than simply by transaction cost. Table 2provides the information on the fee model for U.S. National Exchanges. Table 3at end of this section summarizes studies on potential determinants of order routing decisions and Appendix A presents market microstructure empirical studies on order routing decisions. Table 2. U.S. national exchanges fee schedule. Exchange Fee Model Adding Liquidity Removing Liquidity Net Fee NYSE America Maker–Taker (0.0045)–0.0002 0.0002 (0.0043)–0.0002 Bats EDGX Maker–Taker (0.0017) 0.00265 0.00095 NYSE Chicago Maker–Taker (0.002) 0.003 0.001 NYSE Maker–Taker (0–0.0029) 0.00275–0.003 0.00015–0.003 NYSE Arca Maker–Taker (0.0015) Tape A 0.003 0.0015 (0.002) Tape C 0.003 0.001 Nasdaq Maker–Taker (0–0.00305+) 0.003 <0.003 Bats BZX Maker–Taker (0.002) Tape A 0.003 0.001 (0.0025) Tape C 0.003 0.0005 Nasdaq OMX PSX Maker–Taker (0.0023) 0.003 0.0007 IEX Flat 0.0003 0.0003 0.0006 Bats BYX Taker–Maker 0.0019 (0.0005) 0.0014 Nasdaq OMX BX Taker–Maker 0.0024 0.0003–(0.0027) (0.003)–0.0027 NYSE National Taker–Maker $0.001–$0.0028 (0.0002–0.003) (0.002)–0.0026 Bats EDGA Taker–Maker 0.003 (0.0024) 0.0006 Note: 1. Tape A is NYSE-listed stocks. Tape C is NASDAQ-listed stocks; 2. ATS fees are individually negotiated between the ATS operator and the participant. This table presents all 13 U.S. national exchange fee schedules for per share price $1.00 or above at 8 January 2019. Rebate indicated by parentheses. For some exchanges, the fee and rebates vary based on the trading volume per order. Data are from each exchange’s respective website. First of all, trading venue choice is fundamentally influenced by the trading system structure (market design) in each exchange. The focus of the studies on the type of the trading system has evolved along with the trading system itself. Early papers on trading system structure mainly compare call markets vs. continuous markets and suggest that the call markets improve the information efficiency of overall market welfare, while continuous markets could be complements for call auction markets. The theoretical discussion can be found in Brennan and Cao (1996) and Vayanos (1999), and empirical studies can be found in Amihud and Mendelson (1991); Neal (1992); Biais et al. (1999); and Corwin and Lipson (2000). With the market innovation through time, the discussion of market design shifts to the limit order market and hybrid market. Some theoretical studies include Foucault (1999); Parlour and Rajan (2003); Foucault et al. (2005); Goettler et al. (2005); Hendershott and Moulton (2011), and the recent work by Budish et al. (2019). Notably, there is an uptrend discussion about the role of human intermediation in market design. For example, Venkataraman (2001) argues that the floor-based market structure with human intermediation (ex. NYSE) has lower execution costs than an automated limit J. Risk Financial Manag. 2021,14, 556 8 of 32 order market. Additionally, Bessembinder and Venkataraman (2004) suggest that a central market (downstairs market) has relatively more information and smaller trades than the dealership market (upstairs trading), and traders strategically choose across markets to minimize the expected execution costs. Brogaard et al. (2021) examine the market quality around the COVID-19 pandemic when NYSE suspended floor trading and show that floor trading improves liquidity and price discovery. Table 3. Overview of studies on potential determinants of order routing decisions. Determinants of Order Routing Decisions Theorical Studies Empirical Tests Execution Cost Transaction Fee Limit order trading model with fixed or endogenized fee Colliard and Foucault (2012)Cardella et al. (2017); Malinova and Park (2015); Battalio et al. (2016b); Jørgensen et al. (2018); Comerton-Forde et al. (2018); Clapham et al. (2021) Limit order trading model with differentiating maker & taker fee Foucault et al. (2013) Limit order trading model with fee exogenously Cimon (2021) Execution Quality Inventory model Biais (1993); De Frutos and Manzano (2002)Boehmer et al. (2007); Battalio et al. (2016a); Peterson and Sirri (2003); Thomas et al. (2021); Boehmer et al. (2005); Garvey et al. (2016); Ernst et al. (2021); Thomas et al. (2021) Single period strategic trade model He et al. (2006) Dynamic model Pagano and Röell (1996); He et al. (2006); Degryse et al. (2009); Maglaras et al. (2015); Colliard and Foucault (2012) Information Risk Two-period strategic trade model Ye (2011)Grammig et al. (2001); Jain et al. (2003); Jiang et al. (2012); Nimalendran and Ray (2014); Garvey et al. (2016); Hatheway et al. (2017) Two-period sequential trade model Zhu (2014) Limit order trading model Foucault et al. (2007) Trader Type Informed vs. Uninformed Traders Strategic trade model Kyle (1985) Kavajecz and Odders-White (2004); Garvey and Wu (2011); Jones and Lipson (2004); Ready (2014); Chakravarty et al. (2012); Barber et al. (2008); Chevalier and Ellison (1999); Coval and Stafford (2007); Gao and Lin (2015); Han and Kumar (2013); O’Hara (2015); Boehmer et al. (2021); Jain et al. (2021) Two-period strategic trade model Ye and Zhu (2020) Fast vs. Slow Traders Search and bargaining model Üslü (2019) Brogaard et al. (2015); Hasbrouck and Saar (2013); Hendershott et al. (2011) Sequential trade model Biais et al. (2015) Continuous limit order trading model Budish et al. (2015); Baldauf and Mollner (2020) Dynamic model Ro¸su (2019) Trader’s Behavior and Strategy Limit order trading model Parlour and Seppi (2003) Garvey et al. (2016) Symmetric continuous limit order trading model Kyle et al. (2018) J. Risk Financial Manag. 2021,14, 556 15 of 32 order flow. Significantly, given the GameStop trading frenzy by the retail investors in 2021 13 , the role of retail trading on the overall market quality and price discovery has raised attention. A promising direction for future research may explore the interaction between the retail investor’s attention, market fragmentation, and routing order decisions. 3.2.2. Fast vs. Slow Trader Based on trading speed, microstructure theories separate the traders as fast and slow traders 14 . Traders compete with each other by the reaction speed to new information. Fragmentation induces high-frequency trading in order to take the information advantage. In particular, with technology innovation, some traders utilize algorithmic trading to respond to a market event at the millisecond level (referred as the high-frequency trader). Many theoretical studies focus on discussing the impact of high-frequency trading on market quality and overall welfare. For instance, Üslü (2019) applies the search-andbargaining model to discuss the impact of exogenous heterogeneity in investors’ search speed. The model by Biais et al. (2015) allows the interaction between fast and slow traders and shows that the information advantages from faster traders could result in adverse selection for the slower traders. Budish et al. (2015) provide a model to examine the high-frequency trading on the market design and social welfare. Baldauf and Mollner (2020) extend Budish et al. (2015) to include high-frequency trading into the information acquisition procedure by endogenizing the informed trading and HFT reaction. Furthermore, the theoretical model proposed by Ro¸su (2019) allows one to examine informed trading at different speeds. Many empirical studies show the positive relationship between high-frequency trading (HFT) and market quality in litand off-exchanges. The HFT could potentially lower the adverse selection cost, improve market quality under liquidity, price discovery, and the short-term volatility dimensions (Brogaard et al. 2015;Hasbrouck and Saar 2013; Hendershott et al. 2011). Van Van Kervel (2015) argues that increased number of faster traders could result in more order cancellations in a relatively high-latency venue, creating frictions and harming slow traders. Shkilko and Sokolov (2020) show that the differential in a traders’ trading speed harms market quality. With technology enabling faster speeds, fast traders can actively seek latent liquidity across venues to make an arbitrage profit. Hasbrouck and Saar (2009) document a trading “fleeting orders” phenomenon, namely submitting a limit order and quickly canceling within a second. Hasbrouck and Saar (2009) explain that increased numbers of “fleeting orders” results from new dynamic trading strategies. Additionally, some studies point out that venues with a maker–taker pricing structure may be more favored by faster traders as they could place the limited order to earn the rebates faster than anyone else, and venues with a taker–maker pricing structure may be less attractive to fast traders since the taker–maker venues allow slow trader to pay the maker fee and jump to the head of the queue (O’Hara 2015;Ye and Yao 2014). 3.2.3. Trader’s Behavior and Strategy Trading strategies could also affect the order routing decision since the trade timing and the selected trade venue can materially affect the trader strategy’s success and estimated return. Theoretical models generally use the CAAR model to formalize an investor’s optimal trading strategy to maximize the expected utility, and the reader may refer to McAleer et al. (2016b) who summarize the investors’ utility models and related implications. An experimental work by Frydman et al. (2014) confirms the disposition effect and find that the investor’s decision-making procedure is consistent with the predictions of realization utility. Therefore, the effect of changes in trading behavior on routing preference could be a promising direction for future research. Parlour and Seppi (2003) propose a limit order trading model to incorporate the strategic behavior of traders. Their model assumes trader’s strategies depend on the market current state, and they predict that widened spread leads traders to place more J. Risk Financial Manag. 2021,14, 556 16 of 32 limit orders and fewer market orders. Kyle et al. (2018) propose a symmetric continuoustime model to incorporate the heterogeneity belief among investors and trade speed to trade strategies. Glode and Opp (2020) endogenizes the trader’s expertise in the model and show that the trader’s expertise matters in choosing between the limit-order markets and over-the-counter (OTC) markets 15 .Garvey et al. (2016) empirically examine the trader’s expertise on the routing venue choice and suggest that traders with better skill are more likely to participate in off-exchange trading. 3.2.4. Summary and Further Discussion Alongside the execution cost, studies suggest that the order route decision is also influenced by the types of traders and their trading behavior. On the dimension of the trading information. The studies suggest informed traders prefer to trade in dark pools to hide information, and they are more likely to split orders to smaller sizes and send them over to multiple venues to maximize profits. On the other hand, most orders placed by uninformed traders (retail investors) are internalized or executed in off-exchanges by market makers. On the dimension of the trading speed, the studies show that the fast trader uses a technological advantage to fleet across venues to seek latent liquidity and get arbitrary profit. Traders’ expertise and their trading behavior may influence the order routing decision as well. However, connecting trader’s behavior with the routing venue choice is an important question and yet has not been well explored. Investors’ sentiment is widely studied through the lens of behavioral finance, as much as the anomalies germane to the asset pricing literature16. Thus, it will be worthwhile for future research to link sentiment with the trader’s behavior on the routing venue choice. Especially, as discussed in McAleer et al. (2016a), there are not many theoretical models developed to link behavioral and financial economics to health and medical science. McAleer (2020) discusses risk management measures, such as Global Health Security Index, which could potentially link the market uncertainty with the country’s health security. Still, given the ongoing COVID-19 Pandemic, the health condition and environment’s impact on risk aversion and trading behavior remains largely undefined and is an important direction for future research. 3.3. Market and Stock Characteristics 3.3.1. Market Condition Changes in the market condition alter the order routing decision. McAleer et al. (2016c) examines the global financial crisis in the past two decades and observe a positive relationship between the volatility of stock returns and crisis. Theoretical prediction suggests that the informed trading increases in off-exchanges while overall off-exchange volume share decreases when the bid-ask spread is wider and market volatility is higher (Zhu 2014). Several empirical studies support the predictions in Zhu (2014) 17 .Vuorenmaa (2014) explicitly discusses the lit and dark liquidity around the Global Financial Crisis. Jiang et al. (2012) find that the trading volume shifts from off-exchange to lit-exchanges when the prices are volatile. Furthermore, He et al. (2015) confirm Jiang et al.’s (2012) finding under the international context. Barclay et al. (2003) show that ECNs attract more informed trades in the active and volatile markets. Jurich (2021) shows a negative relation between market volatility and the off-exchange trading volume share. Anselmi et al. (2021) examines the dynamics of the market fragmentation during the COVID-19 pandemic period and find that orders are trading in a more concentrated way and they are moving to a venue with high transparency in the time of market stress. They also observe the overall order flow shifts from the dark to lit-exchanges. 3.3.2. Stock Characteristics Baruch and Saar (2009) develop a model linking asset returns with a firm optimal listing choice. The model shows that on which primary market to list matters for the asset J. Risk Financial Manag. 2021,14, 556 17 of 32 returns. Furthermore, Baruch and Saar (2009) suggest that listing stocks in a market where similar stocks are traded could substantially reduce the information asymmetry, increasing stock value. Harris (2003) suggests that the exchanges operate under ECNs attract more NASDAQ-listed securities. Nguyen et al. (2005) examines the launch of the Archipelago Exchange, which was an ECN, and find that it captures fewer NYSE-listed stocks but more NASDAQ-listed stocks. He and Lepone (2014) show that the dark pools trading volume is positively related to trade size and negatively related to price. Garvey et al. (2016) confirm that the order size is an important influence for a trader’s decision to choose off-exchanges and argues that trading large orders in off-exchanges may present front-running. 3.3.3. Summary and Further Discussion Market condition and stock characteristics potentially affect investor’s routing order decision. Theory suggests that higher market volatility reduces trading at off-exchanges and the listing venue and order size matters for routing decision. The evidence is largely in line with these predictions. 3.4. Trading Technologies The technology innovation on trading speed significantly reduces the latency of information transmission and execution. In this section, we will start with the literature on the fragmentation with trading technology innovation and briefly discuss the theoretical prediction and empirical studies about the impact of the technology on the exchanges 18 , namely speed competition and colocation, on the market quality. For a broad discussion on the impact of technology on the financial market, readers may refer to comprehensive reviews by McAleer et al. (2015) about econometrics with informatics and data mining and by Menkveld (2016) and Zaharudin et al. (2021) about HFT trading. Menkveld (2014) argues that both high-frequency trading (HFT) and market fragmentation resulted from technology innovation. With improved technology, search costs decrease, making the trading floor’s operation more profitable, facilitating more venues to enter the market, thus increasing fragmentation. Technology innovation also lowers the information latency, along with the fragmented markets, makes HFT possible. 3.4.1. Speed Race (Low Latency) To increase the market share, exchanges also compete on the speed to respond to submitted orders. A decrease in communication response speed decreases latency arbitrage, attracting more volumes (Chakrabarty et al. 2021). The limit order book model by Baldauf and Mollner (2020) incorporates the random communication latency within the exchange system. Brolley and Cimon (2020) extend a model from Baldauf and Mollner (2020) by assuming that the market makers were endogenously affected by latency delay. Biais et al. (2015) predict that speed arms race pushes venues to extensively invest in speed technology innovation, 3.4.2. Co-Location With the development of technology and algorithm trading, introducing the colocation services by securities exchanges becomes necessary due to competition. Hau (2001) explains that traders located close to the financial center will have more information advantages than those who do not. The introduction of co-location allows an exchange to reduce latency further, attracts more algorithm trading volumes, and enhances liquidity (Aitken et al. 2017;Brogaard et al. 2015;Frino et al. 2014). 3.4.3. Summary and Further Discussion So far, many studies on the relation between technology innovation and orders routing have focused on the interaction with high-frequency trading and market quality. The effect of big data on trader behavior is still unexplored. A review of the theoretical models, econo- J. Risk Financial Manag. 2021,14, 556 18 of 32 metrics, as well as statistical models about the connection on the big data, computation science, psychology, decision-making, and finance is well beyond the scope of our paper, and we refer the reader to the excellent survey by McAleer et al. (2018b), who provide a comprehensive review of the literature that connects big data, finance, and psychology in both theoretical and empirical way. 4. Regulatory Reforms Implementation of any equity market regulations could facilitate the fragmentations, change venue’s execution quality, and alter traders routing venue preference. In this section, we discuss the major regulatory reforms in the U.S. equity market that impact the market trading environment and present the studies examining the impact of these policies on the routing venue decision. 4.1. Order Handling Rules in 1997 In order to promote the quote competition, the U.S. Securities and Exchange Commission (SEC) implemented new order handling rules (OHRs) on NASDAQ’s dealer market in 1997, requiring market makers to display customer limit orders in their quotes 19 . Barclay et al. (1999) and Weston (2000) show that implementing OHRs reduced spreads and dealers’ rent, suggesting improved market quality. However, Rhee and Tang (2013) argue that, in the long-term, forcing quote competition by policy results in dealers altering their competition strategy from quote competition to payment for order flow competition. They observe a weaker correlation between the trading volume and quote competitiveness after the implementation of the OHRs. 4.2. Decimalization in 2000 In order to promote the price competition, the SEC mandated all exchanges to adopt the decimalization system in 2000, with a reduction in minimum tick size from the previous $1/16 ($0.0625) to $0.0120. The implementation of the decimalization results reduced the trade execution costs, increased quote competition among the exchanges, and narrowed the spreads, thus improving market quality. Under the revenue maximization model developed by Chordia and Subrahmanyam (1995), the reduction in tick size will negatively impact the volume internalization. Kandel and Marx (1999) extend Chordia and Subrahmanyam (1995) by treating spreads, preference trades, and vertical integration as equilibrium outcomes. Their models suggest the decrease in tick size results in asymmetric effects on endogenous variables, such as numbers of market makers, due to the change in the equilibrium. Decimalization changes trader’s order submission strategies as well. Changes in minimum tick size alter traders’ behavior by lowering trader’s ex-ante cost, resulting in more market orders and fewer limit orders. Traders now place fewer large limit order sizes and cancel limit orders more frequently (Bacidore et al. 2003;Bessembinder 2003; Chakravarty et al. 2005;Chung et al. 2004;Huang et al. 2010). Goldstein et al. (2010) examine the effects of decimalization on venue competition and suggests that the impact is heterogeneous across venues. The quote competition further weakens, and the competition among venues switches to best quote improvements. Tang et al. (2011) further support Goldstein et al. (2010) about the decline in the quote competitiveness and point out the reason is the reduction in the number of 100-share NBBO-matching quotes posted by NASDAQ. Garvey et al. (2016) find that traders are more likely to route to off-exchanges venue after the decimalization as the cost aspect of routing decision is now marginalized. 4.3. Reg NMS Rule 611 “The Order Protection Rule (OPR)” and Reg NMS Rule 612 “Minmum Pricing Increment” in 2005 To encourage competition among traders and to improve market liquidity, the SEC implemented the Order Protection Rule (OPR) for intermarket price protection 21 . Based J. Risk Financial Manag. 2021,14, 556 19 of 32 on OPR requirements, each exchange has to “establish, maintain, and enforce written policies and procedures reasonably designed to prevent the execution of trades at prices inferior to protected quotations displayed by other trading centers, subject to an applicable exception”. OPR differentiates exchanges based on the execution speed. The rule classifies electronic exchanges, such as NASDAQ, as the fast market and prohibits it to trade through better prices on other fast markets. At the same time, the restriction does not apply to slow market, which is floor-based exchanges. Many studies raised concerns that the implementation of OPR may negatively impact the market quality (Blume 2007;O’Hara 2004). As OPR fundamentally changes exchanges’ execution probability and speed. Chung and Chuwonganant (2012) find OPR negatively impacts the execution quality in NYSE and AMEX; as a result, they observe an increased trading volume in NASDAQ. Meanwhile, OPR alters trader’s trading strategies. Spatt (2018) points out that OPR encourages traders to split orders across venues to achieve the best execution. The Reg NMS rule 612 “Minimum Pricing Increment” rule prohibits all trading venues to display, rank, or accept orders priced at more than two decimal places for stocks that trade greater or equal to $1.00, while allowing the broker-dealers who operate in offexchanges (OTC non-ATS markets) to offer price improvement in sub-penny increments 22 . As a result, traders can now utilize off-exchanges to bypass existing limit order queues and execute orders more quickly. Kwan et al. (2015) empirically document a remarkable gain in the market share for off-exchanges after the implementation of the Reg NMS rule 612, suggesting minimum pricing increment policy yields a significant competitive advantage for off-exchanges. 4.4. SEC Tick Size Pilot Program in 2015 To examine the impact of the tick sizes on the market quality for small-capitalization firms, in 2016, SEC and FINRA jointly launched a 2-year pilot program, which increases the minimum tick size from $0.01 to $0.05 for three pilot groups 23 . The main interest of the pilot focuses on whether the changes in tick size improves liquidity. In contrast, many empirical studies and the SEC report find that this pilot resulted in a negative impact on market liquidity and cost (Albuquerque et al. 2020;Griffith and Roseman 2019;SEC 2018). Given the operational concerns, the SEC issued a termination of the Pilot two days before the planned expiration date24. However, from the venue competition perspective, several studies show that the tick size pilot has a heterogeneous impact on exchanges. For instance, Comerton-Forde et al. (2019) study the effect of the tick size pilot for inverted fee exchanges and finds that the price discovery process is improved in inverted fee exchanges under the trade-at rule. Consequently, the trading volume share shift to inverted fee exchanges. Cox et al. (2019) reach the same conclusion as Comerton-Forde et al. (2019) that inverted fee exchanges gain more volume share under the tick size pilot. Additionally, Cox et al. (2019) observe that the shift in volume share was from both traditional fee exchanges (maker–taker) and off-exchanges, suggesting that the tick size changes reduce the risk of an informed trader exposing an order. 5. Conclusions With the rapid development of technology and the regulation reforms, trading in the U.S. equities markets is increasingly fragmented. Equity trading in the U.S. is dispersed across 16 national exchanges, more than thirty alternative trading systems, and numerous broker-dealers and wholesalers. On the one hand, the intensified competition lowers the transaction fee and ultimately benefits market participants. On the other hand, varying levels of venue transparency and the heterogeneity in the transaction speeds have raised the risk of adverse selection. Thus, examining routing order decisions is an important topic that is worth exploring. This paper provides a better understanding of the potential driving factors underlying routing order decisions under fragmented markets and identifies several promising directions for future research. J. Risk Financial Manag. 2021,14, 556 20 of 32 We survey a large and growing theoretical and empirical literature about the channels and determinants of routing venue choice under a highly fragmented equity market. The literature referenced in this paper carries important implications for policymakers, regulators, and exchange operators: under highly fragmented markets, routing order decisions are complex and influenced by many factors. First, the routing order decision is fundamentally affected by the market structure design. Different trading system structures provide different liquidity provisions and different degrees of transparency, resulting in differences in terms of execution quality. Execution decisions could be influenced by transaction costs, execution quality, and adverse selection concerns. Moreover, the decision procedure involves multiple trade-offs among the transaction costs, execution quality, and the risk of adverse selection. The nature of the trade-off varies by the type of investor. The informed trader pays more attention to the trade-off between transaction cost and execution quality, while the uninformed trader focuses on the trade-off between the transaction cost and the adverse selection cost. Second, the routing venue choice is influenced by the types of traders as well as their strategies. Informed traders are more likely to split their orders and send them across exchanges to camouflage their trading and maximize their profits. Meanwhile, in the U.S. market, uninformed retail investors mainly place orders through retail brokers, and retail brokers’ routing order decisions are influenced by the order-processing cost. Due to the practice of payment for order flow, most retail uninformed marketable orders are routed in off-exchanges by market makers. Third, the routing order decision depends on market conditions and stock characteristics. Order flow moves to exchanges with higher transparency during periods of high market volatility. In addition, stock listing venues and trade size substantially affect routing choices. Finally, the routing order decision is systematically shaped by technological development and regulatory reforms. We have shown that regulatory reform changes the venue’s execution quality and hence alters traders’ routing venue preference. Author Contributions: Conceptualization, S.M. and L.Z.; methodology, S.M. and L.Z.; validation, S.M. and L.Z.; formal analysis, L.Z.; investigation, L.Z.; resources, L.Z.; writing—original draft preparation, L.Z.; writing—review and editing, S.M.; visualization, L.Z.; supervision, S.M.; project administration, S.M. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Data Availability Statement: All used data are mentioned in the list of references. Conflicts of Interest: The authors declare no conflict of interest. Appendix A Table A1. Summary of market microstructure empirical studies on order routing decisions. Authors Year Data Source Sample Period Methodology Findings Cardella, Hao and Kalcheva 2017 SEC Filings and NYSE’s Trade and Quote (TAQ) 1 January 2008–31 December 2010 Multivariate regression analysis The magnitudes of decreasing in trading activities of take fee and make fee are different Malinova and Park 2015 A proprietary trader-level dataset from Toronto Stock Exchange (TSX) 1 August 2005–30 November 2005 Panel regression analysis An increase in the total exchange fee on Toronto Stock Exchange increases its cum fee effective spread and lowers the limit order fill rate Battalio, Corwin and Jennings 2016 Order data from major broker–dealer’s smart order routing systems and NYSE’s Trade and Quote (TAQ) 1 October 2012–30 November 2012 Univariate analysis and multivariate regression analysis Brokers’ route order decision is primarily based on the fee rather than execution quality J. Risk Financial Manag. 2021,14, 556 21 of 32 Table A1. Cont. Authors Year Data Source Sample Period Methodology Findings Jørgensen, Skjeltorp and Ødegaard 2018 Orderbook from Oslo Stock Exchange (OSE) and Thomson Reuters Tick History database 1 January 2010–31 December 2011 Difference in differences analysis The introduction of a fee on excessive order-to-ratios at the Olso Stock Exchange does not affect the market quality ComertonForde, Malinova and Park 2018 A proprietary transaction-broker level dataset from Investment Industry Regulatory Organization of Canada (IIROC) 1 August 2012–30 November 2012 Multivariate regression analysis and two-stage least squares regression Reducing retail order segmentation enhances liquidity in lit-exchanges Clapham, Gomber, Lausen and Panz 2021 Refinitiv Tick History database 1 May 2016–28 February 2017 Difference in differences analysis The order routing decisions are influenced by fee rebates Boehmer, Jennings and Wei 2007 NYSE’s Trade and Quote (TAQ) and the SEC Dash-5 reports 1 June 2001–31 June 2004 Fixed effects regression The routing decisions are associated with execution quality Battalio, Shkilko and Van Ness 2016 Options Price Reporting Authority (OPRA) and NYSE’s Trade and Quote (TAQ) 1 March 2010–31 June 2010 Fixed effects regression Retail brokers have the incentives to route order based on size of the commission and rebates Peterson and Sirri 2003 NYSE SOD file, BSE BEACON system, CHX order data, CSE preferencing dealers, PSE trading floors and PHLX’s market surveillance department 1 October 1996–30 November 1996 Univariate analysis and ordered probit regression NYSE, which was the primary market, obtains better quotation and execution quality for market orders with smaller effective spreads than other regional exchanges Boehmer, Saar and Yu 2005 NYSE’s Trade and Quote (TAQ), System Order Data (SOD) and Consolidated Equity Audit Trail Data (CAUD) 1 January 2001–31 May 2001 Wilcoxon signed rank test and multivariate regression analysis Improvement in pre-trade transparency enhances market liquidity Garvey, Huang and Wu 2016 A proprietary data from a U.S. direct market access (DMA) broker 1 October 1999–31 May 2006 Two-stage hackman model The time-to-execution is much longer in dark venues than in lit venues, and the average fill rate of marketable order executed at dark venues is lower than at lit venues Ernst, Sokobin and Spatt 2021 NYSE’s Trade and Quote (TAQ) 1 January 2019–31 December 2020 Fixed effects regression The exchange with better execution quality (lower cost and higher fill rate) subsequently attracts more order flow J. Risk Financial Manag. 2021,14, 556 22 of 32 Table A1. Cont. Authors Year Data Source Sample Period Methodology Findings Thomas, Zhang and Zhu 2021 NYSE’s Trade and Quote (TAQ) 1 January 2019–31 June 2018 OLS regression and two-stage least squares regression The dark trading decreases liquidity and increases the post-earnings announcement drift (PEAD) Grammig, Schiereck and Theissen 2001 Transaction-level dataset from IBIS and Frankfurt Stock Exchange 1 June 1997–31 July 1997 Private information (PIN) model by O’Hara (2004) The non-anonymous floor trading system has less informed trading than the anonymous electronic market Jain, Jiang, Mclnish and Taechapiroontong 2003 Transaction-level dataset from London Stock Exchange 1 January 2000–31 December 2000 Private information (PIN) model by Easley et al. (1996) and cross-sectional regression The probability of informed trading is no different on the anonymous market than on the non-anonymous market since the informed traders may split orders and send them to multiple venues Jiang, Mclnish and Upson 2012 NYSE’s Trade and Quote (TAQ) 1 January 2008–30 June 2008 MRR regression by Madhavan et al. (1997) Trading volume shifts from off-exchange to lit-exchanges when the prices are vola-tile Nimalendran and Ray 2014 NYSE’s Trade and Quote (TAQ) 1 June 2009–31 December 2009 Multivariate regression analysis Informed trader tend to split order between lit and off-exchanges and the order executed in lit-exchanges provides some price discovery Hatheway, Kwan and Zheng 2017 Thomson Reuters DataScope database 1 January 2011–31 March 2011 Two-stage hackman model Dark venues may harm the market quality by attracting uninformed order flow away form lit market Kavajecz and Odders-White 2004 NYSE SuperDOT dataset 1 July 1997–30 September 1997 Univariate analysis and multivariate regression analysis Technical analysis and moving average indicators are significantly related to the state of liquidity on the limit order book Garvey and Wu 2011 A proprietary order-level data from a U.S. broker-dealer and Thomson Reuters Tick History database 1 October 1999–31 July 2003 OLS regression The focus of trade-offs among transaction cost, execution risk, and adverse selection risk are different based on the types of the investor Jones and Lipson 2004 A proprietary order-level data from NYSE 1 November 2002–30 November 2002 Vector autoregression Retail order flow has better execution quality than non-retail order flow J. Risk Financial Manag. 2021,14, 556 23 of 32 Table A1. Cont. Authors Year Data Source Sample Period Methodology Findings Ready 2014 NASDAQtrader.com, Ancerno database and NYSE’s Trade and Quote (TAQ) 1 July 2005–30 September 2007 Panel regression analysis Institutional orders with high information have less probability of executing in dark pools Chakravarty, Jain, Upson and Wood 2012 NYSE’s Trade and Quote (TAQ) 1 August 2007–31 May 2008 MRR regression by Madhavan et al. (1997) The informed institutional investor applies the intermarket sweep order (ISO) by breaking up large orders and sending them over to multiple trading venues to maximize fragmentation arbitrage profits and hide information Barber, Odean and Zhu 2008 NYSE’s Trade and Quote (TAQ) and Institute for the Study of Security Markets (ISSM) transaction data 1 January 1983–31 December 2001 Univariate portfolio analysis and Fama-Macbeth cross-sectional regression The signed smaller trades provide a reasonable proxy for individual investor’s activity, and over both short and long horizons, retail trade imbalances forecast future returns Chevalier and Ellison 1999 Morningstar 1 January 1992–31 December 1994 Multivariate regression analysis The agency issues within the mutual fund companies can be attributed to career concerns Coval and Stafford 2007 Spectrum mutual fund holdings database 1 January 1980–31 December 2004 Fama-Macbeth cross-sectional regression The institutional price press creates an incentive to front-run Gao and Lin 2015 Website of the bank that holds the rights to administer the lottery and trading data from Taiwan Economic Journal 1 January 2002–31 December 2009 OLS regression Individual investor tends to trade stocks as a gambling activity Han and Kumar 2013 NYSE’s Trade and Quote (TAQ) and Institute for the Study of Security Markets (ISSM) transaction data 1 January 1983–31 January 2000 Fama-Macbeth cross-sectional regression Stocks with lottery features (high volatility, high skewness, and low prices) are heavily traded by retail investors Boehmer, Jones, Zhang and Zhang 2021 NYSE’s Trade and Quote (TAQ) 1 January 2010–31 December 2015 Fama-Macbeth cross-sectional regression Most marketable orders placed by retail investors in the U.S. equity market are either internalized or executed in by wholesale market makers in off-exchange J. Risk Financial Manag. 2021,14, 556 24 of 32 Table A1. Cont. Authors Year Data Source Sample Period Methodology Findings Jain, Mishra, O’Donoghue and Zhao 2021 SEC Rule 605, SEC Rule 606 and NYSE’s Trade and Quote (TAQ) 1 June 2019–29 February 2020 Univariate analysis and multivariate regression analysis Retail brokers who newly announced zero-commission policy tends to route more orders to the off-exchange market maker in order to gain the payment for order flow Brogaard, Hagströmer, Nordén and Riordan 2015 A proprietary dataset for the exchange colocation service subscription and Thomson Reuters’ Tick History database 1 August 2012–31 October 2012 Probit regression and panel regression Enhanced speed from colocation upgrade benefits market liquidity Hasbrouck and Saar 2013 NASDAQ OMX ITCH dataset 1 October 2007–31 December 2007 and 1 June 2008–30 June 2008 Multivariate regression analysis Increased low-latency activity improves traditional market quality measures Hendershott, Jones and Menkveld 2011 NYSE System Order Data (SOD) 1 December 2002–31 July 2003 Two-stage regression Improving in market’s automation and speed reduces cost of immediacy and improves price discovery He, Jarnecic and Liu 2015 Thomson Reuters Tick Historydatabase 1 March 2007–31 October 2011 Fixed effects regression Trading volume shift from off-exchange to lit-exchanges when the prices are volatile Barclay, Hendershott and McCormick 2003 Nasdaq National Market 1 June 2000–30 June 2000 Variance decomposition by Hasbrouck (1991) ECNs attract more informed trades in the active and volatile markets Jurich 2021 Cboe Global Markets and NYSE’s Trade and Quote (TAQ) 1 September 2018–30 September Multivariate regression analysis There is a negative relation between market volatility and off-exchange trading volume share Anselmi, Nimalendram and Petrella 2021 Fidessa database 1 July 2019–31 July 2020 Fixed effects regression Market order flow at the COVID-19 pandemic is more concentrated and moves to a venue with high transparency Nguyen, Van Ness and Van Ness 2005 The SEC Dash-5 reports, Transaction Auditing Group (TAG) and Market System Inc. 1 April 2002–31 October 2002 Multivariate regression analysis A launch of the Archipelago exchange, which is an ECN, captures fewer NYSE-listed stocks but more NASDAQ-listed stocks J. Risk Financial Manag. 2021,14, 556 31 of 32 Malinova, Katya, and Andreas Park. 2015. Subsidizing Liquidity: The Impact of Make/Take Fees on Market Quality. The Journal of Finance 70: 509–36. [CrossRef] McAleer, Michael. 2020. Prevention Is Better Than the Cure: Risk Management of COVID-19. Journal of Risk and Financial Management 13: 46. [CrossRef] McAleer, Michael, Chia-Lin Chang, and Wing-Keung Wong. 2015. Informatics, data mining, econometrics and financial economics: A connection. Journal of Informatics and Data Mining 1: 1–5. McAleer, Michael, Chia-Lin Chang, and Wing-Keung Wong. 2016a. Behavioural, financial, and health & medical economics: A connection. Journal of Health & Medical Economics 2: 1–4. McAleer, Michael, Chia-Lin Chang, and Wing-Keung Wong. 2016b. Management science, economics and finance: A connection. International Journal of Economics and Management Sciences 5: 1–19. McAleer, Michael, John Suen, and Wing-Keung Wong. 2016c. Profiteering from the Dot-Com Bubble, Subprime Crisis and Asian Financial Crisis. The Japanese Economic Review 67: 257–79. [CrossRef] McAleer, Michael, Chia-Lin Chang, and Wing-Keung Wong. 2017. Management information, decision sciences, and financial economics: A connection. Journal of Management Information and Decision Sciences 20: 1–33. McAleer, M., M.-U. Batmunkh, M. Moslehpour, and W.-K. Wong. 2018a. Confucius and Herding Behaviour in the Stock Markets in China and Taiwan. SSRN Electronic Journal. [CrossRef] McAleer, Michael, Chia-Lin Chang, and Wing-Keung Wong. 2018b. Big Data, Computational Science, Economics, Finance, Marketing, Management, and Psychology: Connections. Journal of Risk and Financial Management 11: 15. [CrossRef] McAleer, Michael, David E. Allen, and Abhay K. Singh. 2019. Daily market news sentiment and stock prices. Applied Economics 51: 3212–35. [CrossRef] McAleer, Michael, Kai-Yin Woo, and Wing-Keung Wong. 2020. Review on Efficiency and Anomalies in Stock Markets. Economies 8: 20. [CrossRef] Menkveld, Albert J. 2013. High frequency trading and the new market makers. Journal of Financial Markets 16: 712–40. [CrossRef] Menkveld, Albert J. 2014. High-Frequency Traders and Market Structure. Financial Review 49: 333–44. [CrossRef] Menkveld, Albert J. 2016. The economics of high-frequency trading: Taking stock. Annual Review of Financial Economics 8: 1–24. [CrossRef] Menkveld, Albert J., Bart Zhou Yueshen, and Haoxiang Zhu. 2017. Shades of darkness: A pecking order of trading venues. Journal of Financial Economics 124: 503–34. [CrossRef] Mishra, Suchismita, Vinh Huy Nguyen, and Le Zhao. 2021. Trading Venue Preference: Critical Role of Institutional Ownership. Miami: Florida International University, Unpublished manuscript. Neal, Robert. 1992. A comparison of transaction costs between competitive market maker and specialist market structures. Journal of Business 65: 317–34. [CrossRef] Nguyen, Van T., Bonnie F. Van Ness, and Robert A. Van Ness. 2005. Archipelago’s move towards exchange status: An analysis of Archipelago trading in NYSE and NASDAQ stocks. Journal of Economics and Business 57: 541–54. [CrossRef] Nguyen, Vanthuan, Bonnie F. Van Ness, and Robert R. Van Ness. 2007. Inter-market competition for exchange traded funds. Journal of Economics and Finance 31: 251–67. [CrossRef] Nimalendran, Mahendrarajah, and Sugata Ray. 2014. Informational linkages between dark and lit trading venues. Journal of Financial Markets 17: 230–61. [CrossRef] O’Hara, Maureen. 2004. Searching for a new center: US securities markets in transition. Economic Review 89: 37–52. O’Hara, Maureen. 2015. High frequency market microstructure. Journal of Financial Economics 116: 257–70. [CrossRef] O’Hara, Maureen, and Mao Ye. 2011. Is market fragmentation harming market quality? Journal of Financial Economics 100: 459–74. [CrossRef] Pagano, Marco, and Ailsa Röell. 1996. Transparency and liquidity: A comparison of auction and dealer markets with informed trading. The Journal of Finance 51: 579–611. [CrossRef] Pagnotta, Emiliano S., and Thomas Philippon. 2018. Competing on Speed. Econometrica 86: 1067–115. [CrossRef] Parlour, Christine A., and Uday Rajan. 2003. Payment for order flow. Journal of Financial Economics 68: 379–411. [CrossRef] Parlour, Christine A., and Duane J. Seppi. 2003. Liquidity-Based Competition for Order Flow. Review of Financial Studies 16: 301–43. [CrossRef] Patel, Jayendu, Richard Zeckhauser, and Darryll Hendricks. 1991. The Rationality Struggle: Illustrations from Financial Markets. The American Economic Review 81: 232–36. Peterson, Mark A., and Erik R. Sirri. 2003. Order Preferencing and Market Quality on U.S. Equity Exchanges. Review of Financial Studies 16: 385–415. [CrossRef] Ready, Mark. 2014. Determinants of Volume in Dark Pool Crossing Networks. Unpublished working paper. University of WisconsinMadison. Available online: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1361234 (accessed on 4 December 2020). Rhee, S. Ghon, and Ning Tang. 2013. Can quote competition reduce preferenced trading? A reexamination of the SEC’s 1997 order handling rules. Accounting & Finance 53: 243–64. [CrossRef] Röell, Ailsa. 1990. Dual-capacity trading and the quality of the market. Journal of Financial Intermediation 1: 105–24. [CrossRef] Ro¸su, Ioanid. 2019. Fast and slow informed trading. Journal of Financial Markets 43: 1–30. [CrossRef] J. Risk Financial Manag. 2021,14, 556 32 of 32 SEC. 2018. Assessment of The Plan To Implement A Tick Size Pilot Program. US Securities and Exchange Commission. Available online: https://www.sec.gov/files/TICK%20PILOT%20ASSESSMENT%20FINAL%20Aug%202.pdf (accessed on 4 December 2020). SEC. 2021. Fast Answer: National Securities Exchanges. US Securities and Exchange Commission. Available online: https://www.sec. gov/fast-answers/divisionsmarketregmrexchangesshtml.html (accessed on 1 September 2021). Shkilko, Andriy, and Konstantin Sokolov. 2020. Every Cloud Has a Silver Lining: Fast Trading, Microwave Connectivity, and Trading Costs. The Journal of Finance 75: 2899–927. [CrossRef] Shleifer, Andrei, and Lawrence H. Summers. 1990. The Noise Trader Approach to Finance. Journal of Economic Perspectives 4: 19–33. [CrossRef] Spatt, Chester. 2018. The new realities of market structure and liquidity: Where have we been? Where are we going? In Public Policy & Financial Economics: Essays in Honor of Professor George G Kaufman for His Lifelong Contributions to the Profession. Singapore: World Scientific Publishing Co., pp. 247–63. Tang, Ning, Andriy Shkilko, and Gregory Stone. 2011. Quote Competitiveness, 100-share Quotes, and Decimalization. Financial Review 46: 89–101. [CrossRef] Thomas, Jacob, Frank Zhang, and Wei Zhu. 2021. Dark Trading and Post-Earnings-Announcement Drift. Management Science. [CrossRef] Üslü, Semih. 2019. Pricing and Liquidity in Decentralized Asset Markets. Econometrica 87: 2079–140. [CrossRef] Van Kervel, Vincent. 2015. Competition for Order Flow with Fast and Slow Traders. The Review of Financial Studies 28: 2094–127. [CrossRef] Vayanos, Dimitri. 1999. Strategic Trading and Welfare in a Dynamic Market. Review of Economic Studies 66: 219–54. [CrossRef] Venkataraman, Kumar. 2001. Automated Versus Floor Trading: An Analysis of Execution Costs on the Paris and New York Exchanges. The Journal of Finance 56: 1445–85. [CrossRef] Vuorenmaa, Tommi. 2014. Lit and Dark Liquidity with Lost Time Data: Interlinked Trading Venues Around the Global Financial Crisis. New York: Springer. [CrossRef] Wermers, Russ. 1999. Mutual fund herding and the impact on stock prices. The Journal of Finance 54: 581–622. [CrossRef] Weston, James P. 2000. Competition on the Nasdaq and the impact of recent market reforms. The Journal of Finance 55: 2565–98. [CrossRef] Wittwer, Milena. 2021. Connecting Disconnected Financial Markets? American Economic Journal: Microeconomics 13: 252–82. [CrossRef] Ye, Mao. 2011. A Glimpse into the Dark: Price Formation, Transaction Cost and Market Share of the Crossing Network (9 June 2011). Available online: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1521494 (accessed on 1 September 2021). Ye, Mao, and Chen Yao. 2014. Tick Size Constraints, Market Structure, and Liquidity. WBS Finance Group Research Paper No. 212. Available online: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2359000 (accessed on 1 September 2021). Ye, Mao, and Wei Zhu. 2020. Strategic Informed Trading and Dark Pools. Available online: https://ssrn.com/abstract=3292516 (accessed on 1 September 2021). Yin, Xiangkang. 2005. A comparison of centralized and fragmented markets with costly search. The Journal of Finance 60: 1567–90. [CrossRef] Zaharudin, Khairul Zharif, Martin R. Young, and Wei-Huei Hsu. 2021. High-frequency trading: Definition, implications, and controversies. Journal of Economic Surveys. [CrossRef] Zhu, Haoxiang. 2014. Do Dark Pools Harm Price Discovery? The Review of Financial Studies 27: 747–89. [CrossRef]