One Size Fits All? High Frequency Trading, Tick Size Changes and the Implications for Exchanges: Market Quality and Market Structure Considerations

This paper offers a systematic review of the empirical literature on the implications of tick size changes for exchanges. Our focus is twofold: first, we are concerned with the market quality implications of a change in the minimum tick size. Second, we are interested in the implications of changes in the minimum tick size on market structure. We show that there is a large body of empirical literature that documents a decrease in transaction costs following a decrease in the minimum tick size. However, even though market liquidity increases, the incentive to provide market making activities decreases. We document a strong link between the minimum tick size regulations and the recent increase in High Frequency Trading (HFT) activity. A smaller tick enhances the price discovery process. However, the question of how multiple tick size regimes affect market liquidity in a fragmented market remains to be answered. Finally, we identify topics for future research; we discuss the empirical literature on the Minimum Trading Unit (MTU) and the recent calls for a minimum resting time for quotes.


Introduction
In many respects, and until recently, changes on the minimum tick size regulations appeared to have been fuelling the race to the bottom for transaction costs. This was primarily the case in the US markets since 2001that is, since the adoption of decimal pricing that slashed costs in terms of a reduction in bid-ask spreads. In this literature review, we critically discuss the implications of changes in tick size regulations on market quality and market structure.
Our focus is twofold: First, we are concerned with the market quality implications of a change in the minimum tick size. In particular, we present the empirical literature concerned with the effect of minimum tick size regulations on trading costs and liquidity. The vast majority of the empirical literature has documented a decrease in spreads and an increase in liquidity following a tick size reduction. However, one stream of the literature is also concerned with the effect of this reduction to quoted depth and the ability of the market to absorb large trades. In addition, we document the strong link between the minimum tick size regulations and the recent increase in High Frequency Trading (HFT). As it will be noted, a small minimum tick size allows high frequency traders (HFTRs) to implement their strategies, whilst a larger relative tick size leads to larger profit by HFTRs due to increased trading activity. Finally, we discuss the implication of the minimum tick size on market volatility.
Second, we are interested in the implications of changes in the minimum tick size on market structure, i.e., the effects of the minimum tick size regulation in different market settings. To this end, we are concerned with the effect of tick size changes on the price discovery process, market making and market quality indicators. As we will discuss in the following sections, the decrease in tick sizes has enhanced the price discovery process but has de-incentivised market makers to provide liquidity. The latter has triggered the recent pilot study by the Securities and Exchange Commission (SEC) to increase the tick size for a sample of less liquid stocks. We subsequently focus on the implications of a change in tick size on market design and also on the interaction between market players, especially between retail and institutional investors.
To an extent, our motivation for this review stems from the SEC's recent introduction of a pilot study for certain small capitalization stocks traded on the NYSE for which the minimum tick size would be increased (see SEC, 2014a). 1 We are therefore in the midst of a potential change in policy in the US stock exchanges that may reverse the changes implemented since 2001. However, in our view, a second recent proposal that is related to the minimum tick size regulationsand is an obvious area for future researchis the suggested changes to the minimum resting time which asks and bids would be required to have on the limit order book. These proposed changes are mostly associated with the implementation of MiFiD II in Europe's financial markets and have, as their primary goal, the curling of HFT in Europe (see Stafford and Barker 2014).
In this literature review, our focus is more on the impact of the minimum tick size regulations on market structure and market quality than on the effect of minimum tick size changes on trading activity and transaction costs. Why the choice to focus on market structure and market quality? The literature is overwhelmingly positive on the effect of decimalisation and the general decrease in tick sizes on transaction costs. However, the problem with a small tick size is that, while the results of low transaction costs are felt by market participants at an absolute level (ie market participants receive smaller transaction costs), the same also applies for market quality. That is, transaction costs have reached a point that may be harmful for the welfare of the exchange. One example of the above is the increased need from the exchanges to provide a constant flow of liquidity in a stable environment; however, the lower the transaction costs, the smaller the incentive of market makers to support the exchange on that task. Therefore, our paper is different from previous studies on the effect of decimalization on trading costs as our goal is to synthesize the literature with market structure and market quality in mind. Thus, we are very keen to offer a perspective to academics, policy regulators and market participants on where the current and future research in this area may develop.
The review is structured as follows: Section 2 gives a general outline of the surveyed papers and discusses our methodological approach to this literature review. Section 3 discusses in detail the 1 See also Weild, Kim and Newport (2012). empirical literature, and Section 4 discusses related research on the minimum trade unit. Section 5 concludes the review but, crucially, it also discusses opportunities for future research.
2. An outline of the surveyed papers and structure of this literature review 2.1. An outline of the surveyed papers The majority of papers concerned with the minimum tick size focus on minimum tick size changes and, in particular, on the implementation of decimal pricing in the US exchanges in April 2001.
Methodologically most studies investigate the effect of tick size changes after controlling for certain stock and exchange characteristics (see Ahn, Can, Chan and Hamao 2007, Bacidore 1997, Chakravarty, Van Ness and Van Ness 2005. In particular, studies rely on one of the following sets of samples: 1. Longitudinal studies, that is, studies which report statistics before and after a tick size change on the same set of assets (see Gibson, Singh and Yerramilli 2003, Goldstein and Kavajecz 2000, Jiang, Kim and Wood 2009. This set of studies benefits from studying the same set of assets, however there is also a risk associated with comparing assets in different sample periods. 2. Cross-sectional studies, that is studies that compare assets that are affected by a minimum tick size change with assets for which the tick size is unchanged. and trade in either the same exchange (see Van Ness 2004, Griffiths, Smith, Turnbull andWhite 1998) or in a separate exchange (Bessembinder 2003, Chung, Charoenwong and Ding 2004, Jiang et al. 2009). The latter set of papers relies on a set of matching methods to produce a set of assets that are comparable across the two exchanges.
3. A third set of studies relies on assets that are cross-listed, that is assets that are trading on more than one exchange where the change affects trading in only one of the exchanges (see Lin, Michayluk, Oppenheimer andSabherwal 2009, Oppenheimer andSabherwal 2003). This is also related to a more recent set of studies concerned with the association of the minimum tick size regulations and the incidence of HFT, in addition to the interaction of market systems (see Bartlett and McCrary 2013, Mahmoodzadeh and Gencay 2014, O'Hara, Yao and Ye 2014. Most studies rely on trade and quote (TAQ) data in order to produce reliable estimators of bid-ask spreads, an indicator of liquidity and trading costs (see Coughenour andHarris 2004, Schultz 2000).
Nevertheless, a smaller set of published papers use daily data (see Al-Yahyaee 2013, Chung, Kim andKitsabunnarat 2005) and a second subset of studies use full limit order book data (see Pan, Song and Tao 2012). The majority of published papers use NYSE and NASDAQ TAQ data (see Chou and Chung 2006, Jones and Lipson 2001, Johnson, Van Ness and Van Ness 2014, O'Hara et al. 2014, and some more recent studies use the National Best Bid and Offer (NBBO) US data. There are also variations in the sample time period. A number of studies attempt to predict the effect of the (then) proposed implementation of decimal pricing on market structure and market quality (see Harris 1991 and1994), whereas most studies are concerned with the ex-post realization of a decrease in the minimum tick size (see Chan and Hwang 2002, Chung, Van Ness and Van Ness 2002, Zhao and Chung 2006. Finally, the most common financial instrument used is common stocks (see , Gerace, Smark and Freestone 2012, Hagströmer and Nordén 2013, but more recent papers which focus on HFT also rely on foreign exchange data (see Mahmoodzadeh and Gencay 2014). A limited number of published papers use mutual fund data (see Bollen and Busse 2006) or data from derivatives exchanges (see ap Gwilym, McManus and Thomas 2005, Stone 2009and Chueh 2000.

Structure of the literature review
An obvious way to present the papers in this literature review is in a chronological order. To an extent, this is a logical approach but one which is largely ineffective: conveying the effect of tick size changes on exchanges becomes increasingly difficult unless the focus is on the main feature of exchanges. To this end, for the purposes of this literature review, we classify research as falling in the following categories with respect to the implications of their findings in market quality and market structure: 1. Market quality: we rely on the definition of market quality used by the London Stock Exchange to discuss the effect of minimum tick size changes on market quality indicators. 2 In this respect, market quality is represented by liquidity, transaction costs and volatility. To this end, our discussion focuses on each one of these market characteristics interchangeably. In addition, we look at two aspects of market quality that are crucial in the implementation of an optimal tick size.
The first relates to execution speed, and refers to HFT. The literature makes a special case on the effect of minimum tick size changes on the success of HFT. The second aspect refers to the effect of the minimum tick size changes on market making. The literature generated by the exchanges is very critical regarding the dire consequences which slashing the minimum tick size has on the ability of market makers to continue supporting the illiquid stocks and Initial Public Offerings (IPOs).
2. Market structure: Crucially, the implementation of the minimum tick size in different market settings determines the success of the regulatory policy of tick size changes. We therefore focus on the way different markets have adjusted to the minimum tick size (the markets) and also the way in which different market participants are affected by the changes (the players). To this end, we also discuss how the minimum tick size changes have altered the interaction between a limit order-book market and dark pools. An important feature of market structure is the facilitation of the price discovery process and in this literature review, we review the papers that show the relationship between the minimum tick size regulations and the price discovery process.
Rather than discussing the papers in detail, we summarize them in separate tables according to their main implications for market structure and market quality. That is, whilst there are obviously some papers whose main findings relate to two or more topics, we focus on the consequences of the findings for our main themes of the literature review. Focusing on market structure and market quality meant dropping a small number of papers that make little or no contribution in these two areas. Our hope is that readers of this literature review will be able to formulate a good understanding of the tick size regulations and the effect of tick size changes on the microstructure of financial markets which will inform their future research.
3. Detailed review of the literature on minimum tick changes 3.1. Effect of tick size changes on market quality indicators 3.1.1. Tick size changes and trading costs In Table 1, we present the first set of studies which focus on the implications for trading costs of a minimum tick change. In Panel A, we present the set of studies focussing on a minimum tick size decrease and in Panel B, we focus on studies that discuss the implications for trading costs of a large minimum tick size. In each panel, references are grouped by sample, and then in ascending order by end date of the used sample. This is done in order to group together studies that have focused on the same market, and to identify within that group any trends emerging over time. *** insert Table 1 around here*** This set of studies focuses mainly on the US decimalization, so the bulk of work is conducted with TAQ data relating to US exchanges. In Panel A, the main findings overall support the hypothesis that a smaller tick size leads to narrower bid-ask spreads. The paper by Harris (1991) originally established that a large tick size may act as a binding constraint for the lower-priced stocks, hence what is important is not only the nominal value of the tick size but also its relative value, namely the value of the tick size in relation to the stock price: the greater the stock price, the less binding is the tick size. Kurov and Zabotina (2005) show that the minimum tick size may act as a binding constraint for the very liquid contracts, however, Bollen and Whaley (1998) and Hsieh, Chuang and Lin (2008) show that whilst spread costs fall following a reduction in tick size, market depth also falls which may increase trading costs for larger trades overall.
In Table 1, Panel B, we present the studies that are concerned with the impact of an artificially large tick size on trading costs. The empirical literature around this subject is relatively limited but one important issue arises: the tendency of investors to use a smaller set of prices which effectively increases the minimum tick size. Studies in this area clearly show that there is a strong positive relationship between execution costs and price clustering (Bessembinder 1997). Ikenberry and Weston (2008) show that this artificially large minimum tick is a product of a fundamental human bias for the more prominent numbers.
In terms of the implications for market structure and in particular with regard to trading costs, the evidence suggests that a decrease (increase) in tick size leads to a decrease (increase) in trading costs, especially for the low-priced shares ( Van Ness, Van Ness and Pruitt 2000). However, negotiation costs also increase as the minimum tick increases. Finally, if the use of a tick size has an embedded human bias, then the evidence suggests that a tick size decrease may not have the desired effect since traders would still continue to use the artificially large tick size.

Tick size changes and market liquidity
In Table 2, we consider the studies that focus on the implications of change in tick size on asset liquidity. From a methodological perspective, there is an overlap in the methods employed for the studies included in Table 1 and in Table 2 as for both sets of studies the bid-ask spread is the main variable of interest. The classification as to whether a study is more relevant to trading costs or liquidity is based on self-selection, namely we allow the study itself to identify its main contribution to the literature. Also, for reasons of clarity, we avoid double-entries across the two tables. *** insert Table 2 around here*** Studies that investigate the effect of a tick size change on liquidity are conducted across a range of markets and instruments, and over a relatively long time-span. As anticipated, most studies report that a decrease in tick size has positive implications for liquidity. In particular, decreasing the tick size almost always increases liquidity for the more heavily-traded stocks (Hameed andTerry 1998 andAnderson andPeng 2014) and for stocks with a larger relative tick size (Aitken and Comerton-Forde 2005). Ahn, Cao and Choe (1996) show that the decrease in tick size has no impact on the liquidity of infrequently traded stocks. Further, a number of studies show that a smaller tick size leads to an increase in negotiation costs which might, to an extent, mitigate the benefits of an increased liquidity (see Hameed and Terry 1998).
The majority of studies in Table 2 show that both spreads and depths at the best quote decline following a tick size decrease. In relation to the latter, ap Gwilym et al. (2005) show that the benefit of a smaller monetary spread outweighs the reduction in quoted depth. Also, traders who tend to trade on the best bid and ask experience an increase in liquidity, yet the opposite effect may be experienced by larger traders (Chung et al. 2005 andHo 2008). Verousis, ap Gwilym and Voukelatos (2015) show that the ability of the options market to absorb large trades diminishes following a tick size reduction. The latter observation reflects the fact that larger traders may exhaust the depth at the best ask and bid, but only a limited number of studies focus on the effect of tick size changes on asset depth beyond the first level of the limit order book (see Table 2 below). Evidently, this is a shortcoming in the literature to date, which is somewhat mitigated by the use of effective spreads as a hybrid measure of liquidity.

Tick size changes and effects on market making
What is of particular interest to changes in the minimum tick size and market structure is the relationship between the former, and market making activities. The professional literature clearly identifies the decrease in the minimum tick size as one of the main reasons why market making has become unprofitable with wider consequences regarding ability to support illiquid stocks and Initial Price Offerings (IPOs). In Table 3, we present the studies that relate the change in the minimum tick size with market making. *** insert Table 3 around here*** Theoretically, Bernhardt and Hughson (1996) show that discretenessthe existence of the minimum tick sizelimits competition, whilst also permitting market makers to offer profitable quotes. The question is therefore, do minimum tick size changes make market making more profitable? Table 3a shows the studies that investigate the implications for market making when there is a decrease in the minimum tick size. Studies in this area show that a decrease in tick size leads to a decrease in market making profits. In particular, Stone (2009) shows that a narrower bid-ask spread redistributes profits from market makers to investors. Bessembinder (2003) also noted that reducing the minimum tick size on NASDAQ equates execution costs of the dealer market with a limit order book market, without having an adverse effect on liquidity supply. A number of interesting patterns in market structure do arise though: in dealer markets, the mechanism through which a reduction in the tick size leads to an increase in spreads is via a decrease in liquidity providers' profits (He andWu 2005 andBacidore 1997). That reduction in profits reduces the incentive of market makers to provide accurate information, therefore the adverse selection component of the spread decreases (Bacidore 2001) whilst also making it easier for market makers to manage their inventories (Chung and Van Ness 2001). Furthermore, market makers are still able to provide liquidity although the incentive to do so is greatly reduced (Stone 2009 andMacKinnon andNemiroff 2004). A crucial finding for market structure is that, for low-volume stocks, the existence of specialists leads to a reduction in trading costs whereas for large stocks, competition amongst dealers proves more beneficial for the market (Chung, Van Ness and Van Ness 2004). Interestingly, in a recent study, Charoenwong, Ding and Thong (2016) show that decimalisation has not affected the flipping strategy of institutions for cold IPOs. However, institutions are found to flip more hot-IPOs post-decimalisation due to the lower cost of flipping for IPOs that have substantial price increases in aftermarket trading.
In Table 3, Panel B, we present the studies that have focused on the implications which increasing the minimum tick size has on market making. Studies in this area have shown that increasing the tick size (i) leads to an increase in market making profits and hence to an increase in liquidity supply by the latter (Bollen, Smith and Whaley 2003) and Anshuman and Kalay 1998) and (ii) helps market makers to recover fixed costs. At the same time, Angel (1997) shows that in a large tick regime, investors are able to supply liquidity by placing limit orders. In Table 3, Panel C, we conclude this section by presenting the studies concerned with the general implications of a minimum tick on market making activities. Ball and Chordia (2001) show empirically that, with the existence of a minimum tick, prices and spreads do not correspond to the equilibrium prices which would exist without a minimum tick size. Crucially, all studies in this field indicate that pricing and competition on exchanges largely depend on the regulations governing the minimum tick size. Chordia and Subrahmanyam (1995) demonstrate that the existence of a finite minimum tick leads naturally to a curtailing of competition via the payment-for-order-flow practices. More importantly, Christie and Schultz (1994) show that the minimum tick may artificially arise due to market maker collusion, and both Bourghelle and Declerck (2004) and Chordia and Subrahmanyam (1995) show that a change in the tick size alters the level of transparency in liquidity supply. Table 3, Panel D, we present the two studies that discuss the implications of a tick size change on broker activities. Crucially, stock splits increase the relative tick size which, as explained above, leads to an increase in market making profits. As a consequence, brokers may have a greater incentive to promote a stock that has seen an increase in its relative tick size because they may capture some of the additional benefit generated by market makers. 3 Whilst there are only two empirical studies in this field, they both show that an increase in the relative tick size supports the broker promotion hypothesis. Importantly, Chou, Lee and Chen (2005) show that abnormal ex-split day returns decrease and abnormal ex-split trading volume increases post-decimalisation which confirms the hypothesis that arbitrageurs engage in more trading activities as transaction costs are reduced.

Tick size changes, execution speed and HFT
Until recently, a largely overlooked component of liquidity was execution speed. In this respect, there are only a handful of earlier studies that investigate the implications for execution speed of a change in the minimum tick size (see Coughenour and Harris 2004). However, this field is now clearly a future area of research as execution speed is the cornerstone of HFT. In Table 4, we present the studies that investigate the implications of a change in the minimum tick size for the occurrence and profitability of HFT strategies. In Table 4, Panel A, we discuss the studies which relate HFT to a small tick size, and in Panel B we refer to studies which relate HFT to a large relative tick size. *** insert Table 4 around here*** In Table 4, Panel A, all studies uniformly agree that a reduction in the minimum tick size leads to an increase in HFT. Mahmoodzadeh and Gencay (2014) show that HFT profitability increases as a smaller tick affords HFTRs the opportunity to front-run individual (manual) traders by implementing sub-penny strategies. A direct implication of the latter is an increase in spreads for the manual traders and a decrease in spreads for the HFTRs. Coughenour and Harris (2004) show that front-running is easier for low-priced stocks and Uno and Shibata (2011) show that the decrease in spreads is also accompanied by an increase in adverse selection costs. So, crucially, the speed of quote adjustment substantially increases after a minimum tick size decrease (Chung, Chuwonganant and Jiang 2008).
As we will discuss in Section 5.2, the suggested minimum resting time regulations target the speed of quote adjustment with an intention to limit HFT. A further area of interest originates from the interaction of HFT with alternative trading systems (or dark pools). To this end, Bartlett III and McCrary (2013) and O'Hara, Saar and Zhong (2015) show that there is often a trade-off between HFT and trading in alternative venues: reducing the tick size leads to an increase in HFT (that is, an increase in displayed liquidity) and a decrease in trading in alternative trading systems (that is, a decrease in un-displayed liquidity). The authors further argue that the recent proposal to increase the minimum tick size for small capitalization stocks may potentially harm organized exchanges and HFT and shift trading to alternative trading systems. In Table 4, Panel B, we show the studies that discuss the implications of a large tick size for HFT and market structure. All studies show that a large relative tick size attracts more HFTRs, thus increasing the latter's liquidity provision. Hagströmer and Nordén (2013) demonstrate that the share of trading activity attributed to HFT strategies increases with the minimum tick size. O' Hara et al. (2013) show that, in contrast to the recent SEC proposals, in today's "high frequency" markets, there is little evidence that stocks with a higher relative tick size (a large tick size relative to the stock price) have greater liquidity. Equally, Yao and Ye (2015) show that a large relative tick size decreases liquidity but increases HFT liquidity provision. From a market microstructure perspective, the latter result has wide implications: increasing the tick size in order to enhance liquidity for the least-active stocks may attract more liquidity supply from HFTRs but the authors find no evidence that it will attract more trading volume. Clearly, this area is under-researched and future research will show how liquidity provision works in both this and alternative market settings.

Tick size changes and volatility
This last sub-section on market quality indicators investigates the effect of a change in tick size on volatility. In Table 5, we present the studies that show the reaction to volatility of a change in the minimum tick size or equivalently the level of price discreteness. Most studies confirm that a large tick size has a negative impact on volatility. Hau (2006) shows that a larger tick size increases the costs of speculation 4 and overall stock return volatility. Ke, Jiang and Huang (2004) show that the tick size is more binding on volatility in the middle of the trading day and Jiang et al. (2009) show that the effect of tick size on volatility is more pronounced on dealer markets rather than on limit order markets. Münnix, Schäfer and Guhr (2010) demonstrate the minimum tick size has a wider impact on the microstructure of financial returns. Crucially, the tick size can alter the tail behaviour of the return distribution; a larger tick size can lead to heavier tails. In relation to the latter and the effect of a minimum tick size on price diffusion, La Spada, Farmer and Lillo (2011) show that a decrease in tick size leads to more volatility clustering, or equivalently to a higher return autocorrelation. 5 3.2. Effect of tick size changes on market structure 3.2.1. Effect of tick size changes on market design

Tick size changes' effects on market design
In this section, we survey the studies that investigate the implications of a tick size change on market design. We sort studies first by sample, and then in ascending order by end date of the used sample.
As expected, several studies present results that may be classified to more than one sub-section but we avoid any overlap by focusing on the main implications for market structure and market quality. In Table 6, the main focus is on how the implementation of the minimum tick size rules affects trading across different trading mechanisms. *** insert Table 6 around here*** Clearly the majority of work on market design involves a comparison of NASDAQ with NYSE, thus most studies concentrate on the comparison of samples between the two exchanges. Nevertheless, the study by Huang and Stoll (2001) concentrates on the differences between NYSE, an auction market, and LSE, a dealer market. The authors argue that microstructure characteristics, such as the tick size, are endogenous to market structure; that is the difference between an auction and a dealer market.
Empirically, the findings of Huang and Stoll (2001) are confirmed by Chung and Chuwonganant (2002) who show that execution costs are lower in auction markets than they are in dealer markets.
Theoretically, for a dealer market, Kadan (2006) shows that the welfare of investors is a function of the number of dealers in the market; if the number of dealers in the market is large, investors will prefer a small tick size. The latter result is in contrast to the policy of reducing the tick size across all contracts because if the number of dealers in a stock is small, then setting a large tick size may benefit investors.
The studies that investigate the effect of tick size changes on the NYSE show that a decrease in tick size leads to a reduction in spreads and depths at the best quote. Bacidore, Battalio and Jennings (2003) argue that a smaller tick leads to less displayed liquidity on the order book, but that that has no effect on execution quality. Goldstein, Shkilko, Van Ness and Van Ness (2010) show that decimalisation increases quote competition between exchanges. Chan and Hwang (2002) argue that market quality increases on a limit order book market after the tick size decrease. However, regarding dealer markets, Bessembinder (2000) argues that the relationship between tick size and market quality is relatively more complex than is hypothesized. In relation to the latter, Chakravarty et al. (2004) and Chung and Chuwonganant (2002) show that the smaller tick increases price competition on the limit order book, hence reducing price rigidity, and Zhao and Chung (2006) show that a smaller tick increases the informational efficiency of prices. The latter is clearly related to price discovery studies which will be discussed in Section 3.2.2. With regard to the implications of a tick size change to market structure, Alexander and Peterson (2002) show that a small tick is in contrast with the objectives of the Uptick Rule. 6 In addition, a smaller tick size encourages front-running in the limit order book (Ronen andWeaver 2001 andPortniaguina, Bernhardt andHughson 2006). Finally, Biais, Bisiere, and Spatt (2010) show the effect of the tick size change on market structure through the change in competition between Island and Nasdaq. In particular, their study shows that Island traders undercut competition with Nasdaq traders by taking advantage of a finer tick size and spreads decreased further in Island after the reduction in the tick size for Nasdaq stocks.

Effect of tick size changes on institutional vs. retail traders
In Table 7, we present the set of studies that discuss the implications of a minimum tick size change both for institutional traders and for retail traders. One difficulty with this type of study is the *** insert Table 7 around here*** Clearly, the most significant finding of this literature is that a reduction in tick size does not have a uniform effect across all trader types. On a limit order market such as the Hong Kong Stock Exchange or the NYSE, reducing the tick size leads to a deterioration in market depth and hence a decrease in liquidity for the larger institutions (Pan et al. 2012 andKavajecz 2000). In relation to the latter, Lin et al. (2009) show that if an exchange facing competition from a another exchange reduces its tick size then institutional order flow may potentially migrate to the competing exchange. Oppenheimer and Sabherwal (2003) and Chakravarty, Van Ness and Van Ness (2005) report that retail traders appear to be trading more frequently with a smaller tick size. 7 Conversely, institutional traders trade less frequently and also fragment their orders at a lesser rate (less stealth trading) which in turn decreases adverse selecting costs for large and medium sized trades. Jones and Lipson (2001) show that the move to a smaller tick size increases execution costs for institutional investors.
However, Chakravarty, Panchapagesan and Wood (2005) document thatwhilst in general the finding of Jones and Lipson (2001) is correctfor the institutional investors who work their orders over multiple days, trading costs declined. Finally, Bollen and Busse (2006) document an increase in trading costs for large orders originating from pension funds, mutual funds and hedge funds, hence confirming the finding that institutional investors may be damaged by a move to a finer price grid.

Tick size changes and dark pool trading
There are a limited (but increasing) number of studies that investigate the implications for market structure in a trading environment that is characterized by market fragmentation. In particular, the element of interest here is the provision of liquidity when an exchange competes with an alternative trading system, such as a dark pool on which there is no regulated minimum tick size. From a theoretical perspective, Buti, Rindi, Wen and Werner (2013) investigate how the tick size affects liquid and less liquid stocks on the limit order book. The authors show that reducing the tick size may have detrimental effects on less liquid stocks which disappear if the limit order book faces competition from alternative trading systems. Crucially, these results tend to support SEC's proposed plans to increase the tick size for the less liquid stocks. These results are confirmed empirically in Werner, Wen, Rindi, Consonni and Buti (2015). It is worth mentioning that these results complement the findings of Bartlett andMcCrary (2013) andO'Hara et al. (2013), discussed in Section 3.1.3. In particular, the findings of the latter show how HFTRs are responsible for the shift in liquidity from a dark pool to the limit order book because they increase the supply of liquidity following a tick size decrease. However, the question of how multiple tick size regimes affect market liquidity in a fragmented market remains to be answered.

Effect of tick size changes on the price discovery process
In this section, we present the studies that investigate the effects of changes in the tick size on the price discovery process. Studies in this area focus on the interaction of trading between the spot and derivatives contracts. We present the set of studies in Table 8. *** insert Table 8 around here*** The empirical literature agrees that a decrease in the minimum tick size enhances the price discovery process (Chen and Gau 2009;Beaulieu, Ebrahim andMorgan 2003 and. In particular, Beaulieu et al. (2003) and Chou and Chung (2006) also document an increased participation of funds in the price discovery process following a decrease in the minimum tick size. Booth and Yüksel (2006) confirm the above findings for the Istanbul Stock Exchange. Finally, Chen, Chou and Chung (2009) show that a small tick reduces the willingness of arbitrageurs to initiate arbitrage trades, a finding that is related to the profitability of investments in a small tick size regime and leads to a loss in pricing efficiency. Taiwan exchanges. Research on the MTU is scant but, as recent research has documented, the pervasiveness of HFT has shifted the interest to this field as HFTRs tend to trade on relatively small quantities. We therefore present the empirical papers in the field with the intention to inform the reader of a possible future topic for research. We present the studies on the MTU in Table 9, Panel B. *** insert Table 9 around here*** Amihud, Mendelson and Uno (1999) investigate the effect of voluntary reductions in the MTU at the Tokyo Stock Exchange; they find an increase both in liquidity and valuation associated with MTU reductions. Hauser and Lauterbach (2003) test the asset pricing effects of MTU changes at the Tel 8 In two related studies, Jacob and Ma (2004) and Graham, Michaely and Roberts (2003) investigate the effect of a tick size decrease on the ex-dividend day stock price behaviour, showing that the existence of a minimum tick is not responsible for the ex-dividend price behaviour, that is the empirical finding that prices drop by less than the dividend amount on the ex-dividend date (see also Bali and Hite, 1998  Exchange), where in 2002 the MTU was reduced to one share by the exchange; they find a substantial increase in liquidity and a concurrent decrease in adverse selection costs after the event.
Related to the research on the MTU, a handful of studies examine the effects and the sources of oddlot trading; these papers mostly focus on the US markets. Odd-lot trades are those trades which are executed at a size lower than the round lot, and they are subject to different handling and reporting rules than the round lot. A recent SEC Release (SEC 2014b) discusses odd lot trading in US markets and how it was affected by changes in reporting requirements. We present the set of empirical studies in this field in Table 9, Panel B. Wu (1972) provides an early study of odd-lot trading and its trend over time. Some papers use odd-lot trades as a proxy for individuals' transactions and investigate time of the week and of the year price anomalies (see Dyl andMaberly 1992, Lakonishok andMaberly 1990). After the advent of high frequency trading however, the assumption that odd-lots are mainly  Amihud et al. (1999) also document positive cumulative abnormal returns after both the announcement and the actual reduction in the MTU. Furthermore, they find that trading volume and liquidity, measured by the Amihud's illiquidity ratio, increase after the MTU changes. Amihud et al. (1999) argue that the value and liquidity effects are due to the increase in the investor base; specifically, if more investors hold the stock, information availability on the fundamental value increases, thereby increasing both liquidity and valuation. Hauser and Lauterbach (2003) examine a set of changesboth increases and decreases, decided by an exchange boardin the MTU at the Tel Aviv Stock Exchange between 1998 and 1999. After MTU increases they find a decrease in trading volume, which is used as a proxy for the investor base, a decrease in valuation and an increase in return volatility, which is used as a proxy of price noisiness; after MTU decreases, they document an increase in trading volume, an increase in valuation and an increase in return volatility. They also estimate a model relating stock returns around the MTU changes to changes in trading volume, which is used as a proxy of trading volume, and in return volatility; consistent with Merton's (1987) model, the coefficient of volume change is positive and the coefficient of volatility change is negative. The cross-sectional variation of the results reveals further interesting differences; in particular, extremely thin trading stocks lose value after an MTU reduction and drive the increase in price noisiness when considering the whole sample. Hauser and Lauterbach (2003) argue that an increase in investor base can be detrimental to value if the joining traders are predominantly noise traders or speculators.
In January 2002, the MTU was reduced to one share for the all the stocks listed on Borsa Italiana. Gozluklu et al. (2015) examine the effects of this natural experiment on market quality. They show that liquidity, measured by the bid-ask spread at the first five levels of the order book substantially decreases after the MTU reduction. Furthermore, they document a decrease in adverse selection costs, measured by the price impact of trades (Hendershott, Jones and Menkveld 2011) and by the adverse selection component of the spread (see Glosten and Harris 1988). On the other hand, informational efficiency measured using random walk tests and in the context of the Hasbrouck (1993) model, is not significantly affected by the microstructure change. Finally they show that retail trading activity, measured by following Barber, Odean and Zhu's (2009) approach and by the proportion of online trading, substantially increases. Gozluklu et al. (2015) compare their results to the predictions of a model with liquidity providers operating under asymmetric information. The model shows that when the MTU constraint is removed, those small liquidity traders that could not hedge their endowment shock in a regime with a MTU, can now perfectly hedge it and enter the market; the increased trading activity of these uninformed agents leads to a reduction in adverse selection costs, which determines a spread decrease.

Research on odd-lot trading
An early study by Wu (1972) 9 examines odd-lot trading between 1937 and 1967. One of the main findings is the steady decline in the proportion of odd-lot trading in the period considered. The paper also documents that odd-lot traders are predominantly net buyers and that they trade against the market. Wu (1972) argues that odd-lots are mostly traded by small investors who are not able to afford to trade on a round-lot basis.
Similarly, a group of studies use odd-lot trading as a proxy for individual investor trading and investigate its effect on market anomalies based on time of the week or time of the year. Lakonishok and Maberly (1990) find that odd-lot trading is higher on Mondays and that the increase in odd-lot trading is driven by sell transactions; they argue that this pattern might partly explain abnormally negative returns over the weekend, which represent a market anomaly often referred to as the "weekend effect". Dyl and Maberly (1992) examine the role of individual investors in the determination of the "January effect", i.e. the tendency of small stocks to earn higher returns in January; they find that the ratio of odd-lot sales to odd-lot purchases substantially decreases at the turn of the year, and that the decrease is highly significant in explaining turn or the year returns.

More recently, O'Hara et al. (2014) investigate the bias arising from the exclusion of odd-lots in TAQ
using data from 2008 and 2009. First, they document that a non-negligible amount of trades are oddlots. Importantly, they find that odd-lots are more likely to occur when trades are initiated by HFTRs; this indicates that in today's markets caution should be exercised when interpreting odd-lot trading as a proxy for individual investor trading. The authors report that 25% of price discovery is accounted for by odd-lot trades; this result suggests that analyses of market efficiency which ignore odd-lots are likely to be substantially biased. 10 Motivated by O'Hara et al. (2014), Johnson et al. (2014) examine the sources and the informativeness of odd-lot trading in a period between 2010 and 2011. In particular, they compare intentional odd-lot trades (the original order is submitted as an odd-lot) and circumstantial odd-lot trades (the original order is submitted for 100 or more shares and subsequently divided into multiple transactions, at least one of which is an odd lot). They first find that slightly more than half of all odd-lot transactions are circumstantial. Johnson et al. (2014) also document that intentional odd-lot trades contribute more to price discovery, calculated using the weighted price contribution, than circumstantial odd-lot trades; moreover, the contribution to price discovery increases when non-high frequency traders provide liquidity, or when high frequency traders transact with non-high frequency traders.

Some concluding remarks
The purpose of this literature review was to discuss the studies which investigate the effect of tick size changes on two main aspects of exchanges: market structure and market quality indicators. In this section, we conclude the literature review, discuss the implications of a possible introduction of a minimum resting time for quotes for exchanges, and discuss areas for future research. We have argued that the problem with a small tick size is that it has reached a level that may be potentially harmful to the welfare of exchanges. SEC's action to introduce a pilot plan for the most illiquid stocks trading at NYSE reflect the latter observationthere have been many calls since the US decimalization where small tick sizes are quoted as the main reason why market making has become unprofitable with wider consequences around the support of illiquid stocks and IPOs. With this observation in mind, we chose to synthesize the literature with respect to the effect of tick size changes on market structure and market quality.
Our focus is twofold: First, we are concerned with the market quality implications of a change in the minimum tick size. In particular, we present the empirical literature that is concerned with the effect of minimum tick size regulations on trading costs and liquidity. The vast majority of the empirical literature has documented a decrease in spreads and an increase in liquidity following a tick size reduction. However, a stream of the literature is also concerned with the effect of this reduction on quoted depth and the ability of the market to absorb large trades. Also, we document the strong link between the minimum tick size regulations and the recent increase in HFT. A small minimum tick size allows HFTRs to implement their strategies, whilst a larger relative tick size leads to larger profit by HFTRs due to increased trading activity.
Second, we are interested in the implications of changes in the minimum tick size on market structure.
To this end, we show that the decrease in tick sizes has enhanced the price discovery process but disincentivised market makers to provide liquidity. Also, the welfare of dealers and investors is a function of the number of dealers in the market; if the number of dealers in the market is large, investors will prefer a small tick size. Institutional investors are also adversely affected by a small tick size; reducing the tick size leads to a deterioration in market depth and hence a decrease in liquidity for the larger institutions. Thus, reducing the tick size may lead to the flight of institutional investor trading to smaller tick size trading venues, yet recent studies show that HFTRs are responsible for the shift in liquidity from a dark pool to the limit order book as they increase the supply of liquidity following the tick size decrease.
Finally, this literature review discussed the empirical literature related to minimum trade size regulations and odd-lot trading. Studies in the field show that reducing the MTU leads to an increase in investors' base which has a positive effect on information availability, thereby increasing both liquidity and valuation. With respect to odd-lot trading, a limited set of recent studies shows that in today's "high frequency markets", odd-lots' contribution to price discovery has increased substantially due to their use by HFTRs.

The debate on the minimum resting time
The minimum resting time indicates the minimum amount of time an order must stay in a limit order book to remain valid. A minimum resting time has often been advocated as a way to reduce systemic risk in markets where high frequency trading is widespread. Critics of this proposal argue that orders subject to a minimum resting time are exposed to higher risk and therefore introducing a minimum resting time would induce traders to widen the spreads. The debate on the minimum resting time was spurred by the "Flash Crash" of May 6, 2010, which is considered by many as partly due to high frequency traders. Recently, during the discussions for the MiFID revision in the European Parliament, one of the most controversial proposals was the introduction of a minimum resting time equal to 500 milliseconds. MiFID II does not include this proposed change. 11 Very little research investigates the effects of a minimum resting time for orders; specifically, we are aware only of two working papers, which use simulated markets and do not find conclusive evidence that market participants benefit from a minimum resting time. The first contribution is provided by Lee, Cheng and Koh (2011); they develop a market simulation where an asset is traded in multiple markets and in which market makers trade with three types of traders: random limit order submitters, trend following agents that apply similar strategies, and arbitrageurs. The design considered is a modification of Lee, Cheng and Koh (2010), who examine position limits as a way to stabilize markets. One of the main results is that patterns similar to the aforementioned flash crash are due to the domination of trading strategies that are responding in the same way to the same set of market variables. The findings of Lee et al. (2011) suggest that reducing the speed of order submission does not reduce the order imbalance which leads to flash crashes. Furthermore, Lee et al. (2011) argue that reducing the speed of order submission induces adjustments which may decrease liquidity. The problem is exacerbated in presence market fragmentation, where traders can move across different markets as a response to differences in speed regulation. The second study, by Brewer, Cvitanic and Plott (2014), examines call auctions, minimum resting time, and circuit breakers (the options considered after shutting the trading are: a one-time call auction, a series of temporary call markets, clear books, temporary suspension of trading for ten seconds without clearing the books) as mechanisms to reduce volatility caused by flash crashes and to facilitate recovery after a crash. They simulate a limit order market with buy and sell orders with random values arriving at random times. A flash crash is induced by introducing a very large order to the market. The three mechanisms tested help to limit volatility and aid the recovery of liquidity. The results show that call auctions are the most effective mechanism to limit the adverse effect of flash crashes. Brewer et al. (2014) caution that the results on minimum resting time are highly dependent on the conditions simulated; in particular, if quick cancellations of orders do not cause instabilities, the results may not hold.

Possible future research topics
In this review, we have identified several areas for future research. The decision of SEC to introduce a pilot study in the US is sufficient to generate a number of interesting studies in the area that will evaluate the outcomes of a "reverse decimalization" policy. It remains to be seen what the future policy will be on minimum tick size changes for illiquid stocks. Similarly, there is a gap in the empirical literature on the incentives of market makers to support IPOs. Future research in this field should identify the willingness of market makers to continue offering market making activities in a low-tick regime. The latter however should be studied in parallel with the presence of HFTRs.
In particular, this literature review clearly identified a shift in market making activities that are substituted by HFTRs. Given that HFTRs are more active in a small-tick size environment, future research needs to look in more detail how HFTRs interact with other investors in markets where the tick size is relatively large and in different market structures. A further area that is still underresearched is the effect of minimum tick sizes on the profitability of Smart Order Routing Systems The proposed implementation of a minimum resting time policy makes it clear that policymakers are concerned with the volume of HFT. However, as we have seen in this literature review, HFTRs have replaced market makers for the more liquid stocks. To date, there is no paper that addresses the issue of an optimal tick size in an environment in which retail investors interact with HFTRs. To conclude, it is our view that we are entering a new phase of policy that will have more idiosyncratic characteristics. With that, we believe that policy regulators are becoming more concerned with how certain policies affect certain areas of the market; future research on tick size changes will identify how market structure is clearly associated with each one of these market segments. The implementation and success of these changes remains to be seen, generating a wide scope for fruitful research in the area.
Finally, the literature on the effect of tick size changes and firm characteristics is relatively scarce. For example, Fang, Noe, and Tice (2009) show that changes in the tick size affect firm characteristics (tick size changes affects liquidity and price informativeness which eventually affects firm value) or Edmans, Fang, and Zur (2013) that suggest tick size changes affect governance. Future research needs to focus on the effect of tick size changes on the value of the firm, therefore linking the market microstructure literature with asset pricing and corporate governance studies. From a policy perspective, clearly regulators have been primarily concerned with the effect of tick size changes on the trading price of the firm. However, the above papers demonstrate that the decision to change the minimum tick size ultimately has an effect on firm valuation.  Given a decision to provide liquidity, an agent has an incentive to do so at smaller price increments (e.g., a smaller spread), but there is a greatly reduced incentive to provide liquidity in the first place.
Bacidore ( Provides an incentive for dealers to make markets and for investors to provide liquidity by placing limit orders Anshuman and Kalay (1998) The minimum tick causes time-varying bid-ask spreads, asymmetric commissions, and market breakdowns The minimum tick permits a competitive market maker to realize economic profits that help recoup fixed costs Gibson, Singh and Yerramilli (2003) NYSE (415) Dec00-Mar01 TAQ US Decimalisation led to a decrease in order-processing costs but not to adverse selection and inventory costs A large tick size allows market makers to enjoy spreads that are larger than their actual costs    Changes in the tick size can affect equilibrium spreads on a dealer market and the relation between tick size and market quality is more complex than the imposition of a constraint on minimum spread widths Biais, Bisiere, and Spatt (2010) NASDAQ & ISLAND (7 pairs) Mar00 & Jun01 NASDAQ Spreads fell for both markets after NASDAQ decimalization Competition among markets complements competition among traders Ronen and Weaver (2001) AMEX (324) Apr97-Jun97 TAQ Amex A reduction in the minimum tick decreases spreads and volatility but not depth Improves market quality but also encourages queuejumping in the order book Chung and Chuwonganant (2002) NYSE (2,223) May97-Jul97 TAQ US The minimum price variation is a binding constraint on absolute spreads even after the tick-size reduction, especially for low-price and/or large-volume stocks Reduces price rigidity and increases price competition  NASDAQ ( Lowers the incentive to offer liquidity and reduces the relative information content of the order book Portniaguina, Bernhardt and Hughson (2006) Simulation Simulation Simulation A smaller tick size facilitates the specialist's ability to step ahead of the limit order book, resulting in a reduction in the cumulative depth of the limit order book at prices above the minimum tick Leads to an increase in the specialist participation and specialist profit increases slightly for small market orders, and considerably for large market orders