Price Discovery Without Trading: Evidence From Limit Orders
THE JOURNAL OF FINANCE VOL. LXXIV, NO. 4 AUGUST 2019Price Discovery without Trading: Evidencefrom Limit OrdersJONATHAN BROGAARD, TERRENCE HENDERSHOTT, and RYAN RIORDAN ABSTRACTWe analyze the contribution to price discovery of market and limit orders by highfrequency traders (HFTs) and non-HFTs. While market orders have a larger individual price impact, limit orders are far more numerous. This results in price discoveryoccurring predominantly through limit orders. HFTs submit the bulk of limit ordersand these limit orders provide most of the price discovery. Submissions of limit orders and their contribution to price discovery fall with volatility due to changes inHFTs’ behavior. Consistent with adverse selection arising from faster reactions topublic information, HFTs’ informational advantage is partially explained by publicinformation.ACCORDING TO THE TRADITIONAL VIEW of price discovery, trades reveal investors’private information while market makers’ quotes reflect public information(see, e.g., Glosten and Milgrom, 1985; Kyle, 1985). Most stock exchanges andfinancial markets have evolved into limit order books where there are no designated market makers and limit orders represent the bulk of activity. Theoretical models of limit order books study informed traders’ choice betweenmarket orders and limit orders. The market/limit order choice of informed anduninformed investors determines the nature of price discovery and adverseselection. In this paper, we use regulatory data that enable the classificationof limit orders and trades by high-frequency traders (HFTs) and non-HFTsto systematically quantify the contribution to price discovery of market andlimit orders by HFTs and non-HFTs, primarily using a vector autoregression(VAR; Hasbrouck, 1991a, 1991b, 1995). We then link these results to theoreticalmodels of limit order books. Jonathan Brogaard is with David Eccles School of Business, University of Utah. TerrenceHendershott is with Haas School of Business, University of California – Berkeley. Ryan Riordanis with Smith School of Business, Queen’s University. The authors thank seminar participantsat the 2015 Cambridge Microstructure Theory and Application Workshop, Australia NationalUniversity, Baruch College, Boston College, Chinese University of Hong Kong, Goethe University,Hong Kong University, Stockholm Business School, UC Santa Cruz HFT Workshop, and Universityof Mannheim for helpful comments. The authors also thank Helen and Victoria asked not to bethanked IIROC for providing data and comments. All errors are our own. This research wassupported by the Social Sciences and Humanities Research Council of Canada and the NorwegianFinance Initiative. Hendershott has provided expert witness testimony in a variety of matters,including an ongoing market manipulation case.DOI: 10.1111/jofi.127691621
1622The Journal of Finance RThe role of HFTs in adversely selecting non-HFTs is widely debated by academics, regulators, and investors, with concerns often focusing on HFTs usingmarket orders to “pick off” stale limit orders (Biais, Foucault, and Moinas,2015; Budish, Cramton, and Shim, 2015; Foucault, Hombert, and Rosu, 2015;Foucault, Kozhan, and Tham, 2017). Relatedly, most empirical literature onprice discovery focuses on the contribution of market orders (Hasbrouck, 1991a,1991b; Brogaard, Hendershott, and Riordan, 2014).1 We find, however, thatHFTs’ limit orders contribute more than twice as much to price discovery astheir market orders. In contrast, non-HFTs’ market orders contribute moreto price discovery than their limit orders. Comparing HFTs to non-HFTs, wefind that HFTs’ market orders are responsible for less price discovery thannon-HFTs’ market orders, while HFTs’ limit orders are responsible for twice asmuch price discovery as non-HFTs’ limit orders. Overall, HFTs’ market ordersplay a smaller role in price discovery while HFTs’ limit orders play a largerrole.2Our results show that more aggressive orders have a higher price impact.3Market orders, the most aggressive order type, have the highest impact, followed by orders that change the national best bid and offer (NBBO), orders atthe NBBO, and orders behind the NBBO. Despite their lower individual priceimpact, limit orders provide the majority of price discovery because they arefar more numerous: market orders represent less than 5% of messages.4 Individual HFT market orders contribute more to price discovery on average than1 Recent empirical literature examines the contribution of both market orders and limit orders toprice discovery. Among others, Hautsch and Huang (2012) quantify the impact of a limit order usinga cointegrated VAR. Cao, Hansch, and Wang (2009) and Cont, Kukanov, and Stoikov (2014) showthat order imbalances predict future price movements. Fleming, Mizrach, and Nguyen (2017) studythe price impact of market and limit orders in U.S. Treasury bonds using a VAR setup similar tothe one used here. These papers focus on the price impact of individual orders. In contrast, we focuson decomposing the total amount of price discovery. In addition, our data identifying HFTs allowus to examine whether orders placed by different traders play different roles in price discovery.2 These results do not necessarily imply that concerns about HFTs are unwarranted. HFTs’market orders contribute some to price discovery and adverse selection. HFTs incorporating information with limit orders can also cause non-HFTs’ limit orders to be adversely selected, whichcould in turn lead to excess intermediation if non-HFTs reduce their use of limit orders (Jovanovicand Menkveld, 2015). However, the relative magnitudes of HFTs’ limit orders and market ordersin contributing to price discovery suggests that HFTs are not primarily using their information inmarket orders to adversely select non-HFTs.3 A number of papers examine HFTs’ trading and price discovery. Brogaard, Hendershott, andRiordan (2014) show that HFTs contribute to price discovery with market orders by trading in thedirection of future price changes. Carrion (2013) finds that market-wide information is incorporatedinto prices quickly on days when HFTs trade more. Conrad, Wahal, and Xiang (2015) find thathigh-frequency trading and quoting correlate with more efficient prices. Chaboud et al. (2014)find that HFTs improve price efficiency through lower return autocorrelations and fewer arbitrageopportunities. Chordia, Green, and Kottimukkalur (2018) show that high-frequency market ordersimpound information quickly following macroeconomic announcements.4 A message refers to any instruction received by an exchange; a message includes marketableorders, limit order placements, limit order cancellations, and limit order replacements. A limitorder refers to a nonmarketable instruction received by an exchange; a limit order includes limitorder placements, limit order cancellations, and limit order replacements.
Price Discovery without Trading1623non-HFT market orders. However, non-HFT market orders are three timesmore likely, making them more important overall. HFT limit order submissions and cancellations are both frequent and informative, leading HFT limitorders to contribute roughly 30% of total price discovery versus roughly 15%for non-HFTs.That HFT limit order submissions have a positive price impact is seemingly at odds with the results in Brogaard, Hendershott, and Riordan (2014)that suggest HFTs’ liquidity-supplying trades have a negative price impact.5However, the analysis in Brogaard, Hendershott, and Riordan (2014) relies onexecuted trades and hence does not capture the effect of limit orders that donot execute. For example, a limit order to buy will not execute if the priceincreases. In this case the limit order contributes to price discovery withouttrading. When a limit order executes, in contrast, its price impact is effectivelythe opposite of the market order that it executes against. For example, whena buy market order executes against a sell limit order, on average the efficientprice will increase. This leads to the buy market order having a positive priceimpact and the sell limit order having a negative price impact upon execution. This is why Brogaard, Hendershott, and Riordan (2014) find that HFTs’liquidity-supplying trades have a negative price impact. The price impact oflimit orders upon submission is the weighted average of the (negative) priceimpact of the limit orders that execute and the (positive) price impact of thelimit orders that do not execute. Given that only 5% of limit orders execute, itis not surprising that the average price impact for executed and nonexecutedlimit orders is positive.Theoretical models of limit order books provide insights into the roles thatdifferent orders by different traders play in price discovery (e.g., Goettler,Parlour, and Rajan, 2009 [GPR]; Hoffmann, 2014).6 These models focus ontraders’ choice between market orders and limit orders based on traders’ information and the state of the limit order book. Limit orders receive ratherthan pay the bid-ask spread, but do not execute with certainty. Market ordersalways execute, but pay the bid-ask spread. When information is more valuable and the spread is narrower, traders prefer market orders to limit orders.5 Brogaard, Hendershott, and Riordan (2014) show that HFTs contribute to price discoverywith market orders by trading in the direction of future price changes. They also find that HFTs’liquidity-supplying trades are in the opposite direction of future price changes. Their results arenot necessarily inconsistent with the results presented here. We show that aggressive limit ordersubmissions and cancellations are associated with positive price impacts at the time of submission.Brogaard, Hendershott, and Riordan (2014) show that orders submitted by HFTs that are notsubsequently cancelled and that execute against more aggressively priced incoming limit ordersare adversely selected.6 Other papers examine limit order trading by informed investors, but provide insights lessdirectly related to HFTs. Kaniel and Liu (2006) theoretically model the order choice of informedtraders. Consistent with GPR, their two-period model finds that informed traders are more likelyto submit limit orders. Bloomfield, O’Hara, and Saar (2005) conduct an experiment that includeslong-lived private information and show that informed trades submit more limit orders. Similarly,Rosu (2019) shows that informed traders tend to use limit orders for moderate levels of mispricingand market orders more extreme mispricing.
1624The Journal of Finance RTraders with different characteristics face different trade-offs in their orderchoice. Traders with no intrinsic motivation to trade (GPR) and fast traders(Hoffmann, 2014) who can revise their orders more often prefer limit ordersbecause execution uncertainty is less costly for them and their limit orders faceless adverse selection, respectively. HFTs fit both of these descriptions. Thesemodels are consistent with our empirical finding that HFTs submit the majorityof limit orders.7 Also consistent with our empirical results, GPR and Hoffmann(2014) find that limit orders play a significant role in price discovery.8GPR and Hoffmann (2014) study closely related models in which traderschoose between market and limit orders and later-arriving traders observe newpublic information.9 While GPR and Hoffmann (2014) find similar results forlimit orders overall and for traders with characteristics shared by HFTs, theirmodels yield different predictions for how their results vary with volatility.10An important difference between GPR and Hoffmann (2014) is that in GPR,investors have different and often large private gains from trade.The basic trade-off in both models is between the risk of nonexecution andthe adverse-selection risk associated with the submission of limit orders. Whenvolatility is high, the picking-off risk is higher. Hoffmann’s (2014) fast traderscan avoid being adversely selected by slow traders but cannot submit marketorders profitably. Therefore, fast traders increase their limit order submissionswhen volatility is high.11 GPR include investors with large private values andspeculators with zero private value. When volatility is high, extreme privatevalue investors submit better-priced limit orders to entice speculators to submitmarkets orders.12 The speculators in GPR then switch from limit to marketorders. We find that HFTs reduce their use of limit orders when volatility7 Jovanovic and Menkveld (2015) model a continuously present intermediary that can constantlyrevise its limit orders as “public” information arrives. This intermediary (HFT) also submits morelimit orders than market orders.8 Prior papers empirically examine limit order usage by non-HFT traders. Collin-Dufresne andFos (2015) show that one group of informed traders, namely 13D activist investors, use limit orders.Anand, Chakravarty, and Martell (2005) show that institutions use limit orders. Our results onnon-HFT limit orders contributing to price discovery are consistent with the use of limit orders bytraders with long-lived information. Using the same regulatory data as in our paper, Korajczykand Murphy (2019) provide some evidence of informed institutions using limit orders.9 Foucault (1999) provides many of the basic building blocks in GPR and Hoffmann (2014). Forexample, in these models adverse selection arises from the arrival of public information and limitsorders not always being immediately cancelable. However, all traders are the same in Foucault(1999), which provides limited insight into HFTs and price discovery.10 Few models examine fast, informed traders’ use of limit or market orders conditional onvolatility. An exception is Baldauf and Mollner (2016). Similar to Hoffmann (2014), their settingallows traders to increase their trading speed, for a fee. They model a dynamic setting withinformation arrivals. Their model suggests that fast, informed traders are more likely to use marketorders when the degree of mispricing is high and limit orders when the degree of mispricing is low.11 Relative to fast traders, slow traders in Hoffmann (2014) submit relatively more limit ordersthan market orders when volatility is high. This is consistent with the model of Foucault (1999), inwhich investors are homogeneous and more limit orders are submitted relative to markets orderswhen volatility is high.12 Bloomfield, O’Hara, and Saar (2005) also study volatility and limit orders. They analyze twotypes of variability: volatility and extremity. Volatility is captured by the distribution of future
Price Discovery without Trading1625is high.13 This suggests that modeling richer heterogenity (large, small, andzero) in the private valuations of trading motives, as in GPR, is important forunderstanding HFTs and limit-order markets.Price discovery switching from limit orders to market orders has implicationsfor market stability and possible market failure.14 Madhavan (1992) showsthat continuous markets can fail when adverse selection is sufficiently high. Ifvolatility increases due to greater private information, then market failure ismore likely. If informed liquidity providers switch from limit orders to marketorders when volatility increases, then market failure is even more likely. Weshow that HFTs reduce their use of limit orders as volatility increases, whichreduces the contribution of their limit orders to price discovery. When volatilityincreases, the market/limit order trade-off between execution speed/certaintyand price increases more in favor of market orders for informed traders thanuninformed traders. This differential trade-off for informed and uniformedtraders raises concerns that endogenous fragility in continuous limit orderbooks. This question represents an important area for future empirical andtheoretical research.Prior literature raises several concerns about HFTs. First, a number of theoretical papers show that fast traders like HFTs can adversely select slowertraders. For example, Foucault, Hombert, and Rosu (2015), Biais, Foucault,and Moinas (2015), and Budish, Cramton, and Shim (2015) show that sometraders trading faster on public signals increases information asymmetry.15Our results lend some support to these concerns. For example, we find that thelarger price impact of HFTs’ orders is explained in part by public information,such as the state of the limit order book and lagged returns in a correlatedasset (e.g., the TSX 60 exchange traded fund). However, our results also suggest that trading on such public information is not the dominant role of HFTsin overall price discovery.16 Second, extant work suggests that HFTs could bevalues whereas extremity is captured by the distance between the previous price and the futurevalue. For distributional volatility conditional on extremity, Bloomfield et al. (2005) find no relationship between limit order submissions and volatility. For their extremity measure of volatility,Bloomfield et al. (2005) find a negative relationship between volatility and the limit order submissions of informed trades. This suggests that long-lived private information may also be able togenerate the negative empirical correlation between volatility and limit order.13 Ahn, Bae, and Chan (2001) show that limit order submissions increase subsequent to increasesin transitory volatility.14 Danielsson, Shin, and Zigrand (2012) and Kirilenko et al. (2017) discuss endogenous extremeevents and the 2010 flash crash. Brogaard, Hendershott, and Riordan (2018) show that the tradesof HFTs supply liquidity more than they demand liquidity during extreme price movements. Unlikeour examination of how HFTs’ limits orders change with volatility, Brogaard, Hendershott, Riordan(2018) compare levels during extreme price movements without controlling for the relative liquiditysupplied and demanded by HFTs outside of extreme price movements. If HFTs supply liquiditymore than they demand liquidity, which is true in our sample, HFTs could decrease their useof limit orders as volatility increases while their trades still supply liquidity more than demandliquidity.15 For empirical evidence, see Brogaard, Hendershott, and Riordan (2018).16 Brogaard, Hendershott, and Riordan (2014) find that HFTs’ trading correlates with publicinformation in past market-wide stock returns and limit order book imbalances. We find that this is
1626The Journal of Finance R“front-running” non-HFTs’ orders by detecting large non-HFT orders that aresplit over time or across exchanges (Hirschey, 2017; Korajczyk and Murphy,2019; van Kervel and Menkveld, 2019). We find that HFTs’ orders generallydo not anticipate non-HFTs’ orders in the same direction and that HFTs mayreact more quickly to public information. For instance, HFT orders that movethe NBBO negatively predict the same non-HFT orders and non-HFT marketorders at the NBBO. While this finding is consistent with HFTs observing andreacting to public signals before non-HFTs are able to react, we also show thatthe contribution of HFTs’ limit orders to price discovery is not due solely totheir orders arriving only slightly ahead of non-HFTs’ limit orders.We also examine price discovery for stocks across markets. In particular,we examine HFTs’ activity and price discovery on each exchange and acrossexchanges. As with the market-wide results, we find that HFTs are the predominant channel of price discovery on each exchange through their limit orders.While significant price discovery occurs within the same second across exchanges, the role of HFTs’ limit orders for price discovery is predominant evenwhen sampling at the one-second frequency and this does not appear to be duesolely to minuscule differences in speed. Finally, HFTs react more to events onother exchanges than non-HFTs, this is consistent with HFTs integrating information across markets. While this seems beneficial in a fragmented market,whether such integration is better than trading on a centralized exchange isan open question.The remainder of the paper proceeds as follows. Section I describes the dataand institutional details. Section II documents market-wide activity and pricediscovery. Section III provides evidence on within- and across-market activityand price discovery. Section IV concludes.I. Data and Institutional DetailsData are provided by the Investment Industry Regulatory Organization ofCanada (IIROC). The data include every message submitted on recognizedequity markets in Canada with masked market IDs, masked participant IDs,security IDs, date and timestamps to the millisecond, order type, order volume,and a buy/sell indicator.17 Importantly, the data identify activities across exchanges as the masked participant IDs remain constant across days, securities,true for HFTs’ limit orders submissions as well. Whether to attribute any HFT contribution to pricediscovery to private information runs into the deeper issue described in Hasbrouck (1991a, 190):“the distinction between public and private information is more clearly visible in formal modelsthan in practice.” Given that HFTs rely only on public information in their trading algorithms, onecan argue that all of their contribution to price discovery is due to public information. However, ifHFTs’ algorithms better interpret public signals (like the short sellers on news days in Engelberg,Reed, and Ringgenberg, 2012), then it is more difficult to characterize HFTs as incorporating purelypublic information.17 The data are structured similar to the NASDAQ ITCH. They contain every message sent byeach participant to the exchange. The messages include the initial order, cancels, and amendmentsto the order. As in the United States, there are a number of different order types, such as hiddenorders and immediate or cancel (IOC) orders, which are flagged in the data. We exclude hidden limit
Price Discovery without Trading1627and markets. IIROC requires exchanges to report messages in a standardizedformat. As such, some order types may be recorded as multiple orders. Forexample, modifications are reported to IIROC as both a cancel and a new order.A. Trading LandscapeCanada has a number of equity markets on which trading is organized.We identify nine in total and present summary statistics on the three largestexchanges.18 Trading on these three exchanges makes up more than 98% of thetotal trading volume in our sample stocks over our sample period.Markets in Canada are similar to U.S. markets in that electronic limit order books observe price-time-display priority. Canadian markets differ fromU.S. markets during our sample period in that Canadian markets are lessfragmented, do not allow subpenny trading, and regulate that dark orders improve the price by half of a tick. Orders in Canada during the sample periodare protected via order protection rules (OPR).19 OPR apply to marketplacesthat provide “automated functionality.” Automated functionality includes automatically displaying and updating the status of each participant’s orders,as well as immediately and automatically accepting incoming orders, executing those orders, and canceling any unexecuted portion of those ordersmarked as immediate-or-cancel (IOC). OPR apply only to visible orders andthe visible parts of orders and require marketplaces to implement rules to prevent trade-throughs, that is executing before “immediately accessible, visible,better-priced limit orders.”In contrast to Regulation NMS in the United States, Canadian marketsimplement full depth-of-book protection. This means that before an order is executed, marketplaces must ensure that all protected orders that are visible atbetter price levels have been executed. Canadian regulations also impose bestexecution obligations on brokers. These regulations require dealers and advisors “to execute a trade on the most advantageous terms reasonably availableunder the circumstances when acting for a client.” See Korajczyk and Murphy(2019) for additional institutional details.The Canadian market has seen a dramatic increase in competition for investor order-flow since 2008. In May of 2007 a consortium of Canada’s largestbanks announced a trading platform designed to compete with the TSX,called Alpha Trading Systems. Shortly thereafter in December of 2007 Chi-Xorders from the order book construction. IOC orders are included as an order and cancel if they arenot executed, and a trade if they are filled. IIROC receive data with homogenized fields from eachexchange in a format that allows for cross-platform integration. Specifically, exchange data mustfollow the Financial Information Exchange (FIX) protocol (http://www.fixtradingcommunity.org/).Any deviation from the FIX implementation must be approved by IIROC with a regulatory-feedcompliant solution. The data are timestamped by each exchange. The exchanges are required tosynchronize their clocks with IIROC, which follows the National Research Council Cesium Clock.18 For an overview of marketplaces as of June 1, 2015, see sis/Documents/SumCompEquityMarkets en.pdf.19 See http://www.osc.gov.on.ca/en/Marketplaces order-protection index.htm.
1628The Journal of Finance Rannounced their intention to commence trading in selected Canadian stocks onFebruary 20, 2008. In response TSX rolled out new trading technology (TSXQuantum) to all TSX-listed stocks. In 2012 TSX’s parent company, the MapleGroup, purchased Alpha and now operates Alpha as a separate exchange withinthe TMX group of exchanges.B. SampleOur sample comprises the 15 securities that are part of the TSX 60, theprimary Canadian equity index, at the end of 2014 that are not cross-listedin the United States; the other 45 stocks in the TSX 60 are cross-listed. Weexclude cross-listed stocks as we cannot measure message activity that occursoff Canadian exchanges in the same way. In addition, cross-listed stocks mayhave different properties (Bacidore and Sofianos, 2002). Table I reports descriptive statistics for the sample stocks: market capitalization, share price, tradesize, number of trades, number of shares traded, dollar volume traded, NBBOquoted half-spread, % HFT, % HFT demand, % HFT supply, and the standarddeviation of returns. The average market capitalization from October 15, 2012to June 28, 2013, the sample period, is Market Cap,20 while the daily standarddeviation of stock returns based on end-of-day prices during the sample period is Std. Dev. of Returns. Market capitalization and the standard deviationof stock returns are based on data from Datastream. All other variables arereported as stock-day averages during the sample period using IIROC data.Table I includes activities from all exchanges, whereas the remaining tablesinclude observations only from the three largest exchanges.The firms in our sample have market capitalization that ranges from 1.95 billion CAD to more than 28 billion CAD. Share prices vary between 20and 76, with the exception of Bombardier, with a price of 4.00. The stocks inour sample are actively traded with between 11.84 million and 70.97 milliontraded per stock-day. The stocks are relatively liquid with quoted half-spreadsbetween 1.38 and 12.64 basis points.C. HFT ClassificationWe classify trader IDs as HFTs using the following criteria over the entiresample period:(i) make up more than 0.25% of trading volume;(ii) have an end-of-day inventory of less than 20% of their trading volume;and20 The sample starting date is just after Canadian regulators began requiring dark liquidityprovision to improve on the best displayed prices by at least 1 cent, or 1/2 cent if the displayedspread is 1 cent. To examine whether our results are sensitive to slow adjustment to this regulatorychange, Internet Appendix Tables AII to AVI repeat the main analyses for the 2013 subsample andshow economically similar results. The Internet Appendix is available in the online version of thearticle on the Journal of Finance website.
Table IMarketCap. ( Billion)(1) 8.00 10.03 6.95 9.90 6.77 10.95 6.96 28.74 11.62 1.95 12.46 12.10 9.61 6.45 9.35 APSNCWNAverage 41.28 25.59 53.40 4.00 20.43 72.35 19.77 33.63 29.24 41.10 52.49 76.46 26.28 48.92 42.50 72.98SharePrice(2) 11,637 4,854 10,517 4,875 4,765 14,821 5,383 6,943 6,307 9,738 10,175 14,217 6,210 11,088 10,066 917.282.992.114.315.251.993.220.91Number ofTrades 45421.56756.68160.60Number ofShares Traded(‘000)(5) 34.98 26.91 24.03 50.42 43.52 25.12 70.97 26.52 45.27 33.09 20.87 60.71 32.39 20.79 32.31 11.84Dollar VolumeTraded ( 894.111.382.173.813.705.77NBBO 15.8%% %11.4%16.6%18.7%14.4%23.0%16.4%22.2%% 2%29.8%12.8%15.6%24.1%31.6%17.7%12.3%9.5%% .560.850.620.920.971.541.08Std. Dev. ofReturns(%)(11)The table reports summary statistics for the 15 noncross-listed stocks in the TSX 60. The sample period is from October 15, 2012 to June 28, 2013.Ticker is the ticker. Market Cap. is the average market capitalization from Datastream, in billions of Canadian dollars. Share Price is the averagetraded stock price. Trade Size is the average trade size in dollars. Number of Trades is the average number of trades, in thousands. Number of SharesTraded is the average number of shares traded, in thousands. Dollar Volume Traded is the number of shares traded multiplied by the stock price, inmillions of dollars. NBBO Quoted Half-Spread is the calendar time weighted one-half quoted differenc
ignated market makers and limit orders represent the bulk of activity. The-oretical models of limit order books study informed traders’ choice between market orders and limit orders. The market/limit order
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