Inferring Public and Private Information from Trades and Quotes

The Financial Review 41 (2006) 95--117

Inferring Public and Private Informationfrom Trades and Quotes

Bart FrijnsAuckland University of Technology

Abstract

We propose a new model that uses nonsynchronous, ultra-high frequency data to analyzethe sequential impact of trades and quotes on the price process. Private information is relatedto the impact of trades and public information to the impact of quotes. The model is extendedto include various other factors that affect public and private information. For 20 active Nas-daq stocks, private information causes, on average, 9.43% of daily stock price movements.Additionally, quotes are more informative when (1) many dealers set the best price and (2)traditional market makers rather than Electronic Communication Networks set the best price.

Keywords: public versus private information, ultra-high frequency data, Nasdaq, marketmicrostructure

JEL Classifications: C32, G15

1. Introduction

It is a well-established notion that stock prices change with the flow ofinformation. When new information arrives, market participants update their beliefs

∗Corresponding author: Department of Finance, Auckland University of Technology, Private Bag 92006,1020 Auckland, New Zealand; Phone: +64-9-921-9999 extn 5713; Fax: +64-9-921-9876; E-mail:[email protected]

I wish to thank Arnold Cowan (the editor), Thorsten Lehnert, Ronald Mahieu, Dimitri Margaritis, FranzPalm, Peter Schotman, Christian Wolff, and two anonymous referees for their valuable comments andsuggestions.

C© 2006, The Eastern Finance Association 95

96 Frijns/The Financial Review 41 (2006) 95–117

about the asset’s value and the new information is incorporated into the stock price.The theoretical microstructure literature distinguishes between public and privateinformation (e.g., Glosten and Milgrom, 1985; Kyle, 1985). Public informationis market-wide information available to all participants. Private information refersto specific information known only by a few traders called insiders. A relevantquestion is to what extent these two sources of information affect the change inprices.

Existing empirical research investigates several aspects of informational asym-metries. Glosten and Harris (1988), for example, determine the cost component ofthe bid-ask spread that is due to the presence of informed traders. Easley et al. (1996)take the position of the market maker and model the probability of trading with aninformed counterparty. For assets traded in several markets, Hasbrouck (1995) devel-ops a measure for informational asymmetries across markets. Madhavan, Richardson,and Roomans (1997) develop a structural model of intraday price formation and usethis model to analyze components of the bid-ask spread, transaction costs, and pricevolatility. Apart from the last study, the question of the relative contributions of publicand private information to the change in prices remains mostly untouched. This paperaddresses that issue.

This paper’s first and main contribution is the proposal of a new model for thedynamics of trades and quotes. The model is designed for ultra-high frequency dataand allows us to determine the extent to which prices change due to public or privateinformation. In a framework similar to Hasbrouck (1993), we decompose prices intoa permanent component (also called the efficient price) and a transitory component.Because trades and quotes concern the same stock, both processes share the sameefficient price and each event (a trade or a new quote) reveals information about thelocation of the efficient price. We associate the quote process with public informationand the trade process with private information.

The model also allows us to test for the relevant time scale of the price process.Clark (1973) introduces the time scale issue and argues that the arrival rate of infor-mation, not calendar time itself, drives the price process. We can address the timescale issue by allowing the innovations in the efficient price to depend on durations.If the variance of the efficient price innovation increases one on one with the timebetween observations (i.e., calendar time affects the price process), the process issaid to evolve in calendar time. If there is no effect of durations on the efficient priceinnovation, then the efficient price process is only driven by the events occurring (theoccurrence of a trade or innovation of a quote). The process is then said to evolve inevent time.

For our final contribution, we apply the model empirically to 20 actively tradedNasdaq stocks. Although actively traded stocks are known to have a lower probabilityof informed trading (Easley et al., 1996), the sample allows us to extend the model andtest for the impact of some additional factors on public and private information. Thefactors are traded and quoted volume, and, more specific to the Nasdaq, the number

Frijns/The Financial Review 41 (2006) 95–117 97

of dealers at the inside quote and the type of dealer at the inside (a traditional marketmaker versus an Electronic Communication Network, or ECN).1

The results indicate that private information causes only a small fraction ofthe change in the efficient price. On a daily aggregated level, private informationaccounts for 9.43% of the daily price changes. Second, we find that durations areslightly negatively related to innovations in the efficient price, which is inconsistentwith the notion that the price process evolves in calendar time. The extensions ofthe model show that large quoted volumes and many dealers at the inside have alarger effect on the innovation in the efficient price. Also, whether market makersor ECNs set the inside matters; when market makers set the inside, quotes are moreinformative.

The model relies on the assumption that the quote process reveals public in-formation and the trade process reveals private information and incorporates thisinformation into the efficient price when a trade or quote innovation occurs.

We provide the following motivation for our approach. Consider a market wherea dealer submits quotes at which she is willing to trade. Trades at these quotes canoriginate from informed or uninformed traders. Informed traders only trade when thetrue value of the asset lies outside the quoted spread. When they trade, they revealinformation about the true value of the asset. Hence, an informed trade has a permanentimpact on the efficient price (Glosten and Harris, 1988; Madhavan, Richardson, andRoomans, 1997). Uninformed traders trade on the basis of public information andhave no additional information beyond that in quoted prices. Therefore, a trade byan uninformed trader has no impact on the efficient price. The impact of the tradeprocess on the efficient price is therefore fully attributable to private information.

Quotes are innovated on the basis of public information plus the information thedealer extracts from order flow. Whenever a quote is innovated this information isincorporated into the efficient price. However, the private information component thatthe dealer extracts from order flow has already been incorporated into the efficientprice when the informed trade took place. The impact of a quote innovation on theefficient price can therefore be attributed to an innovation in public information. Amore elaborate motivation is presented in the next section.

An additional strength of our model is that it does not rely on a specific tradeclassification rule such as that proposed by Lee and Ready (1991). Whereas that clas-sification rule identifies most trades correctly for the NYSE, results for the Nasdaq,the market this study focuses on, are poor (Blume and Goldstein, 1997). Our modelessentially determines the position of trades and quotes relative to the location ofthe efficient price and subsequently determines whether the efficient price should beadjusted upward or downward.

1 For convenience, this paper uses the term “dealer” to refer to either a market maker or an ECN.


2. Model

In this section we develop a model to describe the dynamics of trades andquotes. The model is an unobserved components model similar to Hasbrouck (1993)and decomposes prices into a permanent efficient price component and a transitorynoise component. We extend the Hasbrouck model in two ways. First, our model isdesigned for nonsynchronous, ultra-high frequency data using every transaction orquote innovation that occurs. Second, we allow the innovation in the efficient priceto depend on different sources of information (i.e., public or private information).We start with the decomposition of transaction prices, then we provide the decom-position for the quote process. Finally, we integrate both processes into a singlemodel.

Consider the transaction prices of a single asset. On a given day, let pi be the logprice of the ith transaction, where i = 1, . . . , N .2 This can be a buy or sell transactionand is reported to the system at time ti. We decompose the transaction price into twocomponents. The first is the efficient price component (mi) of the transaction process.The second component captures the microstructure noise (ηi), which includes the bid-ask bounce and other microstructure effects. The decomposition can be expressed as

pi = mi + ηi , (1)

similar to Hasbrouck (1993); Madhavan (2000); and Zhang, Mykland, and Aıt-Sahalia(2004) among others.

On the same day that we observe N trades, we observe M quote innovations.Because quote innovations do not occur at the same time as transactions, we indexall quote innovations with j, where j = 1, . . . , M . The vector qj contains all logquote prices that are innovated at time tj. The vector can be one-dimensional or two-dimensional depending on whether bid, ask, or both quotes are innovated at time tj.For the moment, we assume that both quotes are innovated at tj such that the vectorof quote innovations has dimension 2. Later, this assumption is relaxed to obtain thefull model.

We decompose quotes, similar to the trades decomposition. However, since thedifference between bid and ask price consists of a deterministic part (for example, dueto order processing costs) we decompose the quote process into three components. Thefirst component considers this deterministic part (c). The second component considersthe efficient price, shared by both bid and ask quotes (mj). The last component (υ j )considers the nondeterministic, transitory difference between bid and ask prices. Thedecomposition for quotes reads

q j = c + ιm j + υ j , (2)

where ι is a (2 × 1) unit vector.

2 In fact N varies across trading days. However, for the sake of notational clarity we do not index N.


Because trades and quotes are considered for the same asset, both processes arecointegrated and share the same common trend (m), the efficient price. However, astransactions and quote innovations do not occur simultaneously, information aboutthe efficient price is revealed at different times. To link the trade and quote processwe introduce a single time scale, referred to as event time, which is the time scale inwhich the events occur. In our case the events are the occurrence of a trade or a quoteinnovation. Because every event potentially releases information about the locationof the efficient price, we argue that this is the relevant time scale for the evolution ofthe efficient price process.

Let t� be the time at which we observe any event, where t� = ti ∪ t j and � =1, . . . , L , where L is the total number of events (trades or quote innovations) occurringon each day. The efficient price, common to both trades and quotes, evolves in thistime scale and is assumed to follow a random walk,

m� = m�−1 + σ� ε�, (3)

where ε� is an i.i.d. innovation term with unit variance and the volatility term σ�

measures the size of the innovation. Our main interest is in determining the sizes ofthe innovations due to public and private information, which leaves us with the issueof how to identify public and private information. The model, however, is structuredso that the quote process reveals the public information and the trade process theprivate information. We motivate this below.

Traditional microstructure theory on asymmetric information (e.g., Glosten andMilgrom, 1985; Kyle, 1985) considers two types of traders, informed traders withsuperior information and noise traders. Informed traders derive superior informa-tion from private sources and trade when the true price of the asset is above orbelow quoted prices. When they trade, they reveal information about the locationof the true price. Hence, informed trading has a permanent impact on the effi-cient price of the asset (Glosten and Harris, 1988; Madhavan, Richardson, andRoomans, 1997). Noise traders trade for liquidity purposes and have no informa-tion other than that present in quoted prices. Because the information in quotedprices has already been incorporated into the efficient price at the time quoteswere set, noise traders have no impact on the efficient price. Therefore, the im-pact of trades on the innovation in the efficient price can be attributed to privateinformation.

Similar to noise traders, dealers have access to public information, but alsoextract some additional information from the order flow they receive. The innovationof a quote therefore depends on the innovation in public information and the privateinformation dealers extract from the order flow. This updating of beliefs and quotesof dealers fits the theoretical framework of Kyle (1985) as well as that of Easley et al.(1996). Although the quote is innovated on the basis of public information and part ofthe private information obtained through order flow, the efficient price is not. Privateinformation that dealers derive from order flow has already been incorporated intothe efficient price at the time of the trade. Therefore, the innovation in the efficient


price due to a quote innovation is due to the remaining part: an innovation in publicinformation.

In the discussion above we have assumed that market makers do not have accessto private information. Although it is very unlikely that a market maker would obtainprivate information, as we discuss below, the model and arguments above would stillbe valid if she did. If a market maker obtained private information, she could trade onthis information anonymously on an ECN. In that case her private information wouldreveal itself through the impact of the trade process on the efficient price.

However, given recent evidence, it remains questionable whether Nasdaq marketmakers obtain private information. First, it is doubtful that market makers obtainprivate information through customer orders. Traders with private information avoidtrading through a market maker because this would potentially reveal their informationand identity. Instead, they prefer to trade on an ECN, which guarantees anonymity.Second, the market maker cannot learn from customer orders by stopping them asthe NYSE specialist can (Ready, 1999). When a market order arrives, the marketmaker must execute it at the inside quote or better, or transfer the trade to a dealerthat offers the inside quote. The market maker cannot stop the order and wait forthe arrival of more information. Finally, Ellis, Michaely, and O’Hara (2002); Schultz(2003); and Chung and Cho (2005) consider alternative ways in which market makerscan obtain private information. They show that market makers who are engaged inthe IPO process, or who are affiliated with firms that have analysts covering thestock, have a clear dominance over other market makers. However, this dominancemanifests itself mainly in obtaining preferencing agreements with traders and not somuch in obtaining private information.

A factor that could affect the private information component is the existence ofthe so-called SOES bandits, day traders profiting from the sluggishness of marketmakers to update quotes (Harris and Schultz, 1998). They trade on Nasdaq’s SmallOrder Execution System (SOES) when new public information arrives in the marketand market makers are slow to update quotes. This could result in overestimationof the private information component because it also includes innovations in publicinformation. Although this issue was relevant before the introduction of the OrderHandling Rule (OHR) in 1997, we argue that for the sample in this study (1999) theeffect of SOES bandits is negligible. After the introduction of the OHR, the Nasdaqintroduced several additional rules to limit SOES bandits. A first rule limited tradesize for automatic execution to 100 shares. Second, an order from SOES trader wouldbe returned if the inside quote was set only by an ECN. (Previously, the order wasexecuted with the market maker that had the next best price but at the inside price.)To counteract resequencing of cancelled orders, a final rule was introduced statingthat if an ECN is at the inside alone, the order would be put in a 90-second queue,allowing the market to adjust their prices (see Mizrach and Zhang, 2000 for a moreelaborate discussion).

In summary, the above discussion implies that the trade process reveals privateinformation and the quote process reveals public information. Since the efficient


price (3) is innovated when a trade occurs or a new quote is set, we can determinethe innovation in the efficient price due to these events. We also consider the impactof time on the innovation in the efficient price. Clark (1973) points out that calendartime may not be the appropriate scale for the price process, a notion supported byHarris (1987) and Ane and Geman (2000). Hence, we also allow the innovation inthe efficient price process to depend on durations. The full specification for σ� is

σ� = τδ1� (P�(1 − Q�)σP + Q�(1 − P�)σQ + P� Q�σPQ), (4)

where P� is an indicator variable equal to 1 when a trade occurs at time t� and zerootherwise. Similarly, Q� is equal to 1 when at time t� a quote is innovated and zerootherwise. The impact of a transaction on the innovation in the random walk ismeasured by σ P, the innovation due to the release of a new quote is measured byσQ, and when both events occur we capture the innovation in σPQ. Durations (τ�)are normalized and are defined as the time between events divided by the averageduration (over the whole sample) between events. This normalization causes thevolatility parameters to be interpretable per event, instead of per second. No otherparameter is affected by this normalization. The parameter δ1 measures the impactof time between events on the innovation in the random walk. The parameter valuesof interest are δ1 = 1

2 and δ1 = 0. When δ1 = 12 the variance of the random walk is

proportional to the duration between events and the process evolves in calendar time.When δ1 = 0 the random walk evolves in event time.

Recent research has shown that microstructure noise is not i.i.d. and that it iscorrelated with the efficient price process (see Hansen and Lunde, 2004). We thereforeallow the microstructure noise to correlate with the innovation in the efficient price.We also include duration functions to allow for potential variation in this correlation.In this case we use durations between trades or quotes separately. This is the relevanttime scale for the separate processes because these processes are only observed atthese points in time.

We start again by considering trades. The durations between trades (πP,�) aredefined similar to durations between events (time between transactions divided by theaverage duration of transactions). We decompose the microstructure noise for tradesas

η� = απδ2P,�(P�(1 − Q�)σP + P� Q�σPQ)ε� + u�. (5)

The parameter α governs the correlation between the efficient price innovationand the microstructure noise. Trade noise can only correlate with the innovationdue to trades σ P or with the innovation due to both events σPQ. The parameter δ2

measures the impact that time has on this correlation. When δ2 > 0, long durationsbetween transaction lead to higher correlation between the innovation in the efficientprice and the noise and vice versa. The last part in the equation (u�) is i.i.d. noise.

Similarly, we specify the transitory deviations from the efficient price for theinside quotes. Under the assumption that both quotes are observed at t� we have

υ� = βπδ3Q,�(Q�(1 − P�)σQ + P� Q�σPQ)ε� + e�, (6)


where β is a (2 × 1) parameter vector that governs the correlation between the quotenoise and the innovation in the efficient price. Similar to the noise of the trade process,the quote noise only correlates with the innovation in the efficient price due the tradesσQ or the innovation due to both events σPQ. The relevant durations for quotes are the(normalized) times between quote innovations (πQ,�) and the impact of time on thiscorrelation is measured by δ3. The last part in the equation (e�) is again i.i.d. noise.

In the previous discussion we assumed that all the events occur at every time t�.In practice, trades and quote innovations do not always occur at the same time. Toresolve this issue, let y� be a (3 × 1) observation vector that includes the most recenttransaction price and the most recent quotes at t�. If at t� a transaction is observed, y�includes this new transaction price and the standing quotes at t�. Similarly, when a newquote is released it is included in y�, as well as the other standing quote and the lastobserved transaction price. Since we are interested in the impact of new informationon the innovation in the efficient price, we only want to consider the latest innovationsin y�. We therefore introduce the matrix J� that selects the observations from y� thatare new at t�. This matrix has dimensions (s� × 3), where s� is the number of newobservations at t�.

To illustrate this selection process, consider a new transaction and an innovationin the bid quote at t�. The new trade and the innovated quote are selected from theobservation vector as follows:

J�y� =(

1 0 0

0 0 1

)

p�

ask�

bid�

=

(p�

bid�

).

Applying this pre-multiplication at every point in time, we can select those elementsin y� that have been updated at t�. Further, we can apply the pre-multiplication of J�

to all components in the model.With this pre-multiplication, the full model can be written in state space form.

We obtain

J�y� = J�

(0

c

)+ J�ιm� + J�

(υ�

ν�

),

m� = m�−1 + σ�ε�,

J�

(η�

υ�

)= J�

(α

β

)�

(1 0

0 ι

) (π

δ2P,�(P�(1 − Q�)σP + P� Q�σPQ)

πδ3Q,�(Q�(1 − P�)σQ + P� Q�σPQ)

)ε�

+ J�

(u�

e�

), (7)

where 0 is a (2 × 1) vector of zeros and ι a (2 × 1) vector of ones. With α being a scalarand β a (2 × 1) vector, � is defined as the Hadamard product, an element-by-elementmultiplication.


With the model in state space form we can estimate all its parameters. Treating thenonupdated observations that are not selected by J� as missing observations, we canuse techniques detailed in Harvey (1989) and estimate the model by quasi-maximumlikelihood using the Kalman filter.3 Because the latent, efficient price process is arandom walk, we initialize the system with a diffuse prior by setting the predictionerror variance to a very large number. We exclude the first 50 observations in thecomputation of the likelihood function to let the prediction error variance decrease toits normal level. Although parameters are estimated over multiple days, the system isre-initialized with a diffuse prior at the beginning of each day.

There are a few additional computational features of (7). Since the innovation inthe efficient price depends on the source of the information and on duration, the modeldoes not converge to a steady state.4 This means that the prediction error varianceis different at every observation, so all the steps in the Kalman filter recursionsneed to be reformed, increasing computational effort considerably. Furthermore, aswe select different elements from y� at each observation, treating the multivariatesystem as a univariate system, as proposed by Koopman and Durbin (2000), yieldsno computational advantages.

3. Data

The Nastraq database contains all trades and (dealer and inside) quotes of alllisted Nasdaq stocks within regular trading hours. We consider trades and quotes of20 actively traded stocks for the period February 1, 1999 to July 31, 1999, a totalof 124 trading days. Stocks are selected randomly from those that were included inthe Nasdaq-100 during the year 1999. Table 1 reports company names and tickersymbols.

Nastraq data include the time the trade was reported, the time the trade wasexecuted, price, and volume of the trade. When trades are reported late the tradedata include an indicator explaining the reason for late reporting (these trades areremoved from the data). The inclusion of trade execution times in the dataset providesa great benefit. It is known that high-frequency intra-day stock prices are contaminatedwith microstructure noise. Issues such as the bid-ask bounce, price discreteness, andother microstructure effects contaminate data. One major factor contributing to themicrostructure noise is the time trades are reported. In many cases we observe thattransactions executed at the same point in time are reported at different points in time.Although we opt for reported time as the relevant time scale (because this is the pointin time that the information is released to the market), many reported transactions

3 Quasi-maximum likelihood (QML) estimates the parameters of the model assuming normality, eventhough the true distribution may not be Gaussian. Standard errors cannot be computed in the traditionalway and are computed as proposed by White (1982).

4 Note that the parameters in α and β are only identified as we allow for these time variations.


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3.52

63.3

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are noninformative as later executed trades have already been reported. We thereforeremove all trades that are reported after a more recently executed and reported trade.When trades are executed at the same point in time, we only consider the transactionthat is reported first. This removes a substantial amount of data and minimizes thediscrepancy between executed time and reported time. For the empirical applicationof the model we use reported times, prices, and volumes (volumes are used in theextension of the model).

The quotes used in the main analysis of this study are the National Best Bidand Offer (NBBO) quotes, also called inside quotes. Since the introduction of OHRin 1997, all quotes issued by market makers and ECNs are included in the NBBO.Before the OHR was introduced, the NBBO was computed only on the basis ofquotes issued by market makers, which were known to be noncompetitive due to,for example, collusion among market makers (see Christie and Schultz, 1994, amongothers). After the implementation of the OHR, the public could compete directly withmarket makers’ quotes, increasing competition and decreasing the size of the insidespread (Barclay et al., 1999). Because the inside quotes at the time of our analysisare competitive, they represent the best prices at which market makers or ECNs arewilling to trade.

The inside quote data provided by Nastraq contains the time the new quotes areissued, the best bid and ask quotes, and indicators referring to the status of the quote.From the quote data we remove all nonregular quotes (quotes with a halt indicator).All bid (ask) quotes more than $2 away from the average of the past 50 bid (ask)quotes are removed. Because we are interested in the impact of quote innovations onthe efficient price innovation, we remove all quotes that do not change. For example,when only a bid quote is innovated, the ask quote is removed. Sampling in thismanner has clear advantages to considering the mid quote because a change in themid quote does not identify whether this occurred due to a change in the bid or the askquote.

Table 1 reports summary statistics. The first statistics are computed from thetrade data. These are average daily returns (computed from open to close), dailystandard deviations over the 124 trading days, and average price level. Next we reportthe total number of observations over the 124 trading days. These numbers indicatea large range of activity for the stocks in the sample, where the most active stock,Dell, has 1.36 million observations, and the least liquid stock, Starbucks, has only248,247 observations. The next column reports the percentages of times that onlytransactions are observed. Clearly, there are more transactions than quotes observed.The average percentage of trades is around 80. The next column reports the percentageof quote innovations. These percentages are quotes over total observations, where notransactions are observed. We find, on average, that quotes represent only about 14%of the observations, leaving a remaining 6% of the observations where both a tradeand a quote innovation were observed. Finally, the last three columns report averagedurations between events, quotes, and trades, respectively. These durations againemphasize the difference in the activity of the assets, where the duration between


Table 2

Duration and correlations parameters

This table reports summary statistics for the duration parameters (δ1, δ2, δ3), the parameter relating to thecorrelation between the innovation in the efficient price and trades (α), and the parameters that relate tocorrelation between the innovation in the efficient price and bid and ask quotes (βb, βa, respectively).

Symbol δ1 δ2 δ3 α βb βa

Mean −0.04 −0.09 −0.17 0.23 −0.03 −0.04(Avg. Std. Err.) 0.018 0.219 0.140 0.035 0.027 0.099Median −0.05 −0.07 −0.24 0.22 −0.03 −0.04Std. Dev. 0.050 0.114 0.333 0.158 0.044 0.147Max. 0.07 0.11 0.51 0.69 0.06 0.47Min. −0.13 −0.3 −0.66 −0.02 −0.11 −0.38Sign. > 0 at 1% 1 0 3 17 1 0Sign. < 0 at 1% 11 1 10 0 9 11

quote innovation (on average approximately 60 seconds) is much larger than theduration between transactions (on average about 7 seconds).

4. Results

In this section we present the results of the model proposed in Section 2. We startby discussing some of the parameter estimates of (7). Subsequently, we determinethe total contribution of public and private information in daily price changes, basedon the parameter estimates of (7).

In Table 2 we present the results for the duration parameter estimates and theparameters relating to correlations with the innovation in the efficient price. The firstcolumn in Table 2 presents statistics for δ1, the duration parameter on the innovationin the random walk. This parameter measures the effect of time between events (τ�)on the innovation in the efficient price. The hypothetical values of interest are δ1 = 1

2(a price process that evolves in calendar time) and δ1 = 0 (a price process that evolvesin event time). The hypothesis that the price process evolves in calendar time is easilyrejected; all parameters are significantly different from 1

2 . For δ1 = 0, the results areless conclusive. Overall, we find that the effect of time between events is slightlynegative; 11 out of the 20 stocks report significant negative parameters with a meanparameter value of −0.04. This indicates that when the time between events is shorter,the innovation in the efficient price is larger and vice versa. In general, durations tendto be shorter near the open and close of the market and large in the middle of theday. Hence, the model captures some of the intradaily dynamics observed in stockmarkets.5

5 Alternatively, the diurnality pattern can be included explicitly in the model, by allowing the parametersto depend on the time of the day. However, with the extensions we make later in the paper, the inclusionof this diurnality feature would increase the computational effort in estimating the model considerably.


Table 3

Innovations due to private and public information

This table presents summary statistics for the parameter estimates of the innovation in the efficient pricedue to trades (σP), quotes (σQ), or both (σPQ). All numbers are multiplied by 10. The last column reportsthe correlation between the number of observations for each stock and its parameter estimate.

Mean (Avg. std. err.) Median Std. dev. Max. Min. Correl (nobs)

σP 0.12 0.0041 0.10 0.0756 0.30 0.04 −0.69σQ 0.87 0.0152 0.79 0.4302 2.08 0.35 −0.71σPQ 0.95 0.0304 0.90 0.4544 2.15 0.37 −0.77

The next two columns report statistics on the impact of time between transac-tions (δ2) and quotes (δ3) on the correlation between the innovation in the efficientprice and the microstructure noise. This parameter is mostly insignificant for trades(only one stock reports a significant parameter value). However, the average pa-rameter estimate is negative (−0.09). For quotes, the average parameter estimate isnegative as well (−0.17), where ten stocks report a significantly negative parametervalue. This indicates that when the duration between trades or quotes is short, cor-relations between microstructure noise and the innovation in the efficient price arehigher.

In columns 4 to 6 we consider the parameters that relate to the correlations be-tween the innovation in the efficient price and the corresponding microstructure noise.We find that these parameters are generally positive for transactions and negative forquotes.

In Table 3 we present summary statistics for the parameter estimates of theinnovation in the efficient price. The first row reports statistics on the innovation inthe efficient price due to trades (σ P). We report this parameter multiplied by ten. Thisparameter can be seen as the amount of private information per transaction. The resultsfor the innovation in the random walk due to quote innovations/public information(σQ) are reported in the next row. We find that the contribution to the innovation inthe efficient price due to public information is much larger than the innovation due toprivate information. The final parameter corresponding to innovations in the randomwalk is reported in the last row of Table 3. This parameter considers the innovation inthe random walk when both events occur simultaneously (σPQ). When this happens,both public and private information are released. If only the public information wouldbe incorporated in the efficient price, σPQ would be equal to σQ. However, we observethat σPQ > σQ , indicating that both events are considered.

The last column in Table 3 reports the correlation between the innovation in theefficient price (σ P, σQ, and σPQ) and the total number of observations. All innovationshave strong negative correlations with the innovations in the efficient price. This isexpected, because daily volatility (reported in Table 1) is a function of the number ofdaily observations and the innovation parameters.


The results presented above show that per event, the innovation due to privateinformation is much smaller than the innovation due to public information. How-ever, for all stocks, the frequency of trades is much higher than the frequency ofquote innovations. Therefore, these measures of information cannot be comparedto each other. To obtain comparable measures, we aggregate all the innovations inthe efficient price up to a daily level. When we have the daily variance of the ef-ficient price process we can calculate the fractions of daily variance due to publicinformation, private information, and both. For a particular day, the fractions can becalculated as

PCP =

L∑k=0

τ2δ1� P�(1 − Q�)σ 2

P

L∑k=0

τ2δ1�

(P�(1 − Q�)σ 2

P + Q�(1 − P�)σ 2Q + P� Q�σ

2PQ

) ,

PCQ =

L∑k=0

τ2δ1� Q�(1 − P�)σ 2

Q

L∑k=0

τ2δ1�

(P�(1 − Q�)σ 2

P + Q�(1 − P�)σ 2Q + P� Q�σ

2PQ

) ,

PCPQ =

L∑k=0

τ2δ1� P� Q�σ

2PQ

L∑k=0

τ2δ1�

(P�(1 − Q�)σ 2

P + Q�(1 − P�)σ 2Q + P� Q�σ

2PQ

) ,

where PCP is the daily price change due to private information, PCQ the daily pricechange due to public information, and PCPQ is the daily price change due to bothevents.

In Table 4 we report the fractions of daily variance that each source contributesto the total daily variance of the efficient price. We report the standard deviationsof these fractions over the 124 trading days in parentheses. On average, we find that9.43% of the daily variance can be attributed to private information, considerably lessthan the percentage of variance that can be attributed to public information, which is65.40%. The percentage of daily variance that can be attributed to both constitutesthe remaining part, 25.17.

5. Model extensions

In the previous section we analyzed the information content of quotes and trades(public and private information, respectively). In this section we propose four possible


Table 4

Daily aggregated contributions to the efficient price

This table presents the average percentage contributions of trades, quotes, or both to the daily variance ofthe efficient price over the 124 trading days in the sample (standard deviations of the daily contributionsare reported in parentheses). Mean and median over all stocks are presented in the last rows.

Symbol % due to trades % due to quotes % due to both

AAPL 8.61% (2.60) 75.15% (6.58) 16.24% (5.56)AMAT 8.41% (2.09) 60.95% (5.76) 30.65% (4.85)AMGN 4.25% (1.55) 74.48% (6.09) 21.27% (5.33)AMTD 6.23% (4.02) 66.49% (9.51) 27.29% (9.00)ATHM 3.09% (2.06) 64.92% (10.90) 31.99% (10.07)CIEN 7.06% (2.35) 76.76% (6.78) 16.18% (5.79)COMS 11.88% (5.32) 69.80% (9.00) 18.32% (7.26)CPWR 17.72% (6.20) 66.41% (7.76) 15.88% (4.24)CSCO 7.46% (4.29) 52.16% (6.19) 40.38% (4.96)DELL 10.55% (4.56) 49.77% (8.00) 39.67% (8.24)INTC 12.24% (5.79) 54.01% (6.77) 33.75% (5.59)MSFT 7.55% (3.30) 51.58% (6.82) 40.87% (5.75)NOVL 18.13% (6.52) 69.25% (8.76) 12.62% (4.25)NXTL 5.36% (2.00) 75.23% (7.16) 19.41% (6.98)ORCL 18.37% (8.03) 55.33% (9.15) 26.30% (5.79)PSFT 18.27% (6.50) 70.34% (7.04) 11.39% (3.79)QWST 6.90% (6.54) 64.95% (12.36) 28.14% (8.43)SBUX 5.54% (4.13) 77.59% (9.60) 16.87% (6.61)SUNW 7.48% (2.56) 65.00% (6.67) 27.52% (5.89)WCOM 3.41% (1.22) 67.85% (6.05) 28.74% (5.65)

Mean 9.43% (4.08) 65.40% (7.85) 25.17 (6.20)Median 7.52% 66.45% 26.80%

extensions of the model. These extensions consider the circumstances under whichtrades or quotes are more informative. To analyze this, we consider four additionalfactors that potentially affect the private or public information components. Thesefactors are traded volume, quoted volume at the inside, the number of dealers at theinside, and the type of dealer at the inside (market maker versus ECN). We analyzethe impact of traded volume on the private information component; all other factorsrelate to public information.

To test for the impact of these factors on the different information components weconstruct different categories for the additional factors (high/medium/low volume,many/some/few market makers at the inside, and ECN/market makers/both at theinside), and include these in our state space framework in (7) by modifying equations(4), (5), and (6). For the traded volume we replace σ P by

(D1,� D2,� D3,�)

σP,1

σP,2

σP,3

,


where D1,�, D2,�, D3,� are dummy indicators equal to 1 if the observation falls withinthis category and zero otherwise. For the factors that affect quotes, σQ is replaced by

(D1,� D2,� D3,�)

σQ,1

σQ,2

σQ,3

,

and in all cases σPQ is replaced by

(D1,� D2,� D3,�)

σPQ,1

σPQ,2

σPQ,3

.

Consequently, a Lagrange multiplier (LM) test can be performed to determine whetherthe additional factors improve the model significantly. In addition to the parametersestimated in (7), the model has four additional parameters (two for the innovation inthe efficient price due to trades/quotes and two for the innovation due to both eventsoccurring). As such the LM statistics are χ2 distributed with four degrees of freedomand a critical value of 13.3 at the 1% level. The information from the LM statistics canbe used to determine which extension of the model yields significant improvements.

We first consider whether different trading volumes reveal differences in privateinformation. This allows us to assess whether informed traders prefer to trade largevolumes to exploit the information they have or whether informed traders attemptto hide their information by splitting orders into smaller pieces. Barclay and Warner(1993) suggest that informed traders prefer to trade at medium-sized volumes, be-cause high-volume trades would reveal their information and low-volume trades aretoo costly in terms of transaction fees, results that are confirmed by Chakravarty(2001).6

We obtain traded volumes from Nastraq. To determine the impact of trade vol-ume on the innovation in the efficient price (in this case σP and σPQ) we createthree different categories: low volume (less than 200 shares traded), medium volume(between 200 and 1,000 shares traded), and high volume (more than 1,000 sharestraded). The cut-off points for these categories where chosen such that each categoryhas enough observations. Some summary statistics on traded volume are presented inpanel A of Table 5. Comparing the mean traded volume to the high fraction of volumein the medium and low categories indicates a right skewness in the distribution oftraded volume.

The LM statistics for traded volume are reported in the last column in panelA. For one-half of the stocks we find that the inclusion of traded volume leads toa significant increase in the likelihood of (7). These results are in line with Easley,

6 Another interesting extension related to the impact of private information is to analyze the impact oftrades where spreads are either large or small. Because informed traders only trade when the true priceof the asset is outside the spread, an informed trade occurring at a large spread may have a larger impacton the efficient price than an informed trade occurring at a small spread.


Table 5

Summary statistics and LM test of the model extensions

This table presents summary statistics and information about the percentage of observation in each categoryfor the variables considered in the extended models. The last column reports LM statistics and the numberof stocks for which the statistic is significant at the 1% level (the LM statistics are χ2 distributed with fourdegrees of freedom, having a critical value of 13.3 at the 1% level).

Panel A: Traded volume

Sample (%)

Traded vol. (×100) <200 200–1,000 >1,000 LM statistic

Mean 9.43 37.63 50.11 12.27 21.65Median 9.50 37.74 50.03 13.01 13.15Std. dev. 2.61 7.47 4.44 3.63 19.25Max. 14.79 57.63 58.07 18.54 66.24Min. 3.80 28.24 38.35 4.03 0.44Significant at 1% 10

Panel B: Quoted volume at inside

Sample (%)

Quoted vol. (×100) <500 500–2,000 >2,000 LM statistic

Mean 27.95 23.71 42.25 34.05 473.32Median 23.24 21.62 43.23 33.90 310.30Std. dev. 14.43 11.35 5.61 13.68 462.32Max. 59.87 58.40 51.28 52.18 1947.6Min. 6.99 13.78 33.05 4.61 60.8Significant at 1% 20

Panel C: Number of dealers at inside

Sample (%)

Num. dealers 1 dealer 2–5 dealers >5 dealers LM statistic

Mean 2.82 55.11 30.64 14.25 738.71Median 2.59 52.92 31.50 11.25 521.75Std. dev. 0.90 9.02 5.38 9.03 640.69Max. 4.34 79.09 37.05 30.19 2813.6Min. 1.36 44.00 19.97 0.95 90.7Significant at 1 % 20

Panel D: Type of dealers at inside

Sample (%)

ECN MM Both LM statistic

Mean 42.87 22.44 34.69 561.02Median 41.63 22.18 36.47 437.80Std. dev. 7.76 5.48 8.61 387.34Max. 62.45 32.14 48.11 1388.00Min. 31.69 14.65 16.08 155.10Significant at 1% 20


Kiefer, and O’Hara (1997) who find that only in some cases traded volume containsadditional information.

The second extension we consider is the impact of quoted volume at the inside onthe public information component. Because all trades at Nasdaq have to be executed atthe inside quotes or at better prices, large quoted volumes at the inside indicate dealers’willingness to trade large quantities. Since dealers are risk-averse toward informedtraders, large quoted volumes at the inside indicates they expect the presence offew informed traders. Hence, high quoted volumes at the inside are expected to beassociated with a higher level of public information relative to the amount of privateinformation.

Since the inside quote data of Nastraq do not include quoted volumes at theinside, we use the dealer quote dataset to obtain these volumes. From this datasetwe maintain an array of all the most recent dealer quotes. These dealer quotes arethen matched with the inside quotes. Every time the inside quote is innovated, werecord the total quoted volume at the inside by all dealers. When only a bid or askis innovated we record the associated volume; when both are innovated we considerthe average volume.

Again, three categories are created for quoted volume: low (below 500), medium(between 500 and 2,000), and high (above 2,000). Summary statistics on quotedvolume at the inside are reported in Panel B of Table 5. Mean quoted volume atthe inside is approximately three times the mean traded volume. Again, we observethe same pattern as with trades. A large fraction of the quoted volume lies below themean, indicating a right-skewed distribution.

LM statistics for quoted volume are reported in the last column of panel B.Statistics are highly significant for all stocks and indicate that quoted volume at theinside affects the public information component.

The number of dealers that set the inside is closely related to quoted volume.It differs in one respect, however. A certain amount of volume may be quoted byone single dealer or shared by many. One dealer quoting a large volume can easilywithdraw her quote. When there are many dealers quoting the inside, the inside quotewill be more firm. The number of market makers at the inside is thus informative aboutthe firmness of the inside quote and we expect a large impact of public informationon the efficient price when many dealers set the inside.

Again, we obtain these data from the dealer quote data provided by Nastraq.Dealer quotes are matched with the inside quotes and we record the number ofdealers at the inside. When only one quote (bid or ask) is innovated, we recordthe number of dealers on the innovated quote; when both quotes are innovated, wetake the average number of dealers at the inside. In Panel C of Table 5 we presentsome summary statistics on the number of dealers at the inside quote. On average,there are approximately three dealers at the inside, although the inside quote is set byone dealer more than half the time.

The last column in panel C again reports the LM statistics for the number ofdealers at the inside. As with quoted volumes, all statistics are highly significant.


Compared to the total quoted volume, we find that more dealers at the inside leads toa larger improvement in the likelihood function. We expect that many dealers at theinside will be more informative than few at the inside.

Finally, we consider whether the type of dealer that sets the inside matters. Herewe distinguish between traditional market makers and ECNs. The importance of theseECNs has grown dramatically since the introduction of the OHR. After the introduc-tion, private investors could compete directly with market maker quotes by trading onan ECN. Recent research has indicated that ECNs often quote more efficient pricesthan traditional market makers (Huang, 2002), indicating the importance of ECNs. Asecond argument that motivates a difference between market maker and ECN quotesis provided by Simaan, Weaver, and Witcomb (2003).7 Before the introduction ofthe OHR, Nasdaq market makers used the Instinet ECN as a venue to trade withother market makers and institutional investors. Because there was no need to includethese prices in the NBBO, this caused a discrepancy between prices quoted at Nasdaq(retail prices) and prices quoted on Instinet (wholesale prices). Additionally, due tothe tacit collusion among several leading market makers (see Christie and Schultz,1994), other market makers were reluctant to quote competitively at Nasdaq out offear of retaliation. When the OHR was introduced, all market maker quotes posted atECNs had to be included in the NBBO, effectively annihilating the discrepancy be-tween wholesale and retail prices. It also provided a means for market makers to postcompetitive quotes anonymously, avoiding potential retaliation from other marketmakers. Again, this indicates that ECN quotes may be more efficient. We thereforetest whether quotes of an ECN or market maker are more informative.

We separate dealers into two different categories, market makers and ECNs.Within the ECN category we include regular ECNs, such as Island and Instinet, andthe Chicago Stock Exchange. The market maker category includes all traditionalmarket makers and those entities registered as order entry firms. The latter, however,represent a very small fraction of quotes disseminated by market makers. Again, wematch these quotes with the inside quotes and determine which type of dealer is at theinside (ECNs, market makers, or both). In this case we make no distinction betweenone or both quotes being innovated.

In Panel D of Table 5 we present the percentages of the inside quotes that areset by either ECNs alone, by market makers alone, or by both. Overall, the highestpercentage is found for ECNs at the inside, followed by both. The lowest percentage isfound for only market makers at the inside (these percentages are in line with Simaan,Weaver, and Whitcomb, 2003). The last column in panel D reports the LM statisticsfor the type of dealer at the inside. All statistics are highly significant, indicating thatthe type of dealer at the inside matters.

The LM statistics provide a clear indication of which factors affect the innovationin the efficient price. For the trades, we find significant LM statistics in approximately

7 We thank a referee for pointing this out.


Table 6

Model extension: Number and type of dealer at the inside

This table presents the results for the extended models, where the innovation in the efficient price dependson the number of dealers that are at the inside (Panel A) and on the type of dealer at the inside: marketmaker or ECN (Panel B). We report innovations in the efficient price due to quotes (σQ) and due to both(σPQ) for the different categories. Each panel also reports the number of cases in which parameter estimatesin that category are larger than the parameters in the other categories (e.g., the first number reported inPanel A shows that for all 20 stocks σQ is larger for the 2–5 dealer category than for the 1 dealer category).

Panel A: Number of dealers at the inside

σQ σPQ

1 dealer 2–5 dealers >5 dealers 1 dealer 2–5 dealers >5 dealers

Mean 0.75 0.94 1.12 0.88 0.97 1.10(Avg. std. err.) (0.025) (0.023) (0.020) (0.044) (0.047) (0.041)Median 0.65 0.805 1.075 0.8 0.92 1.095Std. dev. 0.3659 0.4880 0.5055 0.4430 0.5017 0.5020Max. 1.75 2.36 2.46 2.02 2.29 2.37Min. 0.31 0.39 0.42 0.25 0.21 0.292–5 dealers larger 20 165 dealers larger 20 20 19 19

Panel B: Type of dealer at the inside

σQ σPQ

ECN MM Both ECN MM Both

Mean 0.73 0.92 1.01 0.84 0.95 0.96(Avg. std. err.) (0.016) (0.051) (0.020) (0.049) (0.072) (0.059)Median 0.64 0.82 0.92 0.77 0.89 0.94Std. dev. 0.3378 0.4363 0.4827 0.4540 0.5115 0.4797Max. 1.67 2.10 2.40 1.90 2.17 2.18Min. 0.32 0.38 0.42 0.25 0.21 0.29MM larger 20 19

50% of the cases. Hence, we do not expand the model in this direction. For the quotedvolume at the inside, we find all LM statistics to be significant, but we expect greaterimprovement for the number of dealers at the inside. This is one direction in whichwe expand the model. Finally, we expand the model to incorporate information as towho is at the inside—market makers or ECNs.

In Panel A of Table 6 we report the results for the extended model, including thenumber of dealers at the inside. Because the number of dealers at the inside affectsthe parameters σQ and σPQ, only these parameters are reported (the parameter σ P isnot affected much by the inclusion of the dummy variables). There is a very cleartrend for both σQ and σPQ. The more dealers that are at the inside, the larger the effectof a quote innovation on the efficient price. Hence, the more dealers are at the inside,the more informative these quotes are (as the fraction of σQ/σ P increases). Anotherinteresting feature observed from Panel A is the difference observed between σQ and


σPQ. When there are few dealers at the inside, trades clearly add information to theinnovation in the efficient price, because the low category σPQ is larger than σQ.However, when there are many dealers at the inside, the additional information thattrades add disappears, confirming the notion that the presence of private informationdecreases when more dealers are at the inside.

We present results for the innovations in the efficient price when different typesof dealers are at the inside in Panel B of Table 6. Again, only the results for σQ and σPQ

are reported. The effect of the inclusion of these dummy variables again has a smallimpact on the innovation in the efficient price due to trades (not reported). In all caseswe find that market makers are more informative at the inside than ECNs. This may bedue to the fact that ECNs are typically the more efficient dealers (Huang, 2002) andat the inside most of the time. When a market maker then takes the inside, this maybe a strong signal that she is informed about the location of the efficient price. In thecontext of Simaan, Weaver, and Whitcomb (2003), we could argue that the benefitsof the market maker being at the inside (potential profits) outweigh the costs ofretaliation, again providing a strong signal to the market. Another result is that quotesare most informative when both ECNs and market makers are at the inside, confirmingthat more dealers at the inside reveals more information. We finally note that wheneither an ECN or a market maker is at the inside, trades still add some additionalinformation σPQ. However, when both are at the inside the additional information oftrades disappears. This is, of course, related to the result obtained from the numberof dealers at the inside, because both types of dealers at the inside indicates that moredealers are at the inside.

6. Conclusions

We propose a new model to infer public and private information. The model isdesigned for nonsynchronous, ultra-high frequency data and uses all trades and quotesas they arrive. As both trades and quotes are cointegrated, they share a common trend,also called the efficient price. We investigate the impact of trades and quotes on theinnovation in this efficient price. We relate the impact of trades to private informationand the impact of quotes to public information. In addition, the model addresses theissue of the relevant time scale for the price process by including a duration functionin the efficient price process. The model is applied empirically to 20 Nasdaq stocksand is extended to incorporate several (Nasdaq-specific) variables that potentiallyaffect public and private information.

We find that private information explains only a small fraction of the movementin stock prices, on average only 9.43% of daily stock price movements. Testing for theimpact of time on the price process, we find that time has a slightly negative impact onthe innovation in the efficient price, rejecting the notion of the price process evolvingin calendar time and confirming the findings of Clark (1973).

We consider four directions to extend the model. First, we test whether differenttrade volumes reveal differences in private information and find that the inclusion of


trade volume would improve the likelihood function only slightly. Second, we con-sider the impact of quoted volume at the inside on the public information component.We find that quoted volume would improve the likelihood function significantly.Third, and closely related to quoted volume, we consider the impact of the numberof dealers at the inside on the public information component. The inclusion of thisvariable would improve the likelihood function more than quoted volume at the in-side, and the model is extended in this direction. We find that when many dealersare at the inside, inside quotes are more informative. Finally, we test whether type ofdealer (market maker or ECN) at the inside matters. Again, we find that the inclusionof these variables would improve the likelihood function significantly and we extendthe model in this direction. We find that traditional market makers at the inside aremore informative than ECNs at the inside.

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Documents

Inferring Public and Private Information from Trades and Quotes