The Price Impact of Stock Trades:
Evidence from the Prague Stock Exchange
Vít Bubák Filip µZikešy September 12, 2005
Abstract
Using high-frequency trade and quote data from the Prague Stock Exchange, this paper investigates the price impact of stock trades using a vector autore- gressive model. We …nd that (a) full impact of a trade on the security price is not felt instantaneously but a with a protracted lag, (b) as a function of trade innovation size, the ultimate impact of the innovation on the quote is positive, increasing, and convex, and (c) there is a signi…cant causal pattern (acc. to Grange-Sims) running from lagged quote revisions to trades as well as from trades to quote revisions.
Keywords: vector autoregressive model, market microstructure, price impact of stock trades
JEL: G14, G18
1 Introduction
Starting with Kyle (1985), Glosten and Milgrom (1985) and Easley and OHara (1987), market microstructure research has paid a signi…cant attention to the e¤ect of asymmetric information on market prices. Central to the conclusions of the large body of literature on the subject that has since appeared is the fact that if some traders have superior information about the underlying value of an asset, their trades could reveal what this underlying value is and so a¤ect the behavior of a security price. Put di¤erently, trades could convey information and therefore have a persistent impact on the stock price.
The magnitude of the price e¤ect for a given trade size is generally held to be a positive function of the proportion of potentially informed traders in the population, the probability that any of these traders has in fact observed the private information signal, and the precision of the corresponding private information (see OHara, 1995). Given the close dependence of the price impact on these factors, we are
Institute of Economic Studies, Charles University in Prague.
yInstitute of Economic Studies, Charles University in Prague and Institute of Information The- ory and Automation, Academy of Sciences of the Czech Republic. Address for correspondence:
Opletalova 26, 11000 Praha 1, Czech Republic. Email: zikesf@yahoo.com. The …nancial support from GACR and GAUK under grants no. xx/xxx/xx and 487/A-Ek/2005, respectively, is gratefully acknowledged.
provided with a strong motivation for the determination of such impact using a real-world transaction data. Consequently, in the present study we strive to assess the size of the price impact using the high-frequency trade and quote transaction data from the Prague Stock Exchange (PSE).1 As it should become clear in the following section, the market considered here is an order driven specialist market in which the market-maker exposes bid and ask quotes to the trading public.
Over the past twenty years, a large body of theory has evolved that analyzes the market maker’s exposure to trader’s with superior information. With regard to the extent of the information asymmetry, this body of theory leads to two important empirical predictions.
The …rst prediction assumes that the asymmetry is positively related to the spread. Empirical researchers have since sought to …nd measurable proxies to exam- ine posted bid-ask spreads.2 Although such procedure has its advantages (e.g., the bid-ask spreads are relatively easy to observe) there are di¢ culties connected with the price discreteness or the existence of the clearing fees that e¤ectively render the examination of the asymmetric information using the bid-ask spread nontrivial. In other words, it is always di¢ cult to fully resolve which components of the bid-ask spread re‡ect the asymmetric information and which mirror other information such as the transaction costs. On the Czech market,Hanousek and Podpiera(2002) explored the impact of informed trading on the composition of the bid-ask spread.
One of the major conclusions of their study is that the Czech market-maker-based trading system is rather e¢ cient in dealing with informed trading. In fact, according to their study less than 20% of the bid–ask spread is explained by informed trad- ing, which corresponds roughly to the share of the adverse-selection component in developed markets.
Still a di¤erent group of studies has concentrated on the price impact of the trade.
The works ofGlosten and Harris(1988) andFoster and Viswanathan(1988) were the original contributions to have started the line of analyses on the potential impact of the trade on quoted price. Nevertheless, even these analyses were originally based on a number of tenuous assumptions such as serial independence of transac- tion, no delay in the e¤ect of a trade on the price, and a linear trade-price relationship with the intercept corresponding to …xed transaction costs. There are good reasons for questioning these assumptions. In their studies, Garman (1976) and Stoll (1976) were among the …rst to show that inventory control considerations induce se- rial dependencies in trades, as do price pressure e¤ects and order fragmentation. In other models, lagged adjustment to new information and exchange-mandated price smoothing3 may lead to distribution over time of the information impact as well, although we must say the latter is not relevant to the analysis of data from the PSE as (except for very extreme cases) the quotes may be adjusted freely. Finally, the form of the functional relationship between trade size and information is a conse-
1Our analysis is based on an empirical investigation of six of the most active securities traded on the PSE’s main market.
2For one of the …rst studies on the subject, refer to McInish and Wood(1988).
3Price smoothing occurs when the market-maker is compelled to set the quotes in such a way as to ensure a smooth price adjustment path. If this happens, the market-maker may not be able to revise the quotes fully and as immediately as free use of the news would allow.
quence of a fundamentally unobservable cost and information structure, and many better performing structures thence necessarily entail nonlinear e¤ects.
Hasbrouck(1988) has attempted to partially resolve information and inventory control e¤ects according to the persistence of their impact on the security price. Has- brouck has suggested that the inventory control e¤ects be considered as inherently transient, while the information inferred from a trade due to asymmetric information is assumed to be permanently impounded in the stock price. In the study at hand, we follow the work ofHasbrouck(1991a, 1991b) by assuming that such transience characterizes not only inventory control e¤ects but most other non-information im- perfections (e.g. price discreteness, price pressure, or order fragmentation) as well.
Our approach is thus both attractive and practical as it implies that the information e¤ect of a trade be measured as that which persists over a substantial period of time.
One important feature of the approach adopted byHasbrouck(1991a) as well as in this study is its generality. In his earlier paper,Hasbrouck(1988) noted that if there were to be any private information inferred from a trade, it should be in- ferred "[] not from the total trade but from that component which was unanticipated - the trade innovation". Still, to investigate this proposition, the paper assumed that the component of the trade which was unexpected depended solely on knowledge of the past trade history. In other words, the study e¤ectively employed a univariate trade innovation. Hasbrouck (1991a) as well as the present study generalizes the investigation of the implications of trade innovation to incorporate broader infor- mation sets (such as histories of the quote revisions and nonlinear functions of the trade variables) and thence achieves a broader picture of the asymmetry information e¤ect.
We model the trades and quote revisions as a system characterized by auto- and cross-correlations of a very general nature. The information impact of a trade may be formally de…ned as the ultimate persistent impact on the price quoted resulting from the unexpected component of the trade. This persistent impact is preferred to the immediate impact because the latter may be contaminated by transient liquidity e¤ects. Use of the trade innovation (rather than the total trade) as the driving force has the e¤ect of excluding the portion of the trade which is predictable as (by de…nition) it conveys no information. Relating the ultimate price impact to just his trade innovation then e¤ectively makes any concerns about market imperfections unnecessary.
This paper is organized as follows. In Section 2 we provide a short description of the Prague Stock Exchange (PSE), including an introduction into its market mi- crostructure and the trading rules. A major purpose of our analysis is to examine and consequently better understand the dynamics of trade and quote process on a representative central European stock market and this sections should serve as a key part of this understanding. In Section 3, we describe basic methodology and develop the estimation techniques employed in the analysis. We also motivate and interpret the vector autoregression model (VAR model) and show that the VAR modeling strategy applied to trades and quotes allows, at least in principle, a reso- lution between private information (trade innovation) and public information (quote revision innovation). Section 4 describes the dataset and provides the discussion of the results of estimation of a simple bivariate as well as more advanced quadratic
VAR models. Finally, Section 5 summarizes the results and concludes the study.
2 Prague Stock Exchange
Founded in 1992, the Prague Stock Exchange (PSE) is now the leading securities market organizer4 in Central and Eastern Europe (CEE), covering more than 99%
of the total trade value in the Czech Republic and at times up to 50% of the total trade value in the CEE countries. Securities registered on the PSE are traded on three markets: main, secondary, and free markets, where the main market is the most prestigious market on the Exchange.5
The PSE is a fully electronic exchange with the trading based on automated processing of its member’s orders and instructions for the purchase and sale of secu- rities. Trading on the PSE is segmented into two distinct sub-systems with distinct prices: a quote driven system (referred to as SPAD), and an order driven system (described by automatic trades). The SPAD is a price-driven trading system based on the activity of market makers.6 In the period assessed in this study (2004), the system accommodated eight of the most liquid Czech securities (called blue-chips) supported by ten market makers.
Table 1: SPAD Issues
Issue ISIN Std Qt Max Spread AL Qt
Cesky Telecom CZ0009093209 5,000 6 95,000
CEZ CZ0005112300 10,000 2 100,000
Erste Bank AT0000652011 2,000 8 34,000
Komercni Banka CZ0008019106 1,000 20 11,000
Orco LU0122624777 500 10 31,000
Philip Morris CR CS00008418869 100 200 2,200
Unipetrol CZ0009091500 10,000 3 300,000
Zentiva NL0000405173 3,000 8 51,000
Parameters of issues in SPAD as of April 5, 2005. Values for Std Qt (Standard Quantity) and AL Qt (Above-Limited Quantity) are in pieces. Source: PSE.
The SPAD operates in two phases: an open phase and a closed phase. During theopen phase (9:30 to 16:00 CET), all market makers are obliged to publish their quotes (buying and selling prices) for issues for which they act as market makers. It is this period of the trading hours that is directly relevant for our study as the actual
4According to the European Federation of Stock Exchanges, during the …rst 6 months of 2005 the PSE was the most active exchange in Central and Eastern Europe. With nearly EUR 17.5bil of total equity vol traded, the PSE was …rst to Vienna (EUR 16,9bil), as well as Warsaw and Budapest.
5The main market has the most stringent conditions regarding the admission of securities to trading in the market.
6Hanousek and Podpiera(2003) studied the functioning of SPAD since its launch on the PSE in 1998. They conclude that the new system has succeeded in increasing the transparency of the market and that it has improved the price discovery function of the exchange by attracting a large portion of order-‡ow to the main market.
trading takes place then.7 For each security in SPAD, there has to be a minimum of three market makers8 quoting prices. Each market maker is required to quote a buy and a sell price at all times during the open phase for a standardized number of shares or its multiple (maximum quadruple) to be delivered on a T + 3 basis.
The trading committee also sets a maximum bid-o¤er spread for quotes of the same maker to bring prices of purchases and sales closer (refer to Table (1) above).
All quotes of all market makers take the form of a buy or sell instruction sent to the PSE and are immediately displayed via electronic means to all PSE members.
Any member can immediately take the best quote displayed within SPAD, resulting in instructions being matched and a trade being recorded and published. Quotes worse than the current best quotes within SPAD are informative only. Once a given market maker’s quote becomes the best bid or o¤er available within SPAD (i.e., best quote), such quote becomes binding for that market maker. This means that the market maker is obligated to conclude a trade at such bid or o¤er price quoted should any other PSE member choose to accept it. On the other hand, the market maker is free to adjust his quotes up or down based on its assessment of demand and supply in the stock at any time. Once the best quote is accepted and a trade is thus recorded, the respective market maker is allowed up to a 3-minute recovery period to recalculate its positions and reset quotes. The second best indicative quote of another market maker immediately becomes the best quote and is binding from that moment on, until that quote is accepted too, or until a better quote appears within SPAD.
During the open phase, PSE members are allowed to conclude OTC trades with respect to SPAD securities with each other (OTC SPAD trade) only within a narrow price range often referred to as apermitted range. The permitted range is constantly changing as market makers publish their quotes and it is de…ned as an up-to-the- minute price range limited by the price 0.5% below the best SPAD bid at the bottom and by the price 0.5% above the best SPAD o¤er at the top.9 In addition, OTC SPAD trades must be reported to the PSE within a 5-minute deadline after such trade is concluded in order to preserve market transparency. The reason for manda- tory reporting of OTC SPAD trades is to direct PSE members to SPAD and curb OTC trading among them, as OTC is considered less transparent for the market.
Theopening price of an instrument traded in SPAD is equal to the midpoint of the permitted range as of the start of the open phase; in other words, it is calculated based on the quotes of market makers at the start of the session. The closing price of an instrument traded in SPAD is equal to the midpoint of the permitted range at the close of the open phase (16:00 CET). If during the open phase the arithmetical midpoint of the up-to-the-minute permitted range deviates by more than 20% from
7As a result, in the following lines we describe only the trading mechanism relevant to the open phase. For a detailed discussion of the SPAD market as well as the closed phase, refer to Hanousek and Podpiera(2003). For a detailed description of the microstructure of the Prague Stock Exchange, see SeeBubak and Zikes(2005).
8Non-market-making members are subject to limitations as to their daily maximum trading volume with the market makers, as a protection measure for market makers against excessive settlement risks.
9However, OTC SPAD trades with large blocks of shares with total value larger than CZK 40 million can be registered with any price even outside the current permitted range.
the arithmetical midpoint of the permitted range as of the start of the open phase, all quotes by the market makers become informative only, including the best quotes.
Naturally, trades already concluded are not a¤ected by this rule. The reason for this rule is to protect market makers against excessive losses once dramatic price moves occur.
3 Econometric Framework
In this paper we focus on the information content of stock trades within the frame- work of a simple statistical microstructure model that can accommodate both (per- manent) asymmetric information and (transitory) inventory control e¤ects. The underlying microstructure theory as well as statistical issues are discussed in detail inHasbrouck (1991a, 1991b, 2004) and we therefore provide only a brief overview here.
FollowingHasbrouck(1991a, 1991b, 2004) we denote byqtthe quoted midpoint of the prevailing bid and ask prices and by xt the signed traded volume and adopt the following time ordering convention: the prevailing quotes at timetare those set one period before, i.e. qt 1; a trade is executed, xt, nontrade public information arrives and consequently the market maker revises his quotes implying qt:If there is no trade between two consecutive quote revisions we set the correspondingxt to zero.
To develop some intuition for the statistical model we …rst discuss the structural model from which it can be easily derived. The discussion is based onHasbrouck (1991a,1991b). The model is set in transaction time. We assume that the e¢ cient stock price,mt, follows random walk
mt=mt 1+zv2;t+v1;t; (1)
wherev1;tis a white-noise term re‡ecting all public nontrade information, while v2;t is a serially uncorrelated innovation in trades withE[v1;tv2;t j] = 0 for all j: It is therefore only the unexpected part of the trade that conveys information about the e¢ cient price and not the trade itself. The process for the quoted midpoint is given by
qt=mt+a(qt 1 mt 1) +bxt; (2)
0 < a < 1 and b > 0. According to this speci…cation, the quoted mid-price is a function of three components: the e¢ cient price, lagged deviation of the quoted midpoint from the e¢ cient price and the signed volume. This has an inventory control interpretation: following a buy (positive xt) the market maker will raise the quoted midpoint in excess of mt in order to induce sales. The adjustment to the quoted midpoint occurs with lags and thus besides inventory control, it also re‡ects other market imperfections that imply lagged adjustments such as price discreteness, price-dependent trading strategies, etc. The …nal equation of the model is the demand schedule given by
xt= c(qt 1 mt 1) +v2;t; (3)
wherec <0. Altogether, equations (1)-(3) imply the following VAR representation10 for quote revision, de…ned asrt=qt qt 1, and traded volume, xt:
rt = (z+b)xt+ [zbc (1 a)b]xt 1+a[zbc (1 a)b]xt 2+ +v1;t; xt = bcxt 1 abcxt 2 a2bcxt 3+ +v2;t:
The structural VAR model above may, however, be to restrictive from the statistical point of view, and hence we use a more ‡exible VAR speci…cation that also includes lagged quote revisions:
rt = a10+a11rt 1+a12rt 2+ +b0xt+b11xt 1+b12xt 2+ +v1;t; (4) xt = a20+a21rt 1+a22rt 2+ +b21xt 1+b22xt 2+ +v2;t: (5) Since only innovations to trades are assumed to convey information about the e¢ - cient price, the statistical signi…cance of the coe¢ cient b0 is not very informative.
This is because it measures the total impact of both expected and unexpected part of the trade. To identify the informativeness of the trade, we adopt the two measures suggested inHasbrouck(1991a, 1991b, 2004). The …rst approach is based on the cumulated impulse response function which measures the total impact of a shock to trade on the subsequent quote revision. The impulse response function is derived from the moving average representation of the VAR model. De…ning yt = (rt; xt)0 and rewriting the VAR model in (4) and (5) as
Ayt=c+B1xt 1+B2xt 2+ +vt;
where
A= 1 b0
1 ;Bi= a1j b1j
a2j b2j ;c= a0
c0 ;vt= v1;t v2;t ;
the VMA representation is given by (provided it exists)
yt= +"t+ 1"t 1+ 2"t 2+ ;
where"t=A 1vtand the matrices , 1; :::can be found e.g. inHamilton(1994).
The cumulative impulse-response function is then the plot of the partial sums
S("jt) XS s=0
@yi;t+s
@"jt "jt
and it measures the total impact of a shock in"jtonyi;t+S:Setting"jt to a particular value of unexpected dollar volume and choosing S su¢ ciently large then produces a measure of the estimated total impact of a trade innovation on the e¢ cient price.
This is due to the fact that forSsu¢ ciently large all transient microstructure e¤ects die out leaving
An alternative measure of the impact of trade on quote revision is based on random-walk decomposition (Hasbrouck, 1991b). Letwt=mt mt 1be the inno- vation to the e¢ cient price. Then the impact of the trade innovation on the e¢ cient
1 0SeeHasbrouck(1991b) for derivation.
price, conditional on all available information t 1;is E[wtjxt E[xtj t 1]]: A natural measure of the informativeness of trades relative to the total public infor- mation is
V ar[E[wtjxt E[xtj t 1]]]
V ar[wt] Rw;x2 :
This is the proportion of the variation in the shock to the e¢ cient price that can be attributed to the innovation in trade. It is denoted R2w;x because when the public information set includes the trade and quote history and expectations are formed as linear projections, it corresponds to the coe¢ cient of determination in a regression ofwt on the trade innovation. The formula for computing R2w;x from the MA representation is provided inHasbrouck (1991b).
For practical purposes, the in…nite order VAR and VMA must be truncated at some …nite lag. Due to high persistence of quote revisions we choose to trun- cate the VAR model and its VMA representation at 12 and 20 lags, respectively.
A heteroskedasticity-robust version of the Breusch-Goddfrey LM test proposed in Wooldridge(1991) is used to asses the adequacy of the this speci…cation.
4 Data Description
We use high-frequency data on six of the most actively traded stocks listed on PSE’s main market (SPAD) between January 5, 2004, and November 12, 2004. Although there were two more securities listed on SPAD in the period in question, we do not consider these in our analysis11 as their trading generated a relatively small number of transactions.
The data are extracted the same Trade and Quote datasets obtained from the PSE. Prior to constructing the time series of trade and quote revisions in the manner consistent with the model’s notation and methodology, we adjust the data as follows.
First, we remove transactions that took place outside of normal trading hours. In addition, we delete the days on which we know that a signi…cant interruption in trading had occurred. Second, we remove the …rst transaction of each day as it is likely to be in‡uenced by the trading outside of normal trading hours. Finally, in case of quote data, we consider only unique quotation times and hence regard the simultaneously recorded quotes as a single quotation. Following these adjustments, we merge the …les using a data merging program.
The model discussed in the previous section is speci…ed in transaction time.
In other words, the model’s internal clock t is de…ned directly by the transaction sequence. In practice this means that the …rst observation in the sample (i.e., the
…rst trade or quote on January 5, 2004) occurs at time t0. Consequently, the t is incremented each time a new trade or quote is posted. There is one important exception to this rule: followingHasbrouck(1991a), we assign the sametsubscript to a quote revision that occurs within 15 seconds following a trade.
Since the transaction data provided by the PSE are not classi…ed according to the nature of a trade (buy or sell), we use the Lee and Ready (1991) midquote ruleto classify a trade. With this rule, the prevailing quote mid-point corresponding
1 1The two other securities are Ceske Radiokomunikace and Zentiva.
to a trade is used to decide whether a trade is a buy, a sell, or undecided. If the transaction price is higher (lower) than the quote mid-point, it is viewed as a buy (sell). If the price is exactly at the mid-point, the nature of the trade (buy or sell) remains undecided, andxtis set to zero.
It sometimes occurs that multiple trades take place at the same second. We follow Engle and Russell (1998) and treat multiple transactions at the same time as one single transaction and aggregate their trade volume and average prices.
Table 2: Summary Statistics for Trade Data
CEZ Erste KB PMCR Telecom Unipetrol
# of observations 14,297 8,415 20,133 7,843 15,615 3,949
open phase* 14,083 8,161 19,883 7,551 15,380 3,683
avg price (CZK) 323 2,637 2,885 16,390 207 74
avg volume (shares) 10,283 1,402 1,327 142 22,510 26,301 avg volume (CZK mil) 4.510 2.618 3.816 2.343 3.311 1.963 mean duration (sec) 72.2 559.3 51.1 566.4 55.7 1,038.8
- std. deviation 2,798.7 1,556.3 2,419.2 1,668.6 2,659.0 2,260.5 - maximum 17,727 22,915 16,896 21,771 19,069 19,061
Summary statistics for the trade data for CEZ, Erste Bank (Erste), Komercni Banka (KB), Philip Morris CR (PMCR), Cesky Telecom (Telecom), and Unipetrol from January 5 to November 12, 2005.
’Open phase’ shows the number of transactions during open phase (from 9:30 to 16:00) when cleaned of the …rst observation. The statistics describe the adjusted data.
In Table 2, we present basic summary statistics for the trade data. This ta- ble shows that Komercni Banka (KB) is the most frequently traded stock in the sample, with the average duration equal to 51 seconds. Unipetrol is the least fre- quently traded stock of the sample with an average duration of 1,039 seconds, or 17.5 minutes. Average trading volume varies from 142 shares (PMCR) to 26,301 shares (Cesky Telecom).
Table 3 summarizes the basic characteristics of the quote data. As could be ex- pected, the Unipetrol stock exhibits once again the longest (mean) duration between individual quotes.
Table 3: Summary Statistics for Quote Data
CEZ Erste KB PMCR Telecom Unipetrol
# of observations 42,004 34,384 49,534 25,246 26,216 11,529 open phase* 39,608 32,469 46,425 23,335 24,845 10,746 avg mid-quote (CZK) 205.6 2,999 2,898 16,574 323.7 73.3 mean duration (sec) 129.2 156.1 110.6 214.8 205.3 449.9
- maximum 14,752 14,612 9,086 18,197 13,670 21,790
Summary statistics for the quote data for CEZ, Erste Bank (Erste), Komercni Banka (KB), Philip Morris CR (PMCR), Cesky Telecom (Telecom), and Unipetrol from January 5 to November 12, 2005.
’Open phase’ shows the number of transactions during open phase (from 9:30 to 16:00) excluding multiple quotes. The statistics describe the adjusted data.
5 Empirical Results
We begin the empirical analysis with a simple bivariate model outlined in Section (3), equation (4). The model is based on the assumption that quote revisions are linear in the (signed) trade variable and hence presents only a tenuous approximation of the real quote revision process. Indeed, as Hasbrouck (1991a) emphasizes, not only are the underlying cost and information functions unlikely to be linear but "[]
the order entry and trade negotiation processes are almost certainly dependent on trade size". Consequently, a model which is more realistic but still amenable to linear estimation will be considered later in the section.
The present model as well as the ones that follow were estimated using ordi- nary least squares methodology of the multiple-equation system.12 Due to the large number of observations all statistical inferences are drawn on the 0.1% signi…cance level.13
5.1 Simple Bivariate VAR Model
Estimation results for the simple bivariate VAR model for all six stocks under analy- sis are presented in Table (4). The results of the Breusch-Goddfrey LM test for the presence of serial correlation in the residuals as well as the results of an ARCH LM-test (Engle, 1982) are also presented in the table. The latter test provides signi…cant evidence of autoregressive conditional heteroskedasticity in the VAR dis- turbances(v1;t; v2;t), since the null hypothesis of no ARCH-e¤ects is rejected at each reasonable signi…cance level.14
We …rst examine the price equation. Of particular importance are the coe¢ cient estimates of (xt; : : : ; xt 12) corresponding to (b0; b1;1; : : : ; b1;12). The coe¢ cient estimates are all signi…cant with the signi…cance generally decreasing as we move to lower lags.15 The estimates are predominantly positive with a hint of reversal present around the tenth lag. Let us now observe the behavior ofxtwhich implies how much, on average, the quote midpoint is raised immediately following the purchase order.
The impact ofxt is most pronounced in case of Philip Morris CR (PMCR). In fact, the number is more than nine times as large as the second highest estimate in the sample (Erste). For other securities in the sample, the impact ofxtis much smaller.
With the exception of Erste Bank, the lagged values of rt show a statistically signi…cant negative impact of the …rst lag on the quote midpoint. The impact is positive starting with the second lag. In case of Unipetrol, the negative impact is slightly more persistent. From a purely descriptive point of view, this pattern implies negative lag-1 serial correlation in the quote revisions.
Turning to the volume equation, we notice a relatively strong positive autocor- relation in trades re‡ected by the lagged values of xt coe¢ cients corresponding to
1 2The estimation was performed by Ox(version 3.40 for Windows).
1 3Note that the corresponding standard normal critical value for a two-sidedt-test is 3:3.
1 4An obvious extension of the present analysis would be to subsequently de…ne a bivariate GARCH-model that would allow to speci…cally model the conditional hetereskedastic e¤ects found in both returns and trading volume. We leave this possibility for further empirical research.
1 5We must understand that the magnitudes of the coe¢ cients are not very informative, since the volume was arbitrarily rescaled before estimation to ensure numerical stability.
(b0; b2;1; : : : ; b2;12). This is consistent with the observations of Hasbrouck and Ho(1987) andHasbrouck(1988, 1991a), and suggests simply that purchases tend to follow purchases, and similarly for sales. Indeed, as Hasbrouck (1991) points out, "[] this pattern of positive autocorrelation at low lags is highly typical". In particular, we observe a striking absence at low and moderate lags of the trade re- versal consistent with inventory control mechanisms. In this regard, the short-run predominance of positive autocorrelation that we observe is more consistent with lagged adjustment to new information.
Table 4: Estimates of Bivariate VAR Model
CEZ Erste KB PMCR Telecom Unipetrol
rt xt rt xt rt xt rt xt rt xt rt xt
const 0:0027
(3:83) 0:0000
( 0:49)
0:058
( 0:62)
0:0032
( 0:26)
0:028
(2:80) 0:068
( 3:45)
0:047
(0:37) 0:008
( 0:53)
0:003
(1:31) 0:133
( 3:96)
0:003
(2:10) 0:088
( 5:01)
ai1 0:053
( 7:01)
0:809
(5:41) 0:0007
(0:93) 0:0008
(1:00) 0:089
( 2:15)
0:016
(1:09) 0:055
( 5:23)
0:002
(2:61) 0:197
( 10:1)
0:376
( 5:95)
0:054
( 2:35)
0:035
( 0:37)
ai2 0:035
(5:55) 0:826
(6:04) 0:0014
(0:98) 0:0005
(1:00) 0:044
(4:49) 0:038
(4:36) 0:009
(0:93) 0:003
(4:09) 0:032
(3:77) 0:022
( 0:37)
0:008
( 0:31)
0:051
(0:51)
ai3 0:046
(8:34) 0:417
(2:99) 0:0013
(3:30) 0:0002
(0:93) 0:033
(5:11) 0:020
(2:72) 0:064
(5:61) 0:001
(2:02) 0:008
(1:11) 0:169
( 2:48)
0:014
( 1:37)
0:180
(1:49)
... ... ... ... ... ... ...
ai12 0:013
(2:68) 0:225
(1:78) -0:0002
( 0:31) 0:0001
( 2:32)
0:020
(3:11) 0:011
( 1:40)
0:035
(2:39) 0:0004
(0:74) 0:021
(2:81) 0:0242
(0:35) 0:015
(3:21) 0:016
( 0:17)
b0 0:0044
(14:11) - 0:139
(11:97) - 0:066
(11:54) - 1:32
(9:27) - 0:0025
(8:53) - 0:003
(4:31) -
bi1 0:0034
(11:28) 0:076
(11:98) 0:048
(0:99) 0:041
(8:38) 0:060
(9:81) 0:071
(13:38) 1:13
(7:95) 0:048
(5:93) 0:0022
(5:58) 0:011
(1:97) 0:0018
(2:42) 0:017
(2:42)
bi2 0:0019
(8:31) 0:046
(6:42) 0:027
(2:31) 0:048
(5:25) 0:030
(8:42) 0:071
(8:12) 0:245
(3:85) 0:058
(4:14) 0:0018
(5:54) 0:044
(2:76) 0:0019
(3:87) 0:079
(2:41)
bi3 0:0014
(5:51) 0:047
(4:14) 0:017
(2:88) 0:042
(2:48) 0:009
(3:84) 0:044
(5:15) 0:296
(2:92) 0:028
(3:60) 0:0002
(0:51) 0:040
(3:74) 0:0000
( 0:06) 0:034
(2:37)
... ... ... ... ... ... ...
bi12 0:0003
( 1:89)
0:013
(1:62) 0:289
(1:05) 0:004
(0:77) 0:005
( 2:33)
0:018
(2:48) 0:097
( 1:69)
0:008
(1:45) 0:003
( 0:76)
0:014
(1:82) 0:0011
( 1:45)
0:019
(0:85)
R2 0:053 0:021 0:002 0:009 0:055 0:02 0:062 0:012 0:048 0:010 0:008 0:031 ARCH(4) 49:93 362:1 1:88 250:1 348:7 103:0 10:76 26:1 70:9 94:4 0:26 175:1
LM(4) 16:27 12:07 1:81 3:29 1:08 6:61 10:33 4:80 2:02 15:30 8:87 7:14
Coe¢ cient estimates and White heteroskedasticity-robust t-statistics (in parentheses) for the price equation of the simple bivariate VAR model. The set of variables in the model include the price (quote midpoint) change (a) and trade indicator variable (b). ARCH (4) refers to Engle’s (1982) LM test for ARCH e¤ects of order 4 and LM(4) is the hetereskedasticity-robust LM test for autocorrelation in VAR residuals up to lag 4 proposed by Wooldridge (1991).
Asterix denotes signi…cance at 0.1 percent level. The period assessed runs from January 5 to November 12, 2004.
Other than the positive autocorrelation in trades, one of the primary factors in determining the model’s dynamic adjustment path, the pattern of negative lagged rt coe¢ cients in the xt speci…cation also stands out as noteworthy. Speci…cally, this pattern implies a Granger-Sims causality running from lagged quote revisions to trades (q 9 x). Testing for such causal pattern in the sample of data used in the estimation, we conclude that lagged quote revisions do Granger-Sims cause the trades.16 In addition, we also examine the Granger-Sims causality running from
1 6We use a formal Wald test with the null hypothesis that the quote revision (and later trade)
trades to quote revisions(x9q).17 With the exception of the Unipetrol stock, the causality pattern proves once again strongly signi…cant.
Table 5: Summary of Information Content of Trades
CEZ Erste KB PMCR Telecom Unipetrol
b0 0:0044
(14:11) 0:139
(11:97) 0:066
(11:54) 1:32
(9:27) 0:0025
(8:53) 0:003
(4:31)
Pbi 0:011
(17:49) 0:615
(2:35) 0:176
(13:29) 3:09
(10:44) 0:009
(7:98) 0:009
(5:74)
Granger Causality
H0:x9q 455:8 345:0 226:5 214:3 169:7 76:9 H0:q 9x 87:4 688:7 34:4 37:30 68:1 11:1
Random Walk Decomposition
Rw;x2 0:25 0:01 0:28 0:26 0:06 0:04
Cumulative Response (in CZK)
20(1sQ) 0:094 4:62 1:17 10:55 0:016 0:011
Summary of the informativeness of stock trades based on the simple bivariate VAR(12) model.
An alternative way to measure the impact of trade(s) on quote revision is based on random-walk decomposition (Hasbrouck, 1991b). The decomposition allows for an e¤ective extraction of the variation in the shock to the e¢ cient price that is attributable to the innovation in trade. The results of the decomposition are very impressive for three of the six stocks, CEZ, Komercni Banka (KB), and Philip Morris CR (PMCR).
We examine the dynamic and size-dependent properties of the system with a help of a cumulative quote revision function. The Figure (1) below depicts the cumulative response of the quote midpoint for a share of CEZ subsequent to an initial (i.e., time t0) purchase of 10,000 shares of stock. We chose the number of shares as corresponding to the standard (or minimal) quantity of shares that can be
coe¢ cients are zero. The level of signi…cance is once again 0.1%.
1 7In fact, the structure of the model permits the this both contemporaneously and with lags.
This is a natural implication of the fact that the quote revision follows the trade. See Section (3).
traded in the CEZ stock on SPAD.18
0 2 4 6 8 10 12 14 16 18 20
0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
Figure 1: Quote revision process for the CEZ stock implied by the bivariate model. The …gure shows the cumulative quote revision subsequent to initial buy order of (a standard quantity) of 10,000 shares.
The illustration shows that the convergence seems to be quite slow in case of the CEZ. To be exact, it takes about 20 lags for the security securities to reach its convergence level of about CZK 0.09 (see Table 5). Quite interestingly, nearly 80%
of this level is reached already by the8th lag.
The fact that the convergence just discussed is not instantaneous suggests that transient dynamic considerations - the same features to which VAR models in par- ticular are well suited - are important. Still, as we had a chance to observe, the convergence levels are not straight lines and owing to estimation limitations we can only speculate about what might happen at much higher lags if a long-run trade reversal were present.
Clearly, the quote impact calculations implied by VAR estimates of low order would likely overstate the long-run price impact. In other words, the model would catch up the initial positive impact of a trade on the quote, but would miss the subsequent long-run reversion. Hasbrouck(1991) states that if this problem arises, it is most likely to be present in the estimations for stocks of low market values and may cause the estimates of the price impact to be biased upwards. Although at other times, this might be the case of Unipetrol and Philip Morris CR (PMCR), which had relatively lowest market capitalization of all stocks in the period considered, the twelve lags that we use in the estimation makes us con…dent that there is no question of the long-run impact being overstated in the present study.
5.2 Nonlinearities in Trades Quotes Relation
The VAR systems analyzed so far have been simple bivariate models based on the assumption that the dependence between quote revisions and the trades (as proxied by signed trade variable in the estimation) is linear. The quote revision process in particular was modelled as a linear function both of its own lagged values and contemporaneous and lagged values of trades.
1 8We provide the plots of the cumulative responses for the other stocks in the appendix. Refer to Table (1) for the standard quantities of shares used to initialize the corresponding cumulative response functions.
Still, this assumed linearity is at best a questionable approximation of reality. As we already mentioned, not only are the underlying cost and information functions unlikely to be linear but the order entry and trade negotiation processes are almost certainly dependent on trade size (Hasbrouck, 1991a). A more realistic group of models may be developed by moving to multivariate VAR speci…cations. In the following section we …rst develop what could be considered a representative example of such model and include the results of its estimation in the latter paragraphs as well.
One obvious speci…cation for the (multivariate) model involves regressing the quote revision against current and lagged signed powers of the trade variable. The possibility stems from the fact that a function in general may be approximated by a polynomial expansion. The model analyzed here is quadratic. Other than the quote and signed trade variables used earlier, we also add a large trade variable de…ned as[xt]2. The full quadratic VAR model thus includes four linear equations in which each of the four variables is regressed against lagged values of the entire set. The general speci…cation for each equation is:
( )t= X12
i=1
airt i+ X12
i=0
bixt i+ X12
i=1
cix2t i+ ;t ,
where( ) indexes the set of variables in the model.
A …nal note on the model methodology relates to its estimation. Given that none of the variables included in the set were found to be statistically signi…cant linear predictors of[xt]2, we follow Hasbrouck (1991) and do not estimate the equation for[xt]2; in e¤ect, we treat the large-trade variable as exogenous.
As in the previous section, we estimate the quadratic (???) VAR model for each of the six SPAD securities. The results are provided in Table (6).
Table 6: Estimates of the Quadratic (???) VAR Model for CEZ and Telecom
CEZ Erste KB PMCR Telecom Unipetrol
rt xt rt xt rt xt rt xt rt xt rt xt
P12 i=1
ai 0:223
(13:63) 0:027
(6:65) 0:008
(2:88) 0:005
(4:76) 0:185
(5:31) 0:091
(3:27) 0:187
(4:82) 0:004
(2:13) 0:006
(0:21) 0:002
(0:11) 0:027
( 0:52)
0:150
(1:40)
W(ai= 08i) 387:4 104:8 55:1 588:7 198:6 33:86 94:24 36:67 246:4 67:90 27:97 13:20 P12
i=0
bi 1:263
(18:30) 0:260
(12:69) 0:627
(2:47) 0:236
(10:43) 0:177
(13:30) 0:289
(12:87) 3:10
(10:86) 0:203
(7:85) 0:095
(7:94) 0:252
(8:38) 0:120
(5:84) 0:264
(5:08)
W(bi= 08i) 493:9 324:7 410:6 211:4 229:2 386:1 245:4 109:5 161:2 84:6 78:7 69:4 P12
i=1
ci 0:916
(4:26) 0:150
( 1:50)
0:002
(0:40) 0:001
(0:93) 0:001
( 0:87)
0:001
( 1:71)
0:007
(0:75) 0:001
(0:69) 0:002
(1:31) 0:005
( 1:07)
0:020
(2:43) 0:002
( 0:06)
W(ci= 08i) 39:78 15:55 19:72 14:58 18:27 19:18 21:26 8:71 13:56 21:82 15:18 25:79 R2 0:055 0:028 0:002 0:011 0:056 0:023 0:064 0:012 0:048 0:013 0:009 0:033
Estimates of the quadratic vector autoregressive model for CEZ, Erste Bank (Erste), Komercni Banka (KB), Philip Morris CR (PMCR), Cesky Telecom (Telecom), and Unipetrol stocks. The set of variables in the model include the price (quote midpoint) change, the trade indicator variable, the signed trade volume, and the large volume variable. The table contains summary statistics for each group of regression coe¢ cients including the sum of the coe¢ cients in the group and at-statistic for this sum (in parentheses). The results of an F-test of the null hypothesis that all coe¢ cients in the group are zero are available on request. A method proposed by White (1980) was used to obtain heteroskedasticity consistent standard errors. ARCH (4) refers to Engle’s (1982) LM test for ARCH e¤ects of order 4 (the test is chi-2 (4) distributed). The period assessed runs from January 5 to November 12, 2004.
The estimated coe¢ cients are summarized by equation and groups of like vari- ables. For each equation and each type of variable the sum of the coe¢ cients across all 12 lags and thet-statistics associated with this sum are also reported in the ta- bles. The results of the Wald test of the null hypothesis that all coe¢ cients in the group are zero are also presented.
Again, we …rst discuss the estimates for rt equation. For all of the six stocks under analysis, the coe¢ cient sums for(xt) are all positive and strongly signi…cant.
The coe¢ cient sums for(x2t) are also all positive although in case of four of the six stocks (Erste, KB, PMCR, and Telecom), the positive sign is somewhat questionable due to lowert-statistics. Komercni Banka (KB) stock is the only exception in this regard as its coe¢ cient on(x2t) is both negative and statistically very insigni…cant.
In summary, as a function of trade size, we observe the price impact is generally positive, increasing, and convex. Finally in the coe¢ cient sums on(rt)are they are all mostly positive and signi…cant.
In the trade variable regressions xt, a pronounced pattern of positive autocor- relation is clearly visible in case of the signed trade variable (xt). There are no exceptions among the six stocks in this regard. The coe¢ cient sums for the lagged quote revisions (rt) are predominantly positive with a remarkable low t-statistics in case of Cesky Telecom (Telecom) and Unipetrol stocks. The coe¢ cient sums at lagged signed powers of the trade variable(x2t) are either relatively small or again relatively large with respect to other stocks and negative (CEZ, Telecom). Never- theless, these sums remain insigni…cant.
As in the previous section, we investigated the Granger-Sims causality running from quote revisions to each of the trade variables. Using an Wald of the null hypothesis...
Once again, we examine the dynamic and size-dependent properties of the system with a help of a cumulative quote revision function. The Figure (2) below depicts the cumulative response of the quote midpoint for a share of CEZ subsequent to an initial (i.e., time t0) purchase of 10,000 shares of stock. We chose the number of shares as corresponding to the standard (or minimal) quantity of shares that can be
traded in the CEZ stock on SPAD.19
0 2 4 6 8 10 12 14 16 18 20
0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
Figure 2: Quote revision process for the CEZ stock implied by the trivariate model. The …gure shows the cumulative quote revision subsequent to initial buy order of (a standard quantity) of 10,000 shares.
The illustration shows that the convergence seems to be quite slow in case of the CEZ. To be exact, it takes about 20 lags for the security securities to reach its convergence level of about CZK 0.09 (see Table 5). Quite interestingly, nearly 80%
of this level is reached already by the8th lag.
5.3 A Few Notes on Cumulative Quote Revision
The interpretation of the impulse response function m 2;0 , de…ned in (??), as a measure of private information rests on the assumption that 2;0 re‡ects no public information. This assumption follows directly from the dichotomy that pervades most of the formal models of asymmetric information as well as the derived empirical models: in all of these, the trade is driven partially by private information and partially by liquidity needs, but in no part by public information which is relevant to forecasting the value of the security.
In the model that we adopted from Hasbrouck (1991a), the dichotomy is not less apparent. In fact, the equations (??) and (??) identify all public information with the quote revision innovation( 1;t)and all private information with the trade innovation( 2;t). This renders the model very approximative with respect to reality as in practice: a pure dichotomy simply does not hold. The estimated values of
m may then either capture the response of the quote to private information inad- equately or else may re‡ect the response of the quote to public information as well.
We will now consider a few of the imperfections that might upset the dichotomy.
One aspect of the dichotomy implies that the quote revision innovation re‡ects only public information. Since on the PSE the quotes are provided by dealers, this assertion may be violated if the dealers possess (and ultimately use) superior information. In that case, the prevailing quotes may re‡ect the private information (as they are set by the dealers), which will of course not be captured by the impulse response function.
1 9We provide the plots of the cumulative responses for the other stocks in the appendix. Refer to Table (1) for the standard quantities of shares used to initialize the corresponding cumulative response functions.
The other aspect of the dichotomy implies that the trade innovation contains no public information. We may formalize this as the requirement that public infor- mation is not useful in predicting the trade innovation. In reality, this requirement is violated if any of the following takes place at the market: a) the specialists get involved in smoothing the price transition path, and/or b) the quotes and/or limit orders are reported with a lag (stale quotes/limit orders). We assume only these two "imperfections" as they are most often cited in the empirical literature.
If the market-maker is required to show a smooth price transition path, then quotes may not be immediately revised to re‡ect public information. The implica- tions of this are clear: if the market maker is compelled to set the quotes in a such a way as to ensure a smooth price adjustment path (this is indeed the case of most of the exchanges including the PSE), then he may not be able to revise the quotes as fully and as immediately as unconstrained use of the news would imply. As noted in the Introduction, however, the stale quotes do not present a problem for the correct interpretation of the impulse response function for the data from the PSE.
6 Conclusions
The aim of this study has been to analyze the information content of a trade as implied by its e¤ect on the quote revision. In the analysis, we used the data for all stocks traded on the PSE’s main market (SPAD) in the …rst eleven months of 2004.
Entertaining a heuristic approach, we …rst arrived at a robust empirical speci…- cation in which the impact of trade on price due to asymmetric information is both meaningful and observable. In such a model, the information content of a trade may be meaningfully measured as the persistent impact of the unexpected component of the trade; that is, as the ultimate impact of the trade innovation. By focusing on the trade innovation rather than the trade itself, we avoid misleading inferences due to inventory control or other transient liquidity e¤ects. By considering the persistent impact of the innovation, we concentrate on the information ultimately impounded in the price after transient liquidity e¤ects have died out.
Our …ndings for the six securities traded on the PSE are as follows. First, the full impact of a trade on the security price is not felt instantaneously but a with a protracted lag. This conclusion e¤ectively sets an important benchmark for further studies of the PSE. Any analyses of the stocks traded on the PSE which would assume that the full impact of a trade on price is instantaneous would be seriously incomplete. Second, as a function of trade innovation size, the ultimate impact of the innovation on the quote is nonlinear, positive, increasing, and convex. This is a tentative characterization of the trade size-price impact relation. The convexity seems to be a particular feature of the stocks traded on the PSE as, in general, the relationship tends to be concave. Still, results regarding the convex pattern in trade quote relation should be accepted only carefully, as the conclusion is based on the coe¢ cients of only two of the six securities under analysis. Finally, we show that the order ‡ow does not seem to be a¤ected by prior quote revisions. In other words, there does not seem to be Grange-Sims causality running from quote revisions to trades. This …nding is of marginal importance although had the causality been in fact
proved, it would have presented an intriguing reason for practical experimentation.
A number of directions exist for further research along the lines presented in the chapter. The potential studies fall in two groups. In the …rst group lie comparative analyses of the trade impact across …rms which have di¤erent size (market capital- ization) and perhaps also trading patterns. Another important set of issues that belong to this group concerns seasonal behavior of the trade impact such as time-of- day and day-of-week seasonalities. The second class of studies concerns re…nements.
For example, what characterization appears to best describe the price impact as a function of trade size? We leave these and other extensions to further research in the area.
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8 Appendix
0 2 4 6 8 10 12 14 16 18 20
0.02 0.03 0.04 0.05 0.06 0.07 0.08
0.09 CEZ
0 2 4 6 8 10 12 14 16 18 20
1.0 1.5 2.0 2.5 3.0 3.5 4.0
4.5 Erste
0 2 4 6 8 10 12 14 16 18 20
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
KB
0 2 4 6 8 10 12 14 16 18 20
3 4 5 6 7 8 9
10 PMCR
0 2 4 6 8 10 12 14 16 18 20
0.004 0.006 0.008 0.010 0.012 0.014 0.016 Telecom
0 2 4 6 8 10 12 14 16 18 20
0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010 Unipetrol
Cumulative revisions for stocks...
