Assesing the Quality of a Security Market a New Approach to Transaction

8/6/2019 Assesing the Quality of a Security Market a New Approach to Transaction

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The Society for Financial Studies

Assessing the Quality of a Security Market: A New Approach to Transaction- CostMeasurementAuthor(s): Joel HasbrouckSource: The Review of Financial Studies, Vol. 6, No. 1 (1993), pp. 191-212

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Assessing the Quality of aSecurity Market: A NewApproach to Transaction-CostMeasurementJoel HasbrouckNew York University

I discuss a new method for measuring the devia-tions between actual transaction prices andimplicit efficientprices. The approach decomposessecurity transaction prices into random-walk andstationary components. The random-walk com-ponent may be identified with the efficient price.The stationary component, the difference betweenthe efficientprice and the actual transaction price,is termed the pricing error. Its dispersion is a nat-ural measure of market quality. I describe prac-tical strategiesfor estimating these quantities. Fora sample of NYSEstocks, the average pricing errorstandard deviation estimate is roughly 0.33 per-cent of the stock price. If the pricing error is nor-mally distributed and if it is always a positive costincurred by the transaction initiators, the corre-sponding average transaction costfor these trad-ers is 0.26 percent of the stock price. The disper-sion of thepricing error is alsofound to be elevatedat the beginning and end of the trading session.For comments and suggestions, I am indebted to the editors (Michael Gib-bons and Chester Spatt), the two referees (James Stock and Lawrence Harris),Yakov Amihud, Fischer Black, Richard Green, Maureen O'Hara, RobertSchwartz, and workshop participants at Berkeley, Dartmouth, MIT,NewYorkUniversity, Rutgers University, Stanford University, and the Securities andExchange Commission. I am especially grateful to John Campbell for bring-ing the techniques of random-walk decomposition to my attention. All errorsare my own responsibility. I am indebted to the New York Stock Exchangeand the Institute for Quantitative Research in Finance for financial support.The comments and opinions contained in this article are those of the authoronly. In particular, the views expressed here do not necessarily reflect thoseof the directors, members, or officers of the New York Stock Exchange, Inc.Address correspondence toJoel Hasbrouck, NewYork University, Stern Schoolof Business, 44 West Fourth Street, New York, NY 10012.The Review of Financial Studies 1993 Volume 6, number 1, pp. 191-212X 1993 The Review of Financial Studies 0893-9454/93/$1.50


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The Review of Financial Studies / v 6 n 1 1993

It is commonlyheld that in additionto the explicit costs of executinga securitytransaction (such as the commission), the trader ncurs animplicit cost in the difference between the actual transactionpriceand a benchmarkprice that is considered to be in some sense fair orefficient. Measurementof this difference arises in financial marketsanalyses in two related contexts. First,transaction-costmeasurementtraditionallyaims at estimationof this differencefor a buyer or sellerin a specific transaction,usually with the purpose of evaluating thebroker's performance. Second, comparative market analysis seeksaverage transaction-costmeasures, with a view toward determiningmarkets or regulatorystructures under which these costs are mini-mized. In this article, I discuss and implement a class of improvedmeasures that are useful for both purposes.The new measures are based on existing techniques for resolvinga nonstationary time series into a random-walkcomponent and aresidualstationary omponent.'Applied to securitytransactionprices,it is natural to identify the random-walkcomponent as the efficientprice. The residual stationarycomponent, termed here the pricingerror, is taken as the implicit transactioncost. The dispersion of thepricing errormeasures how closely actual transaction prices track arandom walk and is therefore a naturalmeasure of marketquality.2Earlierstudies of transactioncosts have used variousbenchmarksfor comparison with observable transaction prices: the volume-weighted daily averageprice [Berkowitz,Logue, and Noser (1988)],daily high-low midpointprices andclosing prices [Beebower(1989)],and the midpointof the prevailing bid and askquotes [Perold(1988)].These benchmarks often possess the virtue of convenience, but gen-erally lack strong interpretationsas efficientprices.Comparative tudies of marketperformanceand regulatory mpactanalyses usually arebased on posted bid-ask spreads,liquidityratios,orreturnvarianceratios.3Grossmanand Miller (1988) summarizetheproblems with using posted bid-ask spreads and liquidity ratios asmeasures of marketquality. The posted bid-ask spread is twice thetransactioncost for a market-order raderunder numerous restrictive

'See Beveridge and Nelson (1981), Watson (1986), Campbell and Mankiw (1987), and Quah (1990,1992). Stock and Watson (1988) provide a highly readable review.2 Hasbrouck (1991b) uses this approach to characterize the random-walk component implicit in thequotes. As a measure of information asymmetries, in my earlier article I describe a computation ofthe random-walk variance that is explained by trades. In contrast, in the present article I focus onactual transaction prices, and the characterization of the stationary component. The common useof random-walk decompositions leads to methodological similarities, while the divergent aims ofthe two articles lead to substantial differences.

Cooper, Groth, and Avera (1985), Hasbrouck and Schwartz (1988), and Tanner and Pritchett (1992),compare the liquidity in over-the-counter and exchange markets for equities. Neal (1989) contrastsoptions trading on the CBOE and AMEX. For an example of regulatory studies, see the CommoditiesFutures Trading Commission (1989) draft report on dual trading.

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Assessing the Quality of a Security Market

assumptions,including absence of asymmetric nformation.Liquidityratios, which relate price changes to tradingvolume, fail to differ-entiate between transientprice impacts (a sign of illiquidity) andthepersistentimpacts(a consequence of information nferredfromtradesin an efficient market). The variance ratio is defined as the returnvariance per unit time measured over long horizons divided by thatmeasured overshort horizons. The extent to which this ratiodeviatesfrom unity (the value associatedwith a randomwalk) has been usedto measuremarketperformanceby Barnea(1974) andHasbrouckandSchwartz(1988). As summarymeasures, variance ratios suffer fromproblems of sensitivity to the horizons used. Furthermore, here isno general connection between the variance ratio and conventionaltransaction-costmeasures.In the remainder of this article, I deal with the formaldescriptionand implementation of this approach.In Section 1, I introduce thebasic security price decomposition and establish the economic sig-nificanceof the pricingerrorand its dispersion. Inthe threefollowingsections, I describe problemsof inference in progressivelymore com-plex models. In Section 2,1 illustrate the basicprinciples in situationswhere transactionpricesconstitutethe only availabledata. In Sections3 and 4, I discuss the expansion of the conditioning variable set toinclude other variables (prices and trades) with general laggeddependencies. I then turn to empirical implementation. In Section5, I describe estimationstrategies.In Section 6, I reportresults basedon a sample of NYSE irms,and discuss intradaypatterns.I concludewith a brief summary n Section 7.

1. The Transaction Price DecompositionThe models in this article take the logarithm of the observed trans-action price at time t,Pt, as the sum of two components:

Pt= Mt + St. (1)The firstcomponent (mt) is the efficientprice, defined as the expec-tation of the final (end-of-trading)value of the security conditionalon all public informationavailable at time t, including whatever pri-vate informationmay be inferred from the published terms of thetransaction.The second component (st) is the deviationbetween thisefficient price and the actual transactionprice, and is termed thepricing error. For present purposes, t is assumed to index eithertransactionsor brief intervals of natural time.The pricing error s central to this article. It is viewed as impound-ing diversemicrostructure ffectssuch as discreteness, inventorycon-

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The Review of Financial Studies/ v 6 n 1 1993

trol, the non-information-based omponent of the bid-ask spread, thetransientcomponent of the price response to a block trade,etc., whichare not explicitly modeled. The pricing error is related to the trans-action cost in that, as defined, st is the cost for the buyer and -st isthe cost for the seller. The transactioncost for the buyerand that forthe seller sum to zero for all trades. Even if the unconditional expec-tationof Stis zero, however, it does not follow that all tradersconsiderthe pricing error to be a fair-game perturbation, diversifiable overmany transactions. Conditional on trader identity and order place-ment strategy, he pricing error s generally not a fairgame.A market-ordertrader,for example, must expect to incura positive transactioncost on all transactions.4The estimate of the pricing error ora particularransaction,denotedSt(), is a general function of conditioning data. If the estimate issought as an ex post measure, it may incorporate posttrade infor-mation. If the goal is estimation of the cost of a futurecontemplatedtrade,the conditioning data must be restrictedaccordingly.Further-more, st measures the deviation relative to an efficient price [mtin(1)] that impounds the information that the marketinfers from thetrade.Tradersoften view the transaction ost as the differencebetweentheirexecution price andthe price thatprevailed before they enteredthe market("slippage"). This leads to a pricing error differentfromthe one considered here.Forpurposes of assessing marketdesign and regulation, I proposethe standarddeviation of the pricing error,a-,as a summarymeasureof marketquality. Intuitively,this quantity measures how closely thetransactionprice tracks the efficientprice. In the absence of a fullyspecified model of marketoperation, this dispersion does not have adirect transaction-costinterpretation.Its role as a proxy for marketqualityrests solely on the premise that as transactioncosts and otherbarriersto trading are reduced, transactionprices should conformmore closely to efficientprices.From (1) the pricing error is defined only for trades that actuallyoccur. Neither st nor osdirectly reveals anythingabout the privateorsocial cost of forgone trades (except in the sense that the pricingerror mpoundsanimmediacycost). Thisshortcoming applies to mostmeasures based on actualtradedata. One can envision marketregimesthatachieve narrowbid-ask spreads,for example, by excluding trad-ers who are likely to posses superior information. The apparentimprovement in marketquality implied by the smallerspreadis offset

I Nevertheless, it cannot generally be assumed that Is,I is always a cost paid by a public trader to amarket-maker. For example, if inventory control considerations or price continuity requirementsforce a dealer to place quotes sufficiently away from the efficient price, then a market-order tradermay "pay" the spread and yet still have a negative transaction cost.

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(and perhaps outweighed) by the social cost of forgone trades andreduced production of information.Specification(1) is functionally similar to that used in Hasbrouck[1991b, equation (1)], except that in the earlier article I applied thedecomposition to quote-midpoints. Prices are used here because thepresent goal is cost measurementfor actual transactions.Quotes wereused in the earlier article to avoid simultaneity problems involvingtrades.As in the earlierarticle, two assumptionsare imposed on (1):(i) The efficient price follows a random walk:

mt= mt1 + wti, (2)where wtare uncorrelatedincrements,Ewt = 0, Ew2 = a2, and Ewtwr= 0 for t # r.(ii) The pricing error(st) is a zero-mean covariance-stationaryto-chastic process.There are no requirements that stbe serially uncorrelatedor uncor-related with wt.

In the present article, I do not allow for heteroskedasticityin storwt.In the implementation,however, tindexes transactionsrather hannatural time. Periods of elevated returnvariance per unit time (thebeginning and end of trading) are also periods of frequent transac-tions. Harris 1987) suggests that the behaviors of variance,skewness,kurtosis,and first-order utocorrelationof daily stock returnsare con-sistent with a model in which prices and volumes evolve at a uniformrate in event time. Thus, using transaction time ratherthan naturaltime maymitigate return heteroskedasticity. Furthermore,because aprimary ource of returnheteroskedasticity s time-of-day,estimationsbased on time-of-daysubsamples will be presented.The efficientprice process specified in (2) does not include a driftterm.Although the technique can easily be generalized to include aconstant drift, practical econometric considerations favor suppres-sion. The drift is the expected return (per increment in t). Mostmicrostructureapplications of this technique will involve data sam-ples that arebriefin calendarterms.Insuch situations,Merton(1980)notes that the standarderror of the mean estimate is large relativetothe expected return,and that the estimate is not improved by morefrequentsampling. In consequence, he suggests that returnvariancesusing short dataspans will have smaller estimation errorsif they arecentered around zero, rather than the sample mean return. Similarconsiderations are likely to apply in the present situation.This argu-ment also suggests that the effect of ignoring time- and day-of-weekvariationin expected returns found by Harris(1986) is likely to besmall.

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Deviationsfrom random-walkbehaviorin stock returnsat daily andlonger intervalshave been found by Lo and MacKinlay 1988), Famaand French(1988), and Poterbaand Summers(1988), among others.If these deviations are attributedto low-frequencytemporarycom-ponents of stock prices, they should properlybe impounded in thepricing error.The present analysis,which only allows for short-run(several-transaction)serial dependencies, is thereforeprobablymis-specified. However, the present aim is the measurement of the mi-crostructure-relatedcomponent of st, which is presumably due toshort-runphenomena. The misspecificationwill tend to impound thelong-run components in the random-walkportion of the decompo-sition, leaving st to capture the short-runcomponents of interest. InSection 5, I present a simulation that illustrates this point.

2. Inferences Based on Returns OnlyIn the preceding section, I motivated the economic interpretationand importanceof the pricing error.I now turn to estimation of thepricing error and its dispersion. The exposition describes cases ofincreasing complexity. The model in this section uses returns only;thatof the next section uses returnsand signed trades;andthe modelof Section 4 uses broaderand arbitraryets of conditioning variables.With one exception (the lower-bound result), this discussion con-tains no new econometric results. It is a selective summaryof therandom-walkdecomposition literature cited in the introduction,directed at microstructure ssues.

To imbue (1) and (2) with specific economic content and to illus-tratethe econometric inferences, consider a special case with pricingerror:St= awt + m7, (3)

where mts a disturbanceuncorrelatedwith wt.The Roll (1984) bid-ask spread model corresponds to a = 0 and ft = ? (spread)/2 (depend-ing on the sign of the order). Alternatively,suppose that the spreadis due in part to asymmetricinformationrevealed in the trade andthat the trade is the only update to the informationset. This is aspecial case of Glosten (1987), with no nontradepublic information.In this case, a > 0 will capturethe cost-basedcomponent of the bid-askspreadand iqt 0. Amixed case will resultwhen the returnsreflectpublic informationsupplementaryto the trade.The two termsin (3) correspondto components of the pricingerrorthat may be thought of as information-correlated(awt) and infor-mation-uncorrelated(it). This distinction is a useful one for classi-fying microstructureeffects. Information-uncorrelated ricing errors196


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are likely to result from price discreteness, transient liquidity effects,inventorycontrol effects, and "noise" trading.Information-correlatedpricing errorsarise fromadverse-selection effects in the presence offixed transaction costs and from lagged adjustmentto information.To estimate stand as, it is necessary to connect the model to theobservable data. Given (1)-(3), the returnis

rt = Pt- Pt- = Mt-Mt- + St-St-I = Wt + St- St- l (4)Since wtand stare serially uncorrelated (in the present example), rtpossesses nonzero autocovariances at the firstlag only. This in turnimplies that rtmay be represented as a first-ordermoving averageprocess:

rt= ft-aft-1 (5)Two parameters,{a, a-2} fully characterizethe mean and autocovari-ances of the returnprocess. To deduce the returnmean and auto-covariances from the random-walkdecomposition model requiresspecification of three parameters,{a2W,, a-21 This model is thereforeunderidentified. (In this article, I make no assumptionsand attemptno inferences concerning momentsof higher order, such asskewnessand kurtosis.)In the macroeconomic literature,there are two common identifi-cation restrictions.Thefirst,due to Beveridgeand Nelson (BN) (1981),implies for the present model thatr = 0 in (3) [i.e., that the pricingerror s entirely information-correlated "Glosten model")]. The cor-respondence between (4) and (5) then establishes that -t =wt + awt - awt-1. This further implies a = a/(l - a), wt = (1-a)Et, st = a wt, r- = (1 - a)2r2 , and, o-2 a2o-2. By substitution andrecursion, the estimate of the pricing errorfor a particulartransac-tion is

st(rt, rt1, . -. .) =- =-a(rt + art-, + a2rt2 + ). (6)Under the BN restriction, this estimate is exact. In the followingdiscussion, however, it will find application in more general situa-tions.

The second identification restrictionis due to Watson (1986), andimplies for the model (3) that a = 0 [i.e., that the pricing error iscompletely information-uncorrelated("Roll model") and aS =aVThe analysis (slightly more difficult than the BN case) shows5 that2W (1 -a)2a-2 and o-2= ai-2. In contrastwith the BN case, it is notpossible to expressthe pricingerroras an exactfunctionof the current

5The correspondence between (4) and (5) is c,-ae, = w, + i. - i,-,. Taking the variance of eachside establishes (1 + a2)c2 = a2, + 2a2. Taking the first-order autocovariance of each side yieldsaa2 = a2 = a2. These may be solved to give the indicated results.

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disturbance et.Watson shows that the best linear estimate of st basedon current and lagged returns is identical to thatobtained under theBN restriction (6), but that estimates that incorporate future returnswill be superior.Thereare several interesting featuresof these two cases. First,notethat the random-walkvariancea-2 is invariant.This is a general prop-ertyof these decompositions. Intuitively, observed returnscomputedoverprogressively longer horizons aredominated to a greater degreebythe random-walk omponent, irrespectiveof the formof the pricingerror.Since both identification structuresmust be consistent with thesame observed returnprocess (5), it follows that the random-walkvariance must also be the same.Next, note from the expression for a- that feasibility of the Watsonidentification requires a ' 0. This implies that the first-orderauto-covariance of rtis nonpositive. Recall that the Watsonidentificationrestriction (a = 0, a-2 # 0) characterizes the simple Roll bid-askmodel, which is incompatible with a positive returnautocorrelation.In data samples, of course, a positive estimated autocorrelationcanarise from estimation error. [See Harris(1990).]Between the two identification restrictions, the dispersion of thepricing error differs considerably. To get a feel for this difference,note that for a first-orderautocorrelationcoefficient p near zero, themoving-averageparametera is approximately equal to p. For dailystock returns, French and Roll (1986) estimate the first-orderauto-correlation coefficient to be p = - .0115 (their Table 2). The valuesfor a- obtained under the two identification restrictions differby afactorof a, a factorof 100 in this case. The situation is generally betterwith transactionsdata, where a may reach 0.5. Nevertheless, thesecomputationssuggest that the identification issue is of greatpracticalconcern. To make mattersworse, the economics of the problem donot argueconclusively in favorof either identificationrestriction.Theearlier discussion noted that certainplausible microstructureeffectsare likely to be information-correlated,while others are likely to beinformation-uncorrelated.The general lack of identification impairs estimation of stand as,but some results are still attainable.Watsonshows that the estimateof st given in (6) is the best linear estimate based on current andlagged returns not only for the two special cases considered here,but for all feasible identifications [i.e., all values of a and cr in (3)that imply the given {a, a-}].The identification-invarianceof this particular orm of s, leads to alower bound fora 2. To see this, consider the precision (mean-squareerror) of a general estimate of st, s: 0 < E(st - St)2 = Es2 -ES-2Et(s, - 9). If &, s the BN form given in (6), then the last term198


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vanishes, since E,(st - st) = E[E[s,(s,- s,) Irt, rt, .. .]] = 0. Thisestablishes the lowerbound:a- = Es2 < ES2. It should be emphasizedthatthe needed orthogonalitycondition is guaranteedto hold for theBN form of s, only if the model (4) is correctlyspecified.Now since this restriction rules out any information-uncorrelatedeffects, it is at this point a very weak lower bound. It will be shownin the next section, however, that the lower bound can be strength-ened substantiallyby considering variables besides the transactionprices. The model eventually developed in this article is one thatpermitsboth information-correlatedand -uncorrelatedeffects.

Finally, the Watson identification restriction does not provide anupperbound for the pricingerror.In fact,no meaningfulupperboundfor o2 exists: zero autocorrelations n r,do not necessarily imply zeropricing errors.63. Inferences Based on Returns and Trades

In this section, I describe how the price errorframeworkmay bestrengthenedby including explanatoryvariables n additionto prices.The discussion is based on a simple bivariatemodel of prices andtradesthat can be viewed as the reduced form of a reasonable micro-structuremodel.The trade variable at time t is the trade volume x,, signed to bepositive if the agent who initiates the trade is buying and negative ifthe agent is selling. Tradesare assumed to be symmetric:Ext = 0. Itis provisionally assumed that trades and the pricing error are notautocorrelated.(These restrictionswill be dropped in the next sec-tion.) With the availabilityof the trade variable, the random-walkcomponent in (1) may itself be decomposed into two parts:

w,= Y,xt ut. (7)Here, yxtreflects the informationthe marketinfers from the trade.The second part(ut) is an innovationuncorrelatedwith xtthat stemsfrom nontrade public information. The pricing error may also bewritten to reflecta tradecomponent:

s,= axt +3ut +1t, (8)6 Suppose that Var(r,) = 1, with zero autocovariances at all lags. This is consistent with the "natural"model: a random-walk decomposition in which the pricing error is completely absent (s, = 0) andthe efficient price changes have unit variance (a 2 = 1). The autocovariances are also consistent,however, with a model in which the pricing error is perfectly negatively correlated with the changesin the efficient price (s, = -w,), in which case r, = w, - w, + w,_ . This implies Var(r,) = 1 (asrequired), but the pricing error variance is o2 = 1. The example may be extended by allowinglonger lags on the pricing error. If s, =-w, - w,_ , then although Var(r,) = 1 and the returnautocovariances remain at zero, a 2 = 2. In general, the pricing error variance may be made arbitrarily

large by considering longer lags. Quah (1992) discusses related points.

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where rt s a disturbance that is uncorrelatedwith both xtand ut.Thisspecificationassumes that both wtand stare linear in xt, a restrictionthat will be relaxed in the empirical analysis. The behavior of thereturn series implied by the random-walkdecomposition model is

rt= boxt+ b1xt-,+ et- at-1, (9)that is, a regression with a moving-averageerror term. The corre-spondence between (4) [substitutingin from (8)] and (9) shows

b.xt + b1xt-1+ et -aft-= (a + y)xt - axt +1 + + 3)Ut + -7 Ut- -- T7t-i (10)

The random-walkvariance is identified: a- = (bo + b1)2r +(12 -a)2a2. Without additional restrictions, the remaining parameters ofthe random-walkdecomposition are not identified.The BN restriction sets 77t 0 in (8). This implies a =-b,, y = b&+ b,, = a/(l - a), and ut = (1 - a)Et. In addition, a2 = (1 -a)2a2, and therefore, o- = b2a2 + a2-2. The properties of the BNrepresentation in the univariate case apply here as well. A minorgeneralization of Watson (1986) shows that for all feasible identifi-cations, the best linear estimate of the pricing errorbased on currentand lagged returnsand signed tradesis that obtained under the BNidentification restriction.[This estimate is computed by using the BNvalues fora and ,B n (8) and dropping the 7term.] Since this estimateis identification-invariant,he associated os is a lower bound by thesame logic as in the univariate case.

This simple bivariatespecification may be viewed as a represen-tationof a microstructuremodel in the spirit of Glosten and Milgrom(1985). The market consists of a risk-neutraldealer, and informedand uninformed traders. At the close of period t - 1, the tradinghistory and the efficient price mt-1are common knowledge. At thebeginning of period t, public information (ut) arrives,making theexpected securityvalue mt-, + ut.About this value, the dealer postsbid and ask quotes: qtb = mt_1 + ut - c and qa = mt_1 + ut + C,where c is the half-spread.The arriving rader aces these quotes andmay buyorsell one unit of the securityxt= {-1, + 1}. The transactionprice ispt = qb if x, =-1 andpt = q a if xt = + 1. From the relationsPt= mt- + ut + cxt and mt = mt-I + ut + 'yxt, it is apparent that st= P-mt = (c - y)xt. This is identical with (8) with a = (c -),/3 = 0, and 77t= 0 (i.e., the BN restriction). Therefore, st may becomputed directly,and the lower bound is exact. In this example, itis interesting to contrastthe estimated pricing errorvariancewith thebid-ask spread. The half-spread is, of course, c. This overstates thepricing error, because a portion of this (-y)reflects the update to the200


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efficientprice conditional on the trade.The pricingerrorreflectsonlythe remaining component, (c - 7y).4. Inference in the General Multivariate Case

In the previous section, I generalized the basic model of Section 1by permitting inclusion of other variables. In this section, I expandthe model further to allow general serial correlationsin the returns(andother explanatoryvariables).Froma microstructureperspective,this is importantbecause manymarketimperfections lead to laggedeffects. These include inventory control mechanisms, lagged priceadjustment,and price discreteness.The precise natureof these effectsis unknown, however, and there is in consequence no strong priorspecification.As in Hasbrouck (1991a, 1991b), vector autoregression (VAR)pro-vides a useful framework hatis general enough to capturethe unspe-cified lagged dependencies and is also amenable to computation.ArepresentativebivariateVAR nvolving tradesand price changes is

rt= a,rt_1 + a2rt-2 + + blxt-, + b2xt-2 + + V1,t, (1 1)xt= clrt_1 + c2rt-2 + + dlXt-1 + d2Xt-2 + + V2,t

In the present discussion, xtmay be taken as the signed tradevariabledefined in the previoussection. Moregenerally,xtis a column vectorof explanatoryvariables, and bi and di are conformable coefficientmatrices.The innovations are zero-mean, serially uncorrelated dis-turbances.The VARmay be transformedto obtain a vector movingaverage (VMA)representationthat expresses the variables in termsof currentand lagged disturbances [see Judge et al. (1985, p. 657)].A VMAcorrespondingto (II) is

rt = ao V,t + a*v1,1 + a'v1,t-2 + + b*v2, t + b* V2,t-12b*V2,t-2 +

xt= c *v1,t + C*vl,t-1 + c* vl,t2 + + do*v2,t d*v2,t1 (12)+2d*V2,t-2 +For the present calculations, only the rtequation in (12) is used.The underlying random-walkdecomposition model is (1), but withan expanded representationfor the pricing error:

St= aov1,t + aiv1,,1 + * + 0ov2,t+ f1v2,,1+ * U' + 77t+ 'Y77lXt- + *^^' '(13)

where qt is a disturbanceorthogonal to all components of vt.201


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By a slight modification of the computation in the appendix toHasbrouck(1991b), the varianceof the random-walkcomponent maybe computed as

or2=a b*]Cov(v)[: (14)

[In Hasbrouck (1991b) the disturbancecovariancematrix Cov(v) isblock-diagonal, a structure that is not imposed here.] By a minorgeneralizationof the demonstration n Beveridge and Nelson (1981),the a's and g's in (13) may be computed under the BN identificationrestriction (n, y= = 0):

00 00ai =-z a*, t=_ b*. (15)k=j+l 1j+l

When these coefficientsareused in (13) and the tterms aredropped,the result is an identification-invariant est-linearestimate of st con-ditional on current and lagged v. The pricing errorvariancemaybecomputed as

a2 [a1j O]JCov(v) . (16)By the same logic as that used in the discussion of the univariatemodel, this constitutes a lower bound over the more general cases.To analyze the practicalusefulness of the lower bound, it is nec-essary o considerwhat economic forcesmight cause it to be exceeded.Intuitively,the presenttechnique regresses (projects) the actual pric-ing error on a set of known variables. Under the BN model is theone-lag univariate case described in the introduction, the pricingerror is given by (3). Under the BN restriction, w,may be computedfrom past returns. Viewing (3) as a linear regression, the explainedvariance is a2a 2. The true value for a5 is a242, + C2 . The excess is dueto the "residual variance" U2 . This is a general propertyof random-walk decompositions. In the most general multivariatemodel, the"residual" n the pricing error s constituted by the ft components of(13), and these are the terms dropped under the BN restriction.The residuals in a linear regression are uncorrelated with theexplanatoryvariables, and this is true of the projection residual in(3) as well. This immediately leads to the basic principle: anyfactorthat causes -2to exceed its lower bound cannotbe perfectlycorrelatedwith any linear combinationof the explanatoryvariables.The residualflt in the univariatepricing error(3) is uncorrelated with currentandlagged returns. It is not too difficult to conceive of a pricing error202


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component that is uncorrelatedwith lagged returns.In the univariatemodel, a simple fixed-cost (i.e., non-information-based) bid-askspreadsatisfiesthe requirement.In the bivariate model of Section 2, the residual q, in the pricingerror(8) must be uncorrelatedwith current and lagged returnsandtrades. When trades are included, the BN specification picks up thefixed-cost portion of the spread. In seeking factors that might causethe actual value of i- to exceed the lower bound, one is limited tocomponents uncorrelatedwith currentand lagged returnsandtrades.This is a significant restriction. It must be admitted, however, thatsuch components may arise from discreteness in reported prices. Asimulation dealing with this issue is presented in Section 5.The distinction between the use of transactionprices in the presentarticle and the use of quote midpoints in Hasbrouck(1991b) can beexplained as follows. The analysisof the earlier article requiredthatthe contemporaneous causalityrunningfrom tradesto quotes be one-way. This was justified economically by noting that in actual marketoperations the quote is adjusted subsequently to the trade. In theeconometric specifications, this leads to a recursive structure:theearlier article employs a VAR hat is verysimilarto (11), except thatthe returnspecificationincludes the contemporaneous trade,xt.Thedisturbance covariance matrix is consequently block-diagonal, andthe impact of a trade on the quotes may be determined relativelyprecisely. In the present framework,however, no one-way contem-poraneous causality can be asserted a priori for trades and actualtransactionprices. The two are determined simultaneously, often asthe result of negotiation. Trade-price simultaneityalso implies thatit is generally inappropriateto regard the fiv2,ti terms in (13) asmeasuring the pricing error "caused" by a given set of trade inno-vations.7EstimationAn estimated VMA(12) may be obtained by inverting an estimatedVARsimilar to (11) that is truncated at some lag beyond which allserialdependencies are assumednegligible. Equations (13) (with all, = 0) and (15) maybe used to obtain the BN estimate of st.The BN(lower-bound) estimate of asis computed from (16). Standard rrorsfor the BN asestimate and the stestimate [underthe assumptionthat

I The BN estimate of a, does not change when the contemporaneous trade is included in the returnspecification. More generally, the left-hand side of the r, specification in (12) does not changewhen it is written in terms of the transformed disturbances vt = Av, and coefficients [at bt] =[a, b,]A-', for an orthonormal rotation matrix A. Inclusion of the contemporaneous trade simplydiagonalizes Cov(v,).

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The Review of Financial Studies! v 6 n 1 1993

the 1tin (13) equal zero] can be obtained using generalized methodof moments techniques. The present article, however, is concernedonly with summary averages of a, over broad classes of stocks. Inconsequence, the standard error of the mean estimates are easilycomputed, while the standarderrorsfor the individual stocks are notrequired. Furthermore, the techniques are applied to stocks withnumerous observations.As an example, consider a simulation of the model of Section 3.The trades are generated as xt = {+1, -1} with equal probability(implying 2 = 1). The half-spread s c = 0.005. The otherparametersare au = 0.00346 and y = 0002.8 Since st = axt and a = C - , u. =0.003 (roughly 0.3 percent of the stock price). From (7), au= 0.004.The generated sample consisted of 1000 observationson rtand xt.Consider firstanapplication of the simple univariatereturnanalysisdiscussed in Section 2. The estimated variance and first-orderauto-covariance for the generated data were Var(rt) = 0.0000468 and Cov(rt,rt_ ) = 0.0000155, implying a first-order autocorrelation of p = - .331.The correspondingparameters f the first-ordermoving-averagemodelare a = 0.378 and a = 0.0000410. Using the BN identificationrestric-tion, s = 0.0024 (i.e., a 20 percent underestimate). Using the Watsonrestriction,a = 0.0039 (a 30 percent overestimate).Consider next a joint bivariateanalysis of rtand xt. Since these dataaregeneratedfroma known model, one could estimate the reduced-form specification (9) using maximum-likelihood methods. Themethod used here, however, is the vector autoregression methoddescribed in the last section. The estimated bivariateVAR runcatedat one lag is

rt= -0.375rt-1 - 0.00271 xt_1 + v&,t,(-0.88) (-9.27)xt= -10.6rt-, + 0.0729xt-, + V2,(-1.54) (1.55)

CoV(') 0.0003840.005111(ov) [ 000511 0.997 ]The corresponding VMA epresentation (also truncated at one lag) is

rt= v,t -0.0375v,tl - 0.00271v2,t- ,Xt= -10.6v,,t-l + v2,t + 0.0729V2,t-1

These parameters arise as follows. A quarter-spread on a $25 security is a proportional spread of0.01. Of the 0.005 half-spread, -y= 0.002 is assumed due to adverse selection. The intertransactionrandom-walk variance is therefore o2, = 'y2cr1 + r2 = 0.0022(1) + 0.000012 = 0.000016. On anannual basis, assuming 250 trading days and 10 transactions per day, this is 0.04, an annual returnstandard deviation of approximately 20 percent.

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From (14), the variance of the random-walkcomponent may becomputed as2 = [O 63 -0oo27l [0.000038 0.00511[ 0.963aw [0.963 -0.00271] 0.00511 0.997 J[-0.00271J

= 0.0000162.Underthe BN restriction,the estimated pricing error s [from (6) and(15)]

St= 0.00375',,t + 0.00271b2t (17)Given the relativemagnitudesof Var('1,t)andVar(i?,t),g, 0.00271b1,,0.00271xt. (By construction, the coefficient of xt is a = c - =0.003.) The estimatedstandarddeviationis as= 0.0029, which is closeto the assumed value (0.003). The computations cited to this pointare based on one sample draw. Over 30 sample draws,the averagevalue of the asestimates was 0.00303, and the standarddeviation ofthese estimates was 0.000027.Simulations are also useful for investigating the consequences ofmisspecification.As noted earlier, two particularlyproblematic fea-tures of returndata involve fads and discreteness. To investigate thefirst of these, the prices simulated in the first study were perturbedby the addition of a constructed fad of the formf = 0.99835ft1 + mt,where Var(ut) = 8.24 x 10-6 and t is independent of xt and ut. Theseparameters mply a fad with a standard deviation of 0.05 (approxi-mately 5 percent of the stock price) and a half-lifeof 420 transactions.Withthe inclusion of this fad,the pricing errorvariancemaybe writtenas a2 = (0.003)2 + (0.05)2, a value that is stronglydominated by thefad. Fads are generally viewed, however, as arising from considera-tions beyond the short-run operations of the market. In the presentcontext, the relevant question is, to what extent does the asestimatedusing a truncated VARcapturethe microstructure-based omponentof the pricing error?As a large-sample illustration,when a five-lagVARanalysis was implemented for a single draw of 50,000 observa-tions, the estimated caswas found to be 0.00298. In 30 draws of 1000observationseach, the mean and standarddeviation of the estimateswere 0.00308 and 0.00027. These results support the conjecture,advancedin Section 1, that the misspecificationis likely to limit theestimated asto short-runmicrostructureeffects.To study the effects of discreteness, the generated log transactionprices were rounded to the nearest 0.005 (V8 for a $25 security). Therounding elevates the standard deviation of the pricing error. In asingle draw of 50,000 observations, the standard deviation of thegeneratedstwasfound to be 0.00334.The value forosestimatedusingthe VARprocedure was 0.00299. Thus, presumably because the dis-

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creteness disturbance s uncorrelatedwith either tradesor movementsin the efficient price, it is not captured by the BN as measure. Thecontribution of discreteness remains, however, a relativelysmall partof the total.

6. A Profile of the NYSEIn this section, I presentthe computation of the lower-boundpricing-errorvariancecalculations for a sample of NYSE ssues. The aims ofthis analysisare illustrationof the technique, evaluation of patternsin the pricing-errorvariance across market-valuesubsamples, and apreliminary analysis of intradaily patterns. Estimates of individualpricing errors are not computed, since in the absence of knowledgeof trader identity, they are not highly meaningful.The transactionsdatawere collected from the Institute for the Studyof SecurityMarkets(ISSM) tape for the first quarterof 1989. Supple-mentarydata were obtained from the daily CRSPfile. First, for allfirms present on the ISSMand CRSP apes, I computed equity capi-talizations as of the close of 1988, and formed four subsamples basedon these ranked capitalizations.I then applied the analysis to the first50 firms n each subsample that had at least 500 transactionsoverthequarter. (For the lowest-value subsample, only 27 firmssatisfiedthiscriterion.)In constructing the time series of returns and trades, natural timewas ignored. The datawere viewed as an untimed sequence of obser-vations, and the time subscript t was incremented each time a trans-action occurred. Tradeclassifications were made by reference to thequotes. As noted by Hasbrouck (1988) and Lee and Ready (1991),the NYSE reporting process delays most trades relative to quotes,leading to a spurious reversal in the transaction record. In conse-quence, tradeclassificationwasmadeon the basis of quotes prevailingasof five seconds priorto the tradeprinttime. Fortrades that occurredat the midpoint of these quotes, the trade variablex, was set to zero.Overnight returns were not used. The trade/returns process wasassumed to start afresh each morning, at which time lagged valuesof trades and returns were set to zero.Summary tatistics arereportedin Table 1.As expected, beginningshareprice and numberof transactionsarepositivelyrelatedto marketvalue, andthe average og spreadis negatively relatedto marketvalue.The proportionof unclassified trades (roughly42 percent) is slightlyhigher than the 30 percent found by Lee and Ready (in a 1988 non-censored sample). The proportion of unclassified volume is lowerthan the proportion of unclassified trades, suggesting that the mid-point-tradeproblem is less significantfor largertrades.Furthermore,206


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the classificationproportions exhibit a pattern across market-valuesubsamples.The lowest market-value ubsamplehas the smallestmid-point proportions,andwith increasing marketvalue, the proportionsgenerally increase.In Table 1, I present two estimates of the BN pricing errordisper-sion. The first, as,r is based on a five-lag univariateautoregression(i.e., rtwas regressed against {rt_1, . . ., rt_5}). The average for thetotal sample is 0.243 (i.e., approximately0.243 percent of the stockprice). A striking feature of the (s,r averages is that they are substan-tially lower than the corresponding average spreads. For the totalsample, the average log spread is 1.52 percent. If the spread wereentirelydue to liquidityand non-information-relatedransactioncosts(cf. the Roll model), the analysisof Section 1 suggests that the valueof as should be (1.52 percent)/2 = 0.76 percent. At 0.243 percent,the averagevalue of s,r is only about a third of this. The estimatevalues are in some respects sensitive to choice of lag length: Gen-erally,as ncreaseswith the cutoff.9The cross-sectionalpatterns(acrossfirms and across time) remainunaffected,however.Of course, as,r is a lower bound, and from the earlier remarks,itwould be expected to understatethe truevalue of o-sn the presenceof a pricing error component that is uncorrelatedwith information,but correlatedwith trades.Addition of tradevariablesto the explan-atoryvariable set would therefore be expected to strengthen thislower bound. This enhancement was implemented as follows. Fol-lowing Hasbrouck(1991a, 1991b), the signed tradevariableof powerk is defined by xk = sign(xt) Itl k, Thus, x? is an indicator variablethat takes on values in {-1, 0, +1}, xt = xt, and x 1'2 is a signedsquare-roottrade variable (included to allow for concavity in thetrade-price relation). The VARwas then estimated over the four-variableset {rt,x? xt, x1/2}: each variablewas regressed against thefull set through the fifth lag. The simultaneoususe of variouspowersof the tradeis intended to allow for nonlinear dependencies in boththe random-walkand pricing errorcomponents.Averagevalues for these trade-basedestimatesof the standarddevi-ation of the pricing error, denoted as' , are presented in Table 1.These values are generally higher than the corresponding Us,r values.This is most strikingfor the low market-value ubsample. In movingto the higher market-value ubsamples,the discrepancydeclines, andthe highest market-valuesubsample, the trade-basedos's, are only

9This increase may be occurring for methodological reasons. As discussed in Section 4, the pricingerror variance is essentially an "explained variance" in an implicit linear regression. In any givendata sample, such a quantity will tend to increase whenever explanatory variables are added. Theincrease may also represent, however, contributions to the pricing error from economic forcesoperating over horizons longer than the brief spans generally considered in microstructure analysis.

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Table 1Summary statistics by market capitalizationTotal Market-value subsamplessample 1 (Lowest) 2 3 4 (Highest)

No. of firms 175 27 50 48 50Equity capitalization ($MM) 1145 26 93 416 3502Beginning share price ($) 20.05 7.56 11.96 20.37 34.57Average log spread (x 100) 1.52 2.63 1.98 1.29 .70No. of transactions 3489 761 1221 2792 7899Proportion of unclassified .420 .297 .409 .448 .451tradesProportion of unclassified .342 .283 .352 .347 .349volume

(X 100) 0.243 0.305 0.329 0.230 0.136[0.160] [0.182] [0.164] [0.148] [0.064], (X 100) 0.330 0.552 0.411 0.307 0.153[0.235] [0.285] [0.161] [0.238] [0.078]

The sample is drawn from a sample of NYSE firms stratified by market value of equity. The numberof firms in the total sample and in the subsamples is reported in the first line. All other figures inthe table are sample averages. Equity capitalization and beginning share price are taken from theCRSP file. The average log spread for a given firm is an average of the difference between the logof the bid and the log of the ask quotes, weighted by the time over which the quote was in effect(from the ISSM tape, 1989 first quarter). The number of transactions is the number reported onthe ISSM tape for the first quarter of 1989. The pricing-error standard deviations are computedunder the Beveridge-Nelson identification restriction: a,, is based on a univariate autoregressivemodel of the stock return. o.,,, is based on a VAR of returns and trades. Standard deviations of thevariable are given in brackets.

slightly higher than ,sr The trade-baseda,'s remain, however, sub-stantiallylower than the average half-spreads.Indiscussing the magnitudesof these estimates,it is well to empha-size that identification of oSwith an average transaction cost for aparticular raderor class of tradersrequiresfurtherassumptionsaboutthe operationof the market.Empirical mplementation generallyalsorequires identification of those transactions n which the traderspar-ticipated. Approximate inferences can be made under simplifyingassumptions. If it is assumed that the initiatorof a trade (such as amarket-orderrader)always ncurs a positive cost, then the transactioncost is I ,I. (The receipt of this amountby the contrapartys presum-ably compensation for market-making ervices.) If s, were normallydistributed,then the expected transactioncost for these traderswouldbe ElstI= ( 2_/7r)o 0.8 roughly0.8(0.33 percent) = 0.26percentforthe NYSE otalsample. This should be viewed asvery approximatebecause of the assumptions of one-sidedness in the cost, symmetryof buys and sells, and normality.In a pure liquidity model in which all trades occurred at the bidor the ask,and tradesconveyed no information,one would expect tosee asequal to one half the spread. In actuality,the averagevalues

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Table 2Summary statistics by time of dayMorning Midday Afternoon(9:30- (10:00 A.M.- (3:30-

10:00 A.M.) 3:30 P.M.) 4:00 P.M.)Os,r X 100 0.165** 0.197 0.229*[0.117] [0.149] [0.232]

X 100 0.395* 0.218 0.258**[0.618] [0.166] [0.241]Average log spread x 100 1.000* 0.905 0.913[0.623] [0.593] [0.597]The values in the table are sample means and (in brackets) standard deviations of the pricing-errorstandard deviations estimated for each firm in the sample. 0a,r s based on a univariate autoregressivemodel of the stock return. s is based on a VAR of returns and trades. The average log spread istime weighted.

** The estimate differs from the corresponding midday estimate at significance levels of .10 and .05,respectively (using a sign-rank test on the differences).

for the trade-basedas'sare roughly one quarterof the correspondingaverage spreads. There are at least three considerations bearing onthis discrepancy.First,a substantialproportionof the trades occur atthe midpoint of the bid and ask quotes. This decreases the effectivespread. As an offsetting effect, however, the quoted spread is onlyvalid for trades of relatively small size. Largetrades may take placeoutside of the quoted spread. Finally, besides the fixed transactioncosts, the quoted spreadimpoundsanasymmetric nformationchargenot included in the pricing error.In short, the discrepancybetweenthe estimatedpricing-errorstandarddeviation and the half-spread seasily accounted for by considerations that illustrate and reinforcethe conclusion that posted spreads are suspect measures of marketquality.Previous researchhas characterizedbeginning- and end-of-tradingelevations in returns,variances,andvolumes. Spreadshave also beenfound to be higher at the beginning of trading [see Harris (1986,1989), Foster and Viswanathan(1990, 1993), Jain and Joh (1988),Mclnish and Wood (1992), Mulherin and Gerety (1989), and Wood,Mclnish, and Ord (1985)]. Given that the pricing error impoundsmicrostructure ffects thatarelikely to depend on these factors,thereare grounds for expecting beginning- and end-of-tradingpatterns inthe pricing erroras well. To explore this hypothesis, separate esti-mates of the pricing-errorstandarddeviation were computed for thebeginning-of-day (defined as the firsthalf hour of trading), end-of-day (last half hour of trading), and midday.When a 250-transactionminimum was imposed on the subperiods, the sample declined to36 firms. The estimates are reported in Table 2. The trade-basedestimate of asis higher at the beginning and, to a lesser extent, at the

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end of the tradingsession. (This patternis only partiallyconsistentwith thatof the average og spread,which is not substantiallyelevatedat the end of trading.)

7. ConclusionsIn this article,I define the pricing error(s) as the differencebetweenthe actual transaction price and an implicit unobservable efficientprice assumed to follow a random walk. The standard deviation ofthis pricing error(s) naturallyarises as a measure of marketquality.In establishing the correspondence between this model and theobservedtransactionsdata,it is shown that generally neither s,nor asis econometrically identified. It is nevertheless possible to computecertain estimates of these values: a best-linearestimate of stbased oncurrentand lagged dataand a lower bound foro,. Both estimates maybe improved by the addition of explanatoryvariables.If signed tradevariables are included in the estimation set, the estimates are likelyto be quite close to the true values.The empirical implementation surveys estimates of asfor a sampleof NYSE irms.For the full sample, the averagevalue of the estimatedasis approximately0.33 percent of the stock price. The estimates ofasare negatively related to marketvalue, and also exhibit elevationat the beginning and end of the tradingsession.Thereare many directions for furtherresearch. In the area of trans-action-costmeasurement,it would be useful to compute averageval-ues of the pricing error for particular traders or classes of traders.Along the lines of comparativemarketassessment, the financial com-munity is currently experiencing a period of expansion and experi-mentation in alternativemarketregimes. The asstatisticpresented inthis article maybe a useful tool for assessing the fitness of differentmarketstructures.ReferencesAdmati, A. R., and P. Pfleiderer, 1988, "A Theory of Intraday Patterns:Volume and Price Variability,"Revieuwof Financial Studies, 1, 3-40.Barnea, A., 1974, "Performance Evaluation of New York Stock Exchange Specialists," Journal ofFinancial and Quantitative Analysis, 9, 511-535.Beebower, G., 1989, "Evaluating Transaction Cost," in W. H. Wagner (ed.), The Complete Guideto Securities Transactions: Enhancing Investment Performance and Controlling Cost, Wiley, NewYork.Berkowitz, S. A., D. E. Logue, and E. A. Noser, 1988, "The Total Cost of Transactions on the NYSE,"Journal of Finance, 41, 97-112.Beveridge, S., and C. Nelson, 1981, "A New Approach to the Decomposition of Economic TimeSeries into Permanent and Transitory Components with Particular Attention to the Measurementof the 'Business Cycle'," Journal of Monetary Economics, 7, 151-174.

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Campbell,J. Y., and N. G. Mankiw, 1987, "Permanent and Transitory Components in MacroeconomicFluctuations," American Economic Review, 77, 111-117.Commodities Futures Trading Commission, 1989, "Economic Analysis of Dual Trading on Com-modity Exchanges," working paper, Division of Economic Analysis, Washington, D.C.Cooper, K., J. Groth, and W. Avera, 1985, "Liquidity, Exchange Listing, and Common Stock Per-formance," Journal of Economics and Business, 37, 21-33.Fama, E. F., and K. R. French, 1988, "Permanent and Temporary Components of Stock Prices,"Journal of Political Economy, 96, 246-273.Foster, D. F., and S. Viswanathan, 1990, "A Theory of the Interday Variations in Volume, Variance,and Trading Costs in Securities Markets," Review of Financial Studies, 3, 593-624.Foster, D. F., and S. Viswanathan, 1993, "Variations in Trading Volume, Return Volatility and TradingCosts: Evidence on Recent Price Formation Models," Journal of Finance, forthcoming.French, K. R., and R. Roll, 1986, "Stock Return Variances: The Arrival of Information and theReaction of Traders," Journal of Financial Economics, 17, 5-26.Glosten, L.R., 1987, "Components of the Bid-Ask Spread and the Statistical Properties of TransactionPrices," Journal of Finance, 42, 1293-1307.Glosten, L. R., and P. R. Milgrom, 1985, "Bid, Ask and Transaction Prices in a Specialist Marketwith Heterogeneously Informed Traders,"Journal of Financial Economics, 14, 71-100.Grossman, S. J., and M. H. Miller, 1988, "Liquidity and Market Structure," Journal of Finance, 43,617-633.Harris, L. E., 1986, "ATransactions Data Study of Weekly and Intradaily Patterns in Stock Returns,"Journal of Financial Economics, 16, 99-117.Harris, L. E., 1987, "Transaction Data Tests of the Mixture of Distributions Hypothesis," Journalof Financial and Quantitative Analysis, 22, 127-141.Harris, L. E., 1989, "A Day-End Transaction Price Anomaly," Journal of Financial and QuantitativeAnalysis, 24, 29-45.Harris, L. E., 1990, "Statistical Properties of the Roll Serial Covariance Bid/Ask Spread Estimator,"Journal of Finance, 45, 579-590.Hasbrouck,J., 1988, "Trades, Quotes, Inventories and Information," Journal ofFinancial Econom-ics, 22, 229-252.Hasbrouck, J., 1991a, "Measuring the Information Content of Stock Trades," Journal of Finance,46, 179-207.Hasbrouck, J., 1991b, "The Summary Informativeness of Stock Trades: An Econometric Analysis,"Review of Financial Studies, 4, 571-595.Hasbrouck, J., and R. A. Schwartz, 1988, "An Assessment of Stock Exchange and Over-the-CounterMarkets," Journal of Portfolio Management, 14, 10-16.Jain, P., and G.Joh, 1988, "The Dependence Between Hourly Prices and Trading Volume," Journalof Financial and Quantitative Analysis, 23, 269-283.Judge, G. G., W. E. Griffiths, R. C. Hall, H. Lutkepol, and T-C. Lee, 1985, The Theory and Practiceof Econometrics (2d ed.), Wiley, New York.Lee, C., and M. Ready, 1991, "Inferring Trade Direction from Intradaily Data,"Journal of Finance,46, 733-746.Lo, A. W., and A. C. MacKinlay, 1988, "Stock Prices Do Not Follow Random Walks: Evidence froma Simple Specification Test," Review of Financial Studies, 1, 41-66.

211


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Mclnish, T. H., and R. A. Wood, 1992, "An Analysis of Intraday Patterns in Bid/Ask Spreads forNYSE Stocks," Journal of Finance, 47, 753-764.Merton, R. C., 1980, "On Estimating the Expected Return on the Market: An Exploratory Investi-gation," Journal of Financial Economics, 8, 323-361.Mulherin, J. H., and M. S. Gerety, 1989, "Intraday Trading Behavior in Securities Markets: HourlyNYSE Volume and Returns, 1933-1988," working paper, U.S. Securities and Exchange Commission.Neal, R., 1989, "Market Structure and Transaction Costs," working paper, University of Washington.Perold, A., 1988, "The Implementation Shortfall: Paper versus Reality," Journal of Portfolio Man-agement, 14, 4-9.Poterba, J. M., and L. H. Summers, 1988, "Mean Reversion in Stock Prices: Evidence and Impli-cations," Journal of Financial Economics, 22, 27-60.Quah, D., 1990, "Permanent and TransitoryMovements in Labor Income: An Explanation for 'ExcessSmoothness' in Consumption," Journal of Political Economy, 98, 449-475.Quah, D., 1992, "The Relative Importance of Permanent and Transitory Components: Identificationand Some Theoretical Bounds," Econometrica, 60, 107-118.Roll, R., 1984, "A Simple Model of the Implicit Bid-Ask Spread in an Efficient Market," Journal ofFinance, 39, 1127-1139.Stock, J. H., and M. W. Watson, 1988, "Variable Trends in Economic Time Series," Journal ofEconomic Perspectives, 2, 147-174.Tanner, J. E., and J. B. Pritchett, 1992, "The Pricing of Market Maker Services Under Siege: Nasdaqvs. NYSE on Black Monday," in The NASDAQ Handbook, Probus, Chicago.Watson, M. W., 1986, "Univariate Detrending Methods with Stochastic Trends," Journal of MonetaryEconomics, 18, 49-75.Wood, R. A., T. H. Mclnish, and J. K. Ord, 1985, "An Investigation of Transactions Data for NYSEStocks," Journal of Finance, 40, 723-739.

Assesing the Quality of a Security Market a New Approach to Transaction

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