An Analysis of Intraday Patterns in Bid-Ask Spreads for NYSE Stocks

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An Analysis of Intraday Patterns in Bid/Ask Spreads for NYSE Stocks

Thomas H. McInish; Robert A. Wood

The Journal of Finance, Vol. 47, No. 2. (Jun., 1992), pp. 753-764.

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THE JOURNAL OF FINANCE .VOL. XLVII, NO 2 .JUNE 1992An Analysis of Intraday Patterns in Bid/Ask Spreads for NYSE Stocks

T H O M A S H . M C I N IS H and ROBERT A. WOOD"

ABSTRACTThe behavior of time-weighted bid-ask spreads over th e trading day are examined.The plot of minute-by-minute spreads versus time of day has a crude reverseJ-shaped pattern. Schwartz identifies four determinants of spreads: activity, risk,information, and competition. Using a linear regression model, a significant rela-tionship between these same factors and intraday spreads is demonstrated, butdummy variables for time of day have a reverse J-shape. For given values of theactivity, risk, information and competition measures, spreads are higher at thebeginning and end of the day relative to the interior period.

THIS STUDY HAS A dual focus. First, it extends prior work by examiningwhether variables previously found to be determinants of spreads using dat afor intervals of a day or longer also explain spreads during the t rading day.Second, the paper fu rthers previous research concerning intraday patterns inreturns, variability , and volume by examining intraday patterns of spreads.

Schwartz (1988, pp. 419-420) identifies four classes of variables a s deter-minants of bid-ask spreads: activity, risk, information, and competition. Eachof these determinants is considered briefly. Greater trading activity can leadto lower spreads due to economies of scale in t rading costs. Using trading costarguments, previous researchers show that a number of activity variables aresignificant determinants of bid-ask spreads including: (1) the average num-ber of shares traded (Tinic, 1972), (2) the volume (Tinic and West (1972),Branch and Freed (1977), Stoll (1978)), and (3) the number of transactions(Benston and Hagerman, 1974). Copeland and Galai (1983) model the bid-askspread as a free straddle option provided by the market maker and show th atthe bid-ask spread is inversely related to the frequency of trading. Copelandand Galai (1983) note that since less frequent trading usually means lowertrading volume, the bid-ask spread is likely to be inversely related tomeasures of market activity. Inventory control models (Garman (1976), andHo and Stoll (1980, 1981, 1983)) show that uncertainty in the arr iva l of buyand sell orders forces dealers away from the ir optimal inventory position. Inthe model of Amihud and Mendelson (1980), as the marker-maker approachesthe desired inventory position the bid-ask spread is reduced. Hence, if greater

*McInish is th e Wunderlich Chair of Excellence in Finance and Wood is a DistinguishedProfessor of Finance at Memphis State University in Tennessee. The authors wish to thankYakov Amihud, Anat Admati, John Burke, Kalman Cohen, Joel Hasbrouck, Albert (Pete) Kyle,


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754 T he Journal o f Financevolume of trading or larger trade sizes move a dealer away from the desiredinventory position, spreads will increase. If economies of scale predominate,then the following hypothesis would hold.Hypothesis 1: There is a n inverse re lat ionship be tween spreads and tradingactivity.

Researchers examining trading costs find that a dealer's risk of holding asecurity is a significant determinant of the bid-ask spread; these researchersuse measures of total risk (Tinic (1972), Tinic and West (1972), Branch andFreed (1977), Hamilton (1978), Stoll (1978)) and of systematic and unsystem-atic risk (Benston and Hagerman (1974), Stoll (1978)). Given these considera-tions, the following hypothesis would be expected to hold.Hypothesis 2: There i s a direct relationship between th e level o f r isk an dspreads.

Hasbrouck (1988) shows that the spread is related to the specialist'sperceived exposure to private information so that "large trades convey moreinformation th an small trades." Glosten and Milgrom (1985)develop a modelthat deals with how spreads respond to market-generated and other publicinformation. Since dealers perceive that there is a positive probability thatorders originate from informed traders, orders convey information and affectquotations. Schwartz (1988) argues that "it is likely that the spread widensa t times of substantial informational change." Hence, the following hypothe-sis is expected to hold.Hypothesis 3: There is a d irec t relat ionship be tween spreads a nd the am ou ntof information com ing to th e market .A number of researchers using trading cost models have reported an

inverse relationship between the level of competition and spreads (Demsetz(1968), Tinic and West (1972), Benston and Hagerman (1974), Hamilton(1976, 1978), and Branch and Freed (1977)). These considerations lead to thefollowing hypothesis.Hypothesis 4: The re is a n inverse relationship between spreads an d the level o fcompetition.

Turning next to the examination of intraday patterns, Wood, McInish, andOrd (1985), Harris (1986) and McInish and Wood (1990a) show that variabil-ity of returns exhibits a U-shaped pattern over the trading day. Volatility ofreturns is a direct measure of risk and an indirect measure of the level ofinformation (French and Roll, 1986). Since risk is a determinant of spreads,U-shaped patterns in variability of returns suggest the possibility of U-shapedpatterns in spreads with higher spreads at the beginning and end of thetrading day. Further, Jain and Joh (1988) and McInish and Wood (1990b)report intraday U-shaped patterns in volume. Volume of trading is a direct


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755ntraday Pat te rns in B id / Ask Spreadsthis factor suggests a n inverted U-shaped patte rn in spreads. Greater activityand competition a t the beginning and end of the trading day suggests lowerspreads a t these times. Therefore, the joint effect of risk, information, activ-ity an d competition on intraday variability of spreads is indeterminant.

The remainder of this paper is divided into three sections. Section Idescribes the data and methodology. In Section I1 the results are presented.The f inal section provides conclusions.

I. Data and MethodologyA. Description and Preparation o f the DataThe data for this study comprise every quotation (market bid and ask) forNYSE stocks entered into the Consolidated Quotation System by NYSEspecialists for the first six months of calendar year 1989. The quotations wereobtained from tapes provided by the Institute for the Study of SecurityMarkets. These quotations reflect the specialist's own supply/demand, thecrowd, and the book. Hence, these da ta reflect the strategic behavior of thespecialists and other market participants. Each quotation is time stamped tothe nearest second at the time it is provided to quotation vendors by theSecurities Industry Automation Corporation rath er than earlier in the quota-tion generation process. The length of time between the reporting of thequotation by the specialist and the Securities Industry Automation Corpora-tion time stamp may vary slightly depending upon the trade and quoteactivity levels. Quotations that are not firm are not included in the sample.Quotations from regional exchanges and for stocks that trade at a price ofless than $5.00 are excluded and stocks with fewer tha n 150 trades or fewerthan 150 quotes for the calendar year are omitted. Stock were eliminatedbased on their characterist ics for all of 1989 because the empirical tests werereplicated using da ta for the last six months of 1989, bu t these results are notreported because they do not a lt er any of the conclusions.During 1989, trading on the NYSE was conducted from 9:30 A.M. to4:00 P.M. New York time. A minute-by-minute time series of time-weightedpercentage bid-ask spreads over the trading day for the market is con-structed. Also, for use in the regression analysis described below, the tradingday is segmented into one 31-minute interval and twelve successive 30-minuteintervals. The time-weighted bid-ask spread (BAS) for each security for eachinterval is then calculated. The determinants of these BASs are investigated.The way the BASs are calculated is explained with greater specificity below.

Quotations prior to the opening are excluded and no quotation is carriedovernight. Quotations time stamped after the close are also excluded fromthe minute-by-minute analysis, but are included in the last thirty-minuteinterval of the trading day. The time-weighting is based on the number ofseconds the quotation i s outstanding during the one-minute or thirty-minuteinterval. While time-weighting seems to be the best approach for this study,


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756 The Jou rnal of FinanceAfter editing for errors,' a typical percentage bid-ask spread for eachminute of the trading day is created. First, a time-series of second-by-secondpercentage bid-ask spreads is created for each stock. The time-series beginswith the initial quotation each trading day. For a given stock for everysecond during which a quotation is outstanding a percentage bid-ask spreadis calculated as (ask - bid)/((ask + bid)/2). The process is repeated for eachstock. Then, for each trading second of the calendar year, all of the percent-age bid-ask spreads are averaged to create a second-by-second time series of"market" percentage bid-ask spreads. The percentage bid-ask spreads arethen averaged within each trading minute to create a time series of minute-by-minute bid-ask spreads.A time-weighted BAS is then calculated for thirty-minute intervals for usein the analyses described below. A percentage bid-ask spread (BAS) is

computed for every quotation as: BAS = [(ask - bid)/(ask + bid)/21. Supposethat in the interval (T, T') there are N quotation updates, occurring a t timesti, i = 1,...,N, with spreads BAS,, i = 1;. .,N where to = T and t,,, = T'.BAS, is based upon the quotation that is outstanding at time T (i.e., thequotation outstanding at the beginning of the thirty-minute time interval).Note that since quotations from previous days are not used, BAS, does notexist prior to the first quotation of the day. The interval (T, T') is measuredin seconds. For the interval during which the first quotation of the dayoccurs, the time-weighted spread is:

For intervals beginning subsequent to the first quotation of the day, thetime-weighted spread is:N BASi(ti+,- ti)Ci=o (T' - T)

At least five sources of bias are potentially introduced by late initialquotations-weighting, sampling, delayed openings, quotation delay, andresolution of uncertainty.1. Firms that are quoted earlier in the trading day will have a greaterrepresentation in the earlier minutes. Since (as shown below) theseAccording to the Institute for the Study of Security Markets, the error-checking algorithm

looks for a re turn with an absolute value greate r than a limit that i s a decreasing function of theprice of the stock being filtered. Once a potential error is identified, the algorithm looks forreversals. For example, if a stock is trading at $40 per share and a price of $4 is observed, it isclearly an error. Up to five repetitions of the $4 price just described would be identified by thealgorithm. The algorithm also examines the volatility of returns around the suspected errorpattern before flagging the prices a s erroneous. The higher the volatility, the less likely that thesuspected prices would be flagged. Further, the relationship between trades and quotations


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757n t raday Pa t te rns i n B id / A s k S p r e a d sstocks have lower spreads, a downward bias is introduced in the earlyminute-by-minute averages across stocks. This bias exists to a muchlesser extent in the thirty-minute analysis since most stocks will havebeen initially quoted in the first 31-minute interval.

2. Since stocks that a re initially quoted during a n interval will be reflectedin only part of tha t interval, their sampling error for tha t interval willbe larger than would have been the case if the quotation occurredearlier.

3. Delayed openings may result from uncertainty concerning the appropri-ate opening price which, in tu rn , will likely result in increased spreads.

4. Spreads for late initial quotations may be smaller than for earlier initialquotations since the uncertainty associated with equilibrium prices mayhave been resolved partially by the opening of other stocks by the timeof the late quotation.5. The stale quote problem (mentioned earlier) affects both initial inter-vals and subsequent intervals. If a specialist delays a quote revisionafter the arrival of new information, then the new information will havea smaller effect on that interval than if the quotation had been revisedimmediately. Stale quotations can obfuscate intraday pat terns of aparticular stock if quotations are revised quickly in some periods andslowly in others (e.g., when the specialist is busier). Also, stale quota-tions may affect comparisons across stocks if some specialists revisequotations more quickly than others.All statistical tests are performed at the 0.01 level of significance unless

otherwise indicated.B. M ethodology: An aly s i s o f the Data by In tervalA linear regression model is used to test Hypotheses 1-4. In the regres-

sions, BAS is regressed against a variety of independent variables. Since thedistributions of the variables are highly skewed, the square roots of thevariables are used so that outliers do not dominate the results.

Hypothesis 1 is tested using two activity variables. The first is the squareroot of the number of transactions in each issue i in Interval t (TRADES,,,)and the second is the square root of the average number of shares per tradefor each issue i in Interval t (SIZEi,,).Because of economics of scale consider-ations, both TRADES and SIZE are expected to have an inverse relationshipwith bid-ask spread.

As mentioned, previous researchers have shown that a stock's risk isrelated to its spread (Hypothesis 2). Since previous studies of the determi-nants of spreads did not examine intraday spreads using transactions data,these studies typically used measures of total risk and systematic risk, butwith transactions data a unique estimate of risk for very short intradayintervals can be estimated. These measures are more suitable for use in


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758 Th e Journa l o f F inanceeach stock i in Interval t, Mi as the mean of V,,, for stock i over all t and Sias the standard deviation of Vi,, for stock i over all t. The first measure ofrisk for stock i (RISKl,) is Mi and the second measure of risk for stock i inInterval t (RISKS,,,) is (V,,, - M,)/S,. RISKl captures differential risk fromone stock to another and RISK2 (the normalized value of RISK1) capturesdifferential risk from one interval to another for the stock.

As noted above, previous researchers have often used risk measures basedon transaction prices such as systematic risk, unsystematic risk and totalrisk. But for the trade-to-trade data used here, measures of risk based ontransaction prices are significantly affected by bid-ask bounce. Of course,bid-ask bounce is significantly affected by the size of the spread, the variableinvestigated in this study. Hence, trade-based measures of risk are notsuitable for use in this study.2 The risk measures used here are based onvariability of the mid-point of bid and ask quotes and are not affected bybid-ask bounce. It seems reasonable to believe that this measure of variabil-ity reflects the risk faced by the specialist.Schwartz (1988, p. 419) suggests that the effect of information on spreadscould be tested by considering the effect of current trading volume on spreadswhile controlling for a stock's normal trading volume. Volume of trading wasexamined, but the results are not presented because an alternative variableproved superior for testing Hypothesis 3. Specifically, for each security, themean ( X i )and standard deviation (DL) f the square root of the volume pertrade (SIZEi,,) or stock i over all t are calculated. Then, for each security foreach interval, the normalized value of the square root of the number ofshares per trade for stock i in interval t (NSIZE,,,) is calculated: NSIZEi,,=(SIZE,,,- Xi)/Di. NSIZE is used as an explanatory variable. While SIZEcaptures scale economies associated with trade size, NSIZE captures theeffect of unusually large or small trades relative to the average size of tradesduring a given interval for a given stock. Following the arguments ofHasbrouck (1988) periods during which there are relatively more unusuallylarge trades are likely to have greater information flow. Alternately, unusu-ally large trades may capture movement of dealers away from their preferredinventory position (Amihud and Mendelson, 1980).A variable to test Hypothesis 4 is included next. The variable,REGIONAL i,,, is the square root of the ratio of the number of shares of stocki traded on regional exchanges to the number of shares traded on the NYSEduring interval t . This variable captures the extent of competition in thespirit of variables such as th e of the number of dealers used by previousresearchers. These previous measures of the level of competition such as thenumber of market makers or number of markets on which the stock is traded(Demsetz (1968), Tinic and West (1972), Benston and Hagerman (1974),Hamilton (1976, 1978), and Branch and Freed (1977)) are not suitable for usewith transactions data because they do not change over the trading day. Aninverse relationship between BAS and REGIONAL is expected.


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759ntraday Patterns in Bid / Ask SpreadsSeveral researchers (Demsetz (1968), Tinic (1972), Tinic and West (1972),

Benston and Hagerman (1974), Hamilton (1976, 1978), and St011 (1978)) showthat there is an inverse relationship between a stock's price and its spread.Hence, in the regression model presented below, the square root of theaverage price in Interval t (PRICE,,,) is included as a control variable.

The linear model is:BASi,,= bo + b, TRADES,,,+ b, SIZEi,,+ b3 RISK1,

+ bqRISK2,,t+ b,, NSIZE,,, + b6 REGIONAL,,,+ b7 PRICEi,,+ 12 Interval Dummy Variables (numbered 1-9 and 11-13)+ 4 Weekday Dummy Variables + e,,t ( I )

where BAS,,, is the time-weighted percentage bid-ask spread for stock i inInterval t, the remaining variables are as defined in this subsection, b,, b,,b,, b,, b,, b,, b,, and b, (along with b, - b,, for the interval and weekdaydummy variables) are parameters to be estimated and e,,, is a random errorterm. Examination of variance inflation factors from SAS PROC REG for theabove model indicates statistically significant multicollinearity (a varianceinflation factor of 7). While this multicollinearity has undoubtedly reducedthe t-statistics for some of the explanatory variables, it has not resulted inany sign reversals. Given the large sample size and the consistency of theresults for each half of 1989, multicollinearity is not considered to havebiased the test outcome.

If the relationship between BAS and the explanatory variables is assumedto be the same for each interval, then differences in the intercept can becaptured through the use of dummy variables for intervals 1- 9 and 11-13.

There are also four dummy variables that equal 1 if the observation occurson a Monday, Tuesday, Thursday, or Friday, respectively, and 0 otherwise.These are designed to capture potential day-of-the-week effects identified byFrench (1980).

For a given stock for a given interval, if there are no observations of BASor one of the explanatory variables, then that interval is deleted from theanalysis.

11.ResultsA. Minute-by-Minute Analysis

Examination of the mean BASS for each minute of the trad ing day pre-sented in Figure 1 shows that spreads are relatively high at minute three,decline at a decreasing rate until minute 293 and then increase at anincreasing rate until the close of trading. Thus, the plot of spreads over thetrading day exhibits a crude reverse J-shaped pattern. The relatively low


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T h e J o u r n a l o f F in a n ce

0 100 200 300 400Minute of the Trading Day (0= 9:30 a.m)

Figure 1. Mean Bid-Ask Spreads for Each Minute of the Trading Day.Firs t, a time-seriesof second-by-second percentage bid-ask spreads is created for each stock. The time-series beginswith the initial quotation each trading day. For a given stock for every second during which aquotation is outstanding a percentage bid-ask spread is calculated as (ask - bid)/((ask + bid)/2).The process i s repeated for each stock. Then, for each trad ing second of the calendar year, a ll ofthe percentage bid-ask spreads are averaged to create a second-by-second ime series of "market"percentage bid-ask spreads. The percentage bid-ask spreads are then averaged within eachtrading minute to create a time series of minute-by-minute bid-ask spreads.

opened first and therefore have greater weight relative to thinner stocksduring the first few minutes compared with la ter in the trading day.

B. In terval Analys i sThe results of the regression of BAS against the explanatory and dummy

variables are presented in Table I. Recall that BAS is a percentage spreadrather than a dollar-value spread. The coefficients of TRADES and SIZE aresignificantly negative confirming Hypothesis 1. The coefficient of RISK1 issignificantly positive demonstrating that differential spreads across stockscan be explained in part by differences in a stock's risk. The coefficient ofRISK2 is also significantly positive showing that spreads are larger duringintervals with greater risk. Hence, these results are consistent with Hypothe-sis 2. The coefficient of NSIZE, the measure of information flow as reflectedin trades of a n unusual size, is significantly positive supporting Hypothesis 3.The coefficient of REGIONAL is significantly negative demonstrating that


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In t raday Pa t t e rns i n B id / A s k S p r e a d s

Table I Results for the Regression of Percentage Spreads Against

Activity, Risk, Information, Competition and Control Variables Each trading day during t he fi rst six months of 1989 is segmented into one 31-minute intervaland twelve thirty-minute intervals (9:30 A .M . to 10:OO A . M . , etc). Then, for each security i foreach interval t , th e mean value of the following var iables is calculated: (1) th e time-weightedpercentage bid-ask spread BASi,,, (2) the square root of th e number of trades (TRADES,,,), (3)th e squa re root of the number of share s per trade (SIZE,,,), (4) SIZE,,, minus the mean of SIZE,,,for stock i over all t and then divided by the standard deviation of SIZE,,, for stock i over all t(NSIZE;,,), (5) th e square root of the number of trades on regional exchanges relat ive to thenumber on the NYSE (REGIONALi,), and (6) th e square root of the average price (PRICE,,) .Define Via,as the standa rd deviation of the time-weighted average bid and as k for each stock'ininterval t, M, as the mean of V,,, for stock i over all t and S , as the standard deviation of V,,,for stock i over all t . The first measure of risk (R ISKl i) is Mi and the second measure of risk(RISK2i,t) s (V,,, - M, )/S, . BAS,,, is regressed aga inst TRADES, SIZE, RISKl, RISK2, NSIZE,REGIONAL, and PRICE plus dummy variables for each of the 13 interval s (with interval 10omitted) and dummy variables for each day of the week (with Wednesday omitted).

Independent Variables Coefficients t-statisticINTERCEPTTRADESSIZERISKlRISK2NSIZEREGIONALPRICE

Regression ResultsInterval 1Interval 2Interval 3Interval 4Interval 5Interval 6Interval 7Interval 8Interval 9Interval 11Interval 12Interval 13MondayTuesdayThursdayFridayR-squareF-statistic

" Significant at the 0.01 level


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762 The Journal of Financecausality is uncertain. In addition, the control variable PRICE shows thathigher priced stocks have smaller spreads.

The coefficients of the dummy variables for each interval of the trading dayreveal a crude reverse J-shaped pattern strictly declining from Interval 1 toInterval 9 and then strictly increasing from Interval 11 to Interval 13.Hence, after controlling for the determinants of spreads used in this analysis,a reverse J-shape time-of-day component remains. It is possible tha t thetime-of-day dummy variables are capturing a time-of-day preference fortrading (i.e., structural changes in the trading process across the tradingday). Alternately, a variable may be omitted. It is conjectured that a variableis omitted tha t is related to the resolution of risk over the trading day.

The coefficients of the dummy variables for each day of the week are allsignificantly positive indicating that there are differences in spreads by dayof the week, but the levels of the t statis tics indicates tha t weekday patternsare relatively weak compared with the strength of the intraday patterns.Moreover, the pattern is different than th at reported in a n earlier version ofthis paper for five months in 1987, so that the weekday pattern is not stableover time. Further, the regression analysis was repeated for the last sixmonths of 1989, but the results are not shown because the conclusions areidentical to those already presented-only the pattern of the weekday dummyvariables changed.

111.ConclusionsThis paper examines both the intraday behavior and the determinants of

time-weighted percentage bid-ask spreads during the first six months of1989. On a minute-by-minute basis, spreads are shown to have a crudereverse J-shaped pattern.

Previous research has shown that bid-ask spreads are determined byactivity, risk, information, and competition. This paper extends previouswork by using data for 13 intervals of the trading day to examine thedeterminants of spreads on an intraday basis. Using a linear regressionmodel, bid-ask spreads for each interval are regressed against variableshypothesized to be determinants of spreads. The level of spreads is found tobe significantly inversely related to two measures of activity, the number oftrades and the number of shares per trade. The level of spreads is directlyrelated to both differential risk across stocks and differential risk acrossintervals of the trading day. Intervals of the trading day during which thereare trades of an unusually large size have higher spreads reflecting theinformation content of these trades. Greater competition from regional ex-changes is associated with lower spreads. The direction of causality for theinverse relationship between NYSE spreads and regional trading volume isuncertain. Greater regional competition may reduce NYSE spreads, but tightNYSE spreads may result in great regional trading. Consider a Major


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763ntraday Patterns i n Bid / Ask Spreadsbook at that price or better may cause trades to migrate to the regionalexchanges. Suppose th at the NYSE quotation is 20 114 ask and that the sizeof the limit orders at this price is large while, say, the Pacific Exchange askis 20 318. Then, a cross on the NYSE a t 20 114 would require taking all thelimit order shares off the book before executing the cross. But if the cross isexecuted on the Pacific Exchange where the ask of 20 318 indicates thatthere are no limit orders a t 20 114, there is no interference from the limitorder book.

The market microstructure literature has demonstrated that there areintraday patterns in retu rns (Wood, McInish, and Ord, 1985), variability ofreturns (Wood, McInish, and Ord (1985), McInish and Wood (1990a)), thevolume of trading (Jain and Joh, 1988; McInish and Wood (1990b)), thenumber of trades and the number of shares per trade (McInish and Wood,1991b), and daily index autocorrelations (McInish and Wood, 1991a). Hence,it seems reasonable to examine whether there are intraday patterns inbid-ask spreads.3 Consequently, dummy variables for each interval of thetrading day (except one) are incorporated into the linear regression modeldescribed in the previous paragraph. The coefficients of these dummy vari-ables exhibit a reverse J-shaped pattern over the trading day. Spreads arehigher a t the beginning and end of the trading day than would be expectedbased on the values of the determinants of spreads at those times. Thisfinding suggests the need to search for additional determinants of spreadsthat may be especially relevant for explaining intraday variability inspreads.

While there a re also differences in spreads across days of the week, thestrength of these differences is much less than across intervals of the day.Further, there is evidence that the pattern of differences across days of theweek is not stable over time.

REFERENCESAmihud, Yakov and Haim Mendelson, 1980, Dealership market: Market-making with inventory,

Journal of Financial Economics 8, 31-53.Benston, George J. and Robert L. Hagerman, 1974, Determinants of bid-asked spreads in theover-the-counter market, Journa l of F inancial Economics 1, 353-364.

Branch, Ben and Walter Freed, 1977, Bid-asked spreads on the AMEX and the Big Board,Journa l of F inance, 32, 159-163.Brock, William A. and Allan W. Kleidon, 1992, Periodic market closure and trading volumn: a

model of intraday bids and asks, Journa l of Economic Dynamzcs and Control , Forthcoming.Copeland, Thomas E. and Dan Galai, 1983, Information effects on the bid-ask spread, Journa l o f

Finance 38, 1457-1469.Demsetz, Harold 1968, The cost of transacting, Quarter ly Journa l of Economics 82, 33-53.French, Kenneth R., 1980, Stock returns and the weekend effect, Journal of F inancial Eco-nomics 8, 55-70.----- and Richard Roll, 1986, Stock return variances: The arrival of information and thereaction of traders, Journa l of F inancial Economics 17, 5-26.Garman, Mark B., 1976, Market microstructure, Jourrzal of Financial Eco~zomics3, 257-275.


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You have printed the following article:

An Analysis of Intraday Patterns in Bid/Ask Spreads for NYSE Stocks

Thomas H. McInish; Robert A. Wood

The Journal of Finance, Vol. 47, No. 2. (Jun., 1992), pp. 753-764.

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Information Effects on the Bid-Ask Spread

Thomas E. Copeland; Dan Galai

The Journal of Finance, Vol. 38, No. 5. (Dec., 1983), pp. 1457-1469.

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Marketplace Organization and Marketability: NASDAQ, the Stock Exchange, and theNational Market System

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On Dealer Markets Under CompetitionThomas Ho; Hans R. Stoll

The Journal of Finance, Vol. 35, No. 2, Papers and Proceedings Thirty-Eighth Annual MeetingAmerican Finance Association, Atlanta, Georgia, December 28-30, 1979. (May, 1980), pp. 259-267.

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The Dynamics of Dealer Markets Under Competition

Thomas S. Y. Ho; Hans R. Stoll

The Journal of Finance, Vol. 38, No. 4. (Sep., 1983), pp. 1053-1074.

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The Dependence between Hourly Prices and Trading Volume

Prem C. Jain; Gun-Ho Joh

The Journal of Financial and Quantitative Analysis, Vol. 23, No. 3. (Sep., 1988), pp. 269-283.

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The Pricing of Security Dealer Services: An Empirical Study of Nasdaq Stocks

Hans R. Stoll

The Journal of Finance, Vol. 33, No. 4. (Sep., 1978), pp. 1153-1172.

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The Economics of Liquidity Services

Seha M. Tinic

The Quarterly Journal of Economics, Vol. 86, No. 1. (Feb., 1972), pp. 79-93.

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Competition and the Pricing of Dealer Service in the Over-the-Counter Stock Market

Seha M. Tinic; Richard R. West

The Journal of Financial and Quantitative Analysis, Vol. 7, No. 3. (Jun., 1972), pp. 1707-1727.

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An Investigation of Transactions Data for NYSE Stocks

Robert A. Wood; Thomas H. McInish; J. Keith OrdThe Journal of Finance, Vol. 40, No. 3, Papers and Proceedings of the Forty-Third Annual MeetingAmerican Finance Association, Dallas, Texas, December 28-30, 1984. (Jul., 1985), pp. 723-739.

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An Analysis of Intraday Patterns in Bid-Ask Spreads for NYSE Stocks

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