cur after a market has closed or before it has opened, not in the first halfhour of a trading day.Accordingly, because of the way in which we have measured it, anyaccentuation of first half-hour volatility would not be attributed to news perse (either over-night or in general), but to opening prices not reflectingaccurate adjustments to the news. As such, the accentuated first half-hourprice volatility would be evidence of price discovery being a protractedprocess that extends into, and perhaps beyond, the first half-hour period. Forthis reason, a spike for the first half-hour would be a particularly meaningful,inverse measure of market quality.Second Approach: The second approach we have taken to captureaccentuated short-period price volatility is to normalize our volatilitymeasures for each stock so that they can be directly contrasted for pricechanges measured over different returns intervals (half-hour, open-to-close,one-day, one-week, and two-week intervals). To this end, we express all ofthe volatilities for the different measurement intervals we have examined asrates per a half-hour interval, and divide each of them by a stock’s averagemid-day volatility.As we have previously noted, as the interval over which price changesare measured is increased, the standard deviation of volatility, whenexpressed as a rate per a given period (i.e., per half-hour), will not change ifsuccessive price changes are uncorrelated with each other. However, ifreversal behavior increases the frequency with which up ticks arefollowed by down ticks (or down ticks are followed by up ticks), volatility,as we have measured it, will decrease with the length of the measurementinterval. Alternatively, if momentum trading increases the frequency withwhich up ticks are followed by up ticks (or down ticks are followed by downticks), volatility, as we have measured it, will increase with the length of themeasurement interval. It is possible for a momentum move in one directionto end and then be followed by a momentum move in the opposite directionadjust after a market open due to the trading of the informed traders, and that volatility in firsthalf-hour returns may be attributed, in part at least, to the news factor. However, a majorreason for institutional participants to avoid trading at the open may not be that they arecarefully exploiting the value of their private information, but that they are very reluctant toparticipate actively in price discovery. Alternatively stated, an institutional trader likes to seefirst how the market opens, and then to come forth with his or her orders.
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(a large reversal). In such an event, volatility will increase with the length ofthe measurement interval for short intervals, but once the interval islengthened sufficiently to contain the larger reversals, the observed volatilitywill start to decrease.
4.
DATA AND TEST DESIGN
We have assessed the pattern of intra-day price volatility for two U.S.markets (The New York Stock Exchange and Nasdaq), and three Europeanmarkets (Euronext Paris, Deutsche Börse, and the London Stock Exchange).We first describe the transaction price data used in the analysis for each ofthese markets.
4.1
The Data
We studied the transaction records for each of the five markets for theyear 2000. The stocks in our sample are those that make up the major indexfor each of the countries: the S&P 100, the Nasdaq 100, the CAC 40, theDAX 30 and the FTSE 100. We use the TAQ database of the New YorkStock Exchange, the BDM database of Euronext Paris, the Transaction DataService database of the London Stock Exchange, and Deutsche Börse’sTransactions Database.131We have divided each of our five samples into two calendar periods.For each period, the sample comprises all stocks that were in the index at theend of the calendar period, and for which we have data for the entire period.A further criterion for the inclusion of a stock is that at least two trades occurfor the stock in a minimum of 90 percent of the half-hour intervals in thesample period. Our final sample is 72 stocks for NYSE, 80 stocks forNASDAQ, 39 stocks for Euronext Paris, 28 stocks for Deutsche Börse, and,for the London Stock Exchange, 85 stocks for the January to May period,and 88 stocks for the June to December period.Trading at the NYSE and Nasdaq opens at 9:30 am and closes at 4:00pm. Euronext’s trading hours at the beginning of the year 2000 were 9:00am to 5:00 pm. On Aprilthe trading day was extended to 5:30 pm. TheEuronext market opens with a call auction within the first minutes after 9:00
131
The composition of each of the indices underwent several changes during the year 2000.
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am, and closes with a second call auction that takes place about 5 minutesafter the close of the continuous market.132Deutsche Börse’s trading hours at the beginning of 2000 were 9:00 amto 5:30 pm. The trading day in Germany was extended to 8:00 pm on June2nd, 2000. Trading at Deutsche Börse opens with a call auction that takesplace within the first few minutes after 9:00 am. Deutsche Börse also runsan intra-day auction a few minutes after 1:00 pm, and another auction about5 minutes after the close. Before the extended trading hours, the closing callwas held a few minutes after 5:40 pm. After the extended trading hours, thiscall has been kept as a second intra-day auction, and a fourth auction wasintroduced for a few minutes after 8:00 pm to close the market.Trading hours for the London Stock Exchange are 8:00 am to 4:30 pm.Given the one-hour time difference between Great Britain and ContinentalEurope, the start of trading in London is synchronized with the Europeanmarkets. So too are the opening and closing procedures. The Londonmarket opens with a call auction at 8:00 am and, beginning on May 30th,2000, it also ends trading with a second auction that takes place severalminutes after 4:30 pm.The transaction data were filtered for errors. U.S. TAQ data werefiltered with an algorithm developed by Robert Wood. Wood’s procedureexamines all trades where the absolute value of the price change is greaterthat 11 percent. For such price changes, the algorithm examines up to nineprice changes on either side of the suspicious trade, as well as interveningquotes, to determine the likelihood that the trade was reported in error. Forthe current study, less than 0.01 percent of U.S. trades in our database wereidentified as erroneous by this method. We filtered the European data byeliminating every transaction where the absolute value of the log ofconsecutive prices (excluding the overnight price change) was greater than10 percent.133 No observations were removed with this filter for EuronextParis and Deutsche Börse. This is not surprising because both exchanges,being fully electronic, are not as subject to pricing errors. The filterremoved less than 0.6 percent of the London Stock Exchange trades.
132
In call auction trading, orders are batched together for a multilateral trade, at a single price,at a pre-specified point in time. At the call, buy orders at the single clearing price orabove execute, as do sell orders at the single clearing price or below.
133
The European data were provided in a flat file format that cannot be error filtered in themanner applied to the U.S. data.
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4.2
Test Design
For each of the five markets, each trading day is divided into the seriesof half-hour intervals that comprise the day for the market. For each stock ineach of the samples, a price change is recorded for every half-hour tradinginterval in the year 2000. The first trade and the last trade in a half-hourinterval determine the price change for that interval. Specifically, wemeasure the price change as the natural logarithm of the last price divided bythe first price in an interval.134The half-hour price changes are then divided into separate sets: the firsthalf-hour of the day, the second half-hour, and so on through the final halfhour interval of the trading day. Half-hour volatility is then computed foreach stock for each of the intra-day intervals, by taking the standarddeviation of the series of price changes recorded for each of the intervals.Referring to London time, this gives us the 8:00-8:30 volatility, the 8:309:00 volatility, and so on. The first daily intervals include the opening callsin the three European markets and the NYSE.135 Finally, the volatility foreach market, for each half-hour interval in the day, is computed as theequally weighted average volatility across all of the stocks in our sample forthat market and for that interval.
5.
VOLATILITY PATTERNS
We first consider the pattern of volatility over the trading day (FirstApproach). Then we examine how volatility changes as the interval overwhich price changes are measured is lengthened (Second Approach).As noted above, Euronext Paris and Deutsche Börse both extended theirtrading day during 2000, and the London Stock Exchange introduced aclosing call auction during the year. Accordingly, for each of the markets,we have divided the year into two parts: the span of days that preceded therelevant change, and the span of days that followed. Along with beingnecessitated by the market structure change, replicating the analysis for thetwo sub-periods and somewhat differentiated samples of stocks (particularly134
At least two trades must occur in a half-hour interval for a price change to be recorder forthe interval. If less than two trades occur in any interval, we do not ascribe a price changeto it and drop that observation from the sample. However, since we select the most liquidstocks in all markets, we do not lose any observations in our US sample, and we lose lessthan 0.5% of the observations for each market in our European sample.
135
The Nasdaq market does not open with a call.
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for the London market) gives us further confidence that our findings are notthe chance result of the particular calendar period studied.Forcomparability, we divided the NYSE and Nasdaq samples into two subperiods – the first six months and the last six months of 2000.
5.1
Intra-Day Volatility
The half-hour intra-day volatility patterns for each of the five exchangesare displayed in Exhibit 26.
Exhibit 26: Normalized Price VolatilitiesNote: Price change in each half-hour segment is measured as the natural logarithm of the lastprice divided by the first price in the segment. The half-hour price changes are then dividedinto separate sets: the first half-hour of the day, the second half-hour, and so on through thefinal half-hour interval of the trading day. Half-hour volatility is then computed for eachstock for each of the intra-day segments, by taking the standard deviation of the series of pricechanges recorded for each of the segments. The volatility for each market, for each half-hoursegment in the day is computed as the equally weighted average volatility across all of thestocks in our sample for that market and for that interval. The reported volatilities are thennormalized by dividing them by the average of the volatilities from the second half-hoursegment to the second-to-the-last half hour segment. Hence, the reported volatilities arescaled by dividing them by the mean mid-day volatilities.
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To further analyze the intra-day half-hour volatility pattern, we haveseparated the half-hour intervals into four groups: the first half-hour, thesecond half-hour through the second to last half-hour (not shown, butreferred to as Mid-Day), the last half-hour and, where applicable, the briefperiod between the close of the continuous market and the closing callauction (which we label “Closing CALL”). We apply the label “MID” to theaverage of the set of half-hour volatilities for the second half-hour intervalthrough the second to last half-hour interval. We use this average, MID, asa base against which to normalize the volatilities for each of the othergroups. To illustrate, for the NYSE First Period (the first half of 2000), forthe first half-hour, the value of 1.78 in the table indicates that this volatilityis 78 percent higher than that of the average of the eleven mid-day half-hourvolatilities.For Deutsche Börse’s second period, the formal trading hours extend toan 8:00 pm closing. However, examining volume for the 5:30 pm to 8:00pm segment (not shown), reveals that, for all intents and purposes, themarket has effectively continued to close at 5:30 pm.136 Accordingly, wehave calculated the normalized volatility for Deutsche Börse’s second periodby treating the 5:00 pm – 5:30 pm half-hour period as the closing half-hourof the continuous market, by considering the 5:30 pm call to be the closingcall, and by taking “MID” to be the average volatility over the half-hourintervals from 8:30 am through 5:00 pm.Table 1 also presents the volatility of the price changes from the openingtrade to the closing trade. This ratio is labeled “Open-To-Close.” To theextent that price swings which occur during the day have washed out by theclose of trading, we expect Open-To-Close be relatively low (less than 1).To the extent that intra-day trending predominates, we expect the ratio to berelatively high (greater than 1).The story told by Exhibit 26 is clear. The volatility spike for the firsthalf-hour is substantial for all five markets in each of the two calendarperiods. For the London Stock Exchange, volatility in the first half-hour isroughly three times the average of the other periods (excluding the openingand closing half-hour periods), while for the other European and two USexchanges it is about double.
136
Average daily trading volume showed little increase following the lengthening of thetrading day. For the January – May period, Deutsche Börse’s average daily tradingvolume for the average stock in our sample was 1.40 million shares. For the June –December period, the comparable number is 1.37 million shares.
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Volatility at the close is also accentuated, although less so than at theopening. Volatility over the last half-hour is over 50 percent greater than themid-day volatility for the London Stock Exchange in both sub-periods, andover 30 percent greater for Euronext Paris. Volatility at the close is 17percent more for Deutsche Börse in the first period and 15 percent more inthe second sub-period. Nasdaq closing volatility is 55 and 32 percent abovefor periods 1 and 2, respectively, while the NYSE’s closing volatility is 18percent and 10 percent higher.Also of interest in Exhibit 26 is the volatility between the close of thecontinuous market and the closing call auction (Closing CALL).137 Therelative volatility numbers presented in Exhibit 26 show that, for the threeEuropean market centers, some price volatility exists between the close ofthe continuous market and the closing call. The normalized volatility rangesfrom 1.00 to 1.09 for the continental European exchanges. Period 2 for theLondon exchange yields a normalized volatility of 1.50.138 This volatilityspike at London’s closing call may be attributed to meaningful pricediscovery taking place in the closing auction. Interestingly, for the secondperiod for Deutsche Börse, the call auction volatility is only 63 percent ofthe mid-day volatility at the 5:30 pm call, while it is 14 percent greater thanthe mid-day volatility at the 8:00 pm call.139 Apparently, with tradingactivity being relatively low between 5:30 pm and 8:00 pm, meaningfulprice discovery does occur at the final call. This is consistent with Paganoand Schwartz’s (2002) finding that the introduction of the closing call byEuronext Paris in 1996 (thinner stocks) and 1998 (extended to all stocks) didincrease the quality of price determination in that market.Exhibit 26 also shows the normalized open-to-close volatilities. Thevalues for Open-To-Close range from 0.99 to 1.20. While the numbers arepredominantly greater than unity, only the London values are significantlydifference from one. Open-To-Close is highest for the London StockExchange, standing at 1.18 and 1.20 for the first and periods, respectively.For Euronext Paris, Open-To-Close volatility is 1.00 for the first period, and1.05 for the second period. For Deutsche Börse, Open-To-Close is also 1.00
137
We treated the interval from the close of the continuous market to the closing call as if itwere another half-hour period. The treatment is conservative in that the actual time to theclosing call is roughly five minutes.
138
London introduced its closing call on May 30, 2000.
139
This figure is not shown in Exhibit 26.
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for the first period and .99 for the second period.140 Open-To-Closevolatilities for the two U.S. markets in both periods are tightly grouped at1.13 and 1.14.Because of the general lack of significance, interpreting these results asevidence of reversals may be misleading. Nevertheless, as discussed above,values of Open-To-Close of 1.00 or greater (which we have observed) doessuggest that price dislocations attributable to the four market process factors(spreads, market impact, dynamic price discovery and momentum trading)may not have been totally “repaired” by price reversals that have occurredby the end of the trading day. This is because reversal behavior may not beconfined to a single trading day, but could extend into next-day pricebehavior (and, perhaps, beyond). We assess this further in the next subsection.
5.2
Relative Short-Period and Longer-Period Volatility
The longer-period normalized volatilities displayed in Exhibit 26 are forthree measurement intervals – one day, one week, and two weeks. The oneday interval, DAY (the volatility of Close-To-Close returns) captures theprice change from the closing trade on one trading day to the closing tradeon the following trading day. The one-week interval (1WEEK) captures theprice change from the closing trade on one trading day to the closing tradefive trading days later. The two-week interval (2WEEK) captures the pricechange from the closing trade on one trading day to the closing trade tentrading days later.Each of these measures encompasses over-night (and over-weekend)price changes. The over-night price changes reflect the impact of overnightnews releases, x-dividend price behavior, and stock splits, all of which makeour recorded price changes more volatile.141For this reason, anydiminution of volatility as we progress from the intra-day, to the oneday, to the one-week and, finally, to the two-week measurement
140
Interestingly, when for the second period we extend the analysis to the 8:00 pm close,Open-To-Close volatility increases to 1.07.
141
We account for splits and dividends by eliminating the extreme results that stem from suchevents.
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interval, would be particularly strong evidence of reversal behavior instock price changes.142The first contrast of interest is between Open-To-Close and DAY. Forthe NYSE and Nasdaq, DAY is greater than unity with statisticalsignificance, while Open-To-Close is statistically indistinguishable from 1for both markets. For London, on the other hand, Open-To-Close isstatistically different from 1, while Day is indistinguishable from 1. Thus,while the US markets reflect substantial volatility from the prior day’s closeto the subsequent open, the London market reflects substantial meanreversion during the overnight period. For Euronext Paris and DeutscheBörse, both the Day and Open-To-Close measures were indistinguishablefrom unity for the two study periods.For all markets, the normalized volatility successively declines as wemove from DAY, to 2WEEKS. However, this decline is more pronounced(and has higher statistical significance) for the European markets. Thisfinding may reflect, at least in part, the diminishing influence of the bid/askbounce and market impact as the horizon is lengthened. This could alsoreflect the fact that, over an extended period, errors in price discovery arelargely repaired by reversals that bring prices back toward equilibrium. Notealso that the levels of the DAY ratios in the US markets are higher than unitywhereas those in European markets are not. These differences could reflectthe relative practices of intra-day news release in the US and Europe.143Across the five markets, the values for 2WEEKS are generallysomewhat less than those for 1WEEK. However, the one- and two-weekvalues are similar, and it appears that much of the reversal behavior iscaptured by the one-week measure.
142
The price series could, of course, be adjusted for cash and stock dividends and for stocksplits. However, the adjustment factors were not available to us for the current study.
143
It is further interesting to note that all of the estimates of 1WEEK and 2 WEEKS for theEuropean exchanges are less than one, and that some of these deviations are statisticallysignificant. This means that the adjusted volatility of these longer period returns is lessthan average mid-day volatility, and can be taken as evidence of more accentuated midday reversal behavior and/or more protracted trending in the European markets.
172
6.
A Trading Desk’s View of Market Quality
UNANSWERED QUESTIONS
The picture that emerges for each of the five markets we have consideredis one of accentuated short-period volatility, especially at market openings.Daily opening prices are particularly volatile in the British market. We areunable to explain this result fully, but note that trading volume at the open islow for London.144 The lower volume indicates that institutional investors inLondon tend to avoid trading at the open. While institutional traders in theUS may also tend to avoid the open, retail trading interest in the US (andcontinental Europe) provides ample volume at the open and, in so doing,may lead to better price discovery. Additionally, Werner and Kleidon(1996) suggest that the extensive trading of London stocks in the US alterstheir trading behavior in the UK.And so, in establishing our findings, we have not focused on the actuallevels of volatility in the various markets we have studied. Inter-marketdifferences in underlying volatility levels could be attributed to the differentcharacteristics of the stocks traded in the various markets, to differentinherent levels of risk and uncertainty in the various countries the shares aretraded in, and possibly to other factors that we have not taken into accountthat have little to do with market structure per se.Rather, we haveexpressed our key volatility measures in relative terms (namely, relative tomid-day volatility). Doing so provides a cleaner picture of the volatilitypatterns over the course of a trading day, across measurement intervals ofdiffering length, and across different market structures.The five exchanges we have considered represent very different marketstructures. The NYSE is an order driven market that includes market makers(each of the listed companies is allocated to a single specialist). Nasdaq inthe year 2000 (the test year for our study) had predominantly a dealer marketstructure (albeit with some characteristics traditionally associated with orderdriven markets). Paris, London, and Frankfurt utilize automated (i.e., notfloor-based) order-driven trading platforms.145 Consequently, accentuated144
Volume data are presented in Ozenbas (2002).
145
Frankfurt still has a trading floor, although much of the activity has migrated to itselectronic platform, Xetra. Trading on the floor starts at 9:00 a.m., the same time theelectronic market opens, and both venues open with a call auction. Because the call iselectronic on the electronic platform but not on the floor, it is possible for the floor traders
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volatility, especially at the open, cannot be simply ascribed to a specialisttaking into account his or her own inventory considerations, or to order flowbeing fragmented in a competitive dealer market, or to the attributes of anelectronic platform.A number of questions concerning market quality/efficiency on bothsides of the Atlantic could be raised in light of the magnitude of the volatilityrelationships. We have observed volatility spikes ranging from 76 percent to212 percent for the first-half hour of trading, and volatility spikes at the closethat range up to 64 percent. What accounts for them? At each opening,information that has been released since the previous close must beincorporated into prices. In the process, conflicting opinions held by tradershave to be resolved quickly, in an orderly manner, and with a high degree ofaccuracy. Not surprisingly, the opens are typically periods of seriousbuy/sell imbalances that result in opening prices being imperfectly alignedwith their consensus values.It is not normally the case that extensive information is released at theclose. We suggest that the volatility spikes at the close result, in part at least,from the price pressures caused by agents cleaning up orders that must becompleted within the day, and from traders unwinding positions so as to endthe day flat.One market structure innovation that could alleviate price pressures at theclose is the closing call auction that has now been incorporated into each ofthe three European markets. Pagano and Schwartz (2003) found that theintroduction of a closing call in the Paris market resulted in more efficientprice behavior, both in the closing call itself, and in the last fifteen minutesof the continuous market. They posit that availability of the closing callauction makes it safer towards the end of the continuous market forparticipants to be liquidity providers (i.e., to place limit orders) rather than tobe liquidity demanders (i.e., to place market orders). This is because anylimit orders that did not execute in the continuous market could be rolledinto the call. Consequently, books became deeper and price volatility hasbeen better controlled in the continuous market after the introduction of theclosing call.On the other hand, for the five markets that we have studied, the firsthalf-hour volatility measures show that the three European markets that openwith fully electronic calls perform no better by this metric than the two USmarkets that do not (the NYSE’s call is not fully electronic, and Nasdaq hasno formal opening procedure). However, as previously stated, we have beento see the opening price on Xetra, but prices set on the floor openings are not known at thetime of the Xetra call.
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cautious about making cross-market comparisons. For the London market,as we have noted, the particularly sharp volatility accentuation at the opencould be attributed primarily to its heavily institutional nature, and to the factthat the UK institutional investors tend to shy away from trading at theopen. In any event, we anticipate that, for any given market center,proper design and implementation of an electronic call would improvemarket quality, especially if it is designed so as to provide theappropriate incentives for participants to use it. Further investigationof the issue would be desirable.The research could be extended in a number of other ways. The analysisshould be applied to small-cap and mid-cap stocks, in addition to the largecaps that we have focused on in this study. Attention could also be given tothe effect of pre-opening trading on first half-hour volatility. The tradingbehavior of institutional investors, and its effect on the intra-day patterns ofvolatility and volume, needs to be examined. The relationship betweenvolatility and trading volume should be revisited with reference to the intraday patterns we have observed. Of further interest would be an analysis ofhow the intra-day volatility metric has evolved in recent years, a period thathas seen extensive change in the structure of the equity markets. Ofparticular importance would be an examination of the effect that theconversion to decimals in the US that was completed in 2001 had on the USmarkets (one might anticipate a volatility effect to the extent that institutionof the penny tick has affected the liquidity suppliers). Lastly, matchedsamples and/or multivariate statistical techniques should be used so thatmeaningful cross-country comparisons can be derived from the intra-dayvolatility metric.
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