13
by Bruce 1. Jacobs and Kenneth N. Levy Calendar Anomalies: Abnermal Returns at Calendar Turning Points There is overwhelming evidence that abnormal equity returns are associated with the turn of the year, the week and the month, as well as with holidays and the time of day. These returns are not unique to one historical period, nor can they be explained by considerations of risk or value. Tax-loss selling at year-end, cash flows at month-end and negative news releases over the weekend may explain some of these return abnormalities. But human psychology offers a more promising explanation. Calendar anomalies tend to occur at turning points in time. While these artificial moments have little economic significance, investors may deem them important, and behave accordingly. The question remains why these effects, which have been recognized for some years, have not been arbitraged aioay. Trading costs are, of course, an impediment. A portfolio manager ivould not consider liquidating an entire portfolio on a Friday merely in order to avoid experiencing relatively poor weekend returns. But planned trades can be scheduled to take advantage of calendar-based return patterns. Calendar effects should be of particular importance to traders. C ALENDAR ANOMALIES have long been part of market folklore.' Studies of the day-of-the-week, holiday and Janu- ary effects first began to appear in the 1930s."^ And although academics have only recently begun seriously to examine these return pat- terns, they have found them to withstand close scrutiny. Calendar regularities generally occur at cusps in time—the turn of the year, the month, the week, the day. They often have significant economic impact. For instance, the "Blue Mon- day" effect was so strong during the Great Depression that the entire market crash took place over weekends, from Saturday's close to Monday's close. The stock market actually rose on average every other day of the week. Calendar anomalies are often related to other return effects. For instance, some calendar anomalies are more potent for small than for 1. Footnotes appear at end of article. Bruce Jacobs and Kenneth Levy are principals of Jacobs Levy Equity Management, Fairfietd, Neiu jersey. large capitalization stocks. While analysis of cross-sectional effects requires fundamental da- tabases—a relatively recent innovation—the study of calendar anomalies requires only time- dated records of market indexes. Hence calen- dar anomalies can be tracked historically for much longer periods than effects requiring fun- damental data. The availability of a century of data brings enormous statistical power for testing calendar effects, but it also increases the likelihood of data-mining. If enough patterns are tested, some will appear significant merely by chance. In exploring calendar anomalies, therefore, sig- nificance levels must be properly adjusted for the number of hypotheses examined, out-of- sample tests should be encouraged, and only plausible hypotheses considered.* Calendar regularities appear to be even more aberrant than cross-sectional return effects. A skeptic, for instance, might assert that low P/E stocks provide outperformance simply because of their greater riskiness; this argument can be deflected, but it requires potentially controver- FINAMCIAL ANALYSTS JOURNAL / NOVEMBER-DECEMBER 1986 n 2 8

Calender Anomalies Abnormal Returns at Calender Turning Points

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Page 1: Calender Anomalies Abnormal Returns at Calender Turning Points

by Bruce 1. Jacobs and Kenneth N. Levy

Calendar Anomalies: AbnermalReturns at Calendar Turning Points

There is overwhelming evidence that abnormal equity returns are associated with the turn ofthe year, the week and the month, as well as with holidays and the time of day. These returnsare not unique to one historical period, nor can they be explained by considerations of risk or

value.Tax-loss selling at year-end, cash flows at month-end and negative news releases over the

weekend may explain some of these return abnormalities. But human psychology offers amore promising explanation. Calendar anomalies tend to occur at turning points in time.While these artificial moments have little economic significance, investors may deem themimportant, and behave accordingly.

The question remains why these effects, which have been recognized for some years, havenot been arbitraged aioay. Trading costs are, of course, an impediment. A portfolio managerivould not consider liquidating an entire portfolio on a Friday merely in order to avoidexperiencing relatively poor weekend returns. But planned trades can be scheduled to takeadvantage of calendar-based return patterns. Calendar effects should be of particularimportance to traders.

CALENDAR ANOMALIES have longbeen part of market folklore.' Studies ofthe day-of-the-week, holiday and Janu-

ary effects first began to appear in the 1930s."And although academics have only recentlybegun seriously to examine these return pat-terns, they have found them to withstand closescrutiny.

Calendar regularities generally occur at cuspsin time—the turn of the year, the month, theweek, the day. They often have significanteconomic impact. For instance, the "Blue Mon-day" effect was so strong during the GreatDepression that the entire market crash tookplace over weekends, from Saturday's close toMonday's close. The stock market actually roseon average every other day of the week.

Calendar anomalies are often related to otherreturn effects. For instance, some calendaranomalies are more potent for small than for

1. Footnotes appear at end of article.

Bruce Jacobs and Kenneth Levy are principals of Jacobs LevyEquity Management, Fairfietd, Neiu jersey.

large capitalization stocks. While analysis ofcross-sectional effects requires fundamental da-tabases—a relatively recent innovation—thestudy of calendar anomalies requires only time-dated records of market indexes. Hence calen-dar anomalies can be tracked historically formuch longer periods than effects requiring fun-damental data.

The availability of a century of data bringsenormous statistical power for testing calendareffects, but it also increases the likelihood ofdata-mining. If enough patterns are tested,some will appear significant merely by chance.In exploring calendar anomalies, therefore, sig-nificance levels must be properly adjusted forthe number of hypotheses examined, out-of-sample tests should be encouraged, and onlyplausible hypotheses considered.*

Calendar regularities appear to be even moreaberrant than cross-sectional return effects. Askeptic, for instance, might assert that low P/Estocks provide outperformance simply becauseof their greater riskiness; this argument can bedeflected, but it requires potentially controver-

FINAMCIAL ANALYSTS JOURNAL / NOVEMBER-DECEMBER 1986 n 2 8

Page 2: Calender Anomalies Abnormal Returns at Calender Turning Points

sial assumptions about risk modeling.'' Othersmight claim that the low P/E characteristic mere-ly proxies for value (although this argument canalso be rebutted).*^ Risk or value considerationsappear insufficient to explain calendar anoma-lies such as the day-of-the-week effect.

Because calendar anomalies appear relativelyeasy to exploit, their continued existence seemsinexplicable. To arbitrage the P/E effect, forexample, investors would have to increase theirdemand for low P/E stocks; psychological con-siderations may inhibit investors from doingso.^ But to arbitrage the time-of-day effect, inves-tors merely have to schedule discretionarytrades at a more advantageous time of day.

Calendar anomalies are difficult to exploit as astand-alone strategy because of transaction costconsiderations. For instance, full capture of theday-of-the-week effect would require 100 percent turnover per week. Calendar return pat-terns can, however, be of benefit in timing apreconceived trade. While cross-sectional re-turn effects, such as low P/E, might be useful toportfolio managers in selecting stocks, calendaranomalies may be of greater interest to traders.''

The January EffectThe turn of the year is a special time for thestock market. Most individuals have calendartax years, and many firniis close their books atthis time. The turn of the year represents a cleanslate for government, business and consumerbudgeting, as well as for purposes such asinvestment manager performance evaluation.Additionally, investors' cash flows may be jolt-ed by bonuses, pension contributions and holi-day liquidity needs.

Stocks exhibit both higher returns and higherrisk premiums in January.** These results havebeen corroborated in many foreign markets.^But the higher returns accrue primarily to small-er stocks. January does not appear to be anexceptional month for larger-capitalization is-sues.

10

January seasonals have been noted in returnsto a variety of stock characteristics, includingsize, yield and neglect.'' Returns to small size,for example, occur at the turn of the year —specifically, on the last trading day in Decemberand the first four trading days in January.'- Themagnitude of this effect can be substantial. Overthese five trading days from 1970 to 1981, smallstocks provided an average return of 16.4 percent, compared with 1.9 for large stocks.'-*

It is vital to disentangle interrelated effects inattributing returns to stock characteristics inorder to identify properly underlying sources ofreturn. Disentangled return attributions are re-ferred to as "pure" returns, because they arepurified of other related effects. After "purifica-tion," two effects emerge strongest in January.One is a return rebound for stocks with embed-ded tax losses, especially those with long-termlosses. The other is an abnormal return to theyield characteristic, with both zero-yielding andhigh-yielding stocks experiencing the largestreturns.

Other January seasonals appear to be mereproxies for these two effects. In fact, pure re-turns to smaller size (after controlling for otherfactors) exhibit no January seasonal at all. Thereis also evidence of January selling pressure forstocks with long-term gains, apparently due tothe deferral of gain recognition until the newyear. 14

RationalesThe most commonly cited reason for the

January return seasonal is tax-loss-selling re-bound.'*^ That is, taxable investors dump losersin December for tax purposes, and the subse-quent abatement of selling pressure in Januaryexplains the higher returns. The tax-loss expla-nation has been found to be consistent withreturns in many foreign equity markets and forother asset classes, such as corporate bonds. "

But the tax-loss hypothesis does not seemfully satisfactory. First, there is little evidencethat selling pressure near year-end is strongenough to account for the rebound.''' Second, itis not clear why rational investors would awaitthe new year to reinvest, although temporary"parking" of proceeds in cash could account forthe observed seasonality."^ Third, it seems sub-optimal for investors to wait until year-end totransact. Until the Tax Reform Act of 1986,short-term losses sheltered more income fromtaxes than long-term losses. It would thus havebeen preferable to establish tax losses before anasset's holding period became long term.'"*Also, the tax-loss theory would predict a largerrebound for stocks having short-term losses, yetthe January rebound is stronger for stocks withlong-term losses.-" Fourth, market returns priorto the imposition of the U.S. income tax, andreturns in a few foreign countries, appear incon-sistent with the tax-loss explanation.-' In anycase, sophisticated investors should anticipate

FINANCIAL ANALYSTS JOURNAL / MOVEMBER-DECEMBER 1988 D 29

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predictable price patterns and arbitrage themaway.

Tax-loss-selling pressure might be expected tobe stronger in down-market years, when lossesare more prevalent. Also, higher taxable in-comes or higher tax rates may strengthen tax-loss taking. Current evidence of such relation-ships is rather weak.""

Another rationale for the January effect isyear-end "windowdressing.""^^ In this view,some portfolio managers dump embarrassingstocks at year-end to avoid their appearance onthe annual report. Similar stocks are repur-chased in the new year, resulting in the Januaryeffect. This argument also begs the question ofcountervailing arbitrage.

A January risk seasonal might explain thehigher returns at the turn of the year. In fact,beta (systematic risk) and residual risk for smallfirms rise in January."•* According to the CapitalAsset Pricing Model, only systen:iatic risk earnscompensation. While the January increase inbeta for small firms is approximately 30 percent, it is insufficient to explain the Januaryreturn seasonal.

Moreover, risk appears to be priced only inthe month of January. In all other months, thereis no significant relation between risk and re-turn, whether risk is measured in a CAPM orAPT framework, or even without appealing toany particular asset pricing model."'' This re-mains a mystery. Foreign evidence on the pointis mixed. In some countries, risk and returnpatterns do not coincide, belying the risk expla-nation for return seasonality."*"

Alternatively, the January return seasonalmay be compensation for bearing informationalrisk."'' The seasonal may stem from the reduc-tion of uncertainty associated with the dissem-ination of information after the close of the fiscalyear, especially for small, neglected firms. Butinformational risk is not resolved precipitouslyat the turn of the year. Furthermore, a study offirms with non-December fiscal years presentsstronger evidence."'" Such companies do notexperience a return seasonal at the turn of theirfiscal year, as informational risk is resolved, butrather at calendar year-end. Thus informationalrisk appears to be an inadequate explanation ofthe January seasonal.

Cash-flow patterns at the turn of the year mayproduce the return seasonal. Annual bonusesand holiday gifts might be invested in the stockmarket, along with year-end pension plan con-

tributions. Also, savings spent on holiday con-sumption may in part be replenished. In Japan,where bonuses are paid semiannually, equitiesexhibit seasonals in January and June.""^ Onceagain, this predictable return regularity could bearbit raged.

Novel cognitive psychological approaches, in-cluding Prospect Theory and Procedural Rationali-ty, offer substantial insight into market behav-ior." '* Once we entertain the notions thatinvestors are loathe to admit mistakes, tend to"frame" decisions, have finite mental capacity,and generally behave in rather human ways,seemingly irrational market behavior is demys-tified. For instance. Prospect Theory is consis-tent with the predilection of investors to defertax trading until year-end and the finding thatlong-term tax-loss selling is stronger than short-term. These behaviors arise from the use ofyear-end tax planning as a justification for ad-mitting mistakes and from the tendency to ridelosers too long. Procedural Rationality also of-fers clues into behavioral causes for Januaryanomalies, such as the abnormal performanceof both zero and high-yielding stocks.

The Turn-of-the-Month EffectRecent academic studies demonstrate anoma-lous returns at the turn of each month, vindicat-ing the claims of practitioners.^' While not asdramatic as the January effect, this anomaly issubstantial. In fact, turn-of-the-month returnshave alone accounted fully for the positive re-turns generated by the stock market.

Figure A plots average returns to the DowJones Industrial Average for trading days nearmonth-end for the period 1897 to 1986. " Re-turns are high for each trading day from the lastday in the previous month (denoted as day -1)to the third trading day in the current month.These four trading days averaged 0.118 percent, versus 0.015 per cent for all trading days.While this anomaly has existed for almost acentury, it has weakened somewhat in the mostrecent decade. It has, however, been docu-mented in periods both before and after those inwhich it was first identified; this "out-of-sam-ple" evidence rebuts allegations of data-mining.

Might the turn-of-the-month effect merelyproxy for other anomalies? Studies have reject-ed January, day-of-the-week, holiday, tax-loss-selling and size effects as underlying causes.-'^Methodological deficiencies seem an unlikelyexplanation, as various studies have controlled

FINANCIAL ANALYSTS JOURNAL / NOVEMBER-DECEMBER 1988 D 30

Page 4: Calender Anomalies Abnormal Returns at Calender Turning Points

Figure A The Turn-of-the-Month Effect (avercige daily returns)

0.15

0.12-

0.09

Return (per cent)

Day

Trading; Diiy uf thi' Munlh

Data from j . L.ikonishok .ind S. Sinidl, "Ari.'SLMSOIHI Amim.iliosCornfilU,. Mav 1987)-

l? A \llK•lv-^^^l^ ri.T' |.H'i-ti\L'" (]i)lin--on

for dividends, pricing errors and outliers. Also,risk, as measured by standard deviation ofmarket returns, is no higher at the turn of themonth.

Some practitioners have suggested month-end portfolio rebalancing as a possible explana-tion; investors may reinvest accumulated cashdividends at this time. A more convincing ratio-nale is based on higher month-end cash flows,such as salaries. An interest-rate seasonal toTreasury bills maturing at the turn of the monthhas been attributed to investor cash-flow con-siderations.•''' Increased demand for equities atmonth-end might produce the observed returnregularity.

The timing of earnings announcements mayprovide additional insight. While companiesoften disclose good news voluntarily, the publi-cation of bad news is often suppressed until thenext mandatory quarterly report.-*' Moreover,good earnings reports tend to be released fasterthan bad ones. Some observers have suggestedthat the positive returns around the first of eachmonth reflect a clustering of positive earningsannouncements.•''' But while good earningsnews is predominant in the first half of themonth, it is not concentrated in the first fewdays, when the return seasonality occurs. Also,excluding earnings report months from thesample diminishes the effect, but does not elimi-nate it."

The absence of countervailing arbitrage re-mains a puzzle.

The Day-of-the-Week EffectStock returns are intimately tied to the day ofthe week. The market has a tendency to endeach week on a strong note and to decline onMondays. This pattern is deeply ingrained infolk wisdom, as evidenced by the recent bookDon't Sell Stocks on Monday.^^ It is often referredto as the "weekend" or "Blue Monday" effect.

Eigure B illustrates average daily returns ofthe S&P composite for each day of the weekfrom 1928 to 1982.''' Monday is the only downday, and is significantly different statisticallyfrom all other days. The last trading day of theweek—Friday in five-day weeks and Saturdayin six-day weeks—has a substantial positiveaverage return.

The economic magnitude of the effect is nottrivial. Eor an equity portfolio with a cash flowof $100,000 per week, for example, switchingthe sale day from Monday to the previousEriday might earn an additional S14,700 perannum.""'

As with the turn-of-the-month effect, re-searchers have recently verified the existence ofthis anomaly in both earlier and later periodsthan previously studied.*' The robustness of theday-of-the-week effect across time periods at-tests to its stability and defuses any data-miningcriticism.

Day-of-the-week patterns also exist in otherU.S. markets. Because stock option and stockindex futures prices are anchored by the under-lying spot market, a day-of-the-week effect for

FINANCIAL ANALYSTS JOURNAL / NOVEMBER-DECEMBER 1988 Q 31

Page 5: Calender Anomalies Abnormal Returns at Calender Turning Points

Figure B The Day-of-the-Week Effect (avcr.igf daily returns)

-0.20

MON. TUL. WKD. THU. I-RI.S" SAT.

*Fri, 6-Friday in a six-day Irading week. "Fr i . .'i = Friday in d fivf-day trading wwk.Data from D. Keim and R. Stambaugh, "A Further InvesliRatiun of the Wit-kend Effecl in Stock Returns,"/imnni/(if ffmura. July 19M,pp. 819-837.

these derivative securities would not be surpris-ing. Such effects have been found in both mar-kets, even though low transaction costs in thefutures market facilitate arbitrage of this effect.•*-The U.S. Treasury bill and bond markets alsodisplay a weekly pattern similar to that of theequity markets. Most notably, Monday returnsare negative, and more negative for longermaturity instruments."^"'

A day-of-the-week effect is also present inmany foreign equity markets, again with weeksending strong and opening down, and in for-eign exchange rates, which do not offset thelocal currency equity return patterns from theperspective of a U.S. investor.'*' A pattern re-markably similar to the day-of-the-week effecthas even been identified for orange juice fu-tures.'^'' We must thus be cautious in evaluatingpotential explanations that rely on institutionalfeatures peculiar to the U.S. stock market, suchas settlement procedures, specialist behavior ordividend patterns.

The day-of-the-week effect is related to otheranomalies. The weekly pattern is stronger forsmaller-capitalization stocks. In fact, 63 per centof the small-size effect occurs on Fridays."^"There are conflicting findings on the day-of-the-week effect in the month of January.'*^ Interac-tion of day-of-the-week with holiday and time-of-day regularities are discussed below.

RationalesMeasurement error has often been suggested

as a cause of the observed pattern, especiallybecause the effect appears stronger for smaller-capitalization stocks. But this possibility hasbeen rejected by many researchers.'^'^ For exam-ple, an upward bias in Friday closing prices canbe dismissed as an explanation because thecorrelation between Friday and Monday returnsis positive and the highest of any pair of days.Also, a Monday decline is even more likely thanusual after a Friday decline. Explanations in-volving specialists, such as the frequency ofclosing at bid versus ask prices, have also beenrejected by studies utilizing only over-the-counter bids and by others using markets withdifferent structural characteristics.' ''*

Attempts have been made to test variousvalue-based explanations for the day-of-the-week effect. The obvious hypotheses that re-turns accrue during trading time or during clocktime are easily rejected.''" One study found theday-of-the-week effect to be subsun:\ed by op-tions expiration, unexpected inflation and earn-ings surprise events.* ' But options, money sup-ply announcements and other explanatorymeasures utilized did not exist early in thiscentury. Moreover, the one year examined inthis study—1978—was perverse, in that Mon-days were on average up and Fridays down.

FINANCIAL ANALYSTS JOURNAL / NOVEMBER-DECEMBER 1988 D 32

Page 6: Calender Anomalies Abnormal Returns at Calender Turning Points

Others have proposed trade settlement rulesas a partial explanation for stock value fluctua-tions across days of the week.''" While thisrationale has theoretical appeal, the day-of-the-week effect predates the 1968 advent of currentsettlement procedures. The anomaly also existsin foreign countries where settlement proce-dures alone would predict different weekly re-turn patterns. Eurthermore, the effect has beenstronger during periods of lower interest rateswhen, according to this theory, it should havebeen weaker.^^ Einally, the large magnitude ofthe effect clearly swamps an interest-based, oreven a dividend-based, explanation.

Similar arguments apply to explanationsbased on inventory adjustments. Short-sellersmight, for peace of mind, cover positions priorto the weekend, and short again on Mondaymornings. Specialists might close trading onEridays at ask prices. Investors might be moreinclined to throw in the towel after a weekendof introspection."'''' One problem with such ratio-nales is that they seem insufficient to accountfor the ubiquitous nature of the anomaly. Day-of-the-week effects are evident over the entirecentury for which we have data, in spite ofchanging trading mechanics, short-sale regula-tions, methods of investment management andeven modes of communication. Eurthermore,the anomaly is present in foreign equity mar-kets, as well as other asset classes.

Risk considerations also seem inadequate asan explanation of the day-of-the-week effect. Itis difficult to conceive of any market risk factorthat could have varied so systematically overthe past century as to produce the observedreturn regularity. The standard deviation ofMonday returns is the highest of all days, butonly slightly above average. If risk determineddaily returns, Monday would be an above-average day.

Explanations rooted in human nature showpromise. For example, in experimental marketgames conducted by psychologists, an effectsimilar to the day-of-the-week has been ob-served around trading halts.'''^ The day-of-the-week effect has recently been related to thehuman tendency to announce good news quick-ly and defer bad news. The pattern of earningsand other announcements over the week mayactually drive the observed return effect."'*' Weindicated earlier that the entire market declineof the Great Depression occurred on averageover weekends. Not coincidentally, most bad

new s, such as bank closings, was released afterthe Saturday close to allow the market to "ab-sorb the shock" over the weekend. As a morerecent example, the 1987 string of insider trad-ing indictments were generally announced afterthe market close on Eriday."

The Holiday EffectThe unusually good performance of stocks priorto market holidays was first documented overthe 1901-32 period and has since become anarticle of faith among n:\any practitioners. Re-cent academic studies confirn^ the existence ofthe holiday effect.

Eigure C plots the average return for the dayprior to each of the eight market holidays for theperiod 1963 to 1982. ' The average pre-holidayreturn of 0.365 per cent dwarfs the averageregular-day return of 0.026 per cent. In fact, 35per cent of the entire market advance over thisperiod occurred on just the eight pre-holidaytrading days each year.

Another study examining both earlier andlater periods confirmed the existence of theholiday anomaly. ^ This stvidy also identified aholiday-related phenomenon occurring fromDecember 24 to 31 each year. Not only Christ-mas and New Year's Eve, but also the daysbetween the holidays exhibit exceptional re-turns. In fact, the average cumulative return forjust these eight calendar days is a remarkable1.6 per cent. This year-end rally was identifiedin the Dow and may reflect windowdressing inBlue Chip issues towards year-end. In any case,the dollar magnitude of this year-end, large-capitalization-stock rally is several times themagnitude of the more well-known lanuarysmall-size effect.

The holiday anomaly appears fairly stableover time. In the most recent decade, however,pre-holiday returns have not been exceptional.Nevertheless, the effect does not appear to be astatistical artifact. Eor instance, it is not drivenby outliers, as 75 per cent of pre-holiday daysare up, versus only 54 per cent of all trading

The settlement process, discussed as a poten-tial explanation for the day-of-the-week effect,has complex implications for fluctuations invalue around holidays.*'' For example, this the-ory predicts a high Thursday return preceding aEriday holiday, which is what occurs. But itpredicts a lower-than-average Friday return pre-ceding a Monday holiday, and this is not consis-

FINANCIAL ANALYSTS JOURNAL / NOVEMBER-DECEMBER 1988 • 3 3

Page 7: Calender Anomalies Abnormal Returns at Calender Turning Points

Figure C The Holiday Effect (average pre-holiday returns)

New Year's

President's Day

Good Friday

Memorial Day

Fourth of July

Labor Day

Thanksgiving

Christmas

Avg.

0 0.125 0.25 0.375 0.3 0.625 U.7Rt'turn (per cent)

Ddla trom K. Arji'l, "I li^h Stuck Returns Belori' Hdlid.iys" (Slu.in workinj; fi.i[H'r, MIT, 1W41

tent with empirical results. Moreover, the mag-nitude of any value changes occurring becauseof settlement procedures is much too small toaccount for the holiday effect.

Abnormal pre-holiday returns are not attrib-utable to increased risk. In fact, the standarddeviation of pre-holiday returns—0.609—is lessthan the non-holiday volatility of 0.783 percent.''-

Another perspective is afforded by holidaysnot associated with market closings, like St.Patrick's Day or Rosh Hashanah. Such days donot experience abnormal returns.^^ The absenceof anomalous returns may be due to the lack of atrading break or to a lower level of festivity thanthat associated with major market holidays.

In a class by itself—-almost considered theantithesis of a holiday by the superstitious—isFriday the 13th. Studies examining this dayhave had conflicting results. Over the 1940-84period, the Dow was up as frequently on Fridaythe 13th as on a regular Friday."^ For the 1962-85 period, however, the return for the CRSPindex was significantly negative on this day.***There are several ways of reconciling thesefindings. Possibly the market has become moresuperstitious in recent years. Perhaps the large-capitalization Dow stocks are less susceptible toirrationality than smaller stocks. Also, the up-versus-down-day measure utilized in the firststudy may be less appropriate than percentagereturns. If stocks suffer on Friday the 13th,market psychology would appear to be thelikely culprit.

Holiday effects interact with other anomalies.The holiday effect appears to be stronger forsmaller stocks.'^'' It also swamps the day-of-the-week effect. Monday returns preceding a Tues-day holiday are on average positive.''^ Aftercontrolling for the holiday effect, the best day ofthe week shifts from Friday to Wednesday.''**The high frequency of holidays falling on Satur-day, Sunday or Monday benefits the previousFriday's return.

One potential hypothesis is that pre-holidayreturns represent another manifestation of re-turn abnormalities around trading halts, such asweekends. There are important differences,however. While Mondays are on average down,the day after a holiday does not exhibit unusualreturns.''^ Also, the holiday effect is two to fivetimes the strength of the last-trading-day-of-the-week effect, which suggests that more thana simple trading halt is the cause.^"

Another possibility is that holiday euphorialeads to short-covering and general buyingpressure. But there is little evidence of a marketcorrection as holiday spirits subsequently sub-side. While no fully satisfactory explanation ofthe holiday effect has yet surfaced, psychologi-cal reasons appear to be the most promising.

The Time-of-Day EffectStock returns exhibit intraday, as well as inter-day, patterns. The advent of real-time pricingdatabases has only recently allowed academicscrutiny of these effects.

Figure D plots cumulative returns, at 15-

FINANCIAL ANALYSTS JOURNAL / NOVEMBER-DECEMBEK 19S8 D 3 4

Page 8: Calender Anomalies Abnormal Returns at Calender Turning Points

Figure D The Time-of-Day-Effect

0.3

0.2 -

0.1

0.0

- 0 . 1 -

-0 .2

Thursday Wednesday

10:00 11:00 12:00 1:00Time of Day

2:00 3:00 4:00

Data from L. Harris, "A Transaction Data Study of Weekly and Intrad.nly I'.ilHTns in Sunk Rflunis," liiiiniii! nfpp. 99-117.

S Ifi,

minute intervals throughout each trading day ofthe week, for a recent 14-month period on theNYSE. ' Tuesday through Friday exhibit similarpatterns: Prices rise for approximately the first45 minutes, the bulk of the trading day is flat,and another rally takes place in the last 15minutes of the day. The strong opening isroughly attributable to the first three trades ofthe day in each stock, while the strong close isdue primarily to the last trade. On Monday, incontrast, prices during the first 45 minutes oftrading are down sharply, while the rest of theday resembles the other days of the week.

The time-of-day anomaly has been fairly sta-ble in recent decades, except that the "weekendeffect" component has been moving up in time.Prior to 1968, the weekend effect took place allthrough the trading day on Monday, with everyhour's return being negative. Since 1974, theeffect has shifted forward in time to the week-end, with only the first two hours of Monday'strading being down in price.^~ This day-of-week/time-of-day interaction is also related tothe size effect. Most of the weekend declineoccurs prior to Monday's open for large-capital-

ization stocks, but continues into Mondaymorning for smaller stocks. "* Also, the closingprice anomaly has been found to be robustacross days of the week but stronger at the turnof the month.'''*

One study analyzed the close-of-day anomalyin great detail." It found the average return ofthe last trade to equal 0.05 per cent, or 0.6 centsper share. The return was higher, however, thecloser the final trade to the close of business.Final trades occurring after 3:55 p.m. averaged a0.12 per cent return, or 1.75 cents per share.

The closing-price anomaly is unrelated towhether a stock has listed options or is tradedon a regional exchange beyond the NYSE clos-ing time. Results are not due to data errors,because there is little evidence of return rever-sals at the following open. The effect is robustover time and not attributable to outliers.

Do fundamental values rise at the open andclose, causing the observed return pattern? Un-anticipated good news towards the close mightnot be fully reflected in prices until the nextmorning, particularly if specialists dampen therise in order to maintain orderly markets.'*' Of

FINANCIAL ANALYSTS JOURNAL / NOVEMBER-DECEMBER 1988 D 35

Page 9: Calender Anomalies Abnormal Returns at Calender Turning Points

course, this would not explain Monday morn-ing negative returns. And what might accountfor a rush of good news just before the close?While stocks that trade right at the close experi-ence the largest day-end effect, those that donot trade near the close do not catch up bymorning. This seems to rule out the possibilitythat marketwide good news accounts for theday-end return anomaly.

There is a relation between risk and intradayreturns. The unusually high opening and clos-ing returns are more variable than returns dur-ing the rest of the day.''^ Theories have beenproposed that may account for the observedpattern in riskiness.''^ If investors are averse tovolatility, they would require higher expectedreturns at the open and close. But the riskincrease is insufficient to explain the magnitudeof the observed return effect. Furthermore,Monday morning negative returns run counterto this hypothesis.

The open differs from the balance of the dayin some important respects. Opening prices aredetermined by a market call, unlike the continu-ous market-making process the rest of the day.Also, orders at the open are heavily influencedby foreign investors. While opening returnsexhibit greater dispersion, are less normallydistributed and more negatively autocorrelatedthan other returns, it remains unclear why anyof these differences would result in the morningreturn anomaly. ^

Closing prices are also special. They are uti-lized for valuing portfolios, for performanceevaluation, as strike prices for program trades,and for settling options and futures contracts atexpiration. They are the prices reported in thepress and stored in databases. For all thesereasons, closing prices might be likely candi-dates for manipulation, possibly causing theday-end return anomaly. However, volume forday-end trades is not abnormally small, aswould be the case if someone were painting the

Those who must purchase a stock on a givenday might conceivably rush to beat the closingbell, thus placing upward pressure on prices.But the converse should hold for sellers. As theday-end price effect is stronger at the turn of themonth, windowdressing might play a role.Also, about half the effect is attributable tochanges in the frequency of trades at bid versusask prices near the dose, but the cause of thisdistributional shift remains unknown.*^'

As with the holiday and day-of-the-week ef-fects, the day-end return anomaly may relate tothe impending trading halt. As psychologicalexperiments have demonstrated, there may be abehavioral predisposition to bid up prices priorto the close.

ConclusionThe existence of abnormal returns at calendarturning points is indisputable. Moreover, theseeffects are not implausible. A return regularityoccurring at an arbitrary time on an arbitraryday might justifiably be regarded with suspi-cion. But calendar anomalies occur at cusps intime. These turning points have little economicsignificance, but they apparently evoke specialinvestor behavior. Psychology appears to offerthe most promising explanations for this behav-ior.

While cross-sectional return effects should beof interest to portfolio managers, calendar ef-fects may be of greater interest to traders. Bothclasses of anomalies have important implica-tions for market efficiency. •

Footnotes1. For example, see A. Merrill, Behaz'ior of Prices on

Wall Street (Chappaqua, NY: Analysis Press,1966); Y. Hirsch, The Stock Trader's Almanac (OldTappan, NJ: The Hirsch Organization, publishedannually since 1968); and N. Fosback, Stock Mar-ket Logic {Fort Lauderdale, FL: Institute for Econo-metric Research, 1976).

2. M. Fields, "Stock Prices: A Problem in Verifica-tion," Journal of Business, 1931; M. Fields, "Securi-ty Prices and Stock Exchange Holidays in Rela-tion to Short Selling," Journal of Business, 1934,pp. 328-338; and S. Wachtel, "Certain Observa-tions on Seasonal Movements in Stock Prices,"Journal of Business 15, 1942, pp. 184-193.

3. For an elaboration on these points, see J. Lakoni-shok and S. Smidt, "Are Seasonal AnomaliesReal? A Ninety-Year Perspective" (Johnsonworking paper #87-07, Cornell U., May 1987).

4. See B. Jacobs and K. Levy, "Disentangling EquityReturn Regularities: New Insights and Invest-ment Opportunities," Financial Analysts Journal,May/June 1988.

5. See B. Jacobs and K. Levy, "On the Value of'Value'," Financial Analysts Journal, July/August1988.

6. Ibid.7. For portfolio management implications of cross-

sectional return effects, see B. Jacobs and K.Levy, "Disentangling Equity Return Regulari-ties," in Equity Markets and Valuation Methods

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(Charlottesville, VA: The Institute of CharteredFinancial Analysts Continuing Education Series,forthcoming 1988). For trading implications ofcalendar anomalies, see B. Jacobs and K. Levy,"Trading Tactics in an Inefficient Market," in W.Wagner, ed., A Complete Guide to Securities Trans-actions: Controlling Costs and Enhancing Performance(New York: John Wiley, forthcoming 1989).

8. M. Rozeff and W. Kinney, "Capital Market Sea-sonality: The Case of Stock Returns," Journal ofFinancial Economics 3, 1976, pp. 379-402.

9. M. Gultekin and B. Cultekin, "Stock MarketSeasonality: International Evidence," Journal ofFinancial Economics, December 1983, pp. 469-481.

10. Consider the absence of a January seasonal in theDow Jones Industrial Average, noted by Lakoni-shok and Smidt, "Are Seasonal Anomalies Real?"op. cit.

11. See D. Keim, "Size Related Anomalies and StockMarket Seasonality: Further Empirical Evidence,"Journal of Financial Economics, June 1983, pp. 12-32; D. Keim, "Dividend Yields and Stock Re-turns: Implications of Abnormal January Re-turns," Journal of Financial Economics 14, 1985, pp.473-489; and A. Arbel, "Ceneric Stocks: An OldProduct in a New Package," Journal of PortfolioManagement, Summer 1985, pp. 4-13.

12. See Keim, "Size Related Anomalies," op.cit., andR. Roll, "Vas 1st Das? The Turn-of-the Year Effectand the Return Premia of Small Finns," Journal ofPortfolio Management, Winter 1983, pp. 18-28.

13. J. Lakonishok and S. Smidt, "Trading Bargains inSmall Firms at Year-End," journal of PortfolioManagement, Spring 1986, pp. 24-29. Resultscited are for largest and smallest deciles of listedstocks. While large in percentage terms, howev-er, the January effect is less substantial in dollarterms because of the illiquidity of small stocks.

14. See Jacobs and Levy, "Disentangling Equity Re-turn Regularities," op.cit., for a complete discus-sion of January interrelationships.

15. See D. Givoly and A. Ovadia, "Year-End Tax-Induced Sales and Stock Market Seasonality,"Journal of Finance, March 1983, pp. 171-185.

16. M. Gultekin and B. Guitekin, "Stock MarketSeasonality," op.cit., find higher returns coinci-dent with the turn of the tax year in 13 countries,with the exception of Australia. E. Chang and M.Pinegar, "Return Seasonality and Tax-Loss Sell-ing in the Market for Long-Term Governmentand Corporate Bonds," fournal of Fiiumcial Eco-nomics 17, 1986, pp. 391-415.

17. There is no documentation of downward pricepressure on losers at year-end comparable inmagnitude to their subsequent January bounce-back. While J. Lakonishok and S. Smidt, "Vol-ume in Winners and Losers: Taxation and OtherMotives for Stock Trading," Journal of Finance,September 1986, pp. 951-974, show evidence of

tax-motivated trading in December and January,they find other trading motives more important.

18. J. Ritter, "The Buying and Selling Behavior ofIndividual Investors at the Turn of the Year"(Working paper, U. Michigan, July 1987).

19. See G. Constantinides, "Optimal Stock Tradingwith Personal Taxes: Implications for Prices andthe Abnormal January Returns," Journal of Finan-cial Economics, March 1984, pp. 65-89.

20. See K. C. Chan, "Can Tax-Loss Selling Explainthe January Seasonal in Stock Returns?" Journal ofFinance, December 1986, pp. 1115-1128, andJacobs and Levy, "Disentangling Equity ReturnRegularities," op.cit.

21. C. Jones, D. Pearce and J. Wilson, "Can Tax-LossSelling Explain the January Effect: A Note," Jour-nal of Finance, June 1987, pp. 453-461, find nodifference in the January effect pre and post-income tax. For foreign evidence, see P. Brown,D. Keim, A. Kleidon and T. Marsh, "Stock Re-turn Seasonalities and the Tax-Loss Selling Hy-pothesis: Analysis of the Arguments and Austra-lian Evidence,"/o»rnfl/t)/F(>[a/((.7(i/ Economics, June1983, pp. 33-56, and S. Tinic, G. Barone-Adesiand R. West, "Seasonaiity in Canadian StockPrices: A Test of the 'Tax-Loss-Selling Hypothe-sis'," Journal of Financial and Quantitative Analysis,March 1987, pp. 51-63.

22. While Jacobs and Levy, "Disentangling EquityReturn Regularities," op.cit.. found a January tax-loss rebound effect in each year of their sample,the weakest effects occurred in 1981 and 1986,after substantial stock market advances. Howev-er, if there are fewer individual stocks offeringlosses, there may be more tax-loss selling pres-sure on each one.

23. J. Bildersee and N. Kahn, "A Preliminary Test ofthe Presence of Window Dressing," Journal ofAccounting, Auditing & Finance, Summer 1987.

24. See R. Rogalski and S. Tinic, "The January SizeEffect: Anomaly or Risk Mismeasurement?" Fi-nancial Analysts Joumal, November/December1986, pp. 63-70.

25. See S. Tinic and R. West, "Risk and Return:January vs. the Rest of the Year," Journal ofFinancial Economics, December 1984, pp. 561-574,for CAPM; M. Gultekin and B. Guitekin, "StockReturn Anomalies and the Tests of the APT,"Journal of Finance, December 1987, pp. 1213-1223for APT; and E. Chang and M. Pinegar, "AFundamental Study of the Seasonal Risk-ReturnRelationship: A Note," Journal of Finance, Septem-ber 1988, pp. 1035-1039, for more general find-ings.

26. A. Corhay, G. Hawawini and P. Michel, "Sea-sonality in the Risk-Return Relationship: SomeInternational Evidence," Journal of Finance, March1987, pp. 49-68.

27. Arbel, "Generic Stocks," op.cit.

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28. V. Chari, R. Jagannathan and A. Ofer, "FiscalYear End and the January Effect" (Kellogg work-ing paper #20, Northwestern U., January 1986).

29. K. Kato and ]. Schaliheim, "Seasonal and SizeAnomalies in the Japanese Stock Market," Journalof Financial and Quantitative Analysis, June 1985,pp. 243-260.

30. On Prospect Theory and January, see H. Shefrinand M. Statman, "The Disposition to Sell Win-ners Too Early and Ride Losers Too Long: Theoryand Evidence," Journal of Finance, July 1985, pp.777-792, and S. Ferris, R. Haugen and A. Mak-hija, "Predicting Contemporary Volume withHistoric Volume at Differential Price Levels,"Journal of Finance, July 1988, pp. 677-699. OnProcedural Rationality and January, see E. Miller,"Explaining the January Small Firm Effect"(Working paper, U. New Orleans, November1986).

31. R. Ariel, "A Monthly Effect in Stock Returns,"Journal of Financial Economics 18, 1987, pp. 161-174; S. Penman, "The Distribution of EarningsNews Over Time and Seasonalities in AggregateStock Returns," Journal of Financial Economics 18,1987, pp. 199-228; and Lakonishok and Smidt,"Are Seasonal Anomalies Real?" op.cit.

32. Data from Lakonishok and Smidt, "Are SeasonalAnomalies Real?" op.cit.

33. For example, see Ariel, "A Monthly Effect inStock Returns," op.cit. However, Ariel reportsthat when small-capitalization stocks performpoorly, it is generally in the last half of themonth.

34. J. Ogden, "The End of [he Month as a PreferredHabitat: A Test of Operational Efficiency in theMoney Market," Journal of Financial and Quantita-tive Analysis, September 1987, pp. 329-343.

35. M. McNichols, "A Comparison of the Skewnessof Stock Return Distributions in Earnings An-nouncement and Non-announcement Periods"(Working paper #953, Stanford U., June 1987.)

36. See Penman, "The Distribution of Earnings NewsOver Time," op.cit.

37. Ariel, "A Monthly Effect in Stock Returns,"op.cit.

38. Y. Hirsch, Don't Sell Stocks on Monday (New York:Facts on File, 1986).

39. Data from D. Keim and R. Stambaugh, "A Fur-ther Investigation of the Weekend Effect In SlockReturns," Journal of Finance, July 1984, pp. 819-837.

40. See L. Harris, "How to Profit From IntradailyStock Returns," journal of Portfolio Management,Winter 1986, pp. 61-64.

41. Lakonishok and Smidt, "Are Seasonal AnomaliesReal?" op.cit.

42. For options, see D. Peterson, "A TransactionData Study of Day-of-the-Week and IntradayPatterns in Option Returns" (Working paper.

Florida State U., September 1988). For futures, B.Cornell, "The Weekly Pattern in Stock Returns:Cash Versus Futures: A Note," fournn! of Finance,June 1985, pp. 583-588, found no anomaly; how-ever, E. Dyl and E. Maberly, "The Weekly Pat-tern in Stock Index Futures: A Further Note,"Journal of Finance, December 1986, pp. 1149-1152,located an error in Cornell's data set; F. Phillips-Patrick and T, Schneeweis, "Indexes and StockIndex Futures: Dividend and Interest Rate Ef-fects," Journal of Futures Markets, February 1988,pp. 115-120, provide additional evidence.

43. M. Flannery and A. Protopapadakis, "From T-Bills to Common Stocks: Investigating the Gener-ality of lntra-Week Return Seasonality," fournat ofFinance, June 1988, pp. 431-450.

44. J. Jaffe and R. Westerfield, "The Week-end Effectin Common Stock Returns: The InternationalEvidence," Journal of Finance, June 1985, pp. 433-454, find patterns in the U.K., Canada, Japan andAustralia similar to those in the U.S. However, inJapan and Australia, both Monday and Tuesdayare down, not only because of time-zone differ-ences with the U.S. Mixed evidence from otherEuropean countries is reported in G. Hawawini,ed., "European Equity Markets: Price Behaviorand Efficiency" (Salomon Brothers Center/N.Y.U. Monograph #4/5, 1984). On exchangerates, see Jaffe and Westerfield, "The Week-endEffect in Common Stock Returns," op.cit.

45. R. Roll, "Orange Juice and Weather" (UCLAworking paper #10-83, November 1983).

46. D. Keim, "Daily Returns and Size-Related Premi-ums: One More Time," journal of Portfolio Man-agement, Winter 1987, pp. 41-47. However E.Miller, "Why a Weekend Effect?" Journal of Portfo-lio Management, Summer 1988, argues thatintraweek patterns in returns to size are unrelat-ed to the long-run size effect.

47. R. Rogalski, "New Findings Regarding Day-of-the-Week Returns over Trading and Non-TradingPeriods: A Note," journal of Finance, December1984, pp. 1603-1614, demonstrates that the Janu-ary effect dominates the day-of-the-week effect(that is, Mondays are up on average in January)because of the good performance of small-capital-ization stocks, especially during the first fivetrading days in January. M. Smirlock and L.Starks, "Day of the Week and Ihtraday Effects inStock Returns," Journal of Financial Economics 17,1986, pp. 197-210, concur. However, Keim, "Dai-ly Returns and Size-Related Premiums," op.cit.,reports that ihe day-of-the-week effect is notdifferent in January after controlling for the high-er overall market return in that month. AlthoughMondays may be up in January, they lag otherdays, especially Fridays.

48. See F. Cross, "The Behavior of Stock Prices onFridays and Mondays," Financial Anah/sts journal.

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November/December 1973, pp. 67-69; M. Gib-bons and P. Hess, "Day of the Week Effect andAsset Returns," fournal of Business. October 1981,pp. 579-596; Keim and Stambaugh, "A FurtherInvestigation of the Weekend Effect in StockReturns," op.cit.; Jaffe and Westerfield, "TheWeek-end Effect in Common Stock Returns,"op.cit.; L. Harris, "A Transaction Data Study ofWeekly and Intradaily Patterns in Stock Re-turns," fournal of Financial Economics 16, 1986, pp.99-117; and Sn:iirlock and Starks, "Day of theWeek and Intraday Effects," op.cit.

49. Keim and Stambaugh, "A Further Investigationof the Weekend Effect in Stock Returns," op.cit.

50. See K. French, "Stock Returns and the WeekendEffect," fournal of Financial Economics, March 1980,pp. 55-69. The trading-time hypothesis positsthat returns are equal each trading day. Clock-time posits that Monday returns should be threetimes as high as other trading days, because ofthe weekend.

51. D. Whitford and F. Reilly, "What Makes StockPrices Move?" journal of' Portfolio Management.Winter 1985, pp. 23-30.

52. See J. Lakonishik and M. Levi, "Weekend Effectson Stock Returns: A Note," fournal of Finance.June 1982, pp. 883-889; E. Dyl and S. Martin,"Weekend Effects on Stock Returns: A Com-ment," Journal of Finance, March 1985, pp. 347-349; and J. Lakonishik and M. Levi, "WeekendEffects on Stock Returns: A Reply," Journal ofFinance, March 1985, pp. 351-352.

53. Keim and Stambaugh, "A Further Investigationof the Weekend Effect in Stock Returns," op.cit.

54. Miller ("Why a Weekend Effect?" op. cit.) sug-gests that individual investors buy stocks uni-formly over weekdays, at their brokers' urging,but often make sell decisions over weekends.

55. D. Coursey and E. Dyl, "Price Effects of TradingInterruptions in an Experimental Market" (Work-ing paper, U. Wyoming, 1986).

56. Penman, "The Distribution of Earnings NewsOver Time," op.cit.

57. "Federal prosecutors have made several of theirmost important moves in the [insider trading]scandal late on Friday afternoons, when themarket is finished with business and investorscan mull the situation over during the weekend,"noted J. Crudele, "Dow Off 8,68," New YorkTimes, March 14, 1987.

58. Data from R. Ariel, "High Stock Returns BeforeHolidays" (Sloan working paper, MIT, 1984).Returns are for the capitalization-weighted CRSPindex.

59. Lakonishok and Smidt, "Are Seasonal AnomaliesReal?" op.cit.

60. Ariel, "High Stock Returns Before Holidays,"

op.cit.61. See Lakonishik and Levi, "Weekend Effects on

Stock Returns," op.cit.62. Ariel, "High Stock Returns Before Holidays,"

op.cit.63. While Hirsch, Don't Sell Stocks on Monday, op.cit.,

reports that St. Patrick's Day is up more frequent-ly than a normal day (p. 121), the percentagereturn is not abnormal (p. 122).

64. Hirsch, Don't Sell Stocks on Monday, op.cit.. p. 38.65. R. Kolb and R. Rodriguez, "Friday the Thir-

teenth: 'Part VII'^A Note," journal of Finance,December 1987, pp. 1385-1387.

66. Rogalski, "New Findings Regarding Day-of-the-Week Returns," op.cit.

67. Lakonishok and Smidt, "Are Seasonal AnomaliesReal?" op.cit.

68. Ariel, "High Stock Retums Before Holidays,"op.cit.

69. French, "Stock Returns and the Weekend Effect,"op.cit.

70. Lakonishok and Smidt, "Are Seasonal AnomaliesReal?" op.cit.

71. Data from Harris, "A Transaction Data Study ofWeekly and Intradaily Patterns in Stock Re-turns," op.cit.

71. Smirlock and Starks, "Day of the Week andIntraday Effects in Stock Returns," op.cit.. Thisnon-stationarity resolves previously conflictingevidence on the exact timing of the weekenddrop.

73. L. Harris, "A Transaction Data Study of Weeklyand Intradaiiy Patterns in Stock Returns," op.cit.

74. L. Harris, "A Day-End Transaction Price Anoma-ly" (u se working paper, October 1986).

75. ibid.76. Ibid.77. R. Wood, T. Mclnish and K. Ord, "An Investiga-

tion of Transactions Data for NYSE Stocks,"lournal of Finance. July 1985, pp. 723-739. Astrong contemporaneous relation between intra-day returns and trading volume is documented inG. Joh, "The Dependence Between Hourly Pricesand Trading Volume," Journal of Financial andQuantitative Analysis, September 1988.

78. For example, A Admati and P. Ptleiderer, "ATheory of Intraday Trading Patterns" (StanfordU. working paper #927R, August 1987) develop atheory incorporating informational and liquiditytrading that is consistent with the observed pat-tern of volatility.

79. Y. Amihud and H. Mendelson, "Trading Mecha-nisms and Stock Returns: An Empirical Investiga-tion," lournal of Finance, July 1987, pp. 533-555.

80. Harris, "A Day-End Transaction Price Anomaly,"op.cit.

81. Ibid.

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