Jout-naJ of Financial Economics 18 (1987) 161-174. North-Holland

A MONTHLY EFFECT IN STOCK RETURNS

Robert A. ARIEL*

Banrch College, CUNY. New York. NY 10010, USA

Received December 1984, final version received March 1986

The mean return for stocks is positive only for days immediately before and during the first half of calendar months, and indistinguishable from zero for days during the last half of the month. This ‘monthly effect’ is independent of other known calendar anomalies such as the January effect documented by others and appears to be caused by a shift in the mean of the distribution of returns from days in the first half of the month relative to days in the last half.

1. Introduction

This paper documents a curious anomaly in the monthly pattern of stock index returns: stocks appear to earn positive average returns only around the beginning and during the first half of calendar months, and zero average returns during the second half. During the nineteen year span studied, all of the market’s cumulative advance occurred around the first half of the month, the second half contributed virtually nothing to the cumulative gain. The impact of this effect on stock returns is not subtle; its impact is of the same order of magnitude as the well-known weekend effect documented by French (1980) and Gibbons and Hess (1981).

Several other studies report anomalous calendar dependencies in stock returns. First, as noted above, a weekend effect has been identified in stock returns, the most salient characteristic of which is low or negative returns on Mondays, and some evidence suggests that the negative Monday returns could be more a manifestation of a ‘calendar effect’ rather than a pure ‘closed market effect’. For example, French (1980) finds that returns on days following mid-week holidays are not unusually low. Smirlock and Starks (1986) find that aside from positive first-hour returns, hourly returns on Mondays are negative and lower than their counterparts on other trading days. Further, Rogalski

*I would I&e to thank Terry Marsh, who read and commented on several versions of the present paper, thereby contributing markedly to its clarity, and Franc0 Modigliani. Richard Ruback and the other members of the MIT Finance Department where this research was conducted. I would also Iike to thank Richard ROB, Ieuan Morgan, and Ray Ball for commenting on earlier versions of this paper, and Michael Rozeff and Kenneth French (the referees) whose close reading results in substantial improvements and G. William Schwert (the editor).

0304-405X/87/$3.500 1987. Elsevier Science Publishers B.V. (North-Holland)

162 R.A. Ariel, A monrh(r; eflecf rn stock returns

(1984) does find that, over a different time period, most of the negative return from the closing price on Friday, to the closing price on Monday, occurs while the market is closed over the weekend. Since the market is always closed on weekends, it is impossible to tell whether the negative return is due to the weekend or the fact that the market is closed.

Second, a January effect in stock returns has previously been noted. Rozeff and Kinney (1976) demonstrate that unusually high returns accrue to stocks during January, and Keim (1983), Roll (1983), and Reinganum (1983) note that these high January returns accrue disproportionately to small firms and especially during the early days of January. Tax-loss selling pressure has been advanced as the cause of the January effect, but the persistence of this phenomenon in some overseas markets with non-January tax year starting dates [Brown, Keim, Kleidon and Marsh (1983), Gultekin and Gultekin (1983)) suggests that the January effect may be in part an effect induced by the turn of the year - a ‘calendar effect’. Third, a number of stock market advisors have claimed that a monthly pattern exists. These advisors, whose numbers include Merrill (1966) Hirsch (1979), and Fosback (1976), urge their clients to make use of the monthly pattern as a part of their trading strategies, for example by making planned purchases before the start and postponing planned sales until after the middle of the calendar month in order to capture the unusually high returns that accrue in the early days of calendar months.

In section 2, several tests are reported, which show the existence of a monthly pattern in the returns accruing to stocks. In section 3, the results are discussed, and possible biases that might induce the observed effect are considered.

2. The monthly pattern in returns

The tests to be reported employ the Center for Research in Security Prices (CRSP) value-weighted and equally-weighted stock index returns to represent the returns accuring to ‘stocks’. The data span the years 1963 through 1981.

Fig. 1 shows histograms of the arithmetic mean returns for the nine trading days before and after the start of each month for both the CRSP equally- weighted and value-weighted indices; each daily mean is estimated from 228 daily observations [i.e., nineteen years times twelve months].

The resulting histograms show positive returns at the beginning of the month, starting on the last trading day of the previous month and continuing through the first half of the new month, followed by predominantly negative returns after the mid-point of the month.

It is convenient henceforth to define a ‘trading month’ as extending from the last trading day (inclusive) of each calendar month to the last trading day (exclusive) of the following calendar month [i.e., the last trading day of each calendar month is included with the following month].

R.A A reel. A month!v efect m sock returns 163

Old month

I I I I I I I I I I z;wmiY I I I I I I -9 -8 -7 -6 -5 4 -3 -2 -I 0 I 2 3 1 5 6 7 X 9

Old month Ycu month

I I I I I I I I I I I I I I I I I I I -9 -8 -7 -6 -5 -I -3 -2 -I 0 I 2 3 1 5 6 7 8 9

-. IO

Tradmg Days Rclauve to the Begmmng oi the Month

Fig. 1. Histograms of the daily arithmetic mean returns for the nine trading days before and after the start of each calendar month from l/1/1963 through 12/l/1981 for both the CRSP equally-weighted (top panel) and value-weighted (bottom panel) indexes. Nine rather than ten or more days were selected for presentation to prevent overlap between day + 10 and day - 10 of the following month in the minority of months having fewer than twenty trading days. The global

mean is estimated from the returns to all trading days in this nineteen-year period.

164 R.A. Arid, .1 monrh(v effecr rn stock returns

If each trading month is divided evenly in half [with the odd middle trading day, if any, discarded] the mean daily return from the first half of trading months significantly exceeds the mean daily return from the last half of trading months: The r-statistics for the difference of the mean daily returns from the two populations are 6.07 and 4.34 for the equally- and value-weighted indexes, respectively; moreover, the last-half daily means are indistinguishable from zero. [Descriptive statistics on the sub-populations are given in fig. 2.1’ However, no individual seeking to capitalize on the monthly pattern in stock returns would hold stocks for only a single day. Since the high-return and low-return days cluster in the first and last halves of trading months, respec- tively, cumulative returns over these half months constitute an economically j. more relevant measure of the monthly effect. Table 1 (panel I) reports a standard difference-of-the-means test comparing the mean cumufutioe return over the first nine days of trading months with the mean cumulative return over the last nine days of trading months, both for the entire 1963 to 1981 period and for four subperiods.?

For the entire 1963-1981 period, for both indexes, the r-statistic is statisti- cally significant, thereby showing that the mean cumulative return from the first half of trading months significantly exceeds the mean cumulative return from the second half of trading months. In each of the four subperiods for both indexes the point estimate of the mean return from the first half of trading months exceeds the point estimate of the mean return from the last half of trading months, and the r-statistic for the difference of the mean is significant at the 0.05 level in six of the eight comparisons. Interestingly an F-test applied to the ratio of the estimated variances of first nine-day and last nine-day cumulative returns cannot reject the hypothesis of equal variances at the 0.05 level.

‘As a check on the possible bias in the r-statistics induced by autocorrelation in the daily index returns, these returns were regressed against a first half of trading month dummy variable using the Hildreth-Lu autocorrelation correction procedure. This model in essence performs a dif- ference of the means test corrected for autocorrelation. For both indexes the resulting F- and t-statistics on the dummy are significant at the O.OWl level, thereby showing that autocorrelation in the index returns has not induced the significance of the above reported difference-of-the-means t-statistics.

‘In this and in all subsequent tests, the first and last ‘halves’ of trading months were defined (I priori with the intention of using as much of the data as possible in each test. The average month has slightly less than 21 trading days. The difference of the means test employs the first nine trading days to proxy for the ‘first halF and the last nine trading days to proxy for the ‘last half since the test requires a fixed and equal number of days in the first and last halves. Nine rather than ten or more trading days are employed to avoid overlap of the intervals in the significant minority of 32 months [14% of the sample] with fewer than 20 trading days. The x:-test below compares the return from the first half of a trading month with the return from the last half of that same month. In this test, each trading month was divided evenly in half, with the odd day. if any, in the middIe discarded. None of the results to be reported depend crucially on the exact conventions chosen. Also, by convention in this and in all the following tests, the 1963-1981 time period extends from the last trading day of 1962 (inclusive) through the last trading day of 1981 (exclusive), and likewise for all the subperiods examined.

The difference-of-means test applied in table 1 (panel I) presupposes a normal distribution of the cumulative haif month stock retums.3 To check the sensitivity of the conclusion to this assumption the following x2-test can be performed: Divide each trading month so that equal numbers of trading days appear in each half, discarding the odd day, if any, in the middle of the month. Define the cumulative return over each half-month as the product of one plus the daily returns over that period. If the returns for all days of the trading month are drawn from a single distribution, then the probability that the cumulative return from the first half of a trading month will exceed the cumulative return from the second half of that same trading month should be one-half. The x2-test statistics comparing this expectation with the observed results, both for the full nineteen years of data and for the four subperiods previously examined, are reported in table 1 (panel II). For both indexes, for the full 228 months of data, the null hypothesis is rejected for all confidence levels. Moreover, in each of the four subperiods, the monthly effect is present in the expected direction in both indexes; in six of the eight comparisons the test is significant at the 0.05 level.

These differences in average stock returns from days in the first and last halves of trading months are not due to outliers as can be seen from the frequency histogram of those returns in fig. 2. Identical numbers of trading days appear in each of the two populations so the distributions are directly comparable. The extreme tails of the two distributions appear similar. The differing means are due to a slight shift in the overall distributions of the two populations.

The nineteen-year cumulative impact of the differing daily mean returns is profound. The cumulative returns earned over these nineteen years from investing in stocks during only the first half of all trading months [and the comparable cumulative return from the last half of all months] are tabulated below: 4

Nineteen-year cumulative returns

First half of trading month Last half of trading month Nineteen years

Equally-weighted Value-weighted index index

2552.40% 565.40% - 0.25% - 33.80%

2545.90% 339.90%

‘Daily index returns are commonly treated as being normally distributed. The sum of normally distributed variables is itself normal, but the product is not, and hence strictly speaking the cumulative product over nine daily returns cannot be normally distributed, as the test statistics here implicitly assume. As a check on the possibility that this assumption may be biasing the reported results, all tests employing multi-day cumulative returns were repeated using continu- ously compounded returns, with virtually identical results. The multi-day compounded returns are directly examined in these tests since these illustrate the economic returns that could be earned by trading on the basis of the monthly effect.

4The half-month cumulative returns were calculated by dividing each trading month evenly in half, with the odd trading day in the middle of the month, if any, included in the last half cumulative return, resulting in about 5% more days in the last half cumulative return.

J.F.E. G

166 R.A. Ariel. A month!v effecf in stock returw

Table 1

(I) The mean cumulative return from the first nine trading days of each trading montha in the sample, the mean cumulative return from the last nine trading days of each trading month in the sample, and t-statistic for the difference of these two means for the full period and four

suhperiods. (II) Tabulation of the number of times the first half of the trading montha has a higher return than the last half of that same trading month for the full period and four subperiods. and a X*-statistic for the difference between realized and expected frequency of superior first half of trading month

returns.

1963-1981 1963-1966 1967-1971 1972-1976 1977-1981 (228 months) (48 months) (60 months) (60 months) (60 months)

Mean of first nine-day returns (standard deviation)

Mean of last nine-day returns (standard deviation)

t-statistic (implied JJ)~

Mean of first nine-day returns (standard deviation)

Mean of last nine-day returns (standard deviation)

t-statistic (implied p)”

(I) Equally-weighted index

1.411% 1.295% 1.445% (3.71%) (2.45%) (3.36%)

- 0.021% - 0.0125% - 0.002% (3.51%) (2.25%) (4.10%)

4.23 2.70 2.10 (0.00003) (0.007) (0.034)

(I) Value-weighted index

0.826% 0.969% 0.866% (2.70%) (1.17%) (2.40%)

- 0.182% - 0.290% -0.177% (2.65%) (1.86%) (2.95%)

4.01 3.41 2.11

(O.oooo7) w@w (0.035)

1.256% 1.627% (5.16%) (3.07%)

- 0.148% 0.079% (3.94rn) (3.23%)

1.66 2.70 (0.095) (0.007)

0.546% 0.950% (3.30%) (2.95%)

- 0.094% -0.188% (3.07%) (2.39%)

1.09 2.30 (0.28) (0.021)

Frequency of higher first-half returns

XL tc (implied p)

(II) Equal!v-weighted index

155 36 38

29.48 12.00 4.27 ( < 0.00001) (0.0005) (0.04)

38 43

4.27 11.27

(0.04) (O.OOG8)

Frequency of higher first-half returns

X:-t’ (implied p)

(II) Value-weighted index

150 38 38

22.74 16.33 4.27 ( < 0.00001) (O.OOOW (0.04)

37 37

3.27 3.27 (0.07) (0.07)

“A trading month is defined to extend from the last trading day of a calendar month (inclusive) to the last trading day of the following calendar month (exclusive).

bThe implied probability figure assumes a normal distribution for the nine-day holding period returns.

‘X2 with 2 - 1 degrees of freedom calculated as Z(observed - expected)*/expected, where the expected frequency of higher first half-month returns is equal to half the number of months in the test period. This expectation assumes independence of returns between the two halves of the month. The observed autocorrelation between half-months of about 0.2 may bias the X*-statistic.

300 -

of uadmg monrhs

2.0 All orhcr

r

All other -2.0 -1.0 0.0 1.0 2.0 All other

Daily Percent Return

(in 0.2 percent increments)

obwrvalions

Fig. 2. Histograms of daily return frequencies for the CRSP equally-weighted and value-weighted indexes. Intervals are 0.2% wide and each point represents the indicated number of daily observations with returns falling in that interval. The subpopulations were derived by dividing each trading month [defined to extend from the last trading day (inclusive) of each calendar month to the last trading day (exclusive) of the following calendar month] so that equal numbers of trading days fall in each half; in any month with an odd number of trading days, the odd day in the middle of the month was discarded, yielding 2325 observations in each subpopulation. Top panel: Equally-weighted index - First-half daily mean 0.174% (s.d., 0.787%). last-half daily mean 0.004% (s.d., 0.782%). Bosom panel: Value-weighted index - Fist-half daily mean 0.085% (s.d.,

0.770%). last-half daily mean -0.013% (s.d., 0.756%).

of lradmg months

168 R.A. Ariel, A month!v effect in stock returns

During these nineteen years, all of the market’s cumulative advance occurred during the first half of trading months, with the last half of trading months contributing nothing.

3. Discussion of results

The tests reported in section 2 show that significantly different returns accrue to stocks during the first and last halves of trading months. This section considers a variety of possible causes for these differing mean returns.

One puss ut history? Only one sequence of realized returns is available for examination, and it is always possible that, in this particular sequence, it ‘just happened’ that the first half of trading months had higher returns than the last half. However, the available data put restrictions on the sort of happenstance which might have been responsible for this difference. In particular, the histogram of daily return frequencies presented in section 2 shows that a few outhers which happened to fall in the appropriate half of the month are not the source of the difference; rather, a slight shift in the overall distributions of the two populations is responsible for the differing means.

Pre-test bias? Whenever prior information on realized outcomes is employed in formulating a hypothesis which is then tested against the same data, the resulting test statistics will be biased. This is the problem of ‘data mining’. The comparison here between average returns in the first and last half of trading months as opposed to the first and last half of calendar months [i.e.. the high return last trading day of calendar months is included in the first half of trading months] might suggest that a prior data selection search had been undertaken, but not reported.

One way of overcoming pre-test bias is to employ a hold-out sample of data; one ‘mines’ some of the data and then tests resulting conclusions on the remainder. There is an implicit hold-out sample in the present study. As noted in the Introduction, a number of stock market technicians advise that planned purchases be accelerated and sales be deferred to capture the high returns around the beginnings of months, and generally they regard the period of high return as starting on the last trading day of calendar months. For example, Fosback (1976), the editor of the market letter ‘Market Logic’, notes in his book: ‘Stocks have a marked tendency to rise during the first four days of every month and on the last day of every month. Put together, this continuous span of five trading days constitutes the ‘Month-End’ [strength] component.’ Presumably the technicians uncovered the month-end strength by mining the data, but, at least in the case just cited, the mining was completed by 1976, and hence the five years of data since then may be regarded as a hold-out sample. These five years correspond to the last of the four subperiods examined in the tests reported in section 2. The results for this subperiod alone suggest that pre-test bias cannot be the foundation of the monthly effect.

Biased data? All tests were performed on the CRSP daily index returns. CRSP computes the returns for days around the start of calendar months in

R.A. Anel. A month!v effect in stock returns 169

the same manner as they do for all other days. In particular, the stock weights in the value-weighted index are recalculated daily, and new issues are included in both indexes on the first day that they officially trade. Monthly bias in the

index data does not appear to be responsible for the monthly effect. Mismatch between calendar and trading time? The observed monthly effect is

not being induced by a mismatch between calendar time and trading time. In the above tests, months have been divided so that equal numbers of trading days fall into each half. If equal numbers of trading days in the first or last half encompassed a different number of weekends or holidays, different mean returns from market close to market close might occur in the two halves of months. However, since no constant phase relationship exists between weeks and months, different days of the week, including weekends, will be distrib-

uted evenly across the halves of months. Three of the eight usual holiday closings always occur in the first half of months [i.e., New Year, Fourth of July, Labor Day] and four always occur in the last half of months [i.e., Presidents Day, Memorial Day, Thanksgiving, Christmas]. Two holidays, Good Friday and Election Day, either do not occur consistently in the same half of the month, or are not observed every year. In sum, neither holidays nor weekends preferentially fall in the first or last half of months.’

A dividend effect? The monthly effect is not being induced by the concentra- tion of dividend payments in the first or last halves of months.

All tests were performed on the CRSP total return [or ‘dividend reinvest-

ment’] indexes, so preferential dividend payments in the first or last halves of trading months will not bias the temporal pattern of total returns, at least to a first approximation. It could be argued that differential taxation of dividends

and capital gains cause earnings retained in the corporation to be valued differently than earnings paid out as dividends. If, as a result, stock prices fall

on ex-dividend dates by more or less than the dividend payment, and if

dividend payments are concentrated in the first or last half of trading months, an ex-dividend tax effect will remain in the returns.

Three cogent arguments can be raised against the claim that the monthly

effect is an ex-dividend tax effect. First, it is difficult to show that stocks fall on the ex-dividend date by an amount other than the dividend payment; indeed, the empirical evidence on this point is ambiguous. It would be surprising if this effect appeared so unambiguously in the present study when it was not being sought.

Second, a direct examination of the pattern of dividend payments accruing

to S&P 500 index companies during the first and last nine trading days of

‘Holidays may influence the monthly pattern of returns in yet another way. Merrill (1966) and others have noted and Ariel(1984b) has confirmed a tendency for stocks to show very high returns on the trading day prior to market holiday closings. To see if these high preholiday returns are inducing the monthly pattern, the difference-of-the-half-month-means test described in section 2 was repeated after first setting the returns for trading days prior to holidays equal. to the global mean of all days. Resulting r-statistics of 4.14 and 3.89 for the equally- and value-weighted indexes show that high preholiday returns are not inducing the monthly effect.

170 R.A. Ariel, A monthly effecr in stock retums

trading months over the first quarter of 1982 yields the following pattern [adapted from Gastineau and Madansky (1983, table l)]:

Percent of total dividends paid

Jan. Feb. March ---

First nine days 5.2% 43.0% 17.7% Last nine days 5.8% 12.5% 15.8%

Since there is substantial overlap in the composition or the S&P 500 index and the CRSP value-weighted index, a very similar pattern of dividend payments would presumably be found in the latter; a similar pattern would also be found in the other quarters of the year. Note that dividend payments tend to be concentrated in the first half of the second trading month of the quarter. When the difference-of-the-means test of section 2 is repeated on the value-weighted index after excluding the second month of each quarter’[and excluding January as well, for reasons to be discussed shortly] during the 1963-1981 period, the difference between the first half and last half mean return of 1.05% is significant, with a t-statistic of 3.30 for the 133 monthly observations. Assuming that the above pattern of dividend payments is representative of the remainder of the test period, these figures suggest that the temporal pattern in dividend payments did not induce the observed monthly effect.

Third, and most convincingly, a simple order-of-magnitude argument can show that the monthly effect is not being induced by an ex-dividend tax effect. Suppose for the sake of discussion that the dividend yield on the value-weighted index has averaged 6% per year, or 0.5% per month. The observed difference of the mean returns earned by the first over the last half of trading months for the value-weighted index has been 1.008% per month, as reported in section 2, or twice the monthly dividend payments. Even if all dividend payments were concentrated in the same half of the trading month, the ex-dividend tax effect would have to be twice as large as the dividend payment itself [i.e., stock prices would, on average, either have to fall on the ex-dividend date by three times the dividend payment [i.e., by the dividend payment itself, plus an ex dividend tax effect twice the size], or else increase by the amount of the dividend] in order to induce the observed monthly effect. This sort of change in stock prices on ex-dividend dates is not observed.6

61n addition to dividend payouts, the timing of earnings announcements could conceivably influence the temporal pattern of stock returns. In an examination of corporate earnings announcements, Penman (1987) finds that earnings which are accompanied by positive changes in stock prices tend to occur at the beginnings of calendar quarters. To check whether good corporate earnings news during the early part of the first month of calendar quarters could be inducing the observed monthly effect, the difference-of-the-half-month-means test of section 2 was repeated after excluding tb.e first month of each quarter. For the equally- and value-weighted indexes, respectively, the difference between the half month means is 0.905% and 0.846%, with r-statistics for the difference of 2.45 and 2.84, suggesting that the monthly effect is still significant in the remaining months.

R.A. Arrel, A month& efect rn stock rewrm 171

A manifestation of the January efecr? The monthly effect is not merely another manifestation of the ‘January effect’. Keim (1983), Roll (1983) and Reinganum (1983) have noted a tendency for the stocks of small firms to earn significant excess returns in January, with much of the effect concentrated in the first few days of the month. To see if the tests for the monthly effect are reflecting nothing more than unusually high average returns at the beginning of January, the mean nine-day cumulative returns from the beginnings and ends of all trading months except January were examined. For the equally- weighted index, these mean nine-day returns excluding January are 0.998% and - 0.189% [t-statistic for difference of the means = 3.68, implied p = 0.0003] compared with the mean first and last nine-day return from all months from table 1 (panel I) of 1.411% and -0.021% [t = 4.23, implied p = 0.00003]. Comparable figures for the value-weighted index excluding January are 0.765% and -0.242% [t = 3.92, implied p = O.OOOl] compared with the returns from all months from table 1 (panel I) of 0.826% and -0.182% [t = 4.01, implied p = 0.00007].

The effect of excluding January on the nine-day means are appreciable and in the direction predicted by the January effect; for both indexes the means of both the first and the last nine-day cumulative returns are lower when January is excluded, and the reduction is more pronounced for the equally-weighted index as would be expected if the January effect primarily influences small firms. However, even when January is excluded, the monthly effect is still present in the remaining months, as is evidenced by the differing first- and second-half means, and the difference is still statistically significant. Hence the observed difference in the mean returns from the first and last halves of months is caused by something more than the unusually high returns at the beginning of January.

Neither is the observed effect being induced by high returns during the first half of one or a few of the other months. In particular, the high return months of July, November, and December [Rozeff and Kinney (1976)] are not solely responsible for the observed monthly effect. In results not included here [Ariel (1984a)], it was found that for only one of the months, February, does the point estimate of average cumulative returns over the last nine days of the trading month exceed the point estimate of the average cumulative returns over the first nine days, and the corresponding t-statistic for the difference between average returns shows it to be insignificant. For all the remaining months the difference of the means is in the direction expected by the monthly effect; for several of the months and for both indexes the t-statistic on the difference in nine-day mean returns is significant at the 0.10 level (two-tailed) based on that month’s data alone.

SmaNjkms and the monthly effect

The January period of unusually high excess returns for small firms actually starts on the last trading day of December; indeed, the last trading day of

172 R.A. Ariel, A month!v e#ect in stock returns

Table 2

Incremental return earned by small over large firms (estimated by the difference in returns on the equally-weighted and value-weighted indexes) during the first and last nine days of trading months

(excluding January) during 1963-1981 and during two subintervals.

First nine duys

Cumulative mean return (standard deviation) t-statistic

Last nine days

Cumulative mean return (standard deviation) f-statistic

Difference of the means t-statistic for difference

Full period 1963-1981

(209 months)a

0.219% (1.404%) 2.26

0.036% (1.673%) 0.31

0.183% 1.21

Small fiis outperform large firmsb 1963-1968 1974-1981

(154 months)’

0.349% (1.380%) 3.13

0.312% (1.595%) 2.42

0.037% 0.22

Small firms underperform large firmsb 1969-1973

(55 months)” -

- 0.144% (1.406%)

- 0.75

- 0.736% (1.643%)

- 3.29

0.592% 2.01

“The trading month of January is excluded from the sample to eliminate the ‘January effect’ on small firm returns.

bThe months in the two subintervals were previously identified by Brown, KJeidon and Marsh (1983) as those during which small firms had higher on lower risk-adjusted average returns than large firms.

December together with the four trading days of January alone account for 38% of the annual return earned by the equally-weighted index in excess of the value-weighted index [Roll (1983)].

Fig. 1 shows that the monthly seasonal of high stock returns is also especially strong on the last trading day and first four trading days of calendar months, which fact suggests that the incremental return for small firms over large firms should be examined for a monthly component.

The incremental return earned by small over large firms (estimated by the difference between the return earned on the equally-weighted index and the value-weighted index) was separately cumulated during the first nine days, and during the last nine days of each trading month [excluding January]. The means and standard deviations of the first-half month and last-half month cumulative returns are reported in table 2.

During the full 1963-1981 period small firm returns exceeded large firm returns during both the first half and the last half of trading months, but there is no statistically significant monthly seasonal to the small firm superior performance [t-statistic for difference of the half-month means = 1.211.

Examination of only the full 1963-1981 period obscures a potentially important distinction: Small firms have not consistently outperformed large

R.A. Anel, A monrh!v eflecr in stock returns 173

firms. Indeed, during the 1969-1973 period small firms had lower risk-adjust- ed average returns than large firms [Brown, Kleidon and Marsh (1983)]. Accordingly, the years 1963 through 1981 were split into two groups, the 1969-1973 period, and all the remaining years; table 2 reports the same statistics for these two groups of years as it does for the full pooled period. During the years when smah firms earned more than large firms their superior returns accrued uniformly during both the first and last halves of trading months at the rate of roughly 0.3% per ‘half-month’, but there is no evidence of a monthly seasonal to the superior small firm returns [r-statistic for difference of the half-month means = 0.221.

In contrast, during the years when small firms returned less than large firms, a statistically significant monthly seasonal is present [t-statistic for difference of the half-month mean = 2.011, due primarily !o small firm underperformance during the last half of trading months. Moreover, during 36 of these 55 months, the small firm underperformance was larger during the last half than during the first half of that same trading month [x2 test statistic = 5.251, thereby implying that the observed monthly seasonal of small firm underper- formance during the last half of months was not attributable to a small number of outlying months.

To summarize, excluding January, there is little evidence of a monthly component in the incremental return of small over large firms during either the full pooled period or during those periods when small firms earned a premium over large firms. However, during those years when small firms underper- formed large firms, there was a significant monthly component, with small firms doing poorly primarily during the last halves of trading months.

4. Conclusion

The purpose of this paper is to point out the existence of what has been called here a ‘monthly effect’ in stock returns. The magnitude of this effect is by no means small During the nineteen years studied, all of the market’s cumulative advance occurred during the first half of trading months, with the last half of trading months contributing nothing. Moreover, the variation between high and low return days of the month induced by the monthly effect is of roughly the same order of magnitude as the variation between high and low return days of the week reflected in the well-known weekend effect.’

‘The difference between the mean Monday return, the lowest of the week, and the mean Friday return, the highest, for the equally- and value-weighted indexes are 0.323% and 0.233%, respec- tively [Gibbons and Hess (19Sl)l. The corresponding differences between mean daily returns during the first and last halves of trading months (fig. 2) are 0.140% and 0.097% respectively. These latter differences are about 50% as large as the differences induced by the weekend effect. However, unlike the varying weekday returns in vhich successive high return Fridays are separated by low or negative return days, the high return days of the month are clustered. In essence, the first nine days of trading months have returns comparable to seven to nine Fridays in succession.

174 R.A. Ariel. A monrh!v efect in srock returns

Various explanations for this monthly effect have been considered, including the possibility that it is confounded with the previously reported January and small firm effects on stock returns, but none sufficed to explain the observed empirical regularity. However, even though no explanation has been forthcom- ing, the existence of this pattern in the data may need to be considered in other empirical studies, for example in event studies on aggregate stock returns of economic announcements which occur disproportionately in the first or last half of the month.

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