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Differential information and the small firm effect
Journal
of Financial
Economics
DIFFERENTIAL
13 (1984) 283-294.
INFORMATION
North-Holland
AND THE SMALL FIRM EFFECT*
Christopher B. BARRY Southern
Methodnr
Universi[y.
Dallas,
TX 75275, USA
Stephen J. BROWN BellCommunicarions
Research, Murrq,
Yule University,
Received
March
Hill,
NJ 07974, USA
New Haven, CT 06520, USA
1983, final version received January
1984
We examine a model of market equilibrium in which there is less information available about some of the securities in the market than about others. We consider the model as a potential explanation of the well-known small firm anomaly. Using period of listing as a proxy for quantity of information, we find an association between period of listing and security returns that cannot be accounted for by firm size and which is not diminished by an elimination of January returns data from our sample. Thus, we observe a new empirical regularity in the data and refer to the regularity as the ‘period of listing’ effect.
1. Introduction Banz (1981), Reinganum (1981) and others have observed that returns on common stocks appear to be associated negatively with the aggregate market values of the securities. These aggregate market values are referred to as ‘firm size’. Banz (1981) attempted to adjust for risk and found that small firms produce larger risk-adjusted returns than do large firms. Reinganum (1981) showed that this effect appears to remain even after controlling for the earnings yield of the securities. Later, Reinganum (1982) showed that the effect remains even after adjusting for the risk-measurement effects associated with market values. In a series of related papers, Constantinides (1984), Keim
*The views expressed are those of the authors and do not necessarily reflect those of Bell Communications Research Inc. We wish to thank not only the Editor, G. William Schwert. and the referee, Marc Reinganum, for particularly constructive comments, but also Richard Roll, colleagues at Southern Methodist University and Bell Laboratories, and faculty attending a number of workshops at which this work was presented. We also acknowledge the gracious assistance of Steven Wheeler and Deborah Gardner of the NYSE Archives, 0304-405X/84/$3.00~1984,
Elsevier Science Publishers
B.V. (North-Holland)
284
C. B. Barry and S. J. Brown,
Dlferentiul
information
and the small firm effect
(1983), Reinganum (1983) and others have considered further potential explanations of the firm size effect. To date, however, the phenomenon remains an anomaly. In this paper we investigate a possible explanation of the small firm effect that is based on information arguments. The argument is that securities for which there is relatively little information available may be perceived as riskier securities than are securities for which more information is available. Commensurate with that risk, participants in the market may rationally demand a premium to hold such securities. If so, and if risk is measured empirically without rega,d to the amount of information available, then there may appear to be ‘abnormal’ returns for low information securities. To the extent that low market value securities have less information available, it follows that there would appear to be ‘abnormal’ returns associated with small firms. We propose a simple model of differential information. In a related paper [Barry and Brown (1983)], we show that this model is consistent with a variety of information hypotheses. It yields the result implied by Banz (1981) that the perceived risk of low information securities is higher than the perceived risk of high information securities that have the same historical beta. The model suggests a simple proxy for quantity of information: the relative period of listing. The model on which our analysis is based has e@pirical implications which we examine using monthly NYSE security returns for the period 1931-1980. In so doing we observe a new empirical regularity in the data that is associated with the size effect. However, the regularities are also to some extent distinct from the size effect. We refer to the empirical regularities as the ‘period of listing effect’ since the information measure we use is the relative period of time for which securities have been listed. We also study the relation between the period of listing effect and the so-called ‘turn-of-the-year’ phenomenon that has been found to be an important component of the size effect [see, for example, Keim (1983), Roll (1983) and Reinganum (1983)]. We find that the period of listing effect is in no way lessened by eliminating the January returns from our data. The period of listing effect cannot be accounted for by the turn-of-the-year effect. On reflection, it would appear possible to derive a number of alternative theories that might account for the new empirical regularities that we document in this paper. Institutional interest in ‘well established’ securities may create a clientele effect sufficient to explain the listing effect. Such an argument is consistent with the information hypothesis. There are other arguments involving the intrinsic characteristics of small, newly listed corporations - the existence of tax deferrals, growth potential and other intangibles - that assume the capital markets are either imperfect or incomplete. The information hypothesis is not at variance with the efficient markets hypothesis.
C. B. Barry and S. J. Brown,
Differenrlal
injormatron
and the smallJirm
effect
285
In section 2 we describe a model that yields the result that differential information can have an observable effect on market equilibrium. In section 3 we report the results of an empirical evaluation of period of listing as it relates to observed returns and to market values. Conclusions and suggestions for further research are presented in section 4. 2. Differential information and market equilibrium In the concluding section of his paper, Banz (1981) argues that the small firm effect might be due to the relatively limited information available about the smaller firms. Others have provided empirical tests examining the extent to which the effects of earnings announcements on observed returns vary across firm size categories [see Atiase (1982) and Freeman (1982)]. Still others have examined the relation between the size effect and the extent of analyst interest in securities [Arbel and Strebel(1983)]. However, Reinganum and Smith (1983) have pointed out that if the effects of limited information on security risk characteristics are diversifiable, then in principal we should not expect to observe any effects of limited information on average security returns. Thus, it remains to be shown that the relative lack of information represents a source of non-diversifiable risk. Klein and Bawa (1977) present a model in which the set of information is limited to the past historical data. In that model, low information securities have fewer observations than other securities. Low information securities have relatively high estimation risk [in the sense of Bawa, Brown and Klein (1979)], and this leads risk averse investors to diversify away from such securities [Klein and Bawa (1977, theorem 5)]. Equilibrium implications of this result are developed in Barry and Brown (1983), and the result is extended to cases of divergence of opinion and non-stationarity. That paper shows that if we employ the number of observations as a proxy for the degree of relative estimation risk, limited information can have an effect on systematic risk and therefore on required returns. In an equilibrium setting portfolios of low information securities will appear to earn positive abnormal returns and high information securities will appear to earn negative abnormal returns if their betas are measured without regard for differential information and if their average returns are consistent with a CAPM that reflects investor perception of differential information. For this simple model of differential information we take literally the notion that quantity of information is determined by the number of observations or period of listing of the securities. Raiffa and Schlaifer (1961) point out that there is an ‘equivalent sample information’ interpretation of Bayesian prior and posterior distributions for parameters of many common processes, such as the multivariate normal process. While the interpretation is intuitively appeal-
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C. B. Barry and S. J. Brown, D@rential information and the smallfirm e$ect
ing, it is not necessary that the interpretation be taken literally. For example, an analyst assessing a prior distribution over the mean return of a security might assess a normal prior distribution for that mean. Such a prior would be equivalent to having observed a sample of a given number of returns on the security, but the prior may not in fact have been formed solely on the basis of such data. For example, for small firms the set of information might consist of a few data points at which trades occurred plus reports made available to the public by the firm on a periodic basis. For large firms that are widely followed by many analysts, there may be many sources of information. It is reasonable to suppose that ‘equivalent sample information’ is an increasing function of time but that the amount of information per unit time differs across firms. To the extent that the number of observations is related to the length of time for which a security has been listed, our model of relative estimation risk would predict a ‘period of listing’ effect. ’ To the extent that quantity of available information varies between small firms and large firms, it would also predict an apparent ‘small firm’ effect.
3. Differential information and abnormal returns: The empirical evidence In this section we attempt to measure size and differential information effects on the basis of returns realized on a monthly basis for NYSE traded securities for the period 1931 to 1980. We describe the data and empirical procedures used to this end and present the empirical results. We control for systematic risk and find a significant period of listing effect. This effect persists after controlling for size and for the so-called ‘January effect’.
3.1. Data The data used in our study comprises the set of all securities traded on the New York Stock Exchange (NYSE) from December 1926 to December 1980, which are listed on that exchange for a period of at least 61 months and which have at least 21 months of data on the CRSP monthly returns file.’ On leaving ‘Fisher (1959) was, to our knowledge, the first to examine such a hypothesis. He argued that information available about corporate bonds could be measured by period of listing (since last default), and that such a measure of risk is in fact priced in the bond markets. It is interesting to note that his proxy for ‘marketability’ can be interpreted as a proxy for a capitalization variable. ‘Since the securities we study were listed on the NYSE for at least 61 months and rates of return by size, period of listing, and beta categories were not computed for the first 60 months of listing, the results we report cannot be ascribed to the new issue seasoning process [cf. Ibbotson and JalTe (1975)]. At least 20 months of prior data was required in order to estimate beta.
C. B. Barry and S. J. Brown, Differential information and the smallfirm effect
287
the exchange, the security’s return is based on the price at which the security subsequently trades on another exchange. If no such trade is reported, the security is assumed to have a return of minus one.3 We use the CRSP value weighted index as an index of market returns.4 For each month the securities are cross-classified by size (total market value of equity outstanding in the previous month), number of months since the security was first listed on the NYSE,’ and beta estimated on the basis of the previous 60 months using OLS procedures. Size is organized into 6 quantiles, the smallest 6th of all securities going into group 1, the next 6th going into group 2, and so forth. Period of listing is independently organized into 6 groups. Period of listing group 1 corresponds to those securities listed for the least amount of time, and the 6th group corresponds to those securities listed for the longest period. Beta is also classified independently into 6 quantiles, with the smallest betas assigned to the first group and the largest to group 6.6 Each security is assigned to one of the 6 x 6 x 6 cells according to its size, listing and beta classification. Return measures by size, listing and beta are then constructed by equally weighting returns for securities within each of the 216 cells. Cell membership is recomputed each period based on the previous month’s size, period of listing and beta. Thus, 216 time series of returns are obtained due to size, period of listing and beta dating from January 1931 through December 1980. ‘The purpose of this assumption was to eliminate a potential ‘survivorship bias’ that would be present if we had left out securities on the month they were delisted. This assumption might appear to underestimate returns in the month of delisting, since securities may leave the exchange by merger and acquisition as well as by bankruptcy. Excluding securities in the month they were delisted increased returns due to size and listing. As expected the size effect was more pronounced excluding such securities; however, the magnitude and significance of the listing effect were little affected by this change. 4The value weight index was used to maintain comparability of our results with those of Banz (1981) and Reinganum (1981, 1982). Brown and Warner (1980) indicate some of the problems involved in using such an index in abnormal performance studies; for this reason we also studied the effect of using an equally weighted index [cf. Brown, Kleidon and Marsh (1982)]. In results not reported here, we found that while absolute magnitudes were affected, relative magnitudes were unaffected by the choice of weights, ‘The months of listing were determined from the month of first listing on the CRSP tape or, in the case of 459 securities in our sample trading in 1926, the month in which the security was first accepted by the Committee on the List of the New York Stock Exchange. That date was determined from the first listing statement on record in the archives of the NYSE. This is not entirely satisfactory, since the listing statements were preserved only back as far as June 1884. In 9 of 459 cases, the preferred stock was listed prior to capital or common stock issues, Since it was not obvious that there was not a prior capital stock issue listed on the exchange, the date of the preferred issue was taken as the ‘first listing’. 6We further cross-classified the securities by the extent of trading measured by the proportion of the period of listing for which trade data was used to construct rates of return. Results showed that the period of listing and size effects described later in this paper were strongest for the most frequently traded securities.
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and S. J. Brown,
D#erential
information
and the
smallfirm
effect
3.2. Results Table 1 reports average percentage monthly returns measured within size and period of listing groups. The size effect is very clear in these results,’ but the returns are not risk-adjusted. 8 There appears to be a moderate period of listing effect as well, and risk is relatively constant across periods of listing. Note that the size effect appears to be most pronounced among securities in the lowest period of listing group. Similarly, the period of listing effect is most pronounced for the smallest size category and, again, would be minimally affected by risk adjustment. However, the size effect appears to dominate the listing effect in magnitude using these unadjusted average returns. Some authors argue that the size effect is comprised in large part of unusually large returns to small firms in January [Keim (1983), Roll (1983a) and Reinganum (1983)). To examine the effect of these January returns and their relation to period of listing, we replicate the analysis used to construct the first panel of table 1 excluding all January data. The results are shown in the second panel of that table. Note that in this table, the size and period of listing effects in these returns are of a similar order of magnitude. The returns are not risk-adjusted, and it is interesting to note that risk measured by estimate of beta is virtually constant across period of listing categories but varies substantially across size categories. The listing effect appears to be independent of the January anomaly. The period of listing effect in table 1 is especially noticeable among the smallest firms. Within the smallest size category, the average firm size across the 6 period of listing groups is almost constant, and in fact it declines from $10.5 million for listing category 1 to $9.5 million for listing category 6. Again, the betas are nearly constant across these 6 categories. Thus, in the most pronounced case, there appear to be substantial returns associated with firms with low periods of listing, and it does not appear that those returns can be attributed to firm size or to risk.’ The discussion of the previous section suggests one should expect positive abnormal returns for those securities listed for the least amount of time, where abnormal returns are defined relative to systematic risk estimated on the basis
‘The size effect is of an order of magnitude similar to that reported in Banz (1981, table 3). However, table 1 is not directly comparable to Banz’s table 3 since his results were risk-adjusted. ‘Across all firms in our sample average beta (measured on the basis of the prior 60 months of data) varied from 1.22 to 1.19 by listing category, as compared to 1.36 to 1.02 by size for the period 1931-1980. Controlling for size and listing, respectively, did not affect these observed ranges of variation in beta. ‘Table 1 reports average returns, and it is possible that the results are an artifact of not compounding the returns [cf. Roll (1983b)]. Geometric mean returns are of course smaller than the corresponding average returns, and the size premium measured as the difference between geometric mean returns of the smallest and largest size categories falls to 0.77% from the 1.23% apparent from table 1. However, the listing premium actually increases slightly to 0.28% from 0.24%. reflecting the fact that the variability of returns is relatively constant across listing categories.
C. B. Buy
and S. J. Brown,
Differential
tnformatton
and the small firm effect
289
Table 1 Average percentage anced monthly by 1980. and for that classifications and the average return
monthly returns on equally weighted portfolios of NYSE securities rebalsize and period of listing categories, for the period January 1931 to December period excluding the month of January. In each panel the rows give the size the columns the listing classifications: for example, row 3 and column 4 gives for a portfolio comprising for each month all securities in the third sixth of securities by size and fourth sixth of securities by listing. Period of listinga 1
2
1 2 3 4 5 6
2.36 1.51 1.30 1.06 1.16 0.79
2.14 1.55 1.29 1.02 1.00 0.84
Period of listing marginal<
1.40
1.32
Average
1.22
1.21
3
4
(a) Aiidatu
Size’
betad
5 1931-Dec.
(Jun.
2.17 1.29 1.36 1.13 1.10 0.86
6
Size marginafC
Average betad
2.08 1.39 1.26 1.11 1.07 0.85
1.36 1.29 1.23 1.20 1.12 1.02
1980)
1.67 1.30 0.99 1.23 1.18 0.96
1.95 1.25 1.27 1.14 1.16 0.85
1.98 1.19 1.21 1.11 0.89 0.81
1.38
1.27
1.22
1.16
1.21
1.19
1.20
1.19
(b) Excluding
Januq
( Feb. 1931 -Dec.
I9RO)
1 2 3 4 5 6
1.52 1.01 1.04 0.89 1.10 0.77
1.40 1.09
1.20 0.79
0.83 0.72
1.12 0.76
0.90 0.54
1.18 0.88
1.02 0.80 0.90 0.82
1.03 0.90 1.00 0.82
0.62 0.99 1.06 0.96
0.90 0.89 0.96 0.80
0.76 0.76 0.66 0.68
0.93 0.87 0.93 0.79
Period of listing marginal’
1.08
0.99
0.99
0.89
0.89
0.74
Sizeb
aPeriod of listing is defined as the number of prior months the security in question was listed on the CRSP tapes. In the case of 459 securities in oursample listed at any time in 1926, listing is defined relative to the month the security was accepted by the Committee on the List of the NYSE as recorded in the NYSE Archives. The average period of listing in categories 1 through 6 were 89.5, 146.4, 213.6, 291.2, 387.3 and 592.1 months, respectively. ‘Size was defined as the value of equity outstanding of the security in question as of the end of the previous month. The average size (in $M) for categories 1 through 6 were 9.8, 24.9, 49.9, 99.0, 221.5 and 1.197.4, respectively. ‘The size and period of listing marginals give average returns for portfolios constructed on the basis of size alone and of listing alone, respectively. Note that since the number of securities differ from cell to cell and from one period to the next, the marginals are not simple averages of the corresponding elements in the rows and columns of the table. dAverage value of OLS beta estimated on the basis of prior 60 months of data using a value weighted index.
of a regression of past returns on those of the market. In this context the result is intuitive. In common with other studies relating return to beta risk, we use a moving window of at most 60 months to estimate beta. This estimation period is constant across securities, even though at any point of time there may be more information available about some securities than about others. The result
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C. B. Barry and S. J. Brown, DifJerential informatton and the smallJirm effect
than follows if we accept relative period of listing, perhaps controlling for size, as an adequate proxy for this information. One procedure that can be used to estimate abnormal returns is to place securities into beta decile groups for each month using an estimate of systematic risk based on data from the previous 60 months. Then abnormal returns can be calculated as the deviation of individual security returns from the mean return of the cross-section to which that security belongs [cf. Brown, Kleidon and Marsh (1982, fn. 5)]. This procedure assumes that the Capital Asset Pricing Model is correct and that the ‘true’ beta is constant within a given beta decile group. In that event, the expected return is given by Vi E I,
ER,, = (1 - P,)r,, + P,ER,,,
for security i belonging to beta decile group Z which has a true beta of R,. The risk-free rate specific to period t, qr, is observable, but the ex ante expectations of return on the individual security ER;, and market ER,,,,, and RI are not observable. However, since ER,, = ER,, for i, j E I, a measure of abnormal performance specific to security i would be given by e,t = R,, - &I,
Vi E I.
0)
If the CAPM is correct and the true beta RI is constant within the decile groups organized by the estimate of beta using data prior to t, then EE,~= 0 for all i and t. However, if the beta appropriate to the CAPM differs according to period of listing in such a way that the low information beta, fiL., is greater than the high information beta, RH, for given estimate R, we should expect that the difference eL, - .sHrwould be positive within the beta decile group. Average excess returns computed in this way and standardized using the standard deviation computed on the basis of the prior 60 months of data” are “The
average
excess return
for category
I in period
/ is measured
6, = c L/n,,, 1El where E,, is the excess return for security i computed as in eq. (1) and n,, is the number securities in category I. Then the standardized excess returns for category I is defined as
-L/L@ where
SI = ?
S,, = E,,/(
of
r,,/&),
1=l
with S,, being the standardized I, sf[, is estimated from
excess return
for category
I in period
1. The variance
for category
I-1 3,
= ,=;,1
(J;;JIE,,
-fiSJ2/59,
where the ,& term captures the variability that results from the change in the number of securities from period to period. This procedure accounts for potential dependence in the cross-section of excess returns within each size and listing category. The properties for such dependence adjustment are discussed in Brown and Warner (1980).
C. B. Bary
and S. J. Brown,
Differential
information
and the smaNjirm
effect
291
Table 2 Standardized
excess returnsa
by size and period of listing categories to December 1980.
for all months
Period of listing 1
2
3
4
5
6
1 2 3 4 5 6
- 2.60 1.71 -0.26 - 0.82 0.55 - 1.83
2.03 1.99 0.28 - 1.44 -1.42 - 2.25
2.19 0.42 1.18 - 1.03 -0.18 - 2.37
0.52 - 0.64 - 3.13 - 0.45 0.53 -1.55
0.94 - 0.71 -0.56 -1.11 0.21 -2.81
0.68 - 0.84 - 0.26 -0.90 - 2.36 - 2.85
Period of listing marginal
2.20
1.21
1.76
-1.24
- 1.79
-1.70
Size
January
1931
Size marginal 1.97 0.84 - 1.51 - 1.51 -0.36 - 2.68
aThe standardized excess return for category I represents a t-value given by CT= ,S,,/fi, where T= 600. The standardized excess return for category I in period I, S,,, is defined in footnote 10 of the paper, and represents the average excess return for I in t standardized by the standard deviation of excess returns estimated on the basis of 60 months of prior data, after correction for the number of securities in 1.
reported in table 2. From inspection of this table, we find that the size effect does not dominate the period of listing effect when these effects are measured in terms of standardized excess returns. As before, the period of listing effect is more pronounced among small firms than among the larger firms in our sample. The results in the smallest size category are particularly worthy of note. Those small firms listed for the longest periods do not produce statistically significant excess returns. This result suggests there may be an interaction between period of listing and firm size. To explore in some greater detail the interaction between the small firm effect and listing effects we see in the data, consider table 3 which reports the results of using a Fama and MacBeth (1973) procedure to evaluate size and listing premia, allowing for interactions between these effects.” Considering the size effect by itself we find that there is a significant size effect in the overall period, but this effect is apparently insignificant for the post-war period, consistent with the findings of Banz (1981) among others. Considering the “The numbers reported in table 3 represent time series means of OLS estimates based on the cross-section of 216 returns in each month. This procedure assumes the residuals are independent in the cross-section. To examine how sensitive the results might have been to the independence assumption, a GLS procedure was used. First, a 6-factor representation of the 215 x 215 covariante matrix was estimated on the basis of the cross-section of residuals. One of the 216 cells (the last) had to be dropped to factor the estimated covariance matrix (which would otherwise be singular). Then the coefficients reported in table 3 were recomputed using the GLS procedure. The means of the GLS estimates were nearly identical to those reported in table 3, and the significance of nearly ah of the coefficients was higher than reported for the OLS results, The t-value of the period of listing coefficient increased in magnitude from - 2.48 to - 3.99 for the overall period. In the post-war period, the t-value of the period of listing coefficient was unaffected by the use of the OLS procedure, remaining at approximately - 3.06.
292
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B. Barry and S. J. Brown,
Deferential
information
and the
smallfirm
effect
results excluding January, the size effect is, or appears to be, largely confined to the January months of the sample. This result is consistent with the findings of Keim (1983). Controlling for size, beta and the interactions between the variables, there is a listing effect, and this effect persists in the post-war period as well as when the month of January is excluded from the data. However, this effect is strongest for the smallest firms in the sample [the (size x listing) premium is positive, offsetting the listing effect], and this interaction effect is statistically significant in the post-war period, regardless of whether we exclude the month of January from the sample. At first inspection these results appear puzzling. Table 1 demonstrates a substantial size effect, and table 2 shows that this effect persists even controlling for beta. Yet one might conclude from table 3 that the size effect is small. Further examination reveals the source of this apparent contradiction. The first two tables present strong evidence of the interaction between the effects of size Table 3 Cross-section regression of monthly returns against size, period of listing and beta, and interactions between these variables. Mean and t-value of mean (reported in parentheses) are computed on the basis of the time series of regression coefficients for the period January 1936 to December 1980 and the post-war period January 1946 to December 1980 for all months as well as for all months excluding the month of January.a
Intercept Jan. 1936-Dec. 1980
Feb. 1936-Dec. 1980 (excluding Jan.)
0.0195 (3.74)
- 0.0009 (- 2.31)
0.0012 (0.16)
(0.63)
0.0017 (0.41)
0.0004 (1.31)
- 0.0070 (-1.01) Jan. 1946-Dec. 1980
0.0133 (2.54) - 0.0004
( - 0.77) Feb. 1946-Dec. 1980 (excluding Jan.)
Size
0.0004
Period of listing
Beta
Size x period of listing
Period of listing .T beta
- 0.0085 0.0124 (- 2.48) (2.36)
- 0.0003
t - 0.86)
0.0004
- 0.0008
(- 1.98)
(1.46)
0.0092 (1.51)
- o.OOQ2 - 0.41)
0.0026 (0.29)
-O.OC@O - 0.0107 - 0.0013 (-2.96) (-0.24) - 0.02)
0.14 0.10
-O.OOQO ( - 0.01)
0.0004 (1.62)
0.0021 (2.21)
0.13 0.10
0.0001 (0.10)
0.0009 - 0.0083 0.0104 (- 3.04) (2.12) (2.13)
=yo+yl~,,+~~l,,+~~B~,+y~~~,,~,,~+~s~~,,Pk~~+~6~l,,Pk,)+t,,k,.
0.0025 (2.75)
O.CKJO4 (0.25)
0.0009 - 0.0089 0.0027 (1.54) (- 2.59) (0.51)
R2
0.11
0.0011 (0.68)
- 0.0009 (-1.94)
0.0005 (2.31)
0.0014 (1.88)
0.13 0.10
0.0005 (0.26) 0.0007 (2.23)
0.0004 (0.83)
aThe columns in the table give the mean coefficient estifnates ?a, $,,. R
Size .x beta
0.0015 (1.37)
0.14
, ye from the regression
i.j.k=1,....6.
the size. list-
i$kd beta categories for month t - 1, R ,,k, represents the return on the portfolio comprising the ith size, jth listing and k th beta category of securities in month t, s,, represents the logarithm of average size in category i for month t, /,, a measure of relative period of listing given as the logarithm of the ratio of period of listing for group j to that for group 6, and PI, is the average beta for category k, estimated using 60 months of prior data.
C. B. Barv
and S. J. Brown, Differenriul
information
and rhe smallfirm
effect
293
and listing. In fact, this interaction effect is far more significant than the size effect per se. Though not evident in those tables, there is also a strong interaction between the effects of size and beta. It is only after controlling for these interactions that there is a listing effect stable across subintervals of the data, with no independent size effect.‘* In section 2, we argued that relative period of listing should appear in an equilibrium pricing model as a measure of the non-diversifiable risk induced by differential information. However, relative period of listing is not altogether satisfactory as a proxy for differential information because the amount of information per unit time might vary with the size of the firm. This firm size might capture an element of differential information not captured by period of listing. The results in table 3 are consistent with this hypothesis. 4. Summary and conclusion In this paper we examine a model of market equilibrium with differential information. We show that period of listing, a crude measure of differential information, is associated with the well-known firm size anomaly. However, this information argument does by no means fully explain the firm size anomaly, and it is an open question as to whether a more satisfactory measure of information would more completely explain the observed size effect. It is interesting to note that at least one popular explanation of the small firm effect, an explanation in terms of a turn-of-the-year phenomenon, does not in any way diminish the period of listing effect we see in the data. The significance of our results suggests that it might be profitable to pursue other proxies for the quantity of information. The advantage of period of listing as a proxy for quantity of information is its simplicity and the fact that such a measure is robust to the specific information model under investigation. Atiase (1982) and Freeman (1982) analyze the magnitude of the earnings announcement effect as a function of firm size and find that the monotonic relationship can best be explained as an information effect that might explain at least part of the small firm effect. Figlewski (1981) and others have examined the extent of analyst agreement as a measure of relative information, and Barry and Brown (1983) demonstrate that analyst agreement and information availability are closely associated. These alternative characterizations of information appear to be worthy of examination.
“Caution should be exercised in drawing too literal a comparison between table 3 and the previous two tables. Table 3, which presents a summary of cross-section results, is not strictly comparable to the previous tables which present means of time series data, since the number of securities in each category varies considerably through time. The table 3 results were not sensitive to the use of the Fama and MacBeth (1973) procedure: results were even stronger using a stacked regression procedure implemented on the basis of successive 5-year mean returns, suggesting that the results cannot solely be attributed to month-by-month variations in the number of securities in each classification.
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C. B.
Barty and S. J. Brown,
DQjerenrial
information
and the
smallfirm
effect
References Arbel, Avner and Paul Strebel, 1982, The neglected and small firm effects, The Financial Review 17, 201-218. Atiase, Rowland K., 1982, Predisclosure information, firm capitalization and security price behavior around earnings announcements, Unpublished memo. (University of California, Berkeley, CA). Banz, Rolf W., 1981, The relationship between return and market value of common stocks, Journal of Financial Economics 9, 3-18. Barry, Christopher B., 1978, Etfects of uncertain and nonstationary parameters upon capital market equilibrium conditions, Journal of Financial and Quantitative Analysis 13, 419-433. Barry, Christopher B. and Stephen J. Brown, 1983, Differential information and security market equilibrium, Working paper (Edwin L. Cox School of Business, Southern Methodist University, Dallas, TX). Bawa, Vijay S., Stephen J. Brown and Roger W. Klein, 1979, Estimation risk and optimal portfolio choice (North-Holland, Amsterdam). Brown, Phillip, AIlan W. Kleidon and Terry A. Marsh, 1983, New evidence on the nature of size related anomalies in stock prices, Journal of Financial Economics 12, 33-56. Brown, Phillip, Donald B. Keim, Allan W. Kleidon and Terry A. Marsh, 1983, Stock return seasonalities and the ‘tax loss selling’ hypothesis: Analysis of the arguments and Australian evidence, Journal of Financial Economics, 12,105-127. Brown, Stephen J. and Jerold B. Warner, 1980, Measuring security price performance, Journal of Financial Economics 8, 205-258. Constantinides, George M., 1984, Optimal stock trading with personal taxes: Implications for prices and the abnormal January returns, Journal of Financial Economics 13, 65-89. Fama, E. and J. MacBeth, 1973 Risk, return and equilibrium: Empirical tests, Journal of Political Economy 81,607-635. Figlewski, S., 1981, Information diversity and market behavior, Unpublished memo. (New York University, NY). Fisher, L., 1959, Determinants of risk premiums on corporate bonds, Journal of Political Economy 57, 217-237. Freeman, Robert N., 1982, The association between accounting earnings and security returns for large and small firms, Unpublished memo. (University of California, Berkeley, CA). Ibbotson, Roger G. and Jeffrey F. Jalle, 1975, ‘Hot issue’ markets, Journal of Finance 30, 1027-1042. Keim, Donald B., 1983, Size related anomalies and stock market seasonalitv: Further empirical evidence, Journal of Financial Economics 12, 13-32. Klein. Roeer W. and Viiav S. Bawa. 1977. The effect of limited information and estimation risk on optimz portfolio di;ersification; Journal of Financial Economics 5, 89-111. Lindley, D., 1956, A statistical paradox, Biometrika 44, 187-192. Raiffa, H. and R. Schlaifer, 1961, Applied statistical decision theory (M.I.T. Press, Cambridge, MA). Reilly, Frank K. and Eugene F. Drzycimski, 1981, An analysis of the effects of a multi-tiered stock market, Journal of Financial and Quantitative Analysis 16, 559-579. Reinganum, Marc R., 1981, Misspecitication of capital asset pricing: Empirical anomalies based on earnings’ yields and market values, Journal of Financial Economics 9, 19-46. Reinganum, Marc R., 1982, A direct test of Roll’s conjecture on the firm size effect, Journal of Finance 37, 27-35. Reinganum, Marc R., 1983, The anomalous stock market behavior of small firms in January: Empirical tests for year end tax effects Journal of Financial Economics 12, 89-104. Reinganum, Marc R. and Janet K. Smith, 1983, Investor preference for large firms: New evidence on economies of size, Journal of Industrial Economics, 32, 213-227. Roll, Richard, 1981, A possible explanation of the small firm effect, Journal of Finance 36, 879-887. Roll, Richard, 1983a, Vas ist das? The turn of the year effect and the return premia of small firms, Journal of Portfolio Management 9, 18-28. Roll, Richard, 1983b, On computing mean returns and the small firm premium, Journal of Financial Economics 12. 371-386.
of Financial
Economics
DIFFERENTIAL
13 (1984) 283-294.
INFORMATION
North-Holland
AND THE SMALL FIRM EFFECT*
Christopher B. BARRY Southern
Methodnr
Universi[y.
Dallas,
TX 75275, USA
Stephen J. BROWN BellCommunicarions
Research, Murrq,
Yule University,
Received
March
Hill,
NJ 07974, USA
New Haven, CT 06520, USA
1983, final version received January
1984
We examine a model of market equilibrium in which there is less information available about some of the securities in the market than about others. We consider the model as a potential explanation of the well-known small firm anomaly. Using period of listing as a proxy for quantity of information, we find an association between period of listing and security returns that cannot be accounted for by firm size and which is not diminished by an elimination of January returns data from our sample. Thus, we observe a new empirical regularity in the data and refer to the regularity as the ‘period of listing’ effect.
1. Introduction Banz (1981), Reinganum (1981) and others have observed that returns on common stocks appear to be associated negatively with the aggregate market values of the securities. These aggregate market values are referred to as ‘firm size’. Banz (1981) attempted to adjust for risk and found that small firms produce larger risk-adjusted returns than do large firms. Reinganum (1981) showed that this effect appears to remain even after controlling for the earnings yield of the securities. Later, Reinganum (1982) showed that the effect remains even after adjusting for the risk-measurement effects associated with market values. In a series of related papers, Constantinides (1984), Keim
*The views expressed are those of the authors and do not necessarily reflect those of Bell Communications Research Inc. We wish to thank not only the Editor, G. William Schwert. and the referee, Marc Reinganum, for particularly constructive comments, but also Richard Roll, colleagues at Southern Methodist University and Bell Laboratories, and faculty attending a number of workshops at which this work was presented. We also acknowledge the gracious assistance of Steven Wheeler and Deborah Gardner of the NYSE Archives, 0304-405X/84/$3.00~1984,
Elsevier Science Publishers
B.V. (North-Holland)
284
C. B. Barry and S. J. Brown,
Dlferentiul
information
and the small firm effect
(1983), Reinganum (1983) and others have considered further potential explanations of the firm size effect. To date, however, the phenomenon remains an anomaly. In this paper we investigate a possible explanation of the small firm effect that is based on information arguments. The argument is that securities for which there is relatively little information available may be perceived as riskier securities than are securities for which more information is available. Commensurate with that risk, participants in the market may rationally demand a premium to hold such securities. If so, and if risk is measured empirically without rega,d to the amount of information available, then there may appear to be ‘abnormal’ returns for low information securities. To the extent that low market value securities have less information available, it follows that there would appear to be ‘abnormal’ returns associated with small firms. We propose a simple model of differential information. In a related paper [Barry and Brown (1983)], we show that this model is consistent with a variety of information hypotheses. It yields the result implied by Banz (1981) that the perceived risk of low information securities is higher than the perceived risk of high information securities that have the same historical beta. The model suggests a simple proxy for quantity of information: the relative period of listing. The model on which our analysis is based has e@pirical implications which we examine using monthly NYSE security returns for the period 1931-1980. In so doing we observe a new empirical regularity in the data that is associated with the size effect. However, the regularities are also to some extent distinct from the size effect. We refer to the empirical regularities as the ‘period of listing effect’ since the information measure we use is the relative period of time for which securities have been listed. We also study the relation between the period of listing effect and the so-called ‘turn-of-the-year’ phenomenon that has been found to be an important component of the size effect [see, for example, Keim (1983), Roll (1983) and Reinganum (1983)]. We find that the period of listing effect is in no way lessened by eliminating the January returns from our data. The period of listing effect cannot be accounted for by the turn-of-the-year effect. On reflection, it would appear possible to derive a number of alternative theories that might account for the new empirical regularities that we document in this paper. Institutional interest in ‘well established’ securities may create a clientele effect sufficient to explain the listing effect. Such an argument is consistent with the information hypothesis. There are other arguments involving the intrinsic characteristics of small, newly listed corporations - the existence of tax deferrals, growth potential and other intangibles - that assume the capital markets are either imperfect or incomplete. The information hypothesis is not at variance with the efficient markets hypothesis.
C. B. Barry and S. J. Brown,
Differenrlal
injormatron
and the smallJirm
effect
285
In section 2 we describe a model that yields the result that differential information can have an observable effect on market equilibrium. In section 3 we report the results of an empirical evaluation of period of listing as it relates to observed returns and to market values. Conclusions and suggestions for further research are presented in section 4. 2. Differential information and market equilibrium In the concluding section of his paper, Banz (1981) argues that the small firm effect might be due to the relatively limited information available about the smaller firms. Others have provided empirical tests examining the extent to which the effects of earnings announcements on observed returns vary across firm size categories [see Atiase (1982) and Freeman (1982)]. Still others have examined the relation between the size effect and the extent of analyst interest in securities [Arbel and Strebel(1983)]. However, Reinganum and Smith (1983) have pointed out that if the effects of limited information on security risk characteristics are diversifiable, then in principal we should not expect to observe any effects of limited information on average security returns. Thus, it remains to be shown that the relative lack of information represents a source of non-diversifiable risk. Klein and Bawa (1977) present a model in which the set of information is limited to the past historical data. In that model, low information securities have fewer observations than other securities. Low information securities have relatively high estimation risk [in the sense of Bawa, Brown and Klein (1979)], and this leads risk averse investors to diversify away from such securities [Klein and Bawa (1977, theorem 5)]. Equilibrium implications of this result are developed in Barry and Brown (1983), and the result is extended to cases of divergence of opinion and non-stationarity. That paper shows that if we employ the number of observations as a proxy for the degree of relative estimation risk, limited information can have an effect on systematic risk and therefore on required returns. In an equilibrium setting portfolios of low information securities will appear to earn positive abnormal returns and high information securities will appear to earn negative abnormal returns if their betas are measured without regard for differential information and if their average returns are consistent with a CAPM that reflects investor perception of differential information. For this simple model of differential information we take literally the notion that quantity of information is determined by the number of observations or period of listing of the securities. Raiffa and Schlaifer (1961) point out that there is an ‘equivalent sample information’ interpretation of Bayesian prior and posterior distributions for parameters of many common processes, such as the multivariate normal process. While the interpretation is intuitively appeal-
286
C. B. Barry and S. J. Brown, D@rential information and the smallfirm e$ect
ing, it is not necessary that the interpretation be taken literally. For example, an analyst assessing a prior distribution over the mean return of a security might assess a normal prior distribution for that mean. Such a prior would be equivalent to having observed a sample of a given number of returns on the security, but the prior may not in fact have been formed solely on the basis of such data. For example, for small firms the set of information might consist of a few data points at which trades occurred plus reports made available to the public by the firm on a periodic basis. For large firms that are widely followed by many analysts, there may be many sources of information. It is reasonable to suppose that ‘equivalent sample information’ is an increasing function of time but that the amount of information per unit time differs across firms. To the extent that the number of observations is related to the length of time for which a security has been listed, our model of relative estimation risk would predict a ‘period of listing’ effect. ’ To the extent that quantity of available information varies between small firms and large firms, it would also predict an apparent ‘small firm’ effect.
3. Differential information and abnormal returns: The empirical evidence In this section we attempt to measure size and differential information effects on the basis of returns realized on a monthly basis for NYSE traded securities for the period 1931 to 1980. We describe the data and empirical procedures used to this end and present the empirical results. We control for systematic risk and find a significant period of listing effect. This effect persists after controlling for size and for the so-called ‘January effect’.
3.1. Data The data used in our study comprises the set of all securities traded on the New York Stock Exchange (NYSE) from December 1926 to December 1980, which are listed on that exchange for a period of at least 61 months and which have at least 21 months of data on the CRSP monthly returns file.’ On leaving ‘Fisher (1959) was, to our knowledge, the first to examine such a hypothesis. He argued that information available about corporate bonds could be measured by period of listing (since last default), and that such a measure of risk is in fact priced in the bond markets. It is interesting to note that his proxy for ‘marketability’ can be interpreted as a proxy for a capitalization variable. ‘Since the securities we study were listed on the NYSE for at least 61 months and rates of return by size, period of listing, and beta categories were not computed for the first 60 months of listing, the results we report cannot be ascribed to the new issue seasoning process [cf. Ibbotson and JalTe (1975)]. At least 20 months of prior data was required in order to estimate beta.
C. B. Barry and S. J. Brown, Differential information and the smallfirm effect
287
the exchange, the security’s return is based on the price at which the security subsequently trades on another exchange. If no such trade is reported, the security is assumed to have a return of minus one.3 We use the CRSP value weighted index as an index of market returns.4 For each month the securities are cross-classified by size (total market value of equity outstanding in the previous month), number of months since the security was first listed on the NYSE,’ and beta estimated on the basis of the previous 60 months using OLS procedures. Size is organized into 6 quantiles, the smallest 6th of all securities going into group 1, the next 6th going into group 2, and so forth. Period of listing is independently organized into 6 groups. Period of listing group 1 corresponds to those securities listed for the least amount of time, and the 6th group corresponds to those securities listed for the longest period. Beta is also classified independently into 6 quantiles, with the smallest betas assigned to the first group and the largest to group 6.6 Each security is assigned to one of the 6 x 6 x 6 cells according to its size, listing and beta classification. Return measures by size, listing and beta are then constructed by equally weighting returns for securities within each of the 216 cells. Cell membership is recomputed each period based on the previous month’s size, period of listing and beta. Thus, 216 time series of returns are obtained due to size, period of listing and beta dating from January 1931 through December 1980. ‘The purpose of this assumption was to eliminate a potential ‘survivorship bias’ that would be present if we had left out securities on the month they were delisted. This assumption might appear to underestimate returns in the month of delisting, since securities may leave the exchange by merger and acquisition as well as by bankruptcy. Excluding securities in the month they were delisted increased returns due to size and listing. As expected the size effect was more pronounced excluding such securities; however, the magnitude and significance of the listing effect were little affected by this change. 4The value weight index was used to maintain comparability of our results with those of Banz (1981) and Reinganum (1981, 1982). Brown and Warner (1980) indicate some of the problems involved in using such an index in abnormal performance studies; for this reason we also studied the effect of using an equally weighted index [cf. Brown, Kleidon and Marsh (1982)]. In results not reported here, we found that while absolute magnitudes were affected, relative magnitudes were unaffected by the choice of weights, ‘The months of listing were determined from the month of first listing on the CRSP tape or, in the case of 459 securities in our sample trading in 1926, the month in which the security was first accepted by the Committee on the List of the New York Stock Exchange. That date was determined from the first listing statement on record in the archives of the NYSE. This is not entirely satisfactory, since the listing statements were preserved only back as far as June 1884. In 9 of 459 cases, the preferred stock was listed prior to capital or common stock issues, Since it was not obvious that there was not a prior capital stock issue listed on the exchange, the date of the preferred issue was taken as the ‘first listing’. 6We further cross-classified the securities by the extent of trading measured by the proportion of the period of listing for which trade data was used to construct rates of return. Results showed that the period of listing and size effects described later in this paper were strongest for the most frequently traded securities.
288
C. B. Bar?
and S. J. Brown,
D#erential
information
and the
smallfirm
effect
3.2. Results Table 1 reports average percentage monthly returns measured within size and period of listing groups. The size effect is very clear in these results,’ but the returns are not risk-adjusted. 8 There appears to be a moderate period of listing effect as well, and risk is relatively constant across periods of listing. Note that the size effect appears to be most pronounced among securities in the lowest period of listing group. Similarly, the period of listing effect is most pronounced for the smallest size category and, again, would be minimally affected by risk adjustment. However, the size effect appears to dominate the listing effect in magnitude using these unadjusted average returns. Some authors argue that the size effect is comprised in large part of unusually large returns to small firms in January [Keim (1983), Roll (1983a) and Reinganum (1983)). To examine the effect of these January returns and their relation to period of listing, we replicate the analysis used to construct the first panel of table 1 excluding all January data. The results are shown in the second panel of that table. Note that in this table, the size and period of listing effects in these returns are of a similar order of magnitude. The returns are not risk-adjusted, and it is interesting to note that risk measured by estimate of beta is virtually constant across period of listing categories but varies substantially across size categories. The listing effect appears to be independent of the January anomaly. The period of listing effect in table 1 is especially noticeable among the smallest firms. Within the smallest size category, the average firm size across the 6 period of listing groups is almost constant, and in fact it declines from $10.5 million for listing category 1 to $9.5 million for listing category 6. Again, the betas are nearly constant across these 6 categories. Thus, in the most pronounced case, there appear to be substantial returns associated with firms with low periods of listing, and it does not appear that those returns can be attributed to firm size or to risk.’ The discussion of the previous section suggests one should expect positive abnormal returns for those securities listed for the least amount of time, where abnormal returns are defined relative to systematic risk estimated on the basis
‘The size effect is of an order of magnitude similar to that reported in Banz (1981, table 3). However, table 1 is not directly comparable to Banz’s table 3 since his results were risk-adjusted. ‘Across all firms in our sample average beta (measured on the basis of the prior 60 months of data) varied from 1.22 to 1.19 by listing category, as compared to 1.36 to 1.02 by size for the period 1931-1980. Controlling for size and listing, respectively, did not affect these observed ranges of variation in beta. ‘Table 1 reports average returns, and it is possible that the results are an artifact of not compounding the returns [cf. Roll (1983b)]. Geometric mean returns are of course smaller than the corresponding average returns, and the size premium measured as the difference between geometric mean returns of the smallest and largest size categories falls to 0.77% from the 1.23% apparent from table 1. However, the listing premium actually increases slightly to 0.28% from 0.24%. reflecting the fact that the variability of returns is relatively constant across listing categories.
C. B. Buy
and S. J. Brown,
Differential
tnformatton
and the small firm effect
289
Table 1 Average percentage anced monthly by 1980. and for that classifications and the average return
monthly returns on equally weighted portfolios of NYSE securities rebalsize and period of listing categories, for the period January 1931 to December period excluding the month of January. In each panel the rows give the size the columns the listing classifications: for example, row 3 and column 4 gives for a portfolio comprising for each month all securities in the third sixth of securities by size and fourth sixth of securities by listing. Period of listinga 1
2
1 2 3 4 5 6
2.36 1.51 1.30 1.06 1.16 0.79
2.14 1.55 1.29 1.02 1.00 0.84
Period of listing marginal<
1.40
1.32
Average
1.22
1.21
3
4
(a) Aiidatu
Size’
betad
5 1931-Dec.
(Jun.
2.17 1.29 1.36 1.13 1.10 0.86
6
Size marginafC
Average betad
2.08 1.39 1.26 1.11 1.07 0.85
1.36 1.29 1.23 1.20 1.12 1.02
1980)
1.67 1.30 0.99 1.23 1.18 0.96
1.95 1.25 1.27 1.14 1.16 0.85
1.98 1.19 1.21 1.11 0.89 0.81
1.38
1.27
1.22
1.16
1.21
1.19
1.20
1.19
(b) Excluding
Januq
( Feb. 1931 -Dec.
I9RO)
1 2 3 4 5 6
1.52 1.01 1.04 0.89 1.10 0.77
1.40 1.09
1.20 0.79
0.83 0.72
1.12 0.76
0.90 0.54
1.18 0.88
1.02 0.80 0.90 0.82
1.03 0.90 1.00 0.82
0.62 0.99 1.06 0.96
0.90 0.89 0.96 0.80
0.76 0.76 0.66 0.68
0.93 0.87 0.93 0.79
Period of listing marginal’
1.08
0.99
0.99
0.89
0.89
0.74
Sizeb
aPeriod of listing is defined as the number of prior months the security in question was listed on the CRSP tapes. In the case of 459 securities in oursample listed at any time in 1926, listing is defined relative to the month the security was accepted by the Committee on the List of the NYSE as recorded in the NYSE Archives. The average period of listing in categories 1 through 6 were 89.5, 146.4, 213.6, 291.2, 387.3 and 592.1 months, respectively. ‘Size was defined as the value of equity outstanding of the security in question as of the end of the previous month. The average size (in $M) for categories 1 through 6 were 9.8, 24.9, 49.9, 99.0, 221.5 and 1.197.4, respectively. ‘The size and period of listing marginals give average returns for portfolios constructed on the basis of size alone and of listing alone, respectively. Note that since the number of securities differ from cell to cell and from one period to the next, the marginals are not simple averages of the corresponding elements in the rows and columns of the table. dAverage value of OLS beta estimated on the basis of prior 60 months of data using a value weighted index.
of a regression of past returns on those of the market. In this context the result is intuitive. In common with other studies relating return to beta risk, we use a moving window of at most 60 months to estimate beta. This estimation period is constant across securities, even though at any point of time there may be more information available about some securities than about others. The result
290
C. B. Barry and S. J. Brown, DifJerential informatton and the smallJirm effect
than follows if we accept relative period of listing, perhaps controlling for size, as an adequate proxy for this information. One procedure that can be used to estimate abnormal returns is to place securities into beta decile groups for each month using an estimate of systematic risk based on data from the previous 60 months. Then abnormal returns can be calculated as the deviation of individual security returns from the mean return of the cross-section to which that security belongs [cf. Brown, Kleidon and Marsh (1982, fn. 5)]. This procedure assumes that the Capital Asset Pricing Model is correct and that the ‘true’ beta is constant within a given beta decile group. In that event, the expected return is given by Vi E I,
ER,, = (1 - P,)r,, + P,ER,,,
for security i belonging to beta decile group Z which has a true beta of R,. The risk-free rate specific to period t, qr, is observable, but the ex ante expectations of return on the individual security ER;, and market ER,,,,, and RI are not observable. However, since ER,, = ER,, for i, j E I, a measure of abnormal performance specific to security i would be given by e,t = R,, - &I,
Vi E I.
0)
If the CAPM is correct and the true beta RI is constant within the decile groups organized by the estimate of beta using data prior to t, then EE,~= 0 for all i and t. However, if the beta appropriate to the CAPM differs according to period of listing in such a way that the low information beta, fiL., is greater than the high information beta, RH, for given estimate R, we should expect that the difference eL, - .sHrwould be positive within the beta decile group. Average excess returns computed in this way and standardized using the standard deviation computed on the basis of the prior 60 months of data” are “The
average
excess return
for category
I in period
/ is measured
6, = c L/n,,, 1El where E,, is the excess return for security i computed as in eq. (1) and n,, is the number securities in category I. Then the standardized excess returns for category I is defined as
-L/L@ where
SI = ?
S,, = E,,/(
of
r,,/&),
1=l
with S,, being the standardized I, sf[, is estimated from
excess return
for category
I in period
1. The variance
for category
I-1 3,
= ,=;,1
(J;;JIE,,
-fiSJ2/59,
where the ,& term captures the variability that results from the change in the number of securities from period to period. This procedure accounts for potential dependence in the cross-section of excess returns within each size and listing category. The properties for such dependence adjustment are discussed in Brown and Warner (1980).
C. B. Bary
and S. J. Brown,
Differential
information
and the smaNjirm
effect
291
Table 2 Standardized
excess returnsa
by size and period of listing categories to December 1980.
for all months
Period of listing 1
2
3
4
5
6
1 2 3 4 5 6
- 2.60 1.71 -0.26 - 0.82 0.55 - 1.83
2.03 1.99 0.28 - 1.44 -1.42 - 2.25
2.19 0.42 1.18 - 1.03 -0.18 - 2.37
0.52 - 0.64 - 3.13 - 0.45 0.53 -1.55
0.94 - 0.71 -0.56 -1.11 0.21 -2.81
0.68 - 0.84 - 0.26 -0.90 - 2.36 - 2.85
Period of listing marginal
2.20
1.21
1.76
-1.24
- 1.79
-1.70
Size
January
1931
Size marginal 1.97 0.84 - 1.51 - 1.51 -0.36 - 2.68
aThe standardized excess return for category I represents a t-value given by CT= ,S,,/fi, where T= 600. The standardized excess return for category I in period I, S,,, is defined in footnote 10 of the paper, and represents the average excess return for I in t standardized by the standard deviation of excess returns estimated on the basis of 60 months of prior data, after correction for the number of securities in 1.
reported in table 2. From inspection of this table, we find that the size effect does not dominate the period of listing effect when these effects are measured in terms of standardized excess returns. As before, the period of listing effect is more pronounced among small firms than among the larger firms in our sample. The results in the smallest size category are particularly worthy of note. Those small firms listed for the longest periods do not produce statistically significant excess returns. This result suggests there may be an interaction between period of listing and firm size. To explore in some greater detail the interaction between the small firm effect and listing effects we see in the data, consider table 3 which reports the results of using a Fama and MacBeth (1973) procedure to evaluate size and listing premia, allowing for interactions between these effects.” Considering the size effect by itself we find that there is a significant size effect in the overall period, but this effect is apparently insignificant for the post-war period, consistent with the findings of Banz (1981) among others. Considering the “The numbers reported in table 3 represent time series means of OLS estimates based on the cross-section of 216 returns in each month. This procedure assumes the residuals are independent in the cross-section. To examine how sensitive the results might have been to the independence assumption, a GLS procedure was used. First, a 6-factor representation of the 215 x 215 covariante matrix was estimated on the basis of the cross-section of residuals. One of the 216 cells (the last) had to be dropped to factor the estimated covariance matrix (which would otherwise be singular). Then the coefficients reported in table 3 were recomputed using the GLS procedure. The means of the GLS estimates were nearly identical to those reported in table 3, and the significance of nearly ah of the coefficients was higher than reported for the OLS results, The t-value of the period of listing coefficient increased in magnitude from - 2.48 to - 3.99 for the overall period. In the post-war period, the t-value of the period of listing coefficient was unaffected by the use of the OLS procedure, remaining at approximately - 3.06.
292
C.
B. Barry and S. J. Brown,
Deferential
information
and the
smallfirm
effect
results excluding January, the size effect is, or appears to be, largely confined to the January months of the sample. This result is consistent with the findings of Keim (1983). Controlling for size, beta and the interactions between the variables, there is a listing effect, and this effect persists in the post-war period as well as when the month of January is excluded from the data. However, this effect is strongest for the smallest firms in the sample [the (size x listing) premium is positive, offsetting the listing effect], and this interaction effect is statistically significant in the post-war period, regardless of whether we exclude the month of January from the sample. At first inspection these results appear puzzling. Table 1 demonstrates a substantial size effect, and table 2 shows that this effect persists even controlling for beta. Yet one might conclude from table 3 that the size effect is small. Further examination reveals the source of this apparent contradiction. The first two tables present strong evidence of the interaction between the effects of size Table 3 Cross-section regression of monthly returns against size, period of listing and beta, and interactions between these variables. Mean and t-value of mean (reported in parentheses) are computed on the basis of the time series of regression coefficients for the period January 1936 to December 1980 and the post-war period January 1946 to December 1980 for all months as well as for all months excluding the month of January.a
Intercept Jan. 1936-Dec. 1980
Feb. 1936-Dec. 1980 (excluding Jan.)
0.0195 (3.74)
- 0.0009 (- 2.31)
0.0012 (0.16)
(0.63)
0.0017 (0.41)
0.0004 (1.31)
- 0.0070 (-1.01) Jan. 1946-Dec. 1980
0.0133 (2.54) - 0.0004
( - 0.77) Feb. 1946-Dec. 1980 (excluding Jan.)
Size
0.0004
Period of listing
Beta
Size x period of listing
Period of listing .T beta
- 0.0085 0.0124 (- 2.48) (2.36)
- 0.0003
t - 0.86)
0.0004
- 0.0008
(- 1.98)
(1.46)
0.0092 (1.51)
- o.OOQ2 - 0.41)
0.0026 (0.29)
-O.OC@O - 0.0107 - 0.0013 (-2.96) (-0.24) - 0.02)
0.14 0.10
-O.OOQO ( - 0.01)
0.0004 (1.62)
0.0021 (2.21)
0.13 0.10
0.0001 (0.10)
0.0009 - 0.0083 0.0104 (- 3.04) (2.12) (2.13)
=yo+yl~,,+~~l,,+~~B~,+y~~~,,~,,~+~s~~,,Pk~~+~6~l,,Pk,)+t,,k,.
0.0025 (2.75)
O.CKJO4 (0.25)
0.0009 - 0.0089 0.0027 (1.54) (- 2.59) (0.51)
R2
0.11
0.0011 (0.68)
- 0.0009 (-1.94)
0.0005 (2.31)
0.0014 (1.88)
0.13 0.10
0.0005 (0.26) 0.0007 (2.23)
0.0004 (0.83)
aThe columns in the table give the mean coefficient estifnates ?a, $,,. R
Size .x beta
0.0015 (1.37)
0.14
, ye from the regression
i.j.k=1,....6.
the size. list-
i$kd beta categories for month t - 1, R ,,k, represents the return on the portfolio comprising the ith size, jth listing and k th beta category of securities in month t, s,, represents the logarithm of average size in category i for month t, /,, a measure of relative period of listing given as the logarithm of the ratio of period of listing for group j to that for group 6, and PI, is the average beta for category k, estimated using 60 months of prior data.
C. B. Barv
and S. J. Brown, Differenriul
information
and rhe smallfirm
effect
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and listing. In fact, this interaction effect is far more significant than the size effect per se. Though not evident in those tables, there is also a strong interaction between the effects of size and beta. It is only after controlling for these interactions that there is a listing effect stable across subintervals of the data, with no independent size effect.‘* In section 2, we argued that relative period of listing should appear in an equilibrium pricing model as a measure of the non-diversifiable risk induced by differential information. However, relative period of listing is not altogether satisfactory as a proxy for differential information because the amount of information per unit time might vary with the size of the firm. This firm size might capture an element of differential information not captured by period of listing. The results in table 3 are consistent with this hypothesis. 4. Summary and conclusion In this paper we examine a model of market equilibrium with differential information. We show that period of listing, a crude measure of differential information, is associated with the well-known firm size anomaly. However, this information argument does by no means fully explain the firm size anomaly, and it is an open question as to whether a more satisfactory measure of information would more completely explain the observed size effect. It is interesting to note that at least one popular explanation of the small firm effect, an explanation in terms of a turn-of-the-year phenomenon, does not in any way diminish the period of listing effect we see in the data. The significance of our results suggests that it might be profitable to pursue other proxies for the quantity of information. The advantage of period of listing as a proxy for quantity of information is its simplicity and the fact that such a measure is robust to the specific information model under investigation. Atiase (1982) and Freeman (1982) analyze the magnitude of the earnings announcement effect as a function of firm size and find that the monotonic relationship can best be explained as an information effect that might explain at least part of the small firm effect. Figlewski (1981) and others have examined the extent of analyst agreement as a measure of relative information, and Barry and Brown (1983) demonstrate that analyst agreement and information availability are closely associated. These alternative characterizations of information appear to be worthy of examination.
“Caution should be exercised in drawing too literal a comparison between table 3 and the previous two tables. Table 3, which presents a summary of cross-section results, is not strictly comparable to the previous tables which present means of time series data, since the number of securities in each category varies considerably through time. The table 3 results were not sensitive to the use of the Fama and MacBeth (1973) procedure: results were even stronger using a stacked regression procedure implemented on the basis of successive 5-year mean returns, suggesting that the results cannot solely be attributed to month-by-month variations in the number of securities in each classification.
294
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Barty and S. J. Brown,
DQjerenrial
information
and the
smallfirm
effect
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