Journal
of Banking
and Finance
North-Holland zyxwvutsrqponmlkjihgfedcbaZYXWVU
13 (1989) 675-696.
STOCK MARKET
A Re-assessment
ANOMALIES
Based on the UK Evidence
Mario LEVIS*
University
Received
September
of Bath, Bath BA2 7AY, UK
1988, final version
received June 1989
This paper reports evidence documenting
the presence of a number of irregularities
in stock
price behaviour of firms on the London Stock Exchange. The size effect is not only not the sole
anomaly but is not even the most dominant
one. Specifically, investment
strategies based on
dividend yield, PE ratios and share prices appear as profitable,
if not more, as a strategy
concentrating
on firm size. Although there is a large degree of interdependency
between all four
effects, it is still apparent that the dividend yield and PE ratios subsume the size and share price
effects.
1. Introduction
The volume of empirical evidence that followed Banz’s (1981) and
Reinganum’s (1981) seminal papers has firmly established the existence of a
market size anomaly in stock price behaviour. In the process of searching for
explanations for this phenomenon a number of other ‘irregularities’ have
surfaced. The discovery of the January effect, for example, provided further
valuable insight into the size anomaly but in effect added to rather than
resolved the puzzle. Furthermore, it seems that investment strategies based
on earnings or dividend yields have earned, over sufficiently long time
periods, positive and significant abnormal returns. The presence of such
anomalies is not confined to the U.S. market alone.’ Evidence of the size
effect for other markets has been less forthcoming, but the results of Brown,
Kleidon and Marsh (1983) for the Australian market, Berges, McConnell and
Schlarbaum (1984) for Canada, Nakamura and Tarada (1984) for the Tokyo
Stock Exchange and Levis (1985) for the London Stock Exchange (LSE)
point to a similar size anomaly in these markets as well. With regard to the
*An earlier version of this paper was presented at the NATO Advanced Research Workshop
at Sesimbra, Portugal
in April 1988. I gratefully acknowledge
the comments
of the workshop
participants.
‘See for example Gultekin and Gultekin (1983).
0378-4266/89/$3.50
0
1989, Elsevier Science Publishers
B.V. (North-Holland)
676
M. Levis, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONM
Stock market anomalies
dividend and earnings yield effects the evidence for other than the U.S.
market is still scarce.
The main question surrounding these findings is whether such additional
anomalies are independent of or related to market size. The evidence on this
issue is rather controversial. While Reinganum (1981) and Banz and Breen
(1986) argue that the size effect subsumes the PE effect, Basu (1983) asserts
quite the opposite - i.e. size related anomalies disappear when one controls
for the PE effect. Cook and Rozeff’s (1984) investigation of this discrepancy
added to the controversy by concluding that both views are misguided; their
work suggests that ‘both effects (at least) are at work’ (p. 464). In a more
recent paper Jaffe, Keim and Westerfield (1988) reached similar conclusions.
Peavy and Goodman (1983) introduced an additional dimension to the
analysis; they argue that the PE effect may in fact be an industry effect, since
firms in the same industry tend to have similar PE multiples. When,
however, a direct comparison between PE and firm size is undertaken,
Goodman, Peavy and Cox (1986) conclude that size usually serves as a
proxy for the PE effect.
The relation between dividend yields and stock returns has also received
close scrutiny in the academic literature. For example, the studies of
Litzenberger and Ramaswamy (1979), Blume (1980), Gordon and Bradford
(1980), Miller and Scholes (1982) and Elton, Gruber and Rentzler (1983)
point to a positive and significant relation between dividend yield and
returns but disagree about the underlying sources of this relation; while some
attribute it to the disparity in the tax rates for divided yields and capital
gains, others maintain that yield related effects are due to information bias.
Keim’s (1985) evidence provides an alternative view; it indicates a strong
interaction between dividend yield and firm size which suggests that the
positive dividend yield-return relation is a direct result of the concentration
of smaller firms in certain high dividend yield categories.
As the common factor between the three variables - market size, PE
multiples and dividend yields - is the share price, it is not inconceivable that
these three effects may be attributed to some underlying relationship between
share price and stock returns. The evidence of Blume and Husic (1973), Stoll
and Whaley (1983) and Blume and Stambaugh (1983) points to a negative
relation between share prices and stock returns.
It appears that one of the main sources of the continuing controversy
regarding the relative importance of the four documented anomalies is the
fact that they have been investigated separately using different data sets and
various methodologies. This paper provides a systematic examination of the
stock price behaviour of firms on the LSE in search for evidence regarding
the presence and possible interrelations of the market size, dividend yield, PE
multiple and share price effects. Such an analysis is crucial not only because
it provides for the first time a comprehensive evaluation of all four anomalies
M. Levis, Stock market anomalies
611
using a unique set of data under a uniform methodology, but also because it
offers the opportunity to contrast the U.S. stock price behaviour irregularities with that of one of the largest capital markets. If indeed it emerges that
such phenomena are ‘market specific’, it would imply that application of
conclusions drawn from one market to the other is unwarranted and even
misleading. Nevertheless, the implications in terms of investment strategy and
academic research have been already universally adopted.2
Section 2 describes the data and methodology used in this study. Section 3
examines the properties of the portfolios generated under the four ranking
procedures, while sections 4 and 5 provide a detailed analysis of the four
anomalies under investigation and their potential interactions respectively.
Finally, the main conclusions of this study and its implications are outlined
in section 6.
2. The data and methodology zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLK
A. Data and portfolio formation procedures
The data used in this study are from the London Share Price Database
(LSPD) monthly returns tile and source tile. The latter provides the data
required to estimate market value, PE multiples, dividend yields and share
prices, while the former contains monthly rates of return, inclusive of
dividends and capital gains. Market value of the firm is defined as the
market price at the calendar year-end T (T= 1955,1956,. . . ,1983), times the
number of shares outstanding. The dividend yield is measured by the ratio of
the dividends paid during the twelve months period of a calendar year to the
market price of common stock at the end of this year. Earnings per share are
estimated as the twelve months earnings divided by the number of shares
outstanding at the calendar year-end; this estimate over the share price at the
end of the same year determines the PE ratio.3
In the first instance, a single classificatory procedure is used to construct
portfolios for each of the four attributes under investigation. At the end of
each calendar year T firms are ranked separately in ascending order
according to market value, dividend yield, PE ratio and share price. Portfolio
returns are then computed for the 12-month period commencing the
following April, by combining returns of individual firms using equal
‘Dimson and Marsh (1986), for example, have made a strong case for the small size effect to
be incorporated
into the estimation of abnormal returns in event studies.
3This is the definition used by Reinganum (1981), Basu (1983) and Cook and Rozeff (1984). In
case of firms with a calendar fiscal year-end this definition of dividend yield and PE ratio may
incorporate
a look-ahead
bias. [See Banz and Breen (1986) and following note.] Ball’s (1978)
evidence, however, indicates that the likely effects of experimental
bias are not sufficient to
explain the magnitude
of the PE anomaly.
678
M. Levis, Stock market anomalies
weights4 The ranking and portfolio formation procedures for each of the
four attributes were repeated 29 times to cover the period April 1956 to
March 1985. To qualify for inclusion in a given calendar year, a firm need
only possess data for the particular ranking procedure at the end of this year
and a valid rate of return for April of the following year. Every year firms
enter or leave the sample due to merger or bankruptcies. Thus, no survival
bias requirements are imposed on the sample. Given the ambivalent interpretation of negative earnings and following the practice of previous studies, a
firm was dropped from the sample in any year in which it had negative
earnings. A preliminary analysis of the data indicated substantial differences
in data availability when earnings-per-share (eps) were considered. While, for
example, the ranking procedures for market value, dividend yield and share
price resulted in very similar sample sizes, ranging from 1,150 firms in the
beginning of the 70’s to 2,300 in mid-70’s, the PE procedure resulted in a
sample ranging from 770 to 1,920 firms. ’ The differences in the sample size
would be unimportant for the purposes of this study if the missing eps data
were occurring randomly across the quintiles of the four attributes. Since this
was not the case, a direct comparison of the various effects utilising different
sample sizes would be misleading; on the other hand, the adoption of a
unified sample which could satisfy all four criteria in terms of data
availability would result in an even greater reduction of the data set with
undesirable consequences. Thus, the whole analysis is repeated using two
data sets. The full sample is utilised when the market size, dividend yield and
share price (or any combination of them) are used as the ranking procedures.
On the other hand, where the PE ratio is involved, on its own or in
combination with any of the other attributes, a reduced sample is used. Both
sets of results are presented when comparisons among ranking procedures
are in order. A simple MVl notation is used to identify the smaller size
portfolio, based on the full sample, while MVl! denotes the same portfolio
based on the reduced sample.
To control for the interaction effects between the four attributes, combined
portfolios are constructed. Both within-groups only and within-groups plus
‘Starting
the calculation
of portfolio returns in the following April minimises the potential
bias of accumulating
returns over a three-month
period, at the beginning of each year, when the
dividends and earnings assumed known in the dividend yield and PE calculations
are in fact
unknown.
This is the method used by Basu (1983) and Cook and Rozeff (1984). To test,
however, for the extent of this bias the whole analysis was repeated for portfolios running from
January instead of April.
‘For the period January
1956 to December
1974 the sample of companies
on the LSPD
returns file IS somewhat biased towards larger firms. From January
1975 onwards the database
has been extended to cover all listed shares on the London
Stock Exchange
[see Smithers
(1986)]. Thus, the small firm effect reported in this study may be understated
during the former
period. On the other hand, it is worth noting that the increase in the size of the sample on
January
1975 did not result to any significant
change in the monthly rates of return of the
various market size portfolios.
M. Levis, Stock market anomalies
619
randomisation methods are used. According to the former, all firms in either
the full or reduced sample were ranked first by a chosen criterion and
quintiles are formed. Then within each quintile firms are reranked on a
second variable and quintiles are formed within each of the original quintiles;
twenty-five portfolios are formed for each combination of two attributes. The
process was repeated 25 times to generate portfolios within each of the four
characteristics used in this study as a primary variable and the remaining
three as secondary grouping; to cover all possible combinations of attributes
300 (5 x 5 x 3 x 4) portfolios were generated. Within groups portfolios were
created by ranking, for example, first on size and next on dividend yield, PE,
and share price. The within-groups method has been used by Basu (1983),
Banz (1981) and tested by Cook and Rozeff (1984).
The within-groups plus randomisation method was also used by Basu
(1983) and Cook and Rozeff (1984). The randomisation method follows from
the within-groups method described above; the 25 portfolios generated for
each combination of pairs are combined to form the randomised portfolios.
Market size portfolios, for example, are constructed by randomising separately with respect to dividend yield, PE multiple and share price. The
MVl *DV portfolio, for example, includes securities of the first market size
quintile but is drawn from the entire set of dividend yield classes; thus it can
be viewed as being randomised with respect to dividend yield. In a similar
manner, portfolio zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFE
DVl * MV contains firms of the lowest dividend yield but
includes firms from all market size classes, i.e. randomised with respect to
firm size. To cover all pairs of combinations of the four ranking procedures
used in this study, 12 randomisation procedures were required, resulting in
sixty randomised portfolios.‘j
B. Risk adjustment
issues
Abnormal returns (u,,) are estimated by subtracting from the actual
portfolio return (R,,) the returns predicted by the model used, given the
market return (R,,), the risk free rate (Rft) and the parameter estimates (b,).
Two main models were employed in this study:
upt= (R,, - Rft) -Km - R,J
(1)
up,= (R,, - RJ,)- WLt - RI,).
(2)
Model (1) can be regarded as a limiting case of model (2), the simple CAPM
framework, whereby all betas are assumed to be unity and the abnormal
return is estimated by subtracting the market from the portfolio return.
6All within-groups
only and within-groups
plus randomisation
portfolios that include the PE
ratio either as a primary or secondary
ranking variable are based on the reduced sample. All
other portfolios utilise the full set of data available.
M. Levis, Stock market anomalies
680 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
Model (2) involves a two-stage estimation procedure. The first stage consists
of the estimation of the respective beta coefficients. A sixty month base
period is used for this purpose; the first base period is April 1956 to March
1961. In the second stage the base period beta estimates are used to obtain
abnormal returns for a subsequent holdout period. Holdout periods run for
twelve months at a time beginning in April following the base year (April
1961 in the first instance) and running through March of the following year.
Betas are updated annually by rolling over the base period twelve months at
a time. Thus, the last base period is April 1979 to March 1984, while the last
holdout period is April 1984 to March 1985. The total number of months in
the holdout period is 288.
Marsh (1979) concluded that the results are remarkably robust to the
precise variant of the single factor Market Model and to the estimates of
beta. They are, however, very sensitive to the choice of portfolio weighting
scheme, so that quite different abnormal returns were obtained when equally
rather than market value weighted indices were employed. Accordingly,
abnormal returns in this study are estimated using a specially constructed
equally weighted index consisting of all securities on the London Stock
Exchange. Furthermore, given the well-documented problems of thin trading
evident with U.K. data, abnormal returns based on model (2) but using the
Dimson (1979) Aggregated Coefficients (AC) method for beta estimates were
also estimated for all portfolios. Thus, model (2) takes the form:
upr=(Rpt-Rf,)-
;
bpdRm,t+k-Rf,t+k)- zyxwvutsrqponmlkjihgfedcbaZYX
(3)
k=- 1
Following Dimson, aggregated beta coefficients
lagged and one leading market variable.7
are estimated
using five
3. The properties of the four portfolio ranking procedures
A. Rates of return
Table 1 shows the monthly average raw rates of return for the quintiles
generated by each of the four single ranking procedures over the period April
1961 to March 1985. Each panel also shows the standard deviation of the
portfolio (column 2), the mean return per unit of standard deviation (column
4) and the difference between this amount and the corresponding values for
the FTA value weighted and an equally weighted index, are shown in
columns 5 and 6 respectively. These results are directly comparable with the
evidence reported in U.S. studies.
‘Experimentation with a different lag structure indicated that AC beta estimates are robust
around the number of lagging and leading variables adopted in this study.
M. Levis, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONM
Stock market anomalies
681
Table 1
Monthly rates of return and other summary statistics for the full and reduced sample in the
period April 1961 to March 198.5.”
Mean
(1)
(3)-FTA
(4)
(3)-Equal
(5)
Part 1: Full sample
A. Market value
MVl
MV2
MV3
MV4
MV5
1.32
1.19
1.00
0.94
0.90
3.85
4.60
5.26
5.76
6.32
0.343
0.259
0.190
0.163
0.142
0.174
0.090
0.021
-0.006
- 0.027
0.127
0.043
- 0.026
- 0.053
-0.074
B. Dividend yield
DVl
DV2
DV3
DV4
DV5
0.74
0.80
1.03
1.20
1.57
5.22
5.30
5.16
4.90
4.59
0.142
0.151
0.200
0.245
0.342
- 0.027
-0.018
0.031
0.076
0.173
- 0.074
- 0.065
-0.016
0.029
0.126
C. Share price
PRl
PR2
PR3
PR4
PR5
1.33
1.20
1.01
0.93
0.91
4.67
4.96
5.23
5.26
5.14
0.285
0.242
0.193
0.177
0.177
0.116
0.073
0.024
0.008
0.008
0.069
0.026
-0.023
-0.039
-0.039
MVl!
MV2!
MV3!
MV4!
MV5!
1.51
1.16
1.05
0.98
0.87
3.72
4.47
5.30
5.94
6.32
0.406
0.259
0.198
0.165
0.138
0.237
0.090
0.029
-0.004
0.190
0.043
-0.018
-0.051
-0.078
E. Dividend y ield
DVl!
DV2!
DV3!
DV4!
DV5!
0.77
0.91
1.08
1.23
1.55
5.51
5.29
5.05
4.84
4.54
0.140
0.172
0.214
0.254
0.341
- 0.029
0.003
0.045
0.085
0.172
-0.076
-0.044
- 0.002
0.038
0.125
1.47
1.20
1.00
0.95
0.92
4.58
5.06
5.13
5.30
5.20
0.321
0.237
0.195
0.179
0.177
0.152
0.068
0.026
0.010
0.008
0.105
0.021
-0.021
- 0.037
- 0.039
1.48
1.19
1.05
0.95
0.90
4.75
5.01
5.03
5.14
5.24
0.311
0.237
0.209
0.185
0.172
0.142
0.068
0.040
0.016
0.003
0.095
0.021
-0.007
-0.031
-0.044
1.04
1.05
6.14
4.87
0.169
0.216
Part 2: Reduced sample
D. Market value
F. Share price
PRl!
PR2!
PR3!
PR4!
PR5!
G. PE ratio
PEl!
PE2!
PE3!
PE4!
PE5!
H. M arket
indices
FTA value weighted
Equally weighted
“Period April 1961 to March 1985, 288 observations.
682 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
M. Levis, Stock market anomalies
A survey of the results in part 1 of the table, the full sample, indicates that
consistent with other markets, a firm size effect is also evident in the U.K.
data. A direct comparison of the relative magnitude of the size effect across
other capital markets is difficult because of differing time periods and
research design. However, the bulk of the U.S. evidence points to the
presence of a higher size premium than the 5.1 per cent per annum (0.42 per
cent per month) observed for the LSE.8 The U.K. size effect is also markedly
lower than the premium reported by Brown, Kleidon and Marsh (1983) for
the Australian market, Berges, McConnell and Schlarbaum (1984) for
Canada (about 9 per cent per annum) and Nakamura and Tarada (1984) for
the Tokyo Stock Exchange (10.7 per cent per annum). Panel B of the same
table confirms the existence of a positive relation between dividend yield and
returns. The difference between the two extreme yield portfolios is equal to
10.0 per cent per annum, a premium higher than that reported by Keim
(1983) for NYSE firms. The share price ranking procedure in panel C
exhibits a pattern of raw average monthly returns remarkably similar to the
one found for market size. Estimates of the PE effect are shown in part 2 of
the table. For comparative purposes, equivalent estimates for the other three
ranking procedures, based on the reduced sample, are presented as well.
First, it is worth noting the differences due to the sample size on the
portfolio returns reviewed in part 1 of the table. The exclusion of firms with
negative earnings, in conjunction with the missing data, resulted in an
increase of the monthly returns of the first quintile across all three ranking
procedures. Thus, based on the reduced sample, the market size effect reaches
a level of 7.7 per cent per anum over the period April 1961 to March 1985, a
premium comparable to the 9.5 per cent premium reported by Basu (1983)
for NYSE firms. Panel G documents a negative relation between the PE
ratio and rates of return. The average PE effect of 7.0 per cent per annum is
similar to the effect reported by Basu (1977, 1983) and Reinganum (1981). In
short, the monthly average returns of the portfolios based on the four
ranking procedures indicate that during the period April 1961 to March
1985, an investment strategy based on dividend yields would have outperformed a PE ratio strategy by 2.40 per cent per annum and a market size
and a share price strategy by 1.68 and 2.76 per cent per annum respectively.g
‘A decile instead of a quintile classification
augment the size premium markedly. The average
monthly return for the smaller size decile is equal to 1.63 per cent per month producing
a size
premium of 8.6 per cent per annum. Thus in contrast to the U.S. evidence does not appear to be
a linear relationship
between market size and stock returns across all size portfolios.
9A comparison
of these estimates with the equivalent results based on the alternative portfolio
construction
procedures
mentioned in note 3, instantly reveals that the look-ahead
bias problem
is relevant to the U.K. data as well. While the rates of return for market size and share price
portfolios
remain essentially
unchanged
the dividend
yield and PE effects could be biased
upwards by as much as 2.8 per cent per annum over the period under consideration.
M. Lxois, Stock market anomalies
683
Even more interesting, however, are the results shown in column 3 of this
table regarding the variability of the portfolios of the various ranking
procedures. While the total risk of the five dividend yield, PE and share price
portfolios are almost identical, the market size portfolios are strikingly
different both to modern portfolio theory and intuition i.e. the higher returns
of the smaller portfolios appear to be associated with lower levels of total
risk. As a consequence, the mean return per unit of variability of the smaller
market size quintile is more than twice the size of its largest counterpart,
while the U.K. scaled size premium is 1.8 times higher than its U.S.
equivalent. There is little doubt that the low variability of stock returns of
the smaller firms’ portfolios is at least partially, attributable to infrequent
trading. lo The returns per unit of variability for the PE portfolios exhibit a
similar pattern to those found for U.S. data but are consistently about 50 per
cent higher than the estimates reported by Basu (1983). Similar conclusions
are drawn by comparing the abnormal returns (in terms of total risk) earned
by the smallest size portfolio (MVl) for both the equally and value-weighted
market indices. It is also interesting to note that while the market value
(MV) and share price (PR) portfolios earn similar rates of return, hinting at
the possibility of one acting as a proxy for the other, their respective
variances are markedly different; in fact, the standard deviation estimates for
all five share price portfolios are essentially the same. On this evidence alone
it would appear that market size and share price are not perfectly substitutable ranking procedures. This issue is further explored in the following
sections.
B. Autocorrelation and beta coefficients
The first five autocorrelations coefficients for each of the portfolios of the
four different ranking procedures, the OLS as well as the AC beta estimates
are given in table 2. A significant feature relative to the statistics of U.S.
monthly returns is the high-first-order serial correlation ranging from 0.16 to
0.43 for the market value ranking procedure and the significantly higher
order correlations observed for the two smaller portfolios. It is also
important to note the invariably significant first order serial correlations
observed for each of the portfolios by all four ranking procedures. This
discrepancy with the U.S. data is consistent with the view that the problem
of thin trading is more severe in the British market than in the U.S. In spite
of the strong indication of the existence of thin trading the OLS beta
estimates are rather surprising: the beta coefficients range from 0.7 for
smaller size portfolio to 1.21 for MV5; furthermore, the beta estimates for all
“Roll (1981) has shown that infrequent trading causes both covariance and variance terms to
be downwards
biased, while Dimson and Marsh (1983) reported a correlation
coefficient of 0.81
between trading frequency and market capitalisation
for the London Stock Exchange.
684 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
M. Levis, Stock market anomalies
Table 2
OLS, aggregated beta coefficients and autocorrelations
Betas
OLS
A. M arket
MVl
MV2
MV3
MV4
MV5
B.
rl
0.96
1.02
1.07
1.04
0.92
0.43
0.34
0.29
0.27
0.16
1.01
1.06
1.03
1.01
0.95
1.06
0.98
0.98
1.01
0.99
0.98
1.03
1.04
0.99
1.04
r2
r3
r4
r5
0.25
0.14
0.07
0.03
-0.07
0.24
0.19
0.13
0.09
0.11
0.09
0.01
0.00
0.00
0.00
0.08
- 0.07
-0.10
-0.15
-0.15
0.31
0.26
0.27
0.30
0.30
0.09
-0.01
-0.03
0.07
0.09
0.12
0.15
0.13
0.12
0.17
0.01
0.00
0.01
0.00
-0.01
- 0.05
-0.13
-0.12
- 0.09
-0.11
1.04
1.00
0.99
0.99
0.94
0.30
0.29
0.27
0.28
0.26
0.11
0.05
0.03
0.04
- 0.02
0.13
0.13
0.15
0.15
0.09
- 0.02
-0.12
0.03
0.04
0.02
-0.10
-0.12
-0.11
-0.13
-0.13
1.04
1.02
1.02
1.00
0.94
0.31
0.28
0.28
0.28
0.28
0.16
0.07
0.05
0.02
0.09
0.16
0.15
0.14
0.14
0.12
-0.02
-0.01
0.00
0.02
0.01
-0.07
-0.09
-0.12
-0.11
-0.11
0.13
0.29
-0.09
0.06
0.13
0.14
-0.04
0.00
-0.14
-0.09
value
0.70
0.92
1.06
1.15
1.21
PE ratio
PEl
PE2
PE3
PE4
PE5
D.
Autocorrelations
AC
Dividend y ield
DVl
DV2
DV3
DV4
DV5
C.
of rates of return.a
Share price
PRl
PR2
PR3
PR4
PR5
0.94
1.02
1.05
1.06
0.99
FTA value weighted index
Equally weighted index
“OLS and AC betas are estimated using an equally weighted index. The AC beta is
estimated using five lagged and one leading market coefficient.
portfolios of the three other ranking procedures are essentially equal to
unity. It is also worth noticing that the odd disparity between beta estimates
would be markedly amplified if a value weighted index was used as the
market portfolio. When account of thin trading is taken by using the
Aggregated Coefficients method suggested by Dimson (1979), using five
lagged and one leading market coefficient, the smaller firms still do not
emerge as riskier than their larger counterparts. In fact, our results indicate
that all AC beta estimates are not different from unity. This evidence is
obviously in sharp contrast with the U.S. findings but not entirely surprising
for the U.K. framework. Although no formal tests of the risk-return
relationship have been carried out on U.K. data, there is considerable
scattered evidence in a number of studies hinting at some marked deviations
from the CAPM framework. Dimson’s (1979) tables 7 and 8, for example,
show that even when betas are adjusted by the AC method for thin trading,
M. Levis, Stock market anomalies
685
smaller firms appear to be associated with lower betas; the betas of the 20
per cent lowest beta estimates do not exceed 0.9, even when more terms are
added to the regression. Marsh’s (1979) study of U.K. rights issues concludes
that all of the large positive abnormal returns were small companies.
Furthermore, Dimson and Marsh (1983) using the Trade-to-Trade method
for beta estimation still point to the same paradox, i.e. smaller firms have
lower betas than their larger counterparts and the riskiness of smaller firms
is not stationary over time. More recently Corhay, Hawawani and Michel
(1987) concluded that April ‘is the only month of the year during which the
relationship between average portfolios returns and systematic risk is significantly positive on the LSE’ (p. 67).
4. Risk-return relations for the four effects
Table 3 presents three different types of abnormal returns using the
estimates of models (l), (2) and (3). The results for each one of the ranking
procedures, for both the complete and reduced sample, are shown in separate
panels. Panel A, for example, shows the abnormal returns based on each of
the three risk adjustment models estimates for the five non-randomised
market size portfolios and portfolios randomised for dividend yield, share
price and PE ratio. A single notation, i.e. MV, DV, PE, and PR refers to
non-randomised portfolios; randomised portfolios are labelled with a double
code; the smallest market size portfolio, for example, randomised by dividend
yield is labelled as zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCB
MVl * DV. The second part of the code always refers to
the randomisation procedure in operation. The t-values test the hypothesis
that the individual portfolio abnormal return is equal to zero, while the
Hotelling T2-statistic and the corresponding F-values test the hypothesis that
the abnormal return vector for a particular ranking procedure, MVl to MV5
for example, is equal to zero.
Consistent with the pattern of beta estimates shown in table 2, risk
adjustment models (2) and (3) produce market size premiums markedly
higher than model (1) estimates. Thus, the market size effect not only is not
eliminated or reduced but is indeed increased when a CAPM risk adjustment
is applied. On the other hand, given the beta estimates, it is not surprising
that the abnormal returns of the dividend yield, PE and share price
portfolios are remarkably robust to the particular type of model employed
for risk adjustment purposes.
An examination of the non-randomised portfolios across the four panels
suggests the presence of significant abnormal returns for all four ranking
procedures for both the full and reduced samples. It is apparent from the Fvalues, however, that the size effect is not the most pronounced anomaly on
the LSE in comparison to the dividend yield and PE irregularities. The
dividend yield ranking procedure, for example, yields a risk-adjusted
Table 3
Excess returns, based on three models, for straight and randomised portfolios.”
Model (1) zyxwvutsrqponmlkjihgfed
Model (3)
Model (2)
TZ
T2
T2
a$)
Jv,)
up
% J)
Q,)
up
G,)
W ,)
A. Market value
MVl
0.452
MV2
0.196
MV3
- 0.084
MV4
-0.200
- 0.296
MV5
3.74
2.94
- 2.03
- 3.58
-2.34
0.11
6.21
0.330
0.163
-0.111
-0.161
-0.182
2.04
1.92
-2.50
-2.18
- 1.08
0.07
4.15
0.253
0.135
-0.061
-0.128
-0.164
1.77
1.91
- 1.40
- 1.86
- 1.21
0.04
2.24
MVl*DV
MV2*DV
MV3*DV
MV4*DV
MVS*DV
0.416
0.045
-0.096
-0.173
-0.211
4.17
0.69
- 2.43
-3.40
- 1.90
0.10
5.82
0.333
-0.014
-0.086
-0.148
-0.103
2.45
-0.17
-2.17
-2.15
-0.70
0.08
4.68
0.250
-0.011
- 0.078
-0.090
-0.091
1.90
-0.17
- 1.88
- 1.32
-0.76
0.04
2.20*
MVl*PR
MV2*PR
MV3*PR
MV4*PR
MVS*PR
0.329
0.158
-0.092
-0.142
-0.225
3.38
2.67
-2.35
-2.65
-2.13
0.08
4.34
0.222
0.110
-0.081
- 0.093
-0.126
1.70
1.51
- 2.05
- 1.32
- 0.94
0.04
2.39
0.153
0.106
- 0.067
- 0.056
-0.112
1.09
1.74
- 1.56
-0.79
-0.97
0.03
1.50*
MVl!
MV2!
MV3!
MV4!
MV5!
0.607
0.153
- 0.050
-0.190
-0.328
5.65
2.30
- 1.12
-2.83
- 2.45
0.18
10.08
0.508
0.093
- 0.056
-0.133
-0.213
3.28
1.12
- 1.16
- 1.47
- 1.22
0.11
6.00
0.441
0.090
-0.021
- 0.095
-0.197
3.15
1.23
-0.44
- 1.13
-1.41
0.08
4.51
MVl*PE!
MVZ*PE!
MV3*PE!
MV4*PE!
MV5*PE!
0.528
0.085
-0.077
-0.083
-0.258
0.17
5.08
0.422
2.89
0.13
2.73
0.11
0.368
9.98
0.024
0.33
7.24
0.025
0.37
6.20
1.41
- 1.71
-0.074
- 1.58
- 0.049
- 1.03
-0.29
- 1.23
-0.027
0.011
0.14
-2.13 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
-0.143
-0.91
-0.134
- 1.04
%
B. Dioidend yield
DVl
DV2
DV3
DV4
DV5
- 0.330
-0.299
-0.058
0.131
0.537
-4.65
-4.99
- 1.40
3.25
7.30
0.24
13.46
-0.341
-0.302
-0.051
0.129
0.547
-4.30
- 3.90
- 1.09
2.92
6.79
0.23
12.86
-0.330
- 0.269
-0.046
0.128
0.498
-4.72
-4.45
-1.12
3.21
6.50
0.20
11.36
DVl*MV
DV2*MV
DV3*MV
DV4*MV
DVS*MV
-0.346
-0.180
0.001
0.154
0.371
- 5.64
- 4.47
0.03
4.20
6.39
0.19
10.56
-0.357
-0.197
-0.005
0.159
0.400
-5.60
-4.73
-0.14
4.09
6.52
0.19
10.61
-0.338
-0.183
-0.006
0.151
0.377
-5.59
-4.54
-0.18
4.15
6.74
0.19
10.93
DVl*PR
DVZ*PR
DV3*PR
DV4*PR
DVS*PR
-0.359
- 0.242
-0.065
0.166
0.436
-6.32
-5.69
- 1.77
4.45
7.05
0.24
13.39
-0.368
-0.241
-0.061
0.176
0.440
-6.00
-5.12
- 1.60
4.41
6.82
0.21
11.94
-0.351
-0.220
- 0.058
0.158
0.408
-6.29
-4.91
- 1.61
4.28
6.31
0.20
11.27
DVl!
DV2!
DV3!
DV4!
DV5!
-0.344
-0.196
0.003
0.166
0.515
- 5.03
-3.36
0.08
3.36
6.55
0.18
10.16
-0.345
-0.182
0.000
0.164
0.520
-4.34
-2.56
0.00
2.98
5.85
0.15
8.31
-0.302
-0.163
0.003
0.154
0.479
-4.18
-2.79
0.08
3.21
5.74
0.13
7.62
DVl*PE!
DVZ*PE!
DV3*PE!
DV4*PE!
DVS*PE!
-0.215
-0.158
0004
0.094
0.416
- 4.02
-2.96
0.08
2.22
6.10
0.16
9.34
-0.216
-0.148
0.025
0.092
0.400
- 3.62
-2.35
0.52
2.10
5.58
0.14
7.95
-0.183
-0.132
0.021
0.088
0.374
- 3.28
-2.38
0.45
2.12
4.92
0.11
6.32
Table 3 (continued)
Model (2)
Model (1) zyxwvutsrqponmlkjihg
Model (3)
T2
%
TZ
t&J
F&J
up
t&J
TZ
%J
up
t(u,)
F&J
C. PE ratio
PEl!
PE2!
PE3!
PE4!
PE5!
0.422
0.125
-0.018
-0.141
-0.192
5.55
2.55
-0.42
-2.56
-2.39
0.12
6.98
0.440
0.132
0.005
-0.155
-0.221
5.60
2.52
0.12
-2.41
-2.58
0.12
7.13
0.411
0.121
-0.017
-0.118
-0.176
5.52
2.49
-0.41
-2.15
-2.21
0.12
7.06
PEI*MV!
PE2* MV!
PE3*MV!
PE4* MV!
PES*MV!
0.263
0.098
0.007
- 0.065
-0.109
4.40
1.96
0.16
- 1.53
- 1.55
0.07
4.23
0.278
0.118
0.024
- 0.070
-0.151
4.63
2.29
0.55
- 1.56
-2.12
0.08
4.42
0.282
-0.101
0.007
- 0.063
-0.110
4.96
2.02
0.17
- 1.49
- 1.57
0.09
5.25
PEl*DV!
PE2*DV!
PE3 *DV!
PE4*DV!
PES*DV!
0.217
0.027
- 0.046
-0.037
-0.016
3.92
0.51
- 1.02
-0.80
-0.26
0.07
4.11
0.213
0.062
-0.031
-0.035
-0.050
3.79
1.18
-0.66
-0.78
-0.79
0.06
3.26
0.210
0.062
- 0.043
- 0.039
-0.015
3.81
1.17
-0.94
-0.88
- 0.24
0.07
3.88
PEi*PR!
PE2*PR!
PE3*PR!
PE4*PR!
PES*PR!
0.346
0.079
-0.042
- 0.095
-0.135
5.41
1.47
-0.95
-2.02
-1.82
0.11
6.13
0.350
0.095
- 0.023
-0.103
-0.157
5.33
1.71
-0.50
-2.14
-2.04
0.10
5.93
0.335
0.090
- 0.042
-0.085
-0.123
5.28
1.70
-0.95
-1.85
- 1.68
0.11
6.05
D. Price
PRl
PR2
PR3
PR4
PR5
0.335
0.136
-0.089
-0.175
-0.177
3.43
2.68
-2.30
-3.53
-2.41
0.08
4.46
0.314
0.125
- 0.078
-0.154
-0.176
2.42
2.19
- 1.81
-2.47
-1.88
0.05
2.59
0.261
0.123
- 0.059
-0.138
-0.162
2.60
2.44
-1.43
-2.72
- 2.25
0.04
2.47
PRl*MV
PR2*MV
PR3*MV
PR4*MV
PRS*MV
0.140
-0.011
-0.032
-0.032
-0.023
2.10
-0.25
-0.85
-0.84
- 0.43
0.176
0.024
- 0.037
- 0.033
-0.090
2.47
0.49
-0.93
-0.84
- 1.41
0.05
2.75
0.152
0.026
-0.008
0.038
- 0.098
2.28
0.51
-0.21
0.98
- 1.36
0.04
2.35
PRl*DV
PR2*DV
PR3*DV
PR4*DV
PRS*DV
0.278
0.044
-0.132
-0.172
-0.071
3.36
1.02
-3.63
- 3.92
-1.16
0.09
5.33
0.271
0.026
-0.114
-0.174
- 0.049
2.54
0.56
-2.85
-3.56
-0.64
0.07
4.20
0.212
0.048
-0.103
-0.140
- 0.065
2.55
1.10
-2.71
- 3.07
-1.10
0.05
2.96
PRl!
PR2!
PR3!
PR4!
PR5!
0.455
0.128
- 0.096
-0.163
-0.172
5.30
2.65
- 2.05
-2.87
- 2.29
0.431
3.94
0.09
0.10
0.13
0.396
4.39
0.120
2.30
5.07
7.32 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
0.128
2.70
5.62
-0.091
- 1.79
- 0.077
-1.65
-0.133
- 1.90
-0.119
-2.04
-0.153
- 2.07
-0.165
- 1.72
PRl*PE
PR2*PE
PR3*PE
PR4*PE
PRS*PE
0.393
0.054
- 0.046
-0.163
- 0.086
4.88
1.11
- 1.10
-3.09
- 1.21
0.11
6.52
2.83
0.356
0.046
-0.041
-0.124
-0.074
3.61
0.96
-0.95
- 1.98
-0.87
0.08
4.36
0.331
0.063
-0.027
-0.124
- 0.067
4.03
1.34
-0.63
-2.38
-0.98
0.08
4.81
“Based on monthly data for the period April 1961 to March 1985. F-values not significant at
the 5% levels are noted with a ‘*‘.
- Hotelling Ts-statistic
Notation: up - abnormal portfolio return
T2
F(u,) - F-value for T2-statistic.
t(u,) - f-statistic for up
688
M. Levis, Stock market anomalies
premium, based on model 1, of 0.83 per cent per month for the full sample,
which is almost twice the amount of the 0.42 per cent premium observed for
market size effect. Randomising the market size portfolios to account for
dividend yield differences has a definite, albeit marginal, impact on the vector
of abnormal returns; as portfolios MV2 *DV to MV5 *DV become virtually
identical, any remaining indications of a size effect are entirely attributable to
the persistent strength of the MVl*DV portfolio. On the other hand,
applying a market randomisation to the dividend yield portfolios (DVl*MV
to DVS*MV in panel B) has no material impact on either the strength or
configuration of the already documented dividend yield effect.
The reduced sample estimates in panels A and C provide the evidence for
comparing the size versus the PE effects. The F-values for both nonrandomised sets of portfolios indicate abnormal returns significantly different
from zero and almost identical premiums. Moreover, controlling the market
size portfolios for PE differences or the equivalent PE set for size differences
does not alter the essence of these results in any substantive way. On this
basis, the results of this study suggest that both effects were present on the
LSE for the period under consideration. This conclusion is in line with Cook
and Rozeff’s (1984) results but is in contrast to both Basu’s (1983) and
Reinganum’s (1981) findings, which support the superiority of either a PE or
a size effect respectively. It is also interesting to note that the magnitude of
the PE effect is markedly reduced when controlling for dividend yield
differences. The appropriate F-value, in panel C - model 1, is reduced from
7.06 to 3.88 while the PE premium, the abnormal return difference between
portfolios PEl *DV! and PES*DV!, is reduced to 0.23 per cent per month
from the 0.59 per cent equivalent premium present between portfolios PEl!
and PE5!. These results provide further support to the emerging overall
dominance of the dividend yield effect.
With respect to the share price ranking procedure, it is immediately
apparent from the relevant non-randomised portfolios in panels A and D
that the size and price effects are virtually identical both in terms of
premiums and consistency. The noticeable relative prominence evident in the
risk-adjusted returns (models 2 and 3) of market size portfolios is entirely
due to the uncharacteristic nature of their beta coefficients reported in the
previous section. Panel D indicates that the share price effect appears to be
resilient to both the market size and dividend yield randomisation procedures; the vectors of abnormal returns of the share price portfolios
randomised for market size and dividend yield are still significantly different
from zero in spite of the marked reduction of the relevant premiums. This
evidence is in direct contrast to the configuration of market size portfolio
returns observed in panel A. These results lead one to infer that an
investment strategy based on the share price as the sole security selection
criterion is better suited for the investor interested in long term consistent
M. Levis, Stock market anomalies
689
performance but reluctant to restrict individual holdings to shares that
conform to narrow boundaries in terms of market size and dividend yields.
In short, the findings presented in this section are consistent with the
hypothesis that the dividend yield and PE ratio have a significant impact on
the risk-adjusted returns of U.K. firms and are largely independent from each
other and other confounding effects. The market size anomaly resembles in
many respects the share price effect but ceases to be pervasive when such
portfolios are controlled for the differences in dividend yield and share price
effects.
5. Interaction between the four effects
The evidence in the previous section confirms the presence of a significant
dividend yield, PE effects and to a lesser extent a market size and share price
effect as well as during the period April 1961 to March 1985. This evidence,
however, is not sufficient on its own to indicate whether these effects are
homogeneous across each of the particular quintiles of the four ranking
procedures. Thus, the issue investigated in this section is to what extent the
individual effects depended on the particular quintile of the portfolio
formation procedure in operation. If, for example, the dividend yield and the
firm size effect are independent of each other, one would expect the abnormal
return to be enhanced by adhering to a high dividend yield small size
investment strategy. On the other hand, if the two effects are highly
interrelated, then an additive return possibility would not exist, since one
effect would merely serve-as a proxy for the other.
Table 4 presents the abnormal returns using model (1) for all pairs of
primary and secondary portfolio groupings. Each of the four panels (A to D)
refers to one of the ranking procedures as the primary grouping variable and
the other three as the secondary. As the emphasis in this section is on the
search for anomalies within the same quintile of the primary ranking
variable, only the results based on the full sample are presented (portfolios
involve the PE ratio as a primary or secondary variable are based on the
estimates derived from the reduced sample). Thus, accurate comparisons of
abnormal returns can only be made across the quintiles of the same primary
variable and not across quintiles of different primary ranking procedures,
since the reduced sample was found to have a material impact on the excess
return estimates. Due to space considerations, only the estimates based on
model (1) are presented in this paper; given the specific nature of the beta
coefficients, discussed in section 3B, estimates of abnormal returns based on
models (2) and (3) do not alter the substance of the results presented in this
secti0n.l 1
“Detailed
results based on models
(2) and (3) are available
from the author
on request
Table 4
Excess returns of various combination portfolios based on model (1)
UP
r(u,)
Share price
PE ratio
Dividend yield
T2
TZ
TZ
F(u,)
F(u,) zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIH
F&J zyxwvutsrqponmlkjihgfedcbaZY
%J
tw
A. Market value as prwnary group
MVl
1
0.011
0.04
0.14
2
- 0.242
-1.36
8.14
3
0.136
0.87
4
0.446
2.62
5
0.884
4.87
4.40
2.38
2.85
1.33
1.41
0.839
0.406
0.480
0.208
0.272
0.08
4.38
0.564
0.328
0.168
0.202
0.002
2.50
1.85
0.99
1.19
0.01
0.03
1.96*
MV2
1
2
3
4
5
- 0.474
0.020
0.235
0.303
0.505
-3.58
0.19
2.40
3.14
3.97
0.15
8.29
3.01
0.339 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPO
0.04
0.02
0.211
1.52
2.34
1.59
0.186
1.17*
0.215
1.91
-0.016
-0.14
0.148
1.51
0.72
0.079
0.048
0.46
-0.95
-0.136
0.053
0.40
MV3
1
2
3
4
5
-0.398
- 0.277
-0.036
0.095
0.274
-3.67
-3.10
-0.47
1.10
2.74
0.09
5.39
0.150
0.125
- 0.008
- 0.202
-0.170
1.44
1.37
- 0.09
-2.11
-1.52
0.04
2.06*
0.010
- 0.060
- 0.026
- 0.057
-0.172
0.09
-0.57
-0.21
-0.70
-1.72
0.02
0.89*
MV4
1
2
3
4
5
- 0.399
-0.211
-0.157
-0.036
0.151
-3.36
-2.08
- 1.75
-038
1.50
0.06
3.17
0.038
-0.004
-0.155
-0.163
-0.192
0.32
-0.04
- 1.42
- 1.46
- 1.28
0.02
0.91*
0.033
-0.190
-0.195
-0.151
-0.138
-
0.29
1.73
1.91
1.67
1.53
0.03
1.52*
1
2
3
4
5
-
-2.60
- 1.36
- 1.35
-0.38
0.49
0.05
2.67
0.047
-0.210
-0.265
-0.239
-0.322
-
0.30
1.39
1.72
1.56
1.70
0.04
2.34*
- 0.056
-0.163
-0.134
-0.234
-0.235
-0.36
- 1.04
-0.89
- 1.72
- 1.57
0.02
1.17*
MV5
0.432
0.206
0.209
0.053
0.068
PE ratio
Market value
B. Ditlldend yield as primary
Share price
group
DVl
1
2
3
4
0.023
- 0.426
- 0.424
- 0.432
-0.389
0.09
-2.50
-3.31
- 3.30
-2.32
0.10
6.02
- 0.037
-0.319
-0.353
-0.374
- 0.426
-0.33
-3.12
- 3.09
-2.98
- 2.88
0.06
3.73
0.086
-0.340
-0.306
-0.587
- 0.475
004
-2.03
-2.61
-5.61
-3.82
0.16
8.97
DV2
1
2
3
4
5
-0.114
- 0.370
-0.369
-0.170
-0.325
-0.90
-4.34
-3.81
- 1.28
- 1.90
0.14
7.76
-0.009
-0.173
-0.219
-0.218
-0.194
-0.98
- 1.93
-2.24
- 2.08
- 1.42
0.03
1.84*
-0.219
-0.261
-0.361
-0.241
-0.265
- 2.24
- 2.79
-3.55
- 2.24
-2.53
0.09
4.92
DV3
1
2
3
4
5
0.198
-0.131
-0.034
-0.106
-0.156
1.46
-1.47
- 0.45
-1.03
- 1.07
0.02
1.29*
0.030
0.002
0.001
- 0.084
0.069
0.31
0.02
0.01
-0.92
0.69
0.01
0.35*
1
2
0.290
0.263
0.054
- 0.044
0.075
1.86
2.73
0.70
-0.47
0.61
0.06
3.31
0.333
0.245
0.057
0.082
0.054
3.06
2.53
0.69
0.95
0.50
0.853
0.606
0.384
0.303
0.341
4.56
4.67
3.13
3.08
3.08
0.20
11.50
0.722
0.555
0.299
0.399
0.419
4.25
4.25
2.33
3.38
3.06
DV4
4
5
DVS
1
2
4
0.013
0.12
0.000
0.00
0.02
1.11* zyxwvutsrqponm
-0.163
-0.128
-0.061
- 2.05
- 1.56
-0.74
0.05
3.08
0.340
0.252
-0.096
0.039
0.112
2.90
2.75
- 1.25
0.52
1.52
0.09
5.04
0.14
7.64
0.839
0.587
0.411
0.216
0.363
5.54
5.36
3.99
2.27
3.83
0.17
9.48
zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQP
691
M. Levis, Stock market anomalies
Table 4 (continued)
Market value
%
tw
Share price
Dividend yield
TZ
T2
T2
Fb,)
up
t&J
&$I
up
.
t&J
%J
0.182
0.174
0.392
0.419
0.842
1.69
1.70
3.56
3.41
5.68
0.13
7.40
0.912
0.43 1
0.422
0.099
0.182
5.59
3.38
3.83
0.99
1.76
0.14
8.21
0.265
0.161
0.036
0.001
0.076
2.04
1.54
0.38
0.01
0.89
0.03
1.53*
C. PE ratio as pnmary group
PEl
1
2
3
4
5
0.901
0.476
0.243
0.262
0.173
4.41
3.42
2.10
2.29
1.30
0.13
7.44
PE2
1
2
3
4
5
0.158
0.145
0.128
0.163
0.011
0.92
1.26
1.26
1.52
0.07
0.03
1.42*
-0.178
0.062
0.159
0.220
0.323
- 1.90
0.65
1.82
2.28
2.57
0.06
3.12
PE3
1
2
3
4
5
0.413
-0.109
-0.127
-0.083
-0.182
2.78
-1.00
- 1.37
-0.73
-1.23
0.05
2.97
-0.232
-0.185
- 0.046
-0.041
0.235
-2.30
- 2.05
-0.50
-0.51
2.01
0.04
2.05*
0.189
0.040
-0.125
-0.233
-0.103
1.54
0.41
-1.44
- 2.53
- 1.01
0.03
1.74*
PE4
1
2
3
4
5
0.254
-0.109
- 0.305
-0.109
-0.322
1.43
-1.10
-3.06
-0.82
-1.98
0.06
3.19
-0.345
-0.316
- 0.096
-0.075
0.310
- 3.20
-2.89
-0.89
-0.89
2.32
0.06
3.30
0.289
- 0.079
- 0.299
- 0.247
-0.224
2.16
-0.85
- 3.22
-2.21
- 1.93
0.05
2.85
PE5
1
2
3
4
5
0.112
- 0.278
-0.185
-0.178
- 0.349
0.62
-2.30
-1.58
- 1.14
- 1.92
0.04
2.35
-0.344
-0.397
-0.303
-0.081
0.163
-2.58
- 3.02
- 2.38
-0.69
1.44
0.04
2.57
0.002
- 0.236
-0.170
- 0.242
- 0.269
0.01
-2.06
- 1.37
- 1.88
-2.21
0.03
1.43*
PR2
1
2
3
4
5
0.193
0.238
0.178
0.020
- 0.014
1.10
2.07
1.76
0.19
-0.11
PE ratio
Dividend yield
Market value
D. Share price as primary group
2.71
0.05
PRl
1
0.693
2.39
2.87
2
0.394
-0.08
3
-0.012
1.34
4
0.174
0.41
5
0.054
0.03
1.48*
0.057
-0.292
-0.001
0.562
0.834
0.26
- 1.88
-0.01
4.73
5.86
0.16
11.17
0.760
0.522
0.383
0.189
0.124
4.79
3.53
3.05
1.51
0.74
-0.378
0.035
0.114
0.235
0.498
-3.10
0.43
1.31
2.49
4.48
0.12
6.80
0.441
0.172
0.014
0.083
-0.068
3.71
1.73
0.13
0.89
-0.65
0.11
6.21
o.Ot5
3.29
M. Levis, Stock market anomalies
692
Table
Market
4 (continued)
Dividend
value
yield
PE ratio
TZ
%J
UP
F(u,)
zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
as pmary
group
D. Share pee
PR3
1
2
3
4
5
-0.086
0.111
-0.130
-0.151
- 0.040
-0.60
1.27
- 1.34
-1.38
-0.26
0.03
1.79*
-0.349
-0.187
- 0.068
0.035
0.194
-3.69
-2.12
-0.93
0.44
2.21
0.06
3.24
0.117
- 0.053
-0.160
-0.143
-0.144
1.16
-0.54
- 1.80
- 1.56
-1.13
0.02
1.27*
PR4
1
2
3
4
5
-0.011
-0.019
-0.290
-0.129
- 0.243
-0.07
-0.22
-3.23
- 1.09
- 1.47
0.05
2.69
-0.581
- 0.274
-0.177
-0.003
0.275
-5.34
-2.88
- 2.09
-0.04
3.30
0.12
6.92
0.300
-0.179
-0.261
-0.210
- 0.246
3.06
- 1.99
- 2.70
-2.18
- 1.75
0.08
4.54
PR5
1
2
3
4
5
- 0.020
-0.195
-0.081
-0.193
-0.320
-0.15
-2.13
-0.85
- 1.45
- 1.84
0.03
1.86*
-0.505
-0.382
-0.160
- 0.040
0.238
-4.03
-3.34
- 1.65
-0.50
2.97
0.10
5.91
0.058
-0.011
-0.185
-0.346
-0.280
0.60
-0.12
- 1.72
-2.98
- 2.23
0.04
2.45
“Based on monthly data for the period
the 5”/ levels are noted with a ‘*‘.
portfolid-return
Notation:
ug - abnormal
t(u,) - t-statistic for up
April 1961 to March
T2
F(u,)
1985. F-values
not significant
at
zyxwvutsrqponmlkjihgfedcba
- Hotelling
T2-statistic
- F-value for T2-statistic.
The findings of the previous section indicated that the size and PE effects
appear to work independently from each other. Closer investigation of the
evidence in panels A and C, however, reveals that the aggregate results in
table 3 obscure some of the subtleties involved in the interaction between
market size and PE effects. Examination of the five market size portfolios in
panel A indicates that the PE effect is firmly established within the smallest
market size portfolio. The F-values for all other PE portfolios are not
significant or very marginally so at the 5 per cent level. Panel C points to a
very similar picture with regard to the nature of the size effect, i.e. the size
effect is mainly concentrated within the smallest PE quintile; within higher
PE portfolios its presence is at best marginal. Thus, it appears that there is
some degree of interaction between market size and PE predominantly
within the lowest quintiles of the two ranking procedures.
The relation between market size and dividend yield effects is rather more
complicated. A comparison with the estimates in table 3, panel A, confirms
that a combination of small size and high dividend yield generates portfolios
earning consistently higher abnormal returns than the equivalent aggregate
market size portfolios. The F-values in table 4, panel A, point to the presence
of a dividend yield effect at each level of market size; this effect, however,
gradually declines as one moves from portfolio MVl to MV5 but remains
M. Levis, Stock market anomalies
693
significant at the 5 per cent level. Moreover, the dividend yield premium (the
difference between the smallest and largest dividend yield quintile within each
market size portfolio in panel A of the same table) is never lower than 0.5
per cent per month and increases gradually from dividend yield quintile 1 to
5. This evidence, in conjunction with the results of the previous section, leave
little doubt about the pervasive nature and persistence of the dividend yield
effect. On the other hand, closer investigation of the results in panel B casts
further doubts on the eficacy of the size effect. First, observe the inconsistent
pattern of F-values across the five dividend yield portfolios; the size effect
appears not to be entirely independent of the level of dividend yield; its
presence is clearly firmer within the highest dividend yield quintile. Second,
the pattern of abnormal returns for size portfolios within quintiles DVl to
DV3 does not provide unambiguous evidence in support of a size effect since
there is very little to distinguish between the abnormal returns of market size
portfolios 2 to 4. Keim (1985) conjectured that the excess return of dividend
yield portfolios reflects the contents of these portfolios in terms of market
size firms, i.e. a large proportion of smaller firms are concentrated in the high
dividend yield categories. To further investigate the validity of this conjecture
for U.K. data, the average dividend yield of each market size quintile was
computed as well as the composition of these portfolios in terms of dividend
yields. The analysis supports Keim’s hypothesis. The mean dividend yield of
the smaller portfolio is 8.0 per cent in contrast to the 4.6 per cent dividend
yield of its larger counterpart. Furthermore, the smaller market size portfolios contained a disproportionately larger proportion of high dividend yield
firms, while a high concentration of low to medium yield stocks was evident
in larger size portfolios. I2 Although the emerging picture is remarkably
similar to the U.S. evidence, i.e. high concentration of smaller (larger) firms
within the higher (lower) dividend yield groups, on balance the weight of
evidence does not support the notion that the dividend yield is simply a
surrogate for market size.
A direct comparison between the dividend yield and PE effects in table 3
shows that both effects are at work independently. Controlling one for the
confounding effects of the other does not alter the essence of the observed
irregularities. At the same time, it is also clear that the PE effect is markedly
reduced when full account is taken of the differences in dividend yields across
the five PE portfolios. The results in table 4, panels B and C, confirm this
conclusion. Observe, for example, the PE premiums across each of the five
dividend yield portfolios; the largest such premium is evident within the
lowest dividend yield quintile, namely 0.39 per cent per month. Panel C,
however, indicates the dividend yield effect produces premiums consistently
superior. The largest premium for quintile PEl was 0.66 per cent while the
“For
further
details on average
dividend
yields and portfolio
composition
see Levis (1987).
694
M. Levis. Stock market anomalies
lowest, quintile PE3, was 0.47 per cent per month. Thus, there is little doubt
that these effects are to a certain extent interrelated, but the dividend yield
can be still be confidently regarded as the dominant one.
A survey of panels A to D confirms the overall striking resemblance
between the size and price effects mentioned in the previous section. Both
exhibit very similar premiums and F-values across the four panels. Moreover,
a direct comparison between the two provides further support for the notion
that there is a strong relationship between the two. The price effect, for
example, is virtually non-existent within individual market size portfolios. On
the other hand, the presence of a size effect is apparent within the lowest
price quintile only. Further support for this interaction between market size
and share price can also be obtained from an analysis of the mean share
price of each market size quintile and the share price composition of these
quintiles. The average share price of the firms included in the smaller market
size portfolio was equal to 51 pence (in 1984 prices) while that of the largest
was four times higher. Furthermore, about 57 per cent of the population of
firms included in the smaller size portfolio were firms belonging to the lowest
share price quintile. On the other hand, 46 per cent of those in the larger
market size group were also members of the highest share price group.
6. Conclusions
The empirical evidence reported in this paper indicates that at least during
the April 1961 to March 1985 time period the LSE exhibited a number of
irregularities in stock price behaviour. The well documented size effect
appears to be only one of them. Investment strategies based on dividend
yields, PE multiples and share prices seem to be at least as profitable, if not
more, as strategies based on market size. Furthermore, the size effect is not
entirely independent of the other three portfolio formation procedures. The
significant market size effect, for example, is markedly reduced when control
over the differences in dividend yield is exercised. Any further size effects are
attributed entirely to the uncharacteristic nature of beta coefficients observed
for smaller size portfolios. The implied risk-return relation is not altered even
when a Dimson type beta estimate is applied. Closer examination reveals
that the market size effect is not consistent across all dividend yields, PE or
share price quintiles. It is also worth noting that from the configuration of
abnormal returns across the various portfolio formation procedures it is
often hard to distinguish between the size and share price effects. This
evidence lends further credence to the view that these two variables are either
proxies for each other or both are just proxies for more fundamental
determinants of expected returns for common stocks. The dividend yield or
the PE multiple for example, appear as possible candidates for such a proxy.
Their individual effects are still maintained even when control for their
M. Levis, Stock market anomalies
695
reciprocal differences is exercised, in spite of the fact that neither one is
consistent at every single level of the other.
In short, the weight of the evidence presented in this paper raises questions
about the strength of firm size as an independent determinant of the stock
returns generating process. Its strong dependence with the other firm
attributes suggest that it cannot be viewed as either an independent anomaly
or as a profitable investment strategy in its own right. In that sense, the
results also have implications for various types of event studies. If one is to
control for factors other than risk, then the dividend yield and PE multiple
differences might be more appropriate factors. Such adjustments are particularly important for the LSE in view of the fact that the direction of the riskreturn relation is still rather ambiguous.
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