A STATISTICAL STUDY OF U.K. SHARE PRICES
| Date | 01 November 1970 |
| Author | Myles M. Dryden |
| DOI | http://doi.org/10.1111/j.1467-9485.1970.tb00714.x |
| Published date | 01 November 1970 |
A STATISTICAL STUDY
OF
U.K.
SHARE
PRICES
MYLES M.
DRYDEN*
I
The primary purpose of this article is to report the results of a number
of statistical tests carried out
on
time series of daily prices for 15 shares.
A
detailed description of the data
is
provided in Appendix
A.
The results
of
the statistical tests are contained in Section
I1
of this paper. Since most of
these tests are well known very little space is devoted to explaining them
and readers are simply directed to the appropriate sources. It is also well
known that standard statistical tests, such as auto-correlation analysis, may
be inadequate to detect the presence of temporal dependence of non-linear
form.
To
meet this defect Section
I11
provides a full description of another
form of testing appropriate for the study of speculative prices. The results
and conclusions drawn from applying this test to the share price series are
also presented in Section
111.
Section
IV
summarises the main findings and
makes suggestions for future research.
The statistical analyses carried out here have a bearing
on
a number
of economic problems. At a general level there is the question of the effici-
ency of capital markets. Capital markets play an important role in allocating
the Nation's capital resources. One way of evaluating their efficiency in this
process is to examine the behaviour of share prices. Economic theory
suggests that
if
these markets are efficient then the resulting prices should
change over time in a way such that past changes in prices should provide
no
clues to future changes, otherwise there would be opportunities for
making profits and the markets would not be perfect (Samuelson, 1965;
Fama, 1965a, pp. 36-9). More specifically the relevance
of
various theories
of portfolio management depend
on
the underlying statistical properties
of
the constituent share prices.
For
example, the most well known model of
portfolio management, that of Markowitz (1959) rests on the assumption
that
a
share's price can be represented as a random variable having
a
finite
variance.' Research into the statistical properties of share prices has, how-
ever, yielded some cause for questioning the assumption of finite variance
(e.g. Mandlebrot, 1963). Thus knowledge of the statistical behaviour
of
share
prices has implications for public policy questions concerning the efficiency
of
capital markets, the choice of appropriate portfolio management tech-
niques, and many related economic issues.
*I
would
like
to acknowledge the financial support
of
Edinburgh University's
Moray Fund and the assistance
of
various
members
of
the staff
cif
the Edinburgh
Regional Computing Centre.
But
see
Markowitz
(1959),
p.
108
ff.
i
369
3
70
MYLES
M.
DRYDEN
The particular issue considered here is whether or not share prices follow
a
random walk, that is whether a share's price can be represented by the
simple model
:
Pi
=
Pt+
+
ei
where
et
is a random variable, having constant variance, distributed indepen-
dently
of
et-,,
et+,
etc., and where
P,
is the price of a share at time
t.
This
model implies that the probability of a change in price
of
any given magni-
tude
(X)
is independent of the past history
of
such changes, that is
:
Prob{
AP,=X
I
Apt APi-,,
.
.
.
}
=Prob
,'
APt=X
}
,
Since there is evidence to suggest that the variance of price changes depends
on the price level it is customary to replace
Pi
with log
P,
in the above
model (Cootner, 1964, Ch. 7; Fama, 1965a, p. 45). This practice is adhered
to
in the following analysis and constitutes. therefore, a test
of
whether
share price behaviour is a random walk in the logarithm of price.
While almost all of the analyses carried out here have already been
performed on
U.S.
data2 there is not,
so
far as this author
is
aware, a corres-
ponding series of published research on U.K. share prices3 The consensus
of
opinion which emerges from the research on American share prices is
that the empirical evidence gives strong support for accepting the random
walk model.' The difficulties
of
generalising from the evidence provided
by
one security exchange has already been noted by some of the American
researchersS and preliminary studies carried out by this author suggest that
there may
be
more dependence in day-to-day price changes of U.K. share
prices than
is
evident in an examination of American data (Dryden, 1968,
1969a, 1969b. 1970). These findings, however, could only be regarded as
tentative since they were the result
of
analysing the behaviour
of
ensembles
of
share prices rather than the behaviour of the individual share prices.&
In order to keep the discussion presented in Sections
I1
and
111
within
manageable proportions it will
be
necessary to eschew the opportunity to
present
a
fully comparative study, that
is
comparing the results
of
analysing
individual
U.K.
share prices either with the corresponding results
of
Ameri-
can studies or with the results of analysing aggregates
of
U.K.
shares. The
opportunity will be taken, however, to introduce the key points of similarity
Cootner (19641,
Journal
of
Business
(1966) and
Journal
of
Financial and
Quanti-
tative Analysis
(1968)
provide useful collections of papers. In addition the published
work of Fama-which has been particularly influential in the form of analysis adopted
here-constitutes
an
important contribution
to
this field of research. Readers interested
in pursuing the subject should find the extensive bibliography
of
Fama (1965a) very
helpful.
See Taylor
(1969)
for the arguments for more research on British share prices.
'There are
of
course opponents to the random walk theory. Opposition is
frequently found in the technical (professional) literature.
For
example see Levy (1967).
For example see Fama (1965b, p. 299). Some students
of
the London Stock
Exchange have been reluctant to accept theories based on a study of American data;
see, for example, Taylor (1969).
Kendall
(1953)
noted this problem some time ago. It was left to King (1966).
however,
to
provide a detailed analysis of the problem.
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