LIBRARY
OF THE
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
15ev7eT
/-^^
THE BEHAVIOR OF EUROPEAN
STOCK MARKETS
by
Bruno H. ^olnik
#581-71
January 1972
Draft
—
Comments Invited
I am very grateful to Professors Franco Modigliani, Myron
Scholes, Marti Subrahmanyamand and all the members of the M.I.T.
I £
Finance Seminar for their helpful comments and suggestions.
particularly indebted to Professor Jerry Pogue for his constant
help, advice and criticism.
RECEIVED
FEB
iVl.
I.
T.
7 1972
LIbHAHIES
Introduction
Very little work has been done on the European markets, applying the
modern concepts of investment theory, and, except for limited circles, the
"beta revolution" has yet to reach the other side of the Atlantic.
This can
partly be explained by the lesser interest of Europeans in their capital
markets and the air of mystery that tends to surround the financial world.
A second and perhaps more
pragmatic explanation for the small number of
academic studies is the lack of public and organized sources of stock price
data.
Tfie
need (or fashion) for developing a systematic computerized body of
data on the stock markets seems to have arisen more slowly in Europe.
In
regard the body of data used for this study is to the author's know-
this
ledge unique'
1966-1971.
\
It
compiles daily prices of European stocks for the period
The sample includes over 250 stocks from 8 European markets.
Surprisingly enough, one of the early and most basic contributions to
the random work theory originated in the U.K.
trial
did not find any evidence of significant serial
a
Kendall
[23] studied indus-
share indices on tne London Stock Exchange for the period 1928-38; he
correlation.
More recently,
group of English and Scottisn economists have studied U.K. stock market
indices.
For instance Dryden [10] appl ies
a
simple Markov scheme to succes-
sive daily numbers of advances and declines on the London Stock Exchange.
The estimation technique used and the reliability of the estimates are open
to criticism;
besides, the conclusions drawn on individual stocks by using
tnose aggregates are doubtful.
^
According to Dryden
's
results the random
Institute for International Management (Berlin) and the London Business School (Prof. Brealey) have plans to develop computerized stock
Some brokers or
prices files but it is still in the planning process.
advisory firms have their own data but they are rather limited in scope
and not publicly available.
'The
G33y44
walk theory is violated on the London Stock Exchange.
Thus, in his own
words, the probability for a share to go up one day is seven times larger
if it went up the previous day than if it
went down (this implies substantial
positive serial correlation).
Similarly Henri Theil
[36] applies information theory to the daily per-
centage of stocks, advancing, declining or remaining at a constant price on
the Amsterdam Stock Exchange from 1959 to 1963.
Like Dryden, he finds re-
sults inconsistent with a random walk hypothesis and suggesting positive
correlation:
serial
"Tne best prediction
(information theory criterion) for
tomorrow is half way between a longrun average and today's observation."
Fama [16] replicated this test on the New York Stock Exchange but did not
find that present changes could help to forecast future changes in prices.
This brief review summarizes most of the existing literature in this
area of modern capital
theory.
This limited evidence tends to suggest that
European capital markets may tend to behave differently from the American
market.
However any serious investigation of that topic should deal not only
with market indices and aggregates but with
a
representative number of indi-
vidual securities listed on those markets.
After
a
short description of the European markets and of the data, the
random walk hypothesis will be investigated in section
correlation tests to each European market.
II
applying serial
Those tests will be discussed
and their results compared with the empirical evidence presented for the
American market.
In
section III the relation between risk and return is studied using
the market model
to its national
framework.
The systematic risk of each security relative
market index is computed using various time intervals.
The
robustness and stability over time of those estimates is then investigated.
Finally a preliminary attempt has been made in section IV to test the
Capital Asset Pricing Model
for each European market.
Different measures
have been used to determine the relation between expected returns and the
risk borne by the investors.
No literature seems to exist on those topics
as far as European markets are concerned.
Section
1
)
I:
The European Capital Markets
A Short Description of the European Markets
With the exception of Japan all of the major non-American capital
markets are concentrated in Europe, namely:
and Germany,
United Kingdom, France, Italy,
To give some order of magnitude of the various markets,
have included in table I-l
their market value (in billions of US $).
very hard to find consistent data among countries.
I
It is
For instance, some
countries list their government securities on separate markets; similarly
there might exist regional stock exchanges
(e.g.
France) for which data have
not been found.
Table
I-l:
Market value of each country in 1966
(in billions dollars)
NB
This includes the market value of all the securities
:
listed on all the capital markets of each country (excluding
government bonds not listed on the general stock exchange)
with the exceptions of:
only London Stock Exchange
U.K.:
France:
only Bourse de Paris
U.S.A.:
on the NYSE only.
Sources:
Chambre syndicale des Agents de Change
Banca D' Italia
U.K.
London Stock Exchange, Annual report
Germany
Wirtschaft und Statistik
Switzerland
OECD, Committee on Invisible Transactions
Netherlands
Maandstaatistiek van het Financiewezen
Belgium
Commission de la Bourse de Bruxelles
Sweden:
Sveriges Riksbank, Arsbok
Japan:
Bank of Japan
Survey of Current Business
U.S .A.
France
Italy
:
:
:
:
:
:
:
:
One must be aware that each stock market has its own characteristics
inherited from centuries of traditions.
The London Stock Exchange was by far the world's leading capital market
up to world
war
It is still
I.
the most important market place in Europe
(about one third of the current US equities market value).
its
It has
retained
international orientation with several hundreds of foreign stocks listed
on the exchange.^
'
However large fees and transaction costs coupled with
taxes and constraints on foreign investors have not favored its development
in the past few years.
The Jobber plays
a
role similar to the American
^By rule 163(1 )(e) any stock listed on any other Stock Exchange in
world can be dealt in London.
the
specialist; the London Stock Exchange is
a
private organization regulated
only by its members who are collectively liable (brokers and jobbers) for
any insolvency of one of its members.
Interestingly the London Stock Ex-
change parcels out time in its own fashion;
split into 24 "accounts" or trading periods.
begins on a Monday and lasts until
the Stock Exchange year
is
A normal, two-week account
the Friday of the following week.
Account day, the day "all bargains must be settled", checks and transfers
delivered, falls on Tuesday, eleven days after the account is closed.
if a purchase is made on a Monday of a new account,
the investor's check
must be on his broker's desk three weeks and a day later.
a
Thus,
Of course, for
sale the process is the same but reverse--it is the seller who waits
"Contango", known also as carry over, is an arrangement to
for payment.
postpone payment (or delivery) to the following account period.
widely used than in continental
less
Europe.
tradition, organization and volume of transactions makes the
Its
Bourse de Paris the most important capital market in continental
Its
It is
structure serves as
a
prototype for the markets of Belgium, Italy, Spain
and Greece much as the basic organizational
served as
the model
countries.
Europe.
pattern of Germany's exchanges
for those of Austria, Switzerland and the Scandinavian
There are two ways of dealing in France.
The investor can put
francs on the table and purchase stock in the cash market, the "March^ au
Comptant", or he can deal
for settlement at the end of the month in the
forward market, the "March^
today.
Terme" which is cheaper and generally used
For larger stocks, prices are arrived at by yelling, screaming,
and stamping;
criee".
a
As
in brief it is an auction market called
this is the only way
a
"a la
transaction can take place, this system
is
very fair to investors.
In the
forward market no interests are to be
paid for taking a position, although a broker would typically require from
a
small
investor that 25% of the transaction amount be covered by stocks
or cash in his account.
to the following month,
Should one desire to carry forv/ard an open position
it is possible to do so.
volved if buyers match sellers.
If this
No extra costs are in-
is not the case,
interests will
have to be paid--usually between }h and 4 percent a year.
Depending on
whether the stock has risen or not, your account is then credited or debited.
The whole operation is easy and does not involve large costs.
Milan is the largest Italian market; it is
trolled by the government.
a
public institution con-
Although banks are not allowed as members of
the Exchange, they play an important role and they may deal
after trans-
action hours; these transactions are not official nor recorded by the Exchange.
Transactions are settled once
possible.
It is
a
month but
a
carrying forward is
merely considered as an extension of credit with according
interest payments.
Like many other things in Italy, brokerage rates are
negotiable.
One thing is certain about German stock exchanges:
third.
is
keen.
Frankfort and DiJsseldorf compete for first place and the rivalry
The banks replace the traditional
to trading through the exchange.
(free
Because the banks are free to trade
"telephone market" after hours, volume figures give only
figure of shares traded.
to small
broker; they are not restricted
They may also use the "Freie Makler"
market) any time of the day or night.
on this
Hamburg ranks
a
partial
This feature made the German market unattractive
or foreign investors.
There does not exist any "terme", option
or forward market; however investors can still
borrow directly from the
banks without any legally determined margin requirement.
The Amsterdam "Beurs" maintains the old tradition of internationalism
Officially, the Exchange is open only from 1:00
of the Dutch merchants.
to 2:15 p.m.
but arbitrage with other European and American bourses takes
place all day.
(Royal
The six "internationals" dominate the Amsterdam Exchange
Dutch, Unilever, Philips, AKU, Hoogovens and KLM) and represent 33%
of the market value.
Any broker can act as a specialist (hoekman) on the
floor of the exchange.
The man simply appoints himself, telling his col-
leagues he will henceforth deal
This procedure is symoto-
in X securities.
matic of the informality with which the Dutch approach business dealings.
However he rarely takes
a
position in the security.
Of the three major Swiss exchanges Zurich, Basel and Geneva, Zurich
is
the largest and most active.
the criee,
Except for the quotation process, called
the Exchange organization is similar to their German neighbors;
banks are the only members.
Brussels is the seat of the Common Market and de facto capital of
Europe; it is also the capital of the Belgians.
a
They owe their Bourse to
Napoleon decree of the nineteenth Messidor, year IX of the revolution
and its organization is still
comparable to its French equivalent.
Brussels
is certainly a big international market and over a hundred foreign securi-
ties are quoted but for most of the 700 Belgian or African stocks listed
the market is \/ery thin.
If Milan is
quietest.
the noisiest stock exchange in Europe, Stockholm is the
It is against the rules of the exchange for anyone to speak except
the Exchange officials.
All
transactions are handled by an electric switch
board designed fifty years ago by the famous
L.
M,
Ericsson.
However more
than three fifths of the transactions do not go through the Exchange as
i-^
10
banks and brokers can deal with each other.
developed
A neutral
country, Sweden has
strong restrictions against foreign investment.
\/ery
The Swede
public is neither in a very investing mood because of unfavorable tax laws.
These short descriptions are completed in Table 1-2 by the presentation of some basic characteristics of the European capital markets.
A more
detailed description of the functioning of those markets can be found in
OECD [33], J. J. Houriet [18] or EEC [11].
Above all, it should be kept
in mind that the characteristics of various European markets differ sub-
stantially.
The Data
2)
A tape file of prices and daily. returns on 268 stocks of nine European
countries has been constructed.^
'
This includes daily observations for a
five year period from March 1966 to March 1971.
introduced later in
tiie
have March 22, 1971
as
A few stocks have been
sample (generally on January 2, 1967) but all stocks
their last observation.
Capital adjustment of all
sorts
(splits, rights,...) have been care-
fully incorporated and double checked.
This feature can be very important
in some countries firms pay most of their earning in that fashion.
as
Dividends have been integrated in the computation of the returns
=
(r
^
P.
—
+ d
-
^
P
^—^) for all
the major capital markets
(France, UK, Germany,
^t-1
Italy, Belgium), however they have not been included for the Netherlands,
Sweden and Switzerland.
T)
'
"Eurofinance" for providing a tape of prices which
constituted the core of the present body of data.
'We wish to thank
11
In
order to eliminate possible errors in the data,
cated screening process had been designed.
fairly sophisti-
a
'
The list of stocks included in the sample are given in Annex A,
Table A-1
to A-7.
It consists of:
France
UK
Germany
Italy
The Netherlands
Belgium
/^vSwitzerland
^
'Sweden
65 stocks
40 stocks
35 stocks
30 stocks
24 stocks
17 stocks
17 stocks
6
stocks
It should be emphasized that this sample includes all
and generally represents a large percentage of the total
larger stocks
market.
In
the
case of Italy, the thirty stocks represent 77% of the total market figure.
The same figure is reached for the Netherlands
Germany it still
(82%).
For France, UK, and
represents over 50% of the market value of all outstanding
shares.
For each country a daily index is also included for the same
period.
They are either the only representative indices on those markets
or the most widespread in the public:
^
'In
(2)
constructing their CRESP file, Fisher and Lorie used a filter screening
process which they called Super-king.
To establish the efficiency of
the technique used on this European file and upon a suggestion of F.
Modigliani, the screening process has been named "Super Napoleon".
The six Swedish stocks are major European stocks.
Although 5 Spanish
stocks are included in the tape, they are of minor importance and not
considered in this study.
12
Table 1-2:
Stock Market Indices (daily)
France
13
Section II:
1 )
Test of the Random Walk Hypothesis
A Review
The amount of empirical
results to present in this study is overwhelm-
As a rule the French market will
ing.
be used as a basis for the discussion;
similarities or differences with other European markets will then be emphaOf course one topic of considerable importance is the comparison
sized.
between the characteristics of behavior of those European markets and the
American capital market.
As outlined in the introduction,
the development of the random walk
concept originated in some empirical findings (Kendall
et al
.
)
[23], Osborne [34],
that successive price variations were uncorrelated.
of the random walk theory suggested that in fact returns
prices) should be serially uncorrelated.
The refinement
(or changes in log
This simple test performed on the
NYSE yielded very strong empirical support to the random walk hypothesis.
The most comprehensive work in this area is the study by Fama [14] on the
30 Dow Jones
Industrial
stocks on a five year
period (1956-62); for all
differentiating intervals the serial correlation coefficients were small
and generally not significantly different from zero.
This matter seemed
to have been settled for good but recently it has been the object of grow-
ing interest from the rebalancing strategy proponents such as Evans
Latane' and Young [25] or Cheng and Deets [6].
In
[12],
their recent article,
Cheng and Deets emphasized that the rebalancing strategy will work better
than the Buy and Hold strategy (abstracting from the arithmetic vs. geometric
mean controversy) if returns exhibit negative serial correlation.
vestor following the rebalancing strategy maintains
in fixed
(usually equal) money value proportions.
a
An in-
portfolio with stocks
Thus if a stock's price
14
goes down
(relatively) one will buy more of its shares to maintain its pro-
portion in the portfolio; if the returns exhibit negative serial correlation, then its price will
tend to go up the next period and the rebalancing
investor will be better off than the Buy and Hold investor.
This is only
one of the factors suggested to be in favor of the rebalancing strategy but
it is widely claimed
(Cheng and Deets, Jennings [20], etc.).
Reviewing the literature it appears that Cootner
[8] and Moore [32]
found a preponderance of negative signs for weekly changes, as did King
[24] for monthly price relatives.
Although Fama [14] gets to the same con-
clusions for four- and nine-trading day changes, he finds opposite results
positive serial correlation) for daily or long term returns.
(i.e.
Fama's
argument is that it all depends on the period used, as all stocks tend to
follow the market rather closely and thus will have collectively
positive or negative correlation, on the sample
of
tlie
market.
,
a
rather
generated by the movement
On the other side rebalancing strategists assert that serial
correlation will constantly be negative (both arguments are not exclusive).
In this
section,
I
will
first study the distribution of the serial
coefficients for each European country and compare it with the results
found by Fama on a corresponding period (5 years of data).
Then the sta-
tionarity over time of serial correlation coefficients for individual securities will be investigated.
2)
The Results
The period covered consists of 1310 daily observations.
try, we get a distribution of serial
of France by Table II-l
and Figure
1.
For each coun-
coefficients as illustrated in the case
Table II-l
.LuatlAN.Y_JMA:.
Sl£. lAL-jm&P-ElA TTrN
-WEEKS
,S^--P^A^
MOK'TH
15
c
V-
-it
*
^
•*
->
*l
*,
r.
oooc coooooD O O O O
«-
oooo c oo
r
•*
^f
I
C-
ooo co
16
If the returns have finite variance, and in a large sample of time
observations, the standard deviation of
'
cient is given by the Anderson formula:
SD
the serial
P.
P
correlation coeffi
(1
=
/N
where N is the sample size (1310 for daily returns) and
sidered
(1
of all
is
the lag con-
unit in these tests).
The distribution of serial
cal
t
European countries.
correlation coefficients in France is typiIn
Figure
1
the distribution found by Fama
for daily returns on a comparable period is adjacent to the one which was
found for France; the dashed line represents two standard deviations from
zero.
It can be noticed that in the case of France
(like all
European coun-
tries) the distribution for daily changes is much flatter than for America,
without any mode around zero.
serial
Also the percentage of stocks showing
a
correlation larger than twice the standard deviation is greater.
in the case of French daily returns,
Finally, and still
stocks with fairly high coefficients
the American case.
Still
(in absolute value)
there exist some
in comparison with
(2)'
^
looking at Figure 1, it appears that those deviations from the
random walk hypothesis get less significant for longer time intervals.
^^^See Kendall
[23].
^^^Although coefficients greater than two standard deviations are statisti
cally significant, the real magnitude of their effect is still very
small
I
17
Table II-2:
Dally returns
Ser. corr,
j
,
serial correlation
# of positive
,
# of terms
!
!
Average
France
-0.019
Italy
-0.023
!
\2
terms
V
St.Dev.
33/65
41/65
1V30
3^Ao
9/30
21/40
28/35
23/35
I
I
U.K.
0.072
Germany
0.078
Nederland
0.031
I
I
17/24
9/24
7/17
5/17
A7
4/17
I
Belgium
-0.018
j
Switzerland
0.012
Sweden
0.056
i
Standard Diviation
of the coefficients
~_
1/6
3/6
0.035 (estimated)
Table II -3:
France
11
Biweekly returns
,
serial correlation
Serial corr,
of positive
Average
terms
# of terms
^
2
-0.050
21/65
6/65
Italy
0.050
21/30
3/30
U.K.
0.005
20/40
3/40
Germany
0.038
4/35
Nederland
0.052
17/35
16/24
Belgium
0.019
10/17
1/17
3/17
1/17
6/6
0/6
Switzerland
-0.063
Sweden
Standard Deviation
0.070
-
0.09 (estimated)
•
st. dev;
3/24
18
The third plot of Figure
shows the distribution for biweekly returns;
1
the distribution of correlation coefficients assumes a shape more in line
with the random walk theory and the percentage of stocks having
a
coeffi-
cient larger than two standard deviations (dashed line) gets very small
(although some coefficients are fairly high).
Summary statistics on the distribution for each country are given in
Table II-2 and Table II-3.
In
each of these tables, the first column gives
the average over the sample of stocks, the second column gives the percen-
tage of stocks with
a
positive serial correlation and the third column
indicates the number of stocks with
a
correlation coefficient whose abso-
lute value is larger than twice the standard deviation.
The conclusions
that can be reached for any European country are similar to the previous
ones.
As
far as the predominance of negative serial
no evidence can be found on those European results.
correlation is concerned
In
the case of biweekly
returns for example, only two countries exhibit a tendency towards negative
time dependence; France and Switzerland are the only countries to have
a
larger proportion of stocks with negative serial correlation during the
recent years.
Let us now look at the stability of this time dependence relationship
of returns on stocks.
3)
Stability of the Estimates
For this serial correlation to be used in any meaningful way it should
be stable over time.
In
the random walk framework, one would expect that
this time dependence would be purely accidental
and that
a
stock exhibiting
19
more serial correlation than another in one period would not have any
reason (50% chance) to do so in the next period.
for the predictability of those serial
In this
section we look
correlation coefficients on an indi-
vidual basis.
In
order to do so, the total period has been split into two sub-
periods:
period
1:
period 2:
March 1966
-
December 1968
November 1968
-
March 1971
The coefficients have been computed separately on those two periods.
Then cross-section
(product moment) correlations of serial correlation co-
efficients between the two periods have been computed and are shown in
Table II-4.
Table II-4:
Correlation Between Estimates of the Two Periods
SC^/SC^
France
Italy
U.K.
Germany
Netherlands
Belgium
Switzerland
Sweden
20
Surprisingly enough, there is some evidence of stability of those
serial correlation coefficients of individual stocks.
Thus a stock which
tends to exhibit positive (respectively negative) serial correlation in one
period keeps this characteristic in the following periods.
Only in the
case of Great Britain (the most efficient market?) is this property not
displayed.
Comments
4)
The evidence presented above would tend to categorize the European
stocks into two classes:
a)
b)
(1)
stocks with long period fluctuations around the mean
(low frequency),
stocks with short period fluctuations around the mean
(high frequency).
A plot in terms of stock prices would give
Price
Pri ce
» Time
Class a
Positive serial correlation
of returns
A question which might still
'A
-^
Time
Class b
Negative serial correlation
of returns
need to be clarified is to what extent
somewhat identical interpretation calls for varying short term means.
A quick look at the picture shows that these two interpretations
describe exactly the same behavior.
(
21
the existence of time dependence in return is detrimental to the efficiency
of the market.
Fama [15] defines efficiency as a property of the market to
"fully reflect all available information".
the knowledge of historical
According to that definition
prices could not help anyone to make extra
profits in an efficient market.
One possible intuitive explanation is that
some stocks over-react (negative serial
correlation) to new information
while others adjust slowly (positive correlation) to the information.
Several strategies have been designed to take profit of time dependencies
of this or of a more general
kind.
The rebalancing strategy, using nega-
tive dependencies, has been described earlier.
On the opposite side,
various filter techniques (Alexander [1]) have been designed to take ad-
vantage of positive time dependencies.
22
Section III
1)
:
The Market Model Applied to European Markets
The Market Model
Since the investor is assumed to hold a diversified portfolio of stocks,
the measure of security risk which is of interest is not the risk of
a
se-
curity if held separately but the contribution of that security to the overall
risk of the portfolio.
In
other words, the investor
is
concerned only
with that component of security risk which cannot be diversified away.
This
led to the wide acceptance of one measure of risk, namely the coefficient
of non-diversifiable risk or more simply the beta coefficient of the market
model
The interpretation of the beta coefficient as a measure of risk rests
upon the empirical
validity of the market model.
This model asserts that
the return on an asset, for any period, is a linear function of a market
factor common to all assets and of factors unique to that asset:
+3.1, +e.^
a.
with
E(.,t)=0
cov(c,^, Ij) =
(1)
cov(e,.^., c.^) =
C0V(!
for
i
7^
j.
Then
The result of the portfolio diversification effect is that the appro-
priate risk measure for
risk and not its total
a
security is its contribution to the portfolio
risk;
3-
is a measure of the relative, systematic
23
riskiness of security
i.
Let us write the return on each security as;
^t
=
^•^t^^•t
and consider a portfolio invested equally in
n
securities
"
.1
t
"
1=1
^
1=1
"-
^
fi-
The risk of this portfolio will be given by:
var(W.)
=
t
C-i
n
&y
varfl
1
+ -„
^^
)
z
z
cov(e
.^j
It
e
,
jt
),
According to the market model this reduces to:
var(w^)
r
=
2
6_ var(I
£
"
1
)
+ -^
^
n"^
z
i=l
var(e.
),
^'^
This can be written as:
2
where the bar indicates an average.
in the
When the number of securities included
portfolio increases, the last term becomes negligible.
Evans and
Archer [13] have shown empirically that diversification eliminates this last
term very quickly (ten securities achieve a diversification of 93% of the
residual
risk).
approximate
e
Thus for a diversified portfolio the total
var(I
)
and
e
becomes
a
risk will
measure of risk for the portfolio
24
(since
var(L)
to 3
is a
,
is the same for all
portfolios) and 6., as it contributes
measure of risk for the security
i.
Although the linearity assumption of the market model should not be
confused with the Capital Asset Pricing Model of Sharpe [35] or Lintner
[27], this theory of equilibrium provides a theoretical
support for the
market model
Finally, the empirical validity of the model has been extensively sub-
stantiated by its wide application to common stocks listed on the New York
No attempt will
Stock Exchange.
be made now to summarize the almost infi-
nite number of studies in this area.
the American market will
However comparisons with results on
be drawn in this section whenever relevant.
reader not familiar with this approach could consult Blume [4] and
[5
A
],
King [24].
The same methods are used on the European markets and the systematic
risk of a stock
(Beta) is measured by the regression of the returns of the
stock on some comprehensive index of national wealth, e.g. the return on a
domestic stock market index.
Those regressions have been run separately
for each country.
2)
Selection of
(i
)
a
Time Interval
The Problems
A problem remains to be solved regarding the estimation of systematic risk;
it has to do with tne time intervals and the length of the period used to com-
pute those estimates.
As pointed out by Treynor, Priest,
Mheir results are summarized
in Fisher [17],
Friend and Higgins^
25
and others, the correlation between returns of individual
and returns of an index are not very large.
common stocks
This implies that reliable
estimates of the regression coefficients will only be obtained
number of observations.
quire
a
certain number of years of data (e.g. ten).
the structure and characteristics of the firm will
using shorter time intervals
in
a
large
However as time passes
change and the systema-
This would tend to suggest
tic risk cannot be expected to remain constant.
the obsolescence problem.
v/ith
Using monthly observations for instance, will re-
(weekly returns, possibly daily) to minimize
However as Fisher D7
]
pointed out, the errors
measurement can get very large for short time intervals and the returns
on a stock and on the index appear to become less correlated.
Several explanations can be found for this phenomenon which gets even
more important in the European markets which are supposedly thinner and
less efficient.
1)
Errors of measurement in the index and the returns are the major
factors prompting the use of longer time intervals to compute the 6's.
Their influence is much more important for shorter intervals as the index
is
likely to move less than during longer periods and the relative impor-
tance of the measurement errors will decrease.
Several other errors linked
to the imperfections of the index or to the precision of the model will
tend to reduce the observed correlation.
For example the relevant interval
could be the chronological day and not the trading day.
Some authors remark
that stocks might react differently to different "qualitative" changes in the
index; this specialization phenomenon would favor multi-index models but in
the market model
it would simply add to the random term.
26
2)
Black pointed out the problem of non-simultaneity of quotation.
The problem of non-simultaneity of quotation should be emphasized in the
Except for London, most capital markets follow
case of the European market.
the principle of sequential quotation (one stock price is quoted after the
other) with very little subsequent transactions in the day.
imply some kind of two periods model
This would
including adjustment on past informa-
tion:
^Ut
In
-
any event all
^ '
'h
'
^h-^
"H-
indices are imperfect in this case because they are
not homogenous in time.
In
the same spirit, it has been suggested that some
stocks adjust faster than others which means that it would take more than
a
day for some stocks to adjust
(
distributed lag model).
This kind of short
term lag would vanish when longer time intervals are used to compute the
3-.
In
fact one test of market efficiency would be to see how quickly stocks
adjust to information.
Recently
M.
Scholes advanced the idea that more speculative stocks
would adjust faster to new information.
Well
informed investors would in-
vest in high beta stocks because they will be the most sensitive to this
new piece of information once it becomes public.
3)
Some more basic technical
imperfections appear on the European
markets and on the data base which we are using.
prices have been rounded up; this
First in some instances,
(small) error gets relatively smaller for
large price variation, i.e. longer time period.
It should be remembered
that those markets are less well organized than the American market; on
most of them no market index is computed during the session.
Late in the
27
afternoon
index is computed usinq slightly different stock prices
general
a
from those with which we are dealing.
This could be caused by some syste-
matic bias in the construction of the index such as using
P.M. quotation
1
prices or averages of the day or rounding up the prices, etc.
It has been
decided to keep those indices because they are representative of the total
market.
Using an average return over the sample of stocks included in this
study would completely eliminate the small stocks influence.
4)
argument in favor of using monthly returns versus daily
The usual
or weekly returns is that it "reduces the noise" and thus yields better
estimates.
be shown that,
It will
Let us write the model
=
f^i,t
«i
if the model
is
true, this is a fallacy.
for daily returns as:
(^)
"^i^t^^f
Weekly returns (five trading days) will be given by
a
series of sums
This relation is exactly true only if
of five successive daily returns.
one uses logarithm of price relatives which are additive, otherwise it is
only approximate.
Let us assume that this is the case.
5
5
j^l^ ^•,t+k
hv
with var
c.
,
= 4-
a-
var
b.
-
^i
e,
.
'
= ^-
'A'
"^•^F^_?^ ^t+k)
'
5
4^^^ Vk
^v
Let us call
the estimates of the regression using weekly
returns R. ^,
(2)
28
a^ b* the estimates of the regression using daily returns
«it.
If the least square assumptions hold for (1), they also hold for
(2)
Both estimates are unbiased:
=
E(b^) = E{b.)
b.
but
var
e.
-
var b?
'
-
E(I.
^
!)2
E(I,
var
2
e.
-
^
=
var b.
!)2
-
^
t
t
^
^
t'
t'
The comparisons of the variances of bt and b.
is
vn'
11
tell
the more efficient and therefore which one should be used.
us
which one
The comparison
of the two variances is equivalent to the comparison of their denominators,
but:
Z
t
(I. ^
!)2
-
=
L,
-
+ !.,
t
(I.
^
z
(I, - !,)2 + 5
Z
t
^
-
1)2
^
^
z
V
^
(I,.
-
1)2
^
the denominator of var(b*) is greater than that of var(b^.
between:
Z
t
(I,
-
!,)2
and
5
z
t
(I,
,
I)^
)
and the ratio
29
is
a
measure of the loss of precision due to the grouping.
'
It should now be clear that the longer the time interval
less efficient the estimators
(for the same horizon).
used, the
Intuitively this
means that averaging eliminates most of the extreme points useful
estimation.
If,
in the
for example, all monthly returns are identical, the
varia.ice of the estimates become infinite.
In
other words the gain in
noise reduction is always more than offset by the loss of information.
Mean
Daily Return
In
(same units)
Monthly Return
sumnary, measurement errors suggest the use of longer time intervals
to compute the coefficient of systematic risk; however both the
:tt
ee Malinvaud [29], pp. 281-285,
obsolescence
30
problem and estimated efficiency considerations require the use of short
time intervals, possibly days.
(ii
In
)
The solution should lie somewhere in between,
The Experiment
his
recent work, Fisher [17] used as a criterion the stability of
the beta estimates and tried to determine the
"best" number of observations
for his regressions, i.e. the length of the period on which the parameters
are estimated, using (arbitrarily) monthly returns.
ordinary least squares and then
a
He first aoplied
Kalman filter technique and found that
ten years of data should be used, although the evidence produced for the
dominance of 10 years over
5
or 15 years is not overpowering.
to approach the problem by a different
period used,
5
years of data,
I
I
have tried
(but as slippery) slope; fixing the
computed the characteristics of the esti-
mates using different time intervals for the returns, namely day, week,
2
weeks, month.
The averages over aach country of the beta estimates computed on differ-
ent time intervals are given in Table III-l.
This table shows the strong
influence of the measurement errors on daily computations.
However it
appears that their influence gets very small within a week and the subse-
quent improvement in using larger intervals to compute the 6's is rather
small.
zero.
Quite naturally the measurement errors bias the estimates towards
These errors are still present for longer time intervals, but as
expected their relative weight declines quickly for increasing time intervals.
days
Thus for monthly returns only two observations out of the 20 trading
(the first and last day) will
be affected by those errors and the
magnitude of price variation insures against those slight imperfections.
The average standard deviations for
6
are given in Table III-2 and
confirm the econometric argument developed in paragraph (i)-4.
The smallest
31
Table III-l:
Beta computed on different time -intervals
(average on the sample)
1
--
32
are found for daily computations.
variances
efficient estimates of
(minimum variance).
g
These look like the most
However these are biased
estimates because of measurement errors.
Finally, it is interesting to look at the percentage of the variation
of stock returns explained by the market factors; summary results are given
in Table
III-3.
These figures follow the same pattern as the
Due to the measurement errors the R
themselves.
time interval
used.
2
b
estimates
is increasing with the
Let us assume for a moment that the adjustment of
stock prices is not instantaneous but that it takes a few days to fully
reflect some information.
is
not fully efficient.
could be^
A possible model
2
= ^-
^^-^t^^i^t-i
relative to it.
2
market
to explain such a price behavior
'
-•'
-^^-^t-k^s-f
coefficient of the market model
to increase with the interval
low R
a
'
•^it
Then the R
According to Fama's definition [15] such
(R.
.
versus
L)
would be expected
as the delay in adjustment will
get smaller
Then, whenever the lags are important, one would find a
for the market model using daily observations and slowly increasing
with the interval.
Under this interpretation the R
2
coefficients on an
efficient market will quickly reach their stable value (for increasing time
intervals).
"big four"
In fact a
clear difference appears in Table
(France, U.K., Germany and Italy).
adjust more quickly to new information.
1 1
1-3 between the
These four markets seem to
A quick test is obtained by
(T)
perfect market one would expect the adjustment to be instantaneous
with Y,- = ... = n^ =0.
In a
33
computing the ratio
R
month
R^ day
34
These interpretation and conclusions are purely tentative but seem to
be in agreement with the evidence presented here.
This topic ought to be
investigated in more detail.
In
small
conclusion it appears that the influence of measurement errors is
after
a
week
(a
variation of an average beta from 0.92 to 0.95 can
be considered as unimportant).
biweekly intervals.
as
3)
the best interval
It thus seems
indicated to pick weekly or
The case of Germany, which clearly indicates two weeks
prompted the use of biweekly intervals.
Some Summary Statistics on the European Markets
The various estimates and statistics based on biweekly returns for
each stock are given in Appendix A, Tables A-1
been summarized in Table
1 1
to A-7.
These results have
1-4, which gives averages over the countries for
the major parameters.
a
III-4:
Siimmary results for biweekly computations
(all returns expressed in % )
35
(i)
To make intercountry comparisons meaningful, the role of the
indices should first be investigated.
number of stocks
S-
with weight w.
ZW.3.
If the
=
,
If the index is the sum of a certain
then for those stocks we should have:
1.
index is an equal weighted average
However if the index is
Ieb,
It is even
likely that
stocks) will have
a
market weighted average
a
M.
-
z
B-
>>
1
as
the more speculative stocks
ger stocks are generally more conservative.
is
a
beta
On the other hand if the index
broadly based, equal weight average then the average of the beta of
sample of large (and conservative) stocks will be less than one.
the case for France and as expected the average
than one.
In
a
This is
beta is significantly smaller
the case of the London Stock Exchange the index used is the
Financial times
is
(high
relatively smaller weight in the index and because lar-
(30
Industrial) whose collection of stocks (equal weights)
consis tent with our sample, thus explaining that
1
^
^
3-
=
0.98.
36
The same kind of argument can be developed for each country.
'
The percentage of variation of stock prices explained by the market
A study by King [24] provides
factor varies from one country to the other.
some evidence on the relation between market fluctuations and the variability or a typical security's rate of return on the New York Stock Exchange.
Sixty-three common stocks were analyzed, with rates of return computed on
a
monthly basis from June 1927 to December 1960.
risk has decreased since the pre-war periods.
results.
In
a
more recent work and using
The amount of systematic
Table III-5 shows King's
larger sample of stocks (thus
a
less comparable to this study) Blume [4] found results consistent with the
The mean proportion of security risk due to the market
previous ones.
factor was of the order of 30% for the period 1961-1968.
in Europe do not include the dividends,
thus the average Alpha, as given by the CAPM, would be expected to be:
^^The indices universally used
a =
where
(1
-
B)Rp
a
mean Alpha
B
mean Beta
+0x6
Rp risk free rate
D
In
mean dividend rate on the index.
the case of France and for biweekly returns the order or magnitude
would be:
Rp
~
8is-9%
D
~
2%%
a =
(1
-
0.36% biweekly
yearly
0.10%
--
3)Rp + D X
e
^
.18 x
.36 +
.10 = 0.065 +
.10
which matches fairly well with the regression estimate of 0.174.
^0.165
37
Table
1 1 1-5:
Proportion of Security Risk
Attributable to Market Factors
Period
38
characteristic of the samples of stocks and cannot be directly compared.
4)
Stability of the Risk Measures
The problem of stability (and thus predictability) of the systematic
risk has been studied by Blume
[5]
in his doctoral
monthly returns and long periods (set of
7
Using
years) he found high cross-
sectional correlation, even for individual stocks.
correlation for individual stocks was 0.618
dissertation.
.
The product moment
More recently Robert Levy
[26] replicated those tests on the NYSE using weekly returns on shorter
periods
He found that short term betas were less stable.
(one year or less).
Using yearly periods from 1962 tnrough 1970 he found
a
product moment corre-
lation of 0.486.
If the Betas on the European markets were as predictable as on the
NYSE we would expect the correlation coefficients to lie somewhere in between
these two numbers due to the length of the periods we are using (30 months).
As before two subperiods were considered:
March 1966-November 1968
December 1968-March 1971.
Summary indications on the behavior of the European markets in those
periods are given in Table
1 1
1-6.
Similarly the mean values of
t?
and
R^^
for the sampler of stocks included in this study are given in Table III-7.
Finally the product moment correlation coefficient of a,
the two periods are given in Table
1 1
1-8.
e
and
a
between
39
Table
1 1
1-6:
'^
'^rket
summary
,
biweekly computations
(includes only the returns on the Index)
^an
*
Re turn (^)
1st
2nd
periodj period
0.16
0.12
0.49
-0.10
•0.22
U.K.
Q.14
0.90
0.03
-0.48
Germany
0.19
0.^0
-0.05
Netherlands
0.32
OAk
0.18
Belgium
0.05
•0.04
0.15
Switzerland
0.56
1.25
0.17
Sweden
0.1^
0.29
-0.04
France
Italy
Standard deviation
total
(
40
Table III-8:
Correlation Between Estimates
of the Two Periods
41
Section IV:
The Capital Asset Pricing Model Applied to European Capital
Markets
One would expect the market to place
a
positive price on risk bearing.
Traditionally different measures of risk have been used to determine the
relation between expected returns and the risk borne by the investor (total
More recently an equilibrium model
risk or variance, systematic risk,,..).
has been developed and widely used.
It is generally called the Capital
Asset Pricing Model
(CAPM) and is in line with
presented earlier.
This modal will
tlie
diversification arguments
first be described, then the relation
between returns and risk will be empirically investigated on the European
markets.
1
The Capital Asset Pricing Model
)
Sharpe
a
and Lintner [27],bu1 Iding on the market model, have developed
[^35]
theory of equilibrium in the capital markets.
of perfection of the markets.
Using numerous assumptions
It is possible to develop a relationship be-
tween expected returns and non-diversifiaDle risk measures.
risk-free rate, E(R.) the expected return on
a
security
i
and
If Rp is the
E(R|>^)
the
expected return on the market, it can be shown that the following equilibrium relation holds for all securities:
:(R.)
with
-
Rp = 3.(E(R^)
-
Rp)
Cov (R.,R,^)
^i
=
2
°M
This model
is
based on
a
set of fairly restrictive assumptions:
42
a
-
The market is composed of risk-averting investors maximizing
They make all their decisions
their one period expected utility.
on the basis of only two parameters, the mean and standard deviar
tion of the probability distribution of their terminal wealth. ^^'
The mean and variances of returns are supposed to exist over the
period considered.
b
-
Expectations and portfolio opportunities are "homogenous"; that
investors have the same expectations and opportunities.
is, all
c
-
Capital markets are perfect in the sense that all assets are
infinitely divisible; there are no transaction costs or taxes,
and borrowing and lending rates are equal to each other and the
same for all investors.
As far as the empirical
testing of this model is concerned,
arises in the fact that ex ante expectations are unobservable.
difficulty
a
This model
should thus be reformulated in terms of realized returns based on the as(2)
sumptions that expectations are realized ex post on the average^
"
^Mt
.
^^^Mt^
This leads to the model:
Ri
-
Rp - g^CRM
-
Rp) +
H
where the bar denotes average over the period.
Test of the CAPM on the European Markets
2)
(i)
Traditionally it had been considered that higher returns could
be expected on a security investment with higher level
^
Mhis would imply either
risk
a quadratic utility curve or a joint normal
distribution of returns. However Merton [30 ] derived the same
formula under a less restrictive set of assumptions (continuous time
model
(2)
of total
).
See for example, Jensen [21].
I
43
(usually approximated by the variance of returns).
concept has substituted the systematic risk or
g
The diversification
as the appropriate measure
of risk in the risk/expected return relation (CAPM).
proponents of the former relation^
still
of a
Using annual rates of returns
large sample of stocks for the period 1946-63,
that the market places
is
\
a
However there are
G,
Douglas [9] concludes
positive price on risk bearing and that total risk
as good a measure of risk as systematic risk.
However
a
serious problem
of estimation is present due to the correlation between systematic and
risk
total
(3
and a).
first computed the
over
a
e.
10 year period,
the mean annual
Lintner [28] tried to get around that problem; he
of each security of
a
1954-63, using annual
sample of 30, common stocks
returns.
return for each company, R., on the
first-pass regressions and on
(e.) the residual
3.
obtained from the
variance around the first-
His results are
pass regressions.
R.
S
He then regresses
=
0.108 + 0.0636. + 0.237S^(e.),
(0.009)
(0.035)
More recently Miller and Scholes [31] replicated this study on 631
stocks of the CRSP files.
Their results are slightly different for the
same period:
R.
^
=
0.127 + 0.042 3. + 0.310S^(e.)
^
(0.005) (0.006)^
(0.026)
R^ = 0.33,
'Their empirical work has to be based on individual securities, as the
total risk reduces to the systematic risk for diversified portfolio.
44
As
2.0-193 it appears that the intercept term is larger than ex-
Rj^^
pected and the coefficient of
CAPM.
B
smaller than its value indicated by the
Miller and Scholes then investigated econometric biases which could
explain these deviations from the Capital Asset Pricing Model and found their
magnitude to be largely sufficient to create those results:
correlated.
--The residual and systematic risks are still
--The skewness of returns exaggerates the importance of S (e.).
--B.
is only an
estimate for the true systematic risk; this error
in variable strongly biases
the coefficient of
(1
6.
towards
and
''
)
'
the coefficient of residual risk upwards.
This factor should
be emphasized in the Lintner-Miller & Scholes results as they are
using annual observations to compute the Betas.
All
residual
this would imply
a
significant relation between mean return and
variance ex post even if none exists ex ante
.
The same tests have been run for European markets.
The estimated co-
efficients (and their standard deviations) of the regressions of mean rerisk (standard deviation a) and mean returns versus
turns versus total
systematic risk (b.) and residual risk (standard error of the first-pass
regressions) are given in Table IV-l
Let us more specifically consider the last set of regressions.
case of France:
R.
^
0.23
(0:2)
-
0.3
(0.1)
+ 0.09 S.E.
(0.04)
T)
'The estimates are not even consistent or assymptotically unbiased,
.
'
=
In
the
45
table
lV-1:
cross-sectional results
46
the return on the market was less than the risk free rate in that
As
period the negative sign of the coefficient of
B
was to be expected.
As
emphasized previously, the errors in variables due to the measurement of
and SE in first-pass regressions
errors) can easily explain the (spurious) importance of the residual
Besides the residual
3
(and the negative correlation of their
risk.
risk coefficient is only non-negligible (and signifi-
cant) in the case of France, the Netherlands and Belgium.
For all other
countries, and especially Germany or England, it is both small and unsignificant.
One interesting feature should be noticed:
in all
countries syste-
matic and residual risks seem to have opposite influence on the returns of
a
security.
(E(Rj.)
Rp
-
This means that, if, for example, the market goes up
>
0)
investors would be penalized to hold "residual
the opposite, on a down market, securities with high residual
provide
a
residual
Thus while the
good protection.
risk SE. seems to be
a
6-
is a
multiplicator factor,
stabilizator factor against large variations
and intended as a protection against big losses.
However it is most likely
that those findings are simply caused by some statistical
(ii)
risk"; on
risk seem to
bias.
As these regressions did not present any consistent evidence that
the systematic risk was not the appropriate concept as far as the pricing
of risk is concerned, the Capital Asset Pricing Model will
be investigated
in more detail
The analysis has been conducted for each country with individual securities.
As previously the expected returns have been approximated by the mean
returns on the period and the following cross-sectional
'Except Germany where c
^
0.
regression has been
47
run for each country;
= y + vB.
R
+ £.
i=l ,N
N =
number of stocks
where the B.s are the estimates obtained in the first-pass regressions.
The results are given in Table IV-2 along with some plausible estima-
tions of tne regression coefficients assuming that the Capital Asset Pricing
Model
holds.
Those proxy estimates are:
Risk free rate Rp:
for
u_
(biweekly return)
[Mean return on the market (including dividends)]
for
-
[risk free rate]:
v_.
The results of Table IV-2 can be compared with the extensive evidence on
the American market presented by Jacob [19] or Blume [5 ].
On tne French market, the relation between mean return and
R.
^
=
e
is
given by:
0.56 - 0.286.
(0.10) (0.16)^
The signs of the coefficients are in agreement with the CAPM predictions
although the intercept term is somewhat larger than the risk free rate, inducing the slope to be larger (in absolute value) than forecasted.
For
most countries the coefficients are comparable in sign and magnitude with
their CAPM
a
priori estimates.^
'
In
the regression for Swiss stocks the
intercept term is negative but not very significant (while the slope co-
efficient is very significant).
^The sample of Swedish stocks consists of only 6 stocks and one should
have little confidence on the results found for that market.
48
49
In
general the R
2
to those found by Jacob
of those market line regression are low but comparable
[19] on the American market.
least squares were met it can easily be shown that
be estimated using individual
If the assumptions of
tfie
market line should
securities as any grouping of securities
(portfolios) will hield less efficient estimates;
Malinvaud [29] and others
have shown that the only portfolio approach which would yield (almost)
efficient estimators would be the grouping of securities into portfolios by
ascending order of their dependent variable
6.
However we are faced with
the problem of errors in variable which imply biases in the CLS estimates.
In
this case the OLS estimates are not even consistent.
Malinvaud suggests
the application of a grouping technique coupled with the use of an instru-
mental
variable.
The grouping procedure requires the ranking of securities
by ascending order of their 6's and their inclusion in large portfolios.^
'
Black, Jensen and Scholes [3] developed this technique and applied it suc-
cessfully to the American market.
In a
later
stage of this research the
same method will be applied to the four major European stock exchanges.
'This technique nas the advantage to yield assymptotically both consistent
(for very large portfolios) and efficient (for very many portfolios)
The tradeoff between those two properties appears clearly
estimates.
especially when the number of securities is small as it is in the case
of our sample.
None of this property clearly dominates the other.
50
Conclusion
For the first time, this article applies the mean-variance and CAPM
framework to European capital markets.
A sample of over 250 European
stocks has been studied for the period 1966-1971.
First, the random walk hypothesis has been tested on each European
market and the results confronted with comparable evidence on the American
market.
The distributions of serial
correlation coefficients do not look
fully consistent with the random walk hypothesis; in that respect, the
European markets seem less efficient than the New York Stock Exchange.
Surprisingly, individual serial correlation coefficients seem to be rather
predictable on all markets:
tive
(resp.
a
stock displaying
a
price pattern with posi-
negative) serial correlation in one period will keep this
characteristic in the following periods.
In
the traditional market model
tion between risk and return.
framework, we then studied the rela-
The systematic risk of each security rela-
tive to its national market index has been comouted using various time
intervals and the robustness of those estimates tested.
In
general
the use
of daily returns did not yield satisfactory estimates but it turned out
that the markets reflecting new information the most quickly were those
which
a
priori would be thought to be the most efficient (and certainly the
more liquid), i.e. U.K., France, Germany and Italy.
The R-square coefficients
of the regressions of the stocks return versus the market return are of
the order of magnitude of their American equivalent.
The stability over
time of the betas and of various statistics for individual
been investigated with similar results.
stocks has also
51
Finally an attempt has been made to evaluate the market line of the
Capital
Asset Pricing Model for each European market.
generally consistent with
a
priori expectations.
The results are
Different measures of
risk have been used to determine the relation between expected returns and
the risk borne by the investor.
52
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