LIBRARY
OF THE
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
ALFRED
P.
WORKING PAPER
SLOAN SCHOOL OF MANAGEMENT
WEAK-FORM EFFICIENCY IN THE GOLD MARKET*
by
Adrian
WP1013-78
E.
Tschoegl
August 1978
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
WEAK-FORM EFFICIENCY IN THE GOLD MARKET*
by
Adrian
E.
Tschoegl
WP1013-78
August 1978
ABSTRACT
This paper investigates the efficiency of the gold market with respect
to the information contained in sequences of successive price changes.
Tests for serial correlation and modelling the changes as first-order
Markov processes indicate some short-term dependence.
While there is
no reason to believe outsiders can profit from knowledge of these
In addition,
relationships, insiders might, though this is not certain.
the application of a market model to monthly returns for the period
1974-1977 results in the finding that gold's 'alpha' and 'beta' were
positive, but not significantly different from zero.
*
I would like to thank Richard A.
Cohn, Edwin Kuh, and Donald R. Lessard
for their criticism, advice, and assistance.
Weak-Form Efficiency in the Gold Market
I.
Introduction
This paper treats gold as
from
a
financial asset and investigates its
point of view of the Efficient Markets Hypothesis(EMH)
the
strong form of the EMH proposes that all information will be
in
security
prices
in
such
a
way
as
research
into
.
The
impounded
to leave no opportunity for
extraordinary returns based on any information.
begin
price
logical
One
way
to
the degree to which this formulation holds is to
take some extremely simple, widely available item of information and to
see whether one can use it for profitable trading.
inefficient
with
respect
to
simple
information
improbable that it would be efficient with respect
the
If
it
to
market
is
extremely
is
which
some
is
more complex or less freely available.
The paper examines a series of twice-daily prices for gold to determine
whether successive price changes are independent, and if
one
can
use
not,
whether
knowledge of the dependence to generate trading profits.
The techniques used are tests for serial correlation and modelling
the
change sequences as first-order Markov processes.
The paper also applies
returns on gold.
over
a
standard one-factor market
model
to
monthly
This Is an itnorphous test In that it simply oheoks If
some period holders of gold achieved excess risk-adjusted returns
3-
their investment.
on
In
realizations.
while
Thus
the
expected
ante
ex
One can, however, only observe ex
excess risk-adjusted return is zero.
post
market
efficient
an
prove
tests
the
grossly
nothing,
discrepant results would cause one to question either market efficiency
or
the model.
Academic research in the field
gold. Inter national
finance
finance
of
as
has
by-and-large
sub-field of economics has of course
a
discussed it in the context of international reserves
considerations.
payments
ignored
balance
and
However while there are innumerable articles
Spanish,
investigating the efficiency of the US, UK, W.German, French,
Japanese,
and
Israeli
stockmarkets
and
,
market
the
exchange, there is no comparable study of the
gold
legally
or
are
197^^
is
Americans
In
There
sense it dropped from view.
a
number of reasons the gold market might be of interest.
represents
First, it
financial asset market.
the
This
forbidden to hold gold in any form other than as jewelry
coins of numismatic value.
a
foreign
for
market.
probably due in large part to the fact that from 1933 to
were
of
value
a
substantial
Pick (1977)
efficient
highly
estimates that at the end of 1976
of the stocks of gold held by governments and international
organizations was in the vicinity
private
probably
and
of
US$203.7
billion
holdings US$104.9 billion (both amounts based on
price of US$135/oz.).
This compares with
a
and
a
that
of
free-market
capitalization for the
New
York Stock Exchange of US$856 billion, and US$65 billion for the London
Stock Exchange (Capital International Perspective, Jan.
1977).
4-
There are major gold markets in Zurich
London,
,
world's
countries
therefore
expect
markets in most of the
centers.
augment
the
trading is potentially almost
efficient:
between
would
One
New
,
Informal, and often illegal,
Chicago, Hong Kong, and Singapore.
York,
Frankfurt, Par is
the
main
trading
gold market to be highly
continuous
competition
and
markets should reduce the commissions and transaction costs in
The widely dispersed markets
any one market.
not
only
increase
the
overall market's liquidity, but also act as sensors so that information
arising anywhere can very quickly begin to influence prices
market
gold
enables
Thus the
.
one to test the theory of efficient markets in
market in which it was not developed, but
where
a
priori
a
would
one
expect it to hold.
The second reason gold might be of interest is related to
to
for
the first.
opposed
but
While one would expect the market to be highly efficient
the reasons listed above, nevertheless gold is popularly associated
with hoarding,
price
'gold bugs', and apocalyptic visions of the future.
might therefore reflect 'mispricing'
risk-adjusted excess return), if buyers pay
value to them as
political
a
hedge against
the
Its
(in the sense of a negative
a
premium because of gold's
complete
collapse
and monetary systems, or because, being in
national
of
form,
'bearer'
it
enables them to evade taxes or confiscation.
The third reason is
a
technical one.
The London morning and
afternoon
gold price fixings give the researcher ready access to two transactions
prices
per
day.
At
10:30am
and
3:30pm
each
business
day,
representatives of the five firms that form the London gold market meet
5-
and shortly thereafter
fix
a
price that clears the market.
price series are therefore relatively uncontaminated by
of
prices
carried
The fixings
the
over from some earlier transaction.
inclusion
The data does
suffer from some problems since the times are not exact and the volumes
traded are secret.
Even if the volumes traded were known, these
approximations
represent
since
orders internally and only clear
however
imbalances.
their
any particular fixing, the price is still
internally.
do not receive dividend payments.
find,
we
fact
is traded
at
Finally,
gold
Therefore we can be fairly
confident that any signs of non-independence between
that
last
This
transaction price since the
a
firms will use it in matching some orders
changes
many buy and sell
it reasonably certain that even if no gold
makes
holdings
offset
firms
the
would
successive
price
especially in day-to-day data, is due to real
phenomena and is not an artefact of the
way
prices
are
recorded
or
dividends attributed.
The basic model used is as follows:
Z'(t)
(P'(t)
=
where Z'(t)
P(t)
return
P(t-1))/P(t-1)
-
is the
=
r(t)+ e'(t)
percentage return on gold over the period t-1 to
the price of gold at time t,
is
on
assets
of
component of the return.
time t-1.
e'(t)
the
same
risk
r(t)
and
The prime indicates
is assumed
is
the
e'(t)
a
normal
of
is the unexpected
random variable
to have the properties:
rate
t,
as
of
6-
E[e' (t)]
cov
=
(e'(t), e'(t-k))
If r(t)
is a
E[Z'(T)]
=
=
0,
=
t
=1,2, ...k, k<t
constant then
E[r(t)
e'(t)]
+
r(t)
and therefore cov
(
Z
'
(
t) ,Z
'
(
t-k)
)
=
0.
This further implies that:
E[Z'(t)]
=
E[Z'(t) |Z(t-1
that is, the marginal
knowledge
of
the expected
),
and
this
equals zero.
Z(t-k)]
returns
conditional
return
over
implies
that
the
next
period
equal,
or
that
that
already
not
is
Since the covariance of the returns equals
the
correlation
However suppose that r(t)
function of other variables which change
knows
are
the past series of returns provides no information about
incorporated in the return.
zero,
Z(t-2)...
between Z'(t)
is not a
over
and Z(t-k)
constant but rather
time.
If
the
a
market
the relationship, the unexpected portion of the return may still
follow the model:
E[e' (t)]
X
7-
cov(e' (t)
and
,e' (t-1 ))
=
,
E[Z'(t) lZ(t-1 ),Z(t-2), ...Z(t-k)]
=
r(t)
but
E[Z'(t) |Z( t-1 ),Z(t-2),...,Z(t-k)] at E[Z •(!)],
except by chance, and similarly,
cov(Z'(t) ,Z'(t-k))
i
This means that the expectation of the next period's return depends
the
past
series
of returns, the serial correlation of the returns is
not equal to zero, but no consistent excess returns are possible
prices
r(t)
already
is
returns
on
fully
incorporate
not constant,
the
presence
the relevant information.
of
serial
does not prove market inefficiency.
correlation
However if r(t)
and furthermore the period over which one measures it
is
since
Thus if
the
in
is
small
short,
then
one can treat it as constant, and assume
cov(Z'(t) ,Z'(t-k)
)
-
0.
The presence of serial oorrelatlon In the returns then
remains
us
un
8-
indicator
that
market
the
may
with respect to the
inefficient
be
information contained in the return series.
In
Section II we report the means and standard
returns
first-order
processes.
Section
monthly returns.
takes
IV
the
V
applies
a
two
with
series
the
largest
standard market model to four years
of
Section VI summarizes the results.
Distributions
The data consist of the morning (AM)
in London from Jan.
observations
several
and models them as first-order Markov
correlation
serial
Section
Section II.
of
Section III presents the results of tests for serial
series.
correlation.
deviations
the
in
to
Jun
series
and
1975
2,
AM
.
interpolated for the PM fix for Dec 24,
series to the same length.
fixing prices
and afternoon (PM)
30,
1977.
There
were
631
629 in the PM.
Two prices were
1975 and
to
1976
bring
both
Over the period the price of gold fell from
US$l85/troy ounce at the begining of the period to US$143/troy ounce at
the end.
The AM and PM series were used to generate four series of the
form
Z(t)
=
P(t)/P(t-1
)
-1
and four series of absolute changes:
A(t)
=
P(t)
-
P(t-1)
9-
representra)
series
The four
afternoon):
the
b)
morning):
morning-to-morning
the
c)
(afternoon
change
overnight
Table
change.
afternoon-to-afternoon
change
within-day
the
I
(morning
to
subsequent
to
change:
and
presents
their
d)
the
,
means
and
standard deviations.
While the means for all eight
different
negative,
are
none
zero at the 90% confidence level.
from
significantly
are
This indicates that
swamped
over very short periods anticipated changes are completely
the
effect
of
hypothesis that E[r
(
t) +e( t) ]=0
,
One would not reject the
changes.
unanticipated
the
by
and one cannot
infer
E[r(t)]<0.
that
Histograms and Gaussian probability plots all show the distributions of
the
changes
be
to
lepto-kur totic
Gaussian, and have fatter tails.
Mandelbrots'
(1965)
They
.
are
results
These
more peaked than the
are
consistent
findings for cotton and stock
and Fama's (1965)
We will not in this paper enter the debate
price changes respectively.
not
on the nature of the generating processes since this is
for our
with
essential
purposes.
Serial Correlations
Section III.
Even if the distributions of the price changes do
variance,
the
serial
correlation
coefficient
not
have
(RHO)
is
a
finite
still
from some
unbiased estimate of the true serial correlation (Fama,
1965,
results of Wise,
concerning
appropriate
1964).
distribution
below are only indicative.
In
view
of
the
questions
an
the
and the constancy of r(t), the RHOs reported
Nevertheless,
the
discovery
of
strongly
TABLE
I
MEANS AND STANDARD DEVIATIONS
Variable
10-
significant
serial
uncomfortable about
correlation
our
coefficients
hypothesis
of
the
would
leave
independence
us
of
the
unexpected component of successive price changes.
In
that
vein
we
have
calculated
RHOs for four sets of successsive
changes.
Asterisks indicate significance at the 5% level.
a)Z20(t)
and
RHO
=
Z4(t)
.208*
The change from the evening to the following morning
is
strongly
and
positively related to the subsequent morning to afternoon change.
b)
Z4(t)
RHO
=
and Z20(t+1)
.061
The within-the-day change is
positively
weakly
related
to
the
The morning-to-morning change is negatively and weakly related
to
the
and
following over-night change.
c)
Zam( t-1
RHO
=
)
and Zam( t)
-.034
previous morning- to-morning change.
-
d)
Zpm(t-I)
RHO
=
11-
and Zpm (t)
-.099*
change
The afternoon-to-afternoon
tends
reverse
the
indicating
some
to
previous
afternoon-to-afternoon change.
Two of
the
RHOs
four
independence
significant,
are
successive changes.
between
of the RHOs were estimated
by
7(1 /n-1
)
Fama
As
.
notes, if the distributions of returns are 'fat-tailed' rather
(1972)
than Gaussian,
this
significance.
In
method
addition,
results
the
an
in
two
overstatement
day-to-day
series
of
the
both
have
negative first-order serial correlation coefficients, whereas
sets
of
However the standard errors
expression:
the
lack
of
changes
the
two
shorter periods both have positive first-order
over
RHOs.
Osborne
Niederhoffer and
market-makers,
<
0)
a
(1966)
argue
that
in
sequence of orders will generate reversals (i.e.
(RHO
>
0)
when
one type of order predominates.
underlying economic mechanism involves the exhaustion of
which
form
in balance.
a
RHO
generate
when buy and sell orders are equally numerous, and will
continuations
with
markets
limit
The
orders
'reflecting barrier' when buy and sell orders are roughly
Our results are consistent with this argument,
especially
when one supplements it with the possibility that the morning fixing is
less
important
than
the afternoon one.
Each fixing price then is an
-
12-
one to continuation in
outcome of two opposing tendencies:
run,
and
the
short
the
other to reversal over the longer periods.
Over longer
intervals prices are more likely to have adjusted to reflect fully
information
and
the
by
afternoon
fixing in particular buy and sell
orders are likely to be present in equal
afternoon-to-afternoon
series
reversals
proportion.
dominate
Hence
for
change.
the
If
the
continuations, and
there is only weak continuation from the within-the-day change
overnight
new
to
the
morning fixing is less important than the
afternoon it will not completely adjust to
late in the previous afternoon and overnight.
occurring
information
new
The very strong tendency
to continuation from the overnight change to the within- the-day change
will
then
almost
match
the
tendency to reversals due to the longer
elapsed period between morning-to-morning changes.
This explanation depends strongly on the assumption
fixing
that
morning
the
on average represents a smaller volume of trading than does the
afternoon.
The assumption however is not unreasonable if one remembers
that 10:30am in London is 7:30am in New York and 6:30am in Chicago, and
that since 1974 these have become increasingly important gold
markets.
Table II presents the
the
serial
correlation
day-to-day series with lags of from
the
daily
1
coefficients
to 60 trading days.
changes seem random and to damp-out over time.
cannot reject (at the 5% significance level)
the
for
auto-correlation function for the lags of
equal to zero.
The RHOs for
In
fact, we
the null hypothesis
1
two
that
to 10 days is flat and
The Q statistics for Zam and Zpm are
14.96
and
17.03
respectively, with the latter being significant at the 10% significance
o
w
M
u
M
b
o
u
z
o
o
M
M
CO
13-
level
Q
,
£j
n
=
and
where
(RH0(j))»»2
distributed as chi-square with
is
degrees of freedom.
j
the serial correlation coefficient of lag j,
the number of observations.
While the
Q
(
j=
1
,
.
.
.
,
10)
,
RHO(j)
is
and n is the
must
statistics are high, one
remember that the significance is exaggerated because of the fat-tailed
distributions
of
daily
the
returns (Cornell
&
Dietrich,
The
1978).
magnitudes of the serial correlation coefficients of the lagged changes
and of the Q statistics in this study are quite similar to those
just cited in their study of efficiency in the market
authors
by
the
for
foreign exchange.
gold
There is one surprisingly large relation in
complex
trading
strategies
While the results do not rule
next
Section
the
question
out
than taking advantage of day-to-day
dependence, no simple rules spring to mind.
the
the
data between the morning- to-morning changes twenty days apart but
this could easily be due to chance.
more
found
We will defer to later
in
of whether we can use the short-term
dependence we have found to make extraordinary profits.
Section IV.
An
Ma»"kov
alternative
investigate
Transition Probabilities
approach
successive
to
price
the
use
changes
of
is
serial
to
correlations
model the changes as
to
a
-
Markov process.
14-
Doing so requires no assumptions as to the
nature
of
the distribution of the changes.
A
number
authors
of
have
Niederhoffer and OsborneC 1 966
did
Fielitz(1975)
and Fielitz and BhargavaC
,
market
1
973
)
Kingdom,
index, and the latter for
for
and
the
sample of stocks quoted on
a
works
fuller description of the underlying mathematics and some of the
a
Goodman (1957)
state
Transition Probability Matrix(TPM).
states
of
process
be
state
in
j
in
in the previous period.
i
X(t)
,
(
is first-order
Pr[x(t)
=
...x(t-k)
The TPM is
The elements are estimates of
will
system
from
one
a
matrix of conditional
the
process at time (t), and the vertical by the states at
the
time (t-1).
a
The horizontal dimension of the matrix is given by
probabilities.
and
Any Markov Process is completely described by its
another.
to
Anderson
to
the derivation of the tests used below.
for
Markov theory is concerned with the transition of
chain
first
the
further potentialities of this line of analysis, and
state
Dryden(1969)
.
The interested reader is referred to these
the London exchange.
for
particular,
In
investigated stock prices in the US, as
)
did the same for the United
Ryan(1973)
overall
technique.
this
used
t=0
,
1
,
.
.
.
,
T)
,
with
a
probability
that
the
given period, given that it was in
For
a
the
a
stationary
discrete,
Markov
finite number of states, the process
Markov if
s(j)|x(t-1)
=s(i)]
=
s(i)]= Pr[x(t)
=s( j)
I
x( t-1
)
= s( i)
,
x(t-2) = s(i),
-
That is, the probability that x(t)
15-
is
in state
prior
to
at time (t)
depends
and not on the sequence of
only on which state it was in at time (t-1)
states
j
The transition probabilities Pij satisfy the
(t-1).
following conditions:
Pr[X(t)
s(j)|X(t-1)
=
with (i,j
for all T,
(
j=1 ,2,
.
.
.
=
=
s(i)]
=
1.2, ...,m),
Pij(t)
=
Pij(t+1)= Pij
^ Pij ^
1,
and
£j
Pij
=
1,
,k)
Anderson and Goodman (1957)
have shown
the
that
Likelihood
Maximum
Estimator of Pij is:
Pij
=
n(ij)/n(i)
Where n(ij)
or
is the number
of observations in
a
cell, and n(i)'=Sj n(ij)
the total number of observations in the ith row.
In
this
have classified all price changes into one of three states:
change
(NC),
and
down
(D),
defined
paper
we
up (U), no
by the percentage change being
greater than, equal to, or less than zero respectively.
We assume that
the direction of the most recent change depends only on
the
of the preceeding change.
hypothesis
that
direction
We then test the assumption against the null
successive
changes
are
independent.
We also test
whether the results we observe are stationary over the sample period or
not.
We prepared Transition Probability Matrices for the two sets of changes
16-
-
with significant serial correlation coefficients.
results for the sequence Z20(t)
the
Zpm(t-I)
and
Table
ZM(t), and Table IV those for
and Zpm(t).
As one can
III continuations (an up followed
in Table
see,
by
are more probable than reversals (an up followed by
etc.)
vice-versa), which is consistent with the positive
earlier.
observed
coefficients
In
In both tables
down, and
Table IV reversals are more likely
the
series'
RHO.
continuations are almost as likely as reversals and this
contrast
some
in
a
up,
an
correlation
serial
than continuations, and this too is consistent with
stands
presents
III
to Niederhoffer and Osborne's findings that
reversals were twice as likely as continuations.
Their
data
however
covered much shorter trading intervals than does this study.
The test of the null hypothesis that all the rows are identical is from
Anderson and Goodman.
The statistic:
Zij n(i)'- (Pij -P' j)^ /P'
is
is
distributed as chi-square with m(m-1)
the
number
degrees of freedom,
of states of the process (i.e.
P'j=2i n(ij)/Ei Ej n(ij)
(i.e.
the total number
the
results
significant at the
significant
reject the
of
observations
in
For Table
are X**2=20.809 with six degrees of freedom which is
^%
level.
For
Table
IV,
X*»2=13.2749
at the 5% level, but not at the 2.5% level.
null
m
m=3 in this case), and
the jth column divided by the total number of observations).
III
where
hypothesis
that
the
within-the-day
and
is
Thus we would
change
is
TABLE
in
MARKOV TRANSITION PROBABILITY MATRIX
OVER-NIGHT CHANGE AND WITHIN-THE-DAY CHANGE
Z4
Z20
TABLE IV
MARKOV TRANSITION PROBABILITY
MATRIX
^^^^^^^^^^=^2zEVENIN^a^^
^^^^
Zpm(t)
m(t-l)
Note:
elements are actual
TZl
f^^^°"^^
elements
are probabilities and sum
for rounding error.
counts.
Below diagonal
to 1 across rows, except
'^^'^^P'^
'
17-
of the overnight change, but would be much more ambivalent
independent
about dependence between successive evening- to-evening changes.
We also tested whether or not these
The
period.
sample
relations
were
P'(j)
are
replaced
P''(ij)
by
and
m(m-1)(t-1)
X**2=m.1351
Zpm(t-I)
5%
(T=1,...,5).
t
level.
the
are the cell
summation
the
that
over
is
statistic is distributed as X**2 with
The
degrees of freedom.
For the
series
Z20(t)
which is not significant at the 5% level.
and Zpm(t),
except
above,
P''(ij)
where
probabilities based on the entire sample, and
i,j,
over
series were divided into five six-month periods.
The relevant test statistic is similar to the one
the
stable
and
For
Z4(t),
the series
X**2=21.263 which also is not significant at
the
Thus in both cases we would not reject the null hypothesis
that the processes were stable over the sample period.
The next question of course is
whether
one
evidenced in Table III for profitable trading.
the
can
use
the
dependence
To test this we derived
means and variances for Z4(t), conditional on knowing the state of
Z20(t-1
).
with
1)
ELZ4IZ20
>
0]=
2)
E[Z4|Z20
=
0]
=
-.033%
3)
E[Z4|Z20
<
0]
=
-.1%
Green (1968)
.13%
,
,
,
standard deviation of .55%
a
with
with
a
a
standard deviation of .63%
standard deviation of .66%
reports that the commission charged on
a
purchase or sale
-
18-
conducted via the fixing was .00025%.
While this may have changed, the
implication is that if one could buy or sell at the fixing prices,
could
make
albeit
profit,
a
with
some
However to use this
risk.
strategy one must know the fixing price and make one's decision
it is set.
normal
one
before
Purchases or sales outside of the fixing are subject to the
bid/ask
spreads.
For
the sample period this spread seems to
have been on the order of .5 to 1.1%.
Outsiders
would
thus
seem
to
have been unable to make consistent profits from betting the transition
probabilities of the most dependent sequence of changes.
On
Traders at
the other hand, this may not hold for insiders.
are in telephone contact with their parent organizations
are
in
contact
with
traders
in
Zurich,
fixing
a
who
turn
in
All these
New York, etc.
individuals therefore do have some idea of what state will prevail, and
may be able to conduct their transactions at
However
we
changes in
do
the
not
know what price elasticities pertain.
quantities
of
gold
be
no
more
Very small
move
might
offered
prices
Finally, the profits
sufficiently to severely limit potential profits.
may
commissions.
fixing
the
than is required to compensate traders for the time,
telephone bills, and similar costs that
they
incur
in
policing
the
price.
The results from modeling gold price changes as
process
are
the Section.
successive
a
first-order
Markov
similar to those of the authors cited at the beginning of
between
All have found some tendency to non-independence
price
changes.
In
inversely related to the size of
general though the tendency seems to be
the
oompany
whose
atook
is
belnK
19-
examined.
Fiel itz( 975
1
also found that the dependency tended not to
)
be stable over time.
Section
Market Model
V.
This section reports the results
model
exercise was two-fold:
systematic
applying
one-factor
a
of monthly returns on gold.
years
four
to
from
first, to estimate
gold's
market
The purpose of the
'beta',
i.e.
its
risk to see whether this was negative as has been suggested
by some (e.g.
MacDonald
Solnik,
&
and second,
1977)
estimate
its
instance
by
portfolio,
and
to
ex post risk-adjusted excess return.
The market
model
is
standard
a
one
used
as
for
Jensen( 1968)
Rg - Rf
=
where Rg Rm
,
the
+
a
,
riskless
b(Rm -Rf)
and
Rf are the
asset
systematic risk i.e.
portfolio
+
divided
by
e
returns on gold,
respectively,
(b)
the ratio
its
the
of
is
market
a
measure
the
covariance
with
variance of the latter, (a)
measure of the excess return, and
(e)
is
the
of
gold's
the
market
is the Jensen
classical
stochastic
error term.
The
perspective of the test is that of
a
US investor who can construct
20-
-
a
portfolio by choosing from amongst gold, Treasury Bills, and
market portfolio, all of which are denominated in US dollars.
period
is
from January 1974 to December 1977.
calculated from the PM fixing price on the
The test
The returns on gold are
last
trading
day
of
the
The proxy for the riskless asset is the one-month T-bill rate.
month.
For
world
a
the world market
Perspective's
portfolio
Market
World
have
we
This
Index.
market
national
The
indexes
International
is a market-value weighted
index based on indexes of the eighteen largest
world.
Capital
used
stock
markets
of
the
are also market-value weighted
portfolios of stocks, but converted to US$ at current
exchange
We also used two different ways of calculating the return on
rates.
gold
and
degree
the
the market:
a)
b)
Rg
=
P(t)/P(t-1
Rm
=
Index
Rg
=
ln(P(t))
Rm
=
ln(
(
t)
-
)
1
/Index (t-1
-
-
)
1
+
Dividends
ln(P(t-1))
Index(t))
-
InCIndex ( t-1
) )
+
Dividends
The reason for doing this was to take into account to some
mis-specification
of
the
investment
horizon.
regression gives the more accurate estimate
downward.
of
Thus
(b),
This situation reverses for the first model.
but
the
second
biases
(a)
21-
The regression results were (with t-statistics in parentheses):
a)
Rg - Rf
=
0.00539
+
0.02765(Rm
H2 =-0.02138 SER =0.0685 DW =1.25
Rg - Rf
=
0.00321 + 0.03135(Rm
(0.3338)
Rf)
(
/46
-
Rf)
(0.1272)
(0.5439)
b)
-
F
)
=
01 62
(0.1467)
R2 =-0.02126 SER =0.0665 DW =1.30 F(1/46)
In
.
=0.0215
neither regression are the coefficients significant at even the
significance
level,
and
F-tests
the
clearly have to reach to
reject
the
are similarly weak.
hypothesis
null
40%
One would
that
all
the
(b)
for
gold
coefficients were equal to zero.
The positive, albeit insignificantly different from zero,
may surprise some readers.
might
have
(1977)
for
a
There has been
instance, found
the period 1971
the
a
correlation of -0.07
to 1976.
collapse
market
portfolio
&
MacDonald
between
&
gold
Solnik
percentage
Poors Composite Index over
One must remember though that around early to
of
the
Smithsonian agreement resulted in the
floating of the major world currencies.
the
general feeling that
negative correlation with the market.
changes in the gold price and the Standard
mid-'' 973
a
The prices of
both
are determined in world markets.
gold
and
Therefore the
effect of exchange rate changes impart some positive correlation to the
US$ values of both.
The results for the intercept term (a)
are not aonsistent
with
those
22-
-
Jensen, & Scholes (1972)
of Black,
sub-periods
that
Logue
Hughes,
,
betas were
computed
Companies'
risk-adjusted
betas
When the
performance
et al.,
of
were
using
a
)
assets
consistent
are
These authors found that when
.
market
domestic
Multinational
index.
performance exceeded that of domestic firms.
computed
using
a
world
index
though,
the two sets of companies were quite similar.
credence
argued that their results lent
financial
intercepts
had
results
However the
Sweeney( 1 975
&
portfolios
zero-beta
their
significantly greater than zero.
with
who found that in three out of four
are
priced
internationally
Hughes,
notion
the
to
the
that
that this in turn
and
implies that financial markets are integrated internationally.
Gold is pre-eminently an international
surprising
asset
zero.
In
any
still
a
normal return
that
ex
ante
gold
had
a
of
net
These are minimal though (on the order of 0.1%
possible
for
/
storage
annum).
It
is
negative expected excess
to
pay
a
its special services, but that later developments awarded
them an unexpected offsetting bonus.
this possibility.
We can neither confirm nor reject
The most likely explanations for
however remain chance, and/or missing factors.
Section VI.
different
insignificantly
risk-adjusted return because of buying by investors willing
premium
not
case one might expect that it should be positive
merely because investors wish to earn
costs.
perhaps
is
it
that it should have been correctly priced in the sense that
the risk-adjusted excess return ex post was
from
so
Summary
the
positive
(a)
23-
-
This paper has investigated the efficiency of the gold market primarily
sequences
with respect to the information contained in
price
changes.
first-order
changes as
dependence.
profit
tests
Both
from
for
serial correlation and modelling the
processes
Markov
successive
of
indicated
short-term
some
There was no reason to believe though that outsiders could
knowledge
of
relationships.
these
makers and
Market
professional traders might, but it is not clear that they can do so
in
excess of their costs.
The application of
that
for
a
standard market model to monthly returns
the period 1974-1977, the covariance of the return on gold in
excess of the riskless rate with that of the market was
not
revealed
significantly
different
zero.
from
Similarly,
positive,
the
but
excess
risk-adjusted return was also positive, but not significantly different
from zero.
Further research might proceed in the direction
market's
efficiency
with
respect
series of price changes, structural
publicly
available
information.
of
investigating
the
to more complex models of the time
models
At
this
of
price
point
formation,
and
though there is no
reason to suspect that the gold market in general is any less efficient
than any other international asset market.
2U-
-
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