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Under the assumption of RE, the forecast error E ˜ + I is independent of the info
S 2 r and hence of f p r so that /?RE = 0. Also, regardless of how expectations
then under FRU the expected rate of appreciation will equal the forwar
fpt, so that cov(A$+,, f p f ) = 1 and hence ˜ R = 0 (i.e. risk neutrality holds)
risk neutrality hold then /?RE = SRN 0 and hence from (12.30), B = 1, as
we can construct a data series for Et+l =
If we have survey data on
along with the sample analogues of SRE and SRN. The latter provide evide
importance of the breakdown of either RE or risk neutrality in producing the re
First, let us remind ourselves of some problems, outlined in Chapter 5, t
using survey data to test economic hypotheses. The first question that arises
the data is qualitative (e.g. respondents answer ˜up™, ˜down™, or ˜same™) or q
(e.g. respondents answer ˜the exchange rate for sterling in 91 days will be 2
If qualitative date is used then the different methods which are used to transfo
yield different quantitative results for Hence we™can have different sets of q
data purporting to measure the same expectations. Also, if we have quantitativ
may be either for individuals or for averages (or median value) over a group of i
In principle, RE applies to an individual™s expectations and not to an average
a set of individuals.
There is also the question of whether the respondents are likely to gi
thoughtful answers and whether the individuals surveyed remain as a fixed
change over time. Also, when dealing with the FRU proposition the individua
of s;+˜ must be taken at the same time as fr (and st). Finally there is the
whether the horizon of the survey data (on exactly matches the outturn
sr+l. These problems bedevil attempts to draw very firm conclusions from stu
on survey data. Different conclusions by different researchers may be due to su
differences™ in the survey data used.
Let us return to the study by Frankel and Froot (1986, 1987, 1989) who use q
survey data on US respondents. They calculate SRE BRN and using (12.3
that B # 1 (in fact is negative) and that this is primarily attributed to a fa
(i.e. B R E is non-zero). This broad conclusion holds over five (main) currencie
horizons of 1, 3 and 6 months, for data from the mid 1970s and 1980s. MacD
namely that the failure of p # 1 is mainly due to ˜ R # 0. However, this eviden
weak since for three out of the four exchange rates studied RE = BRN= 0 a
one case is /?RN > 0. In fact, BRN = 1.4(t = 0.15) for the sterling effective ra
difficult to interpret results using the effective rate since this is a ˜basket™ of
(each of which has a set of bilateral forward rates).
On balance then there appears to be fairly strong evidence based on regres
survey data (in particular see Froot and Frankel (1989)) that
the forward premium is a biased predictor of subsequent changes in the exc

most of the bias is due to systematic forecast errors and very little to va

the risk premium
the average risk premium is non-zero but it is time invariant and in partic

not vary with the forward discount
The failure of RE may be due to the fact that agents are ˜irrational™ and th
make systematic forecast errors. However, it could equally be due to the fact
take time to learn about new exchange rate processes and while they are lea
make systematic errors because they do not know the true model. This lear
persist for some time if either the fundamentals affecting the exchange rate are
changing or if the influence of noise traders on the market varies over time. A
there may be a ˜Peso problem™ and a failure of FRU may occur even when
rational in the general sense of the word - namely they are doing the best the
the information available.

A prominent feature of the movement in bilateral exchanges is their extreme
Weekly changes are extremely volatile with monthly and quarterly changes less
empiricism tell us that ˜news™, for example new money supply figures or ne
the current account position, can lead foreign exchange dealers to buy and sell
and influence spot and forward rates. Newspaper headlines such as ˜Dollar fa
of unexpectedly high money supply figures™ are not uncommon. The implicat
that if the published money supply figures had been as expected the exchange
have remained unchanged. It is the ˜new information™ contained in the mon
figures that leads FOREX dealers to change their view about future exchange r
to buy and sell ˜today™ on the basis of this ˜news™. On the other hand, expec
that are later confirmed may already be incorporated in the current exchange
implication of an efficient market. For example, another headline might be ˜Exc
improves as President announces lower monetary targets for the future™. The
here is that expected future events may influence the exchange rate today.
We shall use the term ˜news™ as a shorthand solely for unexpected events
in this section is to examine whether the above commonsense notions conc
behaviour of the foreign exchange market may be formally incorporated in the
Two stylised facts about exchange rate volatility have a bearing on the an
follows. We have noted that the predicted change in the exchange rate, gi
forward premium f p , , gives a poor forecast of As,+l on a month-to-month
variance of the actual change in the spot exchange rate can often exceed t
forward discount by a factor of 20 (Frankel, 1982a). This suggests that t
exchange rate changes As,+l are due to ˜new information™ which by definitio
have been anticipated and reflected in the forward discount f p , which preva
previous period.
Second, contemporaneous spot and forward rates move very closely to
example, for the $/E, $/DM $/yen exchange rates the correlation between t
poraneous spot rate and one-month forward rate exceeds 0.99 and correlatio
the corresponding percentage changes in spot and forward rates exceed 0.9
three currencies.

Direct Tests of the News Hypothesis in Spot and Forward Markets
Our first problem is how to measure news or unexpected events. There are
approaches, one using survey data on expectations, another public forecasts an
RE and regression analysis.
Expectations data exist for prices, inflation and output for a number o
countries. Data on interest rate expectations are also available for the US (
et a1 (1985)). Usually, but not always, data on expectations are qualitative. How
are methods for transforming the data into a quantitative figure for expectatio
and Parkin, 1975 and Pesaran, 1987).
Whether we think that economic fundamentals influence the exchange ra
on our model of exchange rate determination. However, given a time serie
data on expectations of relevant variables, E,-IX,, the unexpected or ˜news™ v
simply given by ( X , - E , - l X , ) . Public forecasts of X , (from, for example,
Bank, Treasury or City forecasters) can be used in a similar manner to form
representing ˜news™.
If neither survey data on expectations nor forecast data are available, we ca
pseudo expectations series E,- 1X, and ˜news™ variables ( X , - E,-IX,) using
analysis. For any variable X , we can assume agents make a forecast of X,
values of X , itself and past values of other relevant economic variables 2,:

x, = e l ( w , - l+ e 2 ( ˜ ) ˜+rE,- l
where & ( L ) are polynomials in the lag operator. Equation (12.33) can be v
reduced form of a ˜complete™ economic model. After estimating (12.33) the
X , can be taken as a proxy for agents™ expectations, E,-1X,. The residual fro
namely i?,, measure of the surprise of news about X t , so gf is a proxy for ( X ,
is a
Let us now turn to a general representation of models of the exchange rat
designate :
st = BXr
a white noise error). For example, in some monetary models, X , includes rela
supplies, relative real output and relative interest rates (see Chapter 13). Fro
and (12.35):
+ + + +
/?™(X, - E t - l X f ) w, = s news 0,
St = sp :
where sf = E,-lsf. Thus the forecast error (s, - s f ) is composed of an un
random component 0, and unexpected changes (˜news™) in the fundamental v
that determine s,. If expectations are rational, (X, - E,-IX,) will be orthogona
lated) with any other variables (at t - 1 or earlier), and with error term w f .
Equation (12.36) can only be made operational if we have a model for
relationship between s, and X , should come from some relevant economic
practice there may be several competing hypotheses about the determinants
of the hypothesis that ˜news™ influences the spot (or forward) rate is always te
with a hypothesis about the determination of the equilibrium expected excha
and the expectations generating equation (12.33). Hence, different researcher
different models for s: and E,-1X, often obtain different results when testing
Perhaps the simplest and most straightforward models of the determination of
risk neutrality and RE. UIP with a constant risk premium rp implies s an :
mined by:
+ +
s = sf-l df-l r p

+ CIP) then sf is given by:
If we assume FRU (or UIP

+ rp™
s = f ,-I

Substituting the above expressions for sf in equation (12.36) we obtain:
+ B ™ K - E,-lXf 1 +
- Sr-1 - dl-1) = r p
(Sf Of

= rp˜ + y™(Xt - Er-1X,) + w,
- fr-i

The above equations may be viewed as models embodying UIP RE and F
respectively, but where one is attempting to explain some of the RE foreca
terms of surprises in specific economic variables X,.If the EMH in the spot an
markets holds then one would expect /? and y to be non-zero and for any varia
at time t - 1 or earlier to have zero coefficients when added to either of these
If one uses a specific economic model based on fundamentals then s: in
replaced by the appropriate economic variables PX,. For example, in moneta
of exchange rate determination X , would include relative money supplies in th
and foreign country (see Chapter 13). In this case economic theory would in
˜sign™ one would expect on and hence on the surprise variables ( X , - E,-I
regression (12.36).
The main problem with studies of this type is that there is no general agr
a theory about the economic ˜fundamentals™ that determine the expected (eq
exchange rate . Hence there is no agreement on what variables to include as
an important news item in one period may not be viewed as important at an
period, suggesting that the coefficients /3 and y may not be statistically signi
all subsamples of the data and may appear unstable over time.
It follows from the above that these ˜news regressions™ are unlikely to
insights. In general, the news items (e.g. surprises in interest rates, money s
prices) that are found to be statistically significant (e.g. Frenkel (1981), Copela
still leave much of the variation in the dependent variable in equation (12.3
or (12.40) unexplained - that is there is still a lot of ˜noise™ or ˜news™ in exc
movements which is not explained at all.
Often in these studies lagged news items (e.g. ( X + l - E r - 2 X t - l ) ) are fo
significant. This is a refutation of RE since these lagged forecast errors are kno
t - 1. Such results are indicative of market inefficiency.

In previous sections we have noted that the simplifying assumptions of risk neu
RE are not consistent with the empirical results on FRU and speculation in the s
via the UIP relationship. This section examines two reasons for the apparen
failure of these relationships and the high volatility exhibited by the spot rate
shown how the Peso problem can complicate the interpretation tests of the EM
and forward markets. Second, a study of chartists, a particular form of noise tr
FOREX market allow us to ascertain whether their behaviour might cause d
exchange rate movements and nullify the EMH.

Peso Problem
The apparent failure of the EMH in empirical tests may be illusory because
known as the Peso problem. The Peso problem leads the researcher to measu
tions incorrectly, hence forecasts may appear biased and not independent of i
at time t.
The Peso problem arises from the behaviour of the Mexican peso in the
Although the peso was on a notionally fixed exchange rate against the US doll
consistently at a forward discount for many years, in anticipation of a devaluat
eventually occurred in 1976). Prima facie, the fact that the forward rate for th
persistently below the outturn value for the spot rate (in say three months™ tim
persistent profitable arbitrage opportunities for risk neutral speculators.
The Peso problem arises from the fact that there could be unobservable
unquantifiable) events which may occur in the future, but in our sample of
actually do occur. It is completely rational for an investor in forming his e
to take account of factors that are unobservable to the econometrician. How
event never occurs in the sample of data examined by the econometrician, th
erroneously infer that the agent™s expectations are biased. Hence the econome
believe that he has unearthed a refutation of RE but in fact he has not. This is
holds and US and Mexican interest rates are always equal and constant, then
= sr

where s, is measured as dollars per peso. If the Mexican government™s fixed
rate policy is entirely credible (call this ˜regime 1™) and has been adhered to fo
of years then s,˜+˜ = s,+l = sf for all time periods in regime 1. Hence under
credibility™ expectations are correct in all time periods.
Now suppose that Mexican investors begin to think the government™s comm
fixed exchange rate has weakened and that there is a non-zero probability n th2
will be devalued and a probability (1 - n2) that it will remain ˜fixed™. Call
˜partial credibility™. A rational investor would then have an expectation given

+ (1 - n2)s,+1
(2) (1)
= n2s,+1

sLi)l = exchange rate under the fixed exchange rate, regime 1, s (2)˜ = new
where ,+
(2) (1)
rate under the devaluation, regime 2, that is sf+l > s,+˜ = s:™). Suppose, how
during the ˜partial credibility™ period the Mexican government does nut alter th
rate. The outturn data will therefore be s:˜ = s:™), the existing fixed parity. H
survey data collected over this partial credibility period (which accurately
Etst+l),will not equal the (constant) outturn value sj™)

The ex-post forecast error in the ˜partial credibility™ period using (12.42) is

= s y - E,s,+1 = Q(S, - s,+l) < 0

where we have used s$)l = st(l). Hence the ex-post forecast error, which is ob
we have survey data on expectations, is non-zero and biased. Also if sj™) var
then a regression of G++1 on the actual exchange rate s;” will in general yield
coefficient. The latter coefficient will equal n2, if is constant over the sam
and may be ˜close to™ n is:
2 f! varies only slightly over time (i.e. some omitte
bias will ensue). Hence we have an apparent refutation of the informational
assumption of RE because the forecast error is not independent of informati
t. Notice that even if n2, the probability of the unobserved event, is small th
the forecast error @,+I can still appear large if the potential change in s und
regime is thought to be large (i.e. s!™) - s is large).
Now let us consider the problems caused when we try to test for FRU. If inve
a devaluation of the peso is likely then s$l1 > s!™) and hence from (12.43) w
E,s,+l > sj™) (remember that sf is in units of pesos per US dollar and hence a
in ˜s™ is a devaluation of the peso). Under FRU and risk neutrality, specula
spot rate (i.e. peso at forward discount).
Suppose we had a longer data set which included a period when the Mexic
ment announced a fixed exchange rate but that agents then believe that this
rate might be abandoned in favour of a revaluation of the peso. The above anal
again apply but in this ˜favourable partial credibility period™ (regime 3) the
forecast errors ii˜:would now be positive (and not negative as under regime
with a long enough data set where ˜unfavourable™ and ˜favourable™ unobser
occur equally often, our data set would conform to the RE postulates of unbias
errors and forecast errors that are independent of Qf.
The Peso problem therefore arises because one is testing a hypothesis with
data set, in which there are unobservable yet non-random variables (i.e. the
of changes in government policy). Thus the average of the outturn values for
an accurate representation of agents™ true expectations. The RE assumption
= E&+l

where u,+l is random around zero, does not hold in the ˜short™, partial credibili
The only way one can in principle get round the Peso problem when investig
is to use accurate survey data on expectations to test Etsf+l = fr. However, i
analysing survey data has its own problems. It is possible that Peso problem
prevalent and in any actual data set we have, they do not cancel out. Peso pro
involve an equal frequency of positive and negative ˜events™ with probabilities
of shifts (d™) - d i ) )that just exactly cancel out in the data set available to the
seems unlikely. Clearly a longer data set is likely to mitigate this problem b
not irradicate it entirely. However, for advocates of RE, the apparent failure
statistical tests can always be attributed to ˜hidden™ Peso problems.

Noiser Traders
If one were to read the popular press then one would think that foreign exchan
were speculators, par excellence. In the 1980s, young men in striped shirt
primary coloured braces were frequently seen on television, shouting simultan
two telephones in order to quickly execute buy and sell orders for foreign
The obvious question which arises is, are these individuals purchasing and sell
exchange on the basis of news about fundamentals or do they in fact ˜cha
If the latter, the question then arises as to whether they can have a pervasive
on the price of foreign exchange. As we have seen there have been a large
technically sophisticated tests of market efficiency in the foreign exchange mar
terms of spot speculation (UIP) and speculation in the forward market (FRU)
there has been remarkably little work done on the techniques used by actu
exchange dealers and whether these might cause movements in exchange rates
not related to news about fundamentals. An exception here is the study by
Taylor (1989a) who look at a particular small segment of the foreign exchan
and undertake a survey of chartists™ behaviour. Chartists study only the price m
in the market and base their view of the future solely on past price changes
example, they might use moving averages of past prices to try and predict fu
They may have very high frequency graphs of say minute-by-minute price
and they attempt to infer systematic patterns in these graphs. Consider, fo
the idealised pattern given in Figure 12.2 which is known as ˜the head and
reversal pattern™. On this graph is drawn a horizontal line called ˜the shoulder
pattern reaches point D, that is a peak below the neckline, the chartist would
signals a full trend reversal. He would then sell the currency believing that it
in the future and he could buy it back at a lower price. As another exampl
Figure 12.3, the so-called ˜symmetric triangle™ indicated by the oscillations
on the point at A. To some chartists this would signal a future upward moveme
the interpretation of such graphs is subjective. For chartists as a group to in
market, most chartists must interpret the charts in roughly the same way, other
chartists would do would be to introduce some random noise into prices but
It is well known that chartists also use survey data on ˜market sentiment™. Fo
if ˜sentiment™ is reported to be optimistic about the German economy, the ch
well try and step in early and buy DMs.
The data set on which the Allen and Taylor study is based is rather small.
was conducted on a panel of chartists (between 10 and 20 responded every
the period June 1988-March 1989. They were telephoned every Thursday
for their expectations with respect to the sterling-dollar, dollar-mark and
exchange rates for one and four weeks ahead, yielding about 36 observations
per currency. The survey also asked the chartists about the kind of information
in making their forecasts and who the information was passed on to (e.g. actu
It was found that at the shortest horizons, say intra-day to one week, a
90 percent of the respondents used some chartist input in forming their exc

Figure 12.2 Head and Shoulders. Source: Allen and Taylor (1989b).
Figure 12.3 Symmetric Triangle. Source: Allen and Taylor (1989b).

expectations. As the time horizon lengthens to three months, six months o
the weight given to fundamentals increases and 85 percent of the responde
that over these longer horizons ˜fundamentals™ were more important than cha
However, the chart analysis was always seen as complementary to the ana
on fundamentals and therefore it is possible that chart analysis influences exc
even at these longer horizons.
If one looks expost at the accuracy of the chartists™ forecasts taken as a w
Figure 12.4 for the DM/$, four-week ahead forecasts are fairly typical of the
other currencies. In general Allen and Taylor find:
There is a tendency for the forecasts to miss turning points. On a rising

market the chartists™ expectations underestimate the extent of the rise or f
Prediction errors are noticeably greater at the four-week horizon than at th

horizon. Individual chartist™s forecasts for four-week ahead predictions ar
unbiased but they are biased for the one-week ahead predictions.
For all the chartists taken as a whole, they correctly predict the change in th

rate over one-week and four-week horizons approximately 50 percent of th
is what one would accept if their forecasts were purely due to chance.

However, the above result for all chartists neglects the possibility that individu
might in fact do well and do consistently well over time. In fact there are di
forecast accuracy among the chartists and there are some chartists who are sys
˜good™. However, one cannot read too much into the last result since the tim
the survey is fairly short and in a random sample of individuals one would alw
that a certain percentage would do ˜better than average™ (e.g. 5 percent of the p
Again taking chartists as a whole, Allen and Taylor assess whether they
alternative methods of forecasting. For example, some alternatives examined a
based on the random walk and ARIMA forecasts or forecasts based upon a
exchange rates, the interest rate differential and the relative stock market pe

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