T. Choudhry International Review of Economics and Finance 8 1999 433–453 443
Table 9 Unbiased forward rate hypothesis test
Null Hypotheses—F Statistics Country
H : a
1
5 1
H : a
, a
1
, a
3
5 0, 1, 0 Australia
4.649 4.924
Canada 7.675
3.137 France
0.319 5.231
Germany 0.186
3.939 Hong Kong
131.770 46.462
Italy 0.595
3.224 Japan
3.720 5.199
South Africa 4.723
1.719 U.K.
0.292 107.930
Implies rejection of the null at the 1 level. Implies rejection of the null at the 5 level.
Implies rejection of the null at the 10 level.
of a unit coefficient on the forward rate is accepted only in France, Germany, Italy and the United Kingdom Table 9. This result is quite different from the previous
semi-strong efficiency test Table 6. The null unbiased hypothesis is only found to be true for South Africa Table 9. Thus, once again South African currency is the
only currency that provides evidence supportive of the semi-strong efficiency.
Table 10 provides a comparison between results presented in this article and results of other research articles that apply some form of cointegration procedure.
26
As the table indicates results presented are not identical in each article. Of course along with
the estimation procedure the sample period and the data frequency are also not identical. Most results presented do provide some evidence of the forward rate effi-
ciency. Lack of evidence is noted during the latest floating era. This article and the Corbae et al. 1992 article do help redeem the latest floating era.
4. Mean-reversion in forward premium
As suggested above, violation of the forward rate unbiasedness may be due to the existence of risk aversion on the part of the participants of the foreign exchange
market. Risk averse participants require a premium on forward contracts that exposes them to exchange rate risk. Relying heavily on Crowder 1994, p. 556, the forward
rate consists of the future spot rate, a risk premium d and a rational expectations forecast error e.
f
t
5 s
t
1
1
1 d
t
1
1
1 e
t
1
1
. 9
Furthermore, the future spot rate can be decomposed into current spot rate plus future depreciation.
s
t
1
1
5 s
t
1 Ds
t
1
1
. 10
444 T. Choudhry International Review of Economics and Finance 8 1999 433–453
Table 10 Summary of comparison between our results and others
Article Data
Method Results
Barnhart and Monthly data
Engle and Granger No evidence of the For-
Szakmary 1991 Currencies of Canada,
cointegration method ward rate hypothesis
Germany, Japan, and the UK against the US
dollar 1974–1988
Corbae, Lim, and Weekly data
Canonical cointegra- Some evidence of the
Ouliaris 1992 Currencies of Canada,
tion regressions Forward rate hypothesis
Germany, Swiss, France, Japan, and the
UK against the US dol- lar
1976–1985
Crowder 1994 Monthly data
Johansen cointegra- No evidence of the For-
Currencies of Canada, tion method
ward rate hypothesis Germany, and the UK
against the US dollar 1974–1991
McFarland, Daily data
Phillip and Hasen Some evidence of the
McMahon, and Currencies of Germany,
fully modified ap- Forward rate hypothesis
Ngama 1994 Belgium, France, Italy,
proach and the US against the
UK pound 1922–1925
Phillips, McFarland, Daily data
Fully modified least Some evidence of the
and McMahon Currencies of Belgium,
absolute deviations Forward rate hypothesis
1996 France, Italy, and the
US against the UK pound
1922–1925
Phillips and Daily data
Fully modified least No evidence of the For-
McFarland Currency of Australia
absolute deviations ward rate hypothesis
1997 against the US dollar
1984–1991 This paper
Monthly data Fractional cointegra-
Some evidence of the Currencies of Australia,
tion and the Harris- Forward rate hypothesis
Canada, France, Ger- Inder cointegration
many, Honk Kong, It- method
aly, Japan, South Africa, and the UK against the
US dollar 1985–1996
T. Choudhry International Review of Economics and Finance 8 1999 433–453 445
Table 11 Forward premium unit root test results: KPSS test
Lags Australia
Canada France
Germany H Kong
Italy Japan
S Africa U.K.
8.413 2.192
1.240 4.551
4.028 0.859 1.338
2.585 3.565
3 2.450
0.762 0.393 1.330
1.290 0.292
0.479 0.956 0.115
6 1.486
0.499 0.248
0.789 0.908
0.194 0.298
0.603 0.692
Implies rejection of the null of stationarity at the 1 level. Implies rejection of the null of stationarity at the 5 level.
Implies rejection of the null of stationarity at the 10 level. KPSS critical value: 0.739 1, 0.463 5 and 0.347 10. Source Kwiatkowski et al. 1992.
Substituting Eq. 10 into Eq. 9, we get f
t
2 s
t
5 Ds
t
1
1
1 d
t
1
1
1 e
t
1
1
. 11
Eq. 11 shows that the forward premium f
t
2 s
t
is the sum of the spot rate deprecia- tion, risk premium and rational expectations error.
27
Given that the spot rate deprecia- tion and the rational expectation error are stationary,
28
if the risk premium is covariance stationary, then the forward premium must be stationary and the spot and the forward
rate are cointegrated with the cointegrating vector of 1, 21; consequently the unbi- ased hypothesis holds Baillie Bollerslev, 1994a.
29
We conduct unit root tests GPH and KPSS to check for the stationarity of the forward premium f
t
2 s
t
. Table 11 presents the results from the KPSS tests with 0, 3 and 6 lags. The KPSS test is applied without a trend, thus the null hypothesis is
stationarity with a drift. The null is rejected at all lags length in six cases: Australia, Canada, Germany, Hong Kong, South Africa, and the United Kingdom. The null of
stationarity is accepted using 3 and 6 lags in the case of Italy and using only 6 lags for France and Japan. Given the cointegration tests results and the unbiased test
results, a nonstationary forward premium for Canada and South Africa and a stationary premium for Italy is quite surprising.
30
Baillie and Bollerslev 1994a indicate that forward premium may be a long memory process; in other words, it may be a fractionally-integrated process, so that imposing
a value of 0 and 1 for d may be too restrictive. Baillie and Bollerslev, applying maximum likelihood estimations methods, find evidence indicating the forward premium to
be fractionally integrated for several currencies. Table 12 shows results from the GPH tests of unit root in the nine forward premiums under consideration. Tests are
conducted for two different values of m, i.e., 0.55 and 0.60. The hypothesis testing regarding the value of d is based on two tests: a two-sided test where the null is d 5
1 and alternate null is d ? 1; and a one-sided test where the null is as before d 5 1 and the alternate null is d , 1 or d . 1. If the two-sided test is unable to reject the
null of d 5 1 then the second test is not considered. For Australia, France, Germany, Japan, South Africa, and the United Kingdom the null of d 5 1 is not rejected using
both values of m. Once again, the South African result is quite surprising given the cointegration and unbiased hypothesis results. The Canadian results show the forward
446 T. Choudhry International Review of Economics and Finance 8 1999 433–453
Table 12 Foward premium unit root test results: GPH test
Country m 5
0.55 m 5
0.60 Australia
d 5 0.9284
d 5 0.8066
20.3248 21.0235
Canada d 5
0.9046 d 5
0.6386 20.4326
21.9123
c,e
France d 5
0.9168 d 5
0.7122 20.3772
21.5227 Germany
d 5 1.0255
d 5 0.8293
0.1155 20.9033
Hong Kong d 5
0.3971 d 5
0.5622 22.7336
a,d
22.3166
b,e
Italy d 5
0.5773 d 5
0.6885 21.9165
c,e
21.6482
a,e
Japan d 5
0.6912 d 5
0.7742 21.4002
21.1946 South Africa
d 5 1.2064
d 5 0.8240
0.9359 20.9312
U.K. d 5
0.8085 d 5
0.7960 20.8681
21.0793
a
Implies rejection of the null of the one-sided test at the 1 level.
b
Implies rejection of the null of the one-sided test at the 5 level.
c
Implies rejection of the null of the one-sided test at the 10 level.
d
Implies rejection of the null of the two-sided test at the 1 level.
e
Implies rejection of the null of the two-sided test at the 5 level. t
-statistics in parentheses. Two-sided test H
: d 5 1 and H
1
: d ? 1. One-sided test H
: d 5 1 and H
1
: d , 1. Two-sided critical values: 2.576 1, 1.960 5, and 1.645 10.
One-sided critical values: 2.326 1, 1.645 5, and 1.282 10.
premium to be fractionally integrated when m is equal to 0.60. In both tests, the alternate null hypotheses are accepted. Results from Hong Kong and Italy show long
memory forward premium using both values of m.
31
The difference in the KPSS and the GPH tests results are quite considerable especially for Canada and Hong Kong.
32
Fig. 1 shows the autocorrelation function of the nine forward premiums and the 5 confidence interval two standard error. Interpretation from the figure is quite difficult
but the forward premium from Australia, France, Germany, Japan and the United Kingdom seems to decay to zero quite slowly.
Our results basically imply two points: first, forward premiums may have a long memory as indicated by Baillie and Bollerslev 1994a; and second, the nonstationary
forward premium may not be the cause behind the failure of the forward rate unbiased- ness. Other factors cited earlier may be responsible. Baillie and McMahon 1989 and
McFarland et al. 1994 suggest that the failure of rational expectations may also be a reason behind the lack of the unbiasedness of the forward rate. Frenkel 1980
T. Choudhry International Review of Economics and Finance 8 1999 433–453 447
Fig. 1.
Autocorrelation function
of forward
premium.
448 T. Choudhry International Review of Economics and Finance 8 1999 433–453
provides evidence of the failure of the unbiased hypothesis during the 1920s due to the absence of rational expectations. Our results also indicate that the definition of
the forward premium may very much dictate mean-reversion. Results provided in our article advocate the need for further research in this field.
5. Conclusions
