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Journal of Banking & Finance 24 (2000) 787±807
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Eciency tests in the French derivatives market
Chun I. Lee a, Kimberly C. Gleason b, Ike Mathur

c,*

a

c

Texas Southern University, Houston, TX 77004, USA
b
Bentley College, Waltham, MA 02154, USA
Department of Finance, College of Busines, Southern Illinois University, Carbondale, IL 62901,
USA
Received 15 September 1997; accepted 24 May 1999

Abstract
The French derivatives market, the Marche 

a Terme International de France (MATIF) or the French International Futures and Options Exchange is one of the major
derivatives markets in the world. The eciency of four ®nancial contracts traded on the
MATIF-CAC40 Index Futures, ECU Bond Futures, National Bond Futures, and PIBOR 3-Month Futures are examined in this paper. Test results from serial correlations,
unit root tests, and variance ratio tests provide overwhelming evidence that the random
walk hypothesis cannot be rejected for these contracts. Ó 2000 Elsevier Science B.V. All
rights reserved.
JEL classi®cation: G15; C22; G13
Keywords: Market eciency; MATIF; Random walk

1. Introduction
With over 70 million contracts traded in 1997, the Marche a Terme International de France (MATIF) in Paris is one of the major derivatives markets in

*

Corresponding author. Tel.: +1-618-453-1421; fax: +1-618-453-5626.
E-mail address: imathur@siu.edu (I. Mathur).

0378-4266/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 3 7 8 - 4 2 6 6 ( 9 9 ) 0 0 0 6 7 - 9

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C.I. Lee et al. / Journal of Banking & Finance 24 (2000) 787±807

the world and has attracted many foreign investors. 1 Anticipating the eventual
realization of the European Monetary Union (EMU) and single currency,
which has been named Euro from its previous name of European Currency
Unit (ECU), the MATIF, now more than ever, is gearing toward internationalization by o€ering products and expanding trading that appeal to global
investors. Examples of these e€orts include the o€ering of ECU-denominated
products and the GLOBEX-partnership with the Chicago Mercantile Exchange. As MATIF clearly states in its 1996 annual report, in the new ®nancial
environment, the battle for market share will be won not only by technical
advances but also by the competitiveness of markets. From the investors' point
of view, one of the important aspects regarding the latter is the issue of market
eciency.
Previous studies have sought to emphasize the importance of MATIF in
global risk management strategies. For example, Geman and Schneeweis
(1993, p. 18) mention that ``MATIF ranks among the world's largest futures markets with a wide range of risk management instruments including
commodity futures, the three-month PIBOR contract, the CAC40 stock
index, the National and the ECU long-term contract''. They go on to
argue for using the National futures contract in global risk management

strategies.
In a similar vein, Chow et al. (1996, p. 1695) state that ``among major futures exchanges only MATIF o€ers a 24-hour non-interrupted trading cycle
accommodating two distinct trading mechanisms ± normal trading hours are
conducted through an open-outcry system on the ¯oor, while after-hours
trading occurs through an automated continuous auction system on GLOBEX, with no trading recess between these two sessions''.
Given both the popularity and the innovativeness exhibited by MATIF, a
natural question to ask is related to the eciency of the ®nancial futures
traded on it. Thus, the purpose of this paper is to conduct comprehensive
eciency tests on the returns of ®nancial futures contracts traded on the
MATIF. These tests are signi®cant for two reasons. First, despite MATIF's
global perspective, little research to date has been done to examine the eciency of products traded on the market. Second, even among studies that
test for eciency in well-established markets, the evidence is mixed. By examining the MATIF, employing the re®ned variance estimator of serial
correlations of Diebold (1986) and the variance ratio tests of Lo and
MacKinlay (1988) that adjust for heteroscedasticity, further evidence on
market eciency is obtained that can shed additional light on the price
behavior of assets.

1

In 1996, approximately 40% of MATIFÕs open interest was held by non-residents.

C.I. Lee et al. / Journal of Banking & Finance 24 (2000) 787±807

789

2. The random walk hypothesis and market eciency
Given that this paper deals with eciency of the French derivatives market
MATIF, it is interesting to note that the concept of eciency was originally
advanced by the French economist Louis Bachelier (1967). Subsequently, researchers such as Working (1934), Cowles and Jones (1937), Kendall (1953)
and Fama (1965) examined serial correlation coecients for successive price
changes to test whether they were statistically equal to zero to establish the
random walk nature of stock prices.
More recently, researchers have supplemented serial correlation and run
tests with unit root tests developed by Dickey and Fuller (1979, 1981), and
others, to test for market eciency. For example, Arshanapalli and Doukas
(1994) use unit root tests to examine stationarity before studying common
trends in currencies. The augmented Dickey±Fuller (ADF) test commonly used
in eciency tests has the null hypothesis that the series has a unit root. Thus,
the ADF test often is complemented by another test that has series stationarity
as the null hypothesis.

Unit root tests on occasion fail to detect deviations from a random walk in
time series. Thus, the variance ratio test developed by Lo and MacKinlay
(1988), and extended into a multivariate setting by Chow and Denning (1993),
has been used more recently in eciency tests. For example, Liu and He (1991)
use the variance ratio test to examine the random walk hypothesis for a series
of ®ve exchange rates. Ayadi and Pyun (1994) use the variance ratio test to
show that after adjusting for both serial correlation and heteroscedasticity, the
random walk hypothesis cannot be rejected in the Korean Stock Exchange. Lee
and Mathur (1999) use this methodology to show that four futures contracts
traded on the Spanish futures markets are ecient.
While the recent papers cited above provide evidence in support of market
eciency, it is far from clear that all markets are ecient. For example, a
recent paper by Fujihara and Mougoue (1997) provides evidence of dependence in petroleum futures. Similarly, Becker et al. (1996) provide evidence
suggesting that the reaction of bond futures trading in the US and the UK to
new information does not appear to be consistent with market eciency. Thus,
eciency in any market should not be assumed without subjecting it to a
thorough examination.

3. Data and methodology
3.1. The MATIF

Futures and options in France are traded on the MATIF, located in Paris.
Founded in February 1986, it is equally owned by banks, insurance companies

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C.I. Lee et al. / Journal of Banking & Finance 24 (2000) 787±807

and the Society des Bourses Frantaises (the French Stock Exchange). Developing its global appeal has been one of its major objectives in recent years.
Since 1993, with the joint development of GLOBEX with the Chicago Mercantile Exchange (CME) and Reuters, its products can be traded around the
clock. An agreement with the CME was signed on November 20, 1996, that
allows its medium- and long-term interest-rate products to be traded on the
¯oor of the CME. With its long-term ECU-contracts well accepted by investors, the MATIF is expecting to be well ahead of its European competitors in
the battle over contracts denominated in the Euro.
In addition to long-term ECU futures, contracts traded in the MATIF include those based on a stock index (CAC40 index futures), long-term interest
rates (National bond futures and options), short-term interest rates (futures
and options on 3-month Pibor ± Paris Interbank O€ering Rates, the benchmark for short term French franc deposits), currencies (USD/FRF, USD/
DEM, DEM/FRF, DEM/ITL, and GBP/DEM options), and commodities
(European Milling Wheat, European rapeseed, white sugar, and potato). All of
its four ®nancial futures contracts have been ocially recognized by the CFTC.
Trading on the MATIF is conducted via the system of open outcry and afterhour GLOBEX trading. The open outcry system is used during normal business

hours, which vary among products, ranging from 8:30 A.M. to 7:30 P.M.
The after-hour trading is mainly conducted via the GLOBEX system and the
hours also vary among contracts. Some (e.g., ECU contracts) cover the entire
time span, while others cover the majority of the hours when the open outcry
system is not in use. Since November 8, 1995, MATIF has become the ®rst open
outcry market to have GLOBEX as a back-up trading system for use when open
outcry trading is interrupted by outside events.
3.2. Data
Daily opening and closing prices, from the inception of trading to April 30,
1997, of the nearby contracts of the four ®nancial futures traded on the
MATIF were obtained from MATIF and are used in the present study. The
four contracts, along with the beginning dates for the available data, are
CAC40 Index Futures (CAC), 881109, ECU Bond Futures (ECU), 901018,
National Bond Futures (NNN), 860220, and PIBOR 3-month Futures (PIB),
880908. The rest of the products are ignored due to the small number of observations as a result of their short history of trading. The underlying instrument for the CAC is the CAC40 index, which is based on 40 major stocks that
account for almost 70% of the volume transacted on the Paris Stock Exchange's monthly settlement market. For the ECU, it is a pool of 6±10-year
ECU-denominated national bonds with a 5.5% coupon. For the NNN, a pool
of 7±10-year French Treasury bonds is utilized. For the PIB, the 90-day Pibor
deposit of 5 000 000 French Francs is used. The stipulation in the 1995 Madrid

C.I. Lee et al. / Journal of Banking & Finance 24 (2000) 787±807

791

meeting of the European Union Heads of States that starting January 1, 1999,
debt issued by EMU member states are to be denominated in the Euro, will
make the ECU contracts even more attractive in the years to come. The CAC is
the most liquid stock index futures contract in Europe, the NNN was the
second most traded long-term interest rate futures contract in the world in
1995, and the PIBOR futures and options contracts are among the ®ve most
actively traded short-term derivatives contracts in the world. 2
The nearby contracts (i.e., contracts nearest to delivery) are examined because, in general, they are the most active contracts. A switch from the nearby
contracts to the contracts next nearest to delivery is made during the delivery
month of the nearby contracts. The plots for the opening and closing prices for
the four contracts are shown in Fig. 1. 3

3.3. Methodology
To examine the di€erence in volatility during trading and non-trading periods, both close-to-close (RC±C ) and open-to-open (RO±O ) returns are used and
calculated as follows:
RC±Ct ˆ Ln…PCt =PCtÿ1 †

and
RO±Ot ˆ Ln…POt =POtÿ1 †:
Serial correlations, unit root tests, and variance-ratio tests are used to test
for the eciency of four ®nancial futures contracts traded on the MATIF. The
tests are complementary in nature. Thus, by employing all three of them, the
robustness of the conclusions can be better established.
The unit root tests developed by Dickey and Fuller (1979, 1981) (ADF tests)
have been used by, among others, Arshanapalli and Doukas (1994), and
Szakmary et al. (1995) to test for eciency. With a unit root ± an I(1) process ±
as the null hypothesis, the following regression on the natural logarithm of
prices is estimated:
Dpt ˆ g0 ‡ g1 T ‡ g2 ptÿ1 ‡

L
X
ci Dptÿi ‡ lt ;

…1†

iˆ1

where T is the number of observations.
2

See http://www.matif.fr for additional statistics.
The ECU ®gures show a sharp price adjustment, which is due to an interest rate adjustment
made by MATIF.
3

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C.I. Lee et al. / Journal of Banking & Finance 24 (2000) 787±807

Fig. 1.

The ADF procedures are appropriate for testing for a unit root. However,
the way the null hypothesis for the ADF test is tested is not very informative
regarding the presence of a unit root. That is, the ADF tests are not very

C.I. Lee et al. / Journal of Banking & Finance 24 (2000) 787±807

793

Fig. 1. (Continued)

powerful against relevant alternative hypotheses. This lack of power in rejecting the null hypothesis of a unit root can be addressed by conducting
alternative tests of stationarity. This issue is addressed by using the KPSS test

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C.I. Lee et al. / Journal of Banking & Finance 24 (2000) 787±807

of Kwiatkowski et al. (1992), which is speci®cally designed to test the null
hypothesis of stationarity and a unit root as the alternative hypothesis. The test
statistic is calculated as
gs ˆ T ÿ2

T
X

St2 =S 2 …L†;

…2†

tˆ1

where L is the lag parameter, St is the cumulative sum of the residuals (et ) from
a regression
of the series on a constant and a linear trend (i.e.,
P
et ; t ˆ 1; 2; :::; T ) and where
St ˆ
T
L
T
X
X
X
et etÿS ;
…3†
S 2 …L† ˆ T ÿ1 e2t ‡ 2T ÿ1 …1 ÿ S=…L ‡ 1††
tˆ1

Sˆ1

tˆS‡1

The null hypothesis of stationarity is rejected in favor of the unit root alternative if the calculated test statistic exceeds the critical values estimated in
Kwiatkowski et al. (1992, Table 1, p. 166).
The presence of a unit root supports the random walk hypothesis, implying
market eciency. However, studies (e.g., Liu and He, 1991) have shown that
unit root tests do not uniformly detect departures from a random walk. The
variance ratio test developed by Lo and MacKinlay (1988) has been used as an
alternative to test the random walk hypothesis. Lo and MacKinlay (1989) show
that the variance ratio test is more powerful than either the Box±Pierce or ADF
tests against several alternative hypotheses, including AR(1), ARIMA(1,1,1)
and ARIMA(1,1,0) processes. Given the premise that the variance of random
walk increments in a ®nite sample increases linearly with the sampling interval,
variance ratio tests examine whether the ratio of variances of di€erent intervals
weighted by their length is one. If pt is the natural logarithm of price series,
then the random walk hypothesis states that pt follows the following form:
pt ˆ W ‡ ptÿ1 ‡ et ;

…4†

and the variance of its qth-di€erenced series, fpt ÿ ptÿq g, is q times the variance
of its ®rst-di€erenced series, fpt ÿ ptÿ1 g. Given q ‡ 1 observations of the price
series, p1 ; p2 ; p3 ; . . . ; pnq‡1 , the ratio of 1/q of the variance of the series
fpt ÿ ptÿq g to the variance of the series fpt ÿ ptÿ1 g shouldPequal one.
P The
variance ratio of q-di€erenced series is de®ned as VR…q† ˆ r2c …q†= r2a …q†:
Additional details are provided in the Appendix A.
4. Empirical evidence
4.1. Basic statistics
Table 1 presents the basic statistics of daily returns. The returns are not
normally distributed. Rather, they are characterized by signi®cantly high

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C.I. Lee et al. / Journal of Banking & Finance 24 (2000) 787±807
Table 1
Basic statistics for returns a
CAC
O±O
Observations
Mean b
Std. dev. b
T-statistics
Skewness
Kurtosis

ECU
C±C

O±O

NNN
C±C

O±O

PIB
C±C

O±O

C±C

2110
2110
1630
1630
2839
2839
2156
2156
2.58
2.69
)0.20
)0.20
0.81
0.79
0.24
0.25
126.02 119.40
77.79
73.82
49.67
45.05
15.52
13.98
0.94
1.0
)0.11
)0.11
0.87
0.93
0.73
0.82
)0.28
)0.18
24.41
25.70
0.50
0.70
4.70
6.27







4.28
3.96
30.21
90.35
9.63
17.17
90.33 115.91

a

O±O is the open-to-open returns, C±C the close-to-close returns.
Expressed in basis points.
*
Signi®cant at the 10% level.
b

skewness and kurtosis. For all four contracts, the open-to-open returns have
higher standard deviation than the close-to-close returns, suggesting higher
volatility during trading hours, as documented in the literature by, e.g., French
and Roll (1986). Furthermore, volatility varies by contract, with the CAC
being the most volatile, and the PIB having the lowest volatility.
4.2. Serial correlations
Table 2 reports the serial correlations of returns. It appears that, except for
ECU, lag-one serial correlations are signi®cant for returns. However, further
examination based on the heteroscedasticity-adjusted estimates developed by
Diebold (1986) indicates that none of the daily returns is serially correlated.
The Box±Pierce Q statistics con®rm this ®nding. Before adjusting for heteroscedasticity, the white noise hypothesis is rejected for all except the close-toclose returns on CAC and ECU, while the adjusted Box±Pierce Qs show that
the white noise hypothesis cannot be rejected for any of the series.
4.3. Unit root test results
Table 3 reports the results of the unit root tests. Panel A shows that the null
hypothesis of one unit root cannot be rejected for any of the four contracts.
The evidence from the KPSS tests in Panel B shows that the null hypothesis of
no unit root is signi®cantly rejected for all contracts, thus further supporting
the ®nding of unit roots in the returns series. This overwhelming evidence of
unit roots presented in Table 3 provides further support for the eciency of
these four futures contracts traded on the MATIF.
4.4. Variance ratio test results
Table 4 provides further strong evidence that the random walk hypothesis
cannot be rejected for the price series. The variance ratios for lags from 1 to 16

796

Table 2
Serial correlations of returns
Lag

2

3

4

5

6

7

8

9

ECU

NNN

O±O

C±C

O±O

C±C

)0.0680
(0.0218) a
(0.4494) b
0.0105
(0.0219)
(0.1783)
)0.0365
(0.0219)
(0.3290)
0.0271
(0.0219)
(0.2851)
0.0152
(0.0219)
(0.2137)
)0.0523
(0.0219)
(0.3939)
)0.0408
(0.0220)
(0.3479)
)0.0027
(0.0220)
(0.0868)
0.0173
(0.0220)
(0.2281)

)0.0142
(0.0218)
(0.2173)
)0.0063
(0.0218)
(0.1440)
)0.0304
(0.0218)
(0.3183)
0.0500
(0.0218)
(0.4099)
)0.0466
(0.0218)
(0.3945)
0.0188
(0.0249)
(0.4597)
0.0163
(0.0249)
(0.4290)
0.0097
(0.0249)
(0.3318)
)0.0393
(0.0249)
(0.6644)

)0.0577
(0.0248)
(0.7644)
)0.0019
(0.0249)
(0.1384)
0.0076
(0.0249)
(0.2785)
0.0134
(0.0249)
(0.3688)
0.0507
(0.0249)
(0.7166)
)0.0222
(0.0219)
(0.2717)
)0.0252
(0.0219)
(0.2897)
)0.0174
(0.0219)
(0.2404)
0.0182
(0.0219)
(0.2482)

0.0397
(0.0248)
(0.6684)
0.0128
(0.0248)
(0.3802)
0.0157
(0.0248)
(0.4207)
0.0590
(0.0248)
(0.8139)
0.0132
(0.0249)
(0.3859)
0.0203
(0.0249)
(0.4534)
)0.0374
(0.0249)
(0.6150)
)0.0162
(0.0250)
(0.4049)
(0.0242
(0.0250)
(0.4970)

O±O
)0.1735
(0.0218)
(1.7288)
0.0851
(0.0219)
(1.2112)
0.0737
(0.0219)
(1.1277)
0.0655
(0.0219)
(1.0623)
0.1018
(0.0219)
(1.3245)
)0.0056
(0.0219)
(0.3099)
0.0359
(0.0220)
(0.7860)
0.0607
(0.0220)
(1.0233)
)0.0867
(0.0220)
(1.2211)

PIB
C±C
)0.1591
(0.0218)
(1.8276)
0.1659
(0.0218)
(1.8680)
0.1061
(0.0218)
(1.4921)
0.0625
(0.0218)
(1.1440)
0.0949
(0.0218)
(1.4123)
0.0364
(0.0219)
(0.8741)
)0.0503
(0.0219)
(1.0283)
0.1380
(0.0219)
(1.7016)
)0.1015
(0.0219)
(1.4607)

O±O

C±C

)0.0698
(0.0218)
(3.6594)
)0.0036
(0.0219)
(0.8346)
0.0084
(0.0219)
(1.2673)
)0.0741
(0.0219)
(3.7753)
0.0566
(0.0219)
(3.2994)
)0.0558
(0.0219)
(3.2755)
)0.0116
(0.0220)
(1.4964)
0.0132
(0.0220)
(1.5931)
)0.0008
(0.0220)
(0.3902)

0.0453
(0.0218)
(3.2856)
0.0160
(0.0218)
(1.9571)
)0.0594
(0.0218)
(3.7578)
0.0387
(0.0218)
(3.0377)
)0.0460
(0.0218)
(3.3127)
)0.0507
(0.0219)
(3.4766)
)0.0048
(0.0219)
(1.0739)
)0.0027
(0.0219)
(0.7976)
)0.0328
(0.0219)
(2.7976)

C.I. Lee et al. / Journal of Banking & Finance 24 (2000) 787±807

1

CAC

10

)0.0161
(0.0250)
(0.4251)
0.0142
(0.0250)
(0.4003)
0.0230
(0.0250)
(0.5087)

0.0202
(0.0219)
(0.2611)
0.0176
(0.0219)
(0.2439)
0.0131
(0.0220)
(0.2102)

(0.0042
(0.0250)
(0.2078)
(0.0465
(0.0250)
(0.6867)
(0.0294
(0.0250)
(0.5468)

0.0909
(0.0220)
(1.2519)
)0.0947
(0.0220)
(1.2763)
0.0782
(0.0220)
(1.1610)

0.0823
(0.0219)
(1.3139)
)0.0867
(0.0219)
(1.3484)
0.0618
(0.0220)
(1.1400)

)0.0007
(0.0220)
(0.3599)
)0.0393
(0.0220)
(2.7504)
)0.0052
(0.0220)
(0.9971)

0.0235
(0.0219)
(2.3667)
)0.0022
(0.0219)
(0.7294)
0.0098
(0.0220)
(1.5278)

Box±Pierce
Q(12)

26.8630

17.9916

19.4052

14.5364

197.5224

271.6149

39.4763

29.1593

Adjusted
Box±Pierce
Q(12)

0.1068

0.0842

0.0395

0.0319

0.0552

0.0545

0.0017

0.0001

11

12

a

Standard deviation of serial correlations.
b
Heteroscedasticity-adjusted standard deviation based on Diebold (1986).
*
Signi®cant at the 10% level.
**
Signi®cant at the 1% level.

C.I. Lee et al. / Journal of Banking & Finance 24 (2000) 787±807

0.0274
(0.0220)
(0.2864)
0.0111
(0.0220)
(0.1824)
)0.0091
(0.0220)
(0.1629)

797

798

C.I. Lee et al. / Journal of Banking & Finance 24 (2000) 787±807

Table 3
Unit root tests
CAC
Panel A: ADF test

a

ECU

NNN

PIB

Test statistic is the t-statistic
P on g2 from the regression
Dpt ˆ g0 ‡ g1 T ‡ g2 ptÿ1 ‡ ci DptÿI ‡ lt

Open-to-open returns
Test statistics
Lags in ADF

)3.0406
1

)1.6363
1

)1.9352
1

)2.9071
1

Close-to-close returns
Test statistics
Lags in ADF 2

)3.0242
1

)1.6919
1

)1.8209
1

)2.9607
1

Panel B: KPSS test b

P 2 2
ÿ2
St =S …L†, where
The test
P statistic is T
St ˆ et ; t ˆ 1; 2; . . . ; T , and
P
P
P
S 2 …L† ˆ T ÿ1 e2t ‡ 2T ÿ1 …1 ÿ S=…L ‡ 1†† et etÿs .
The et s are the residuals from a regression of the series being tested
on a constant and trend

Open-to-open returns
Test statistics2 : L ˆ 0
Test statistic: L ˆ 9
Test statistic: L ˆ 29

4.9822
0.5177
0.1862

13.3372
1.3491
0.4611

24.8383
2.5429
0.8856

26.9694
2.7297
0.9312

Close-to-close returns
Test statistic: L ˆ 0
Test statistic: L ˆ 9
Test statistic: L ˆ 29

5.0160
0.5207
0.1871

13.3466
1.3505
0.4618

24.8943
2.5469
0.8872

27.0804
2.7387
0.9343

a

Critical values are )3.13, )3.41, and )3.96 at the 10%, 5%, and 1% levels, respectively. The null
hypothesis that the series is I(1), i.e., non-stationary, is rejected if the test statistic exceeds the
critical value.
b
Critical values are 0.146 and 0.216 at the 5% and 1% levels, respectively. The null hypothesis of
stationarity is rejected if the test statistic exceeds the critical values.
*
Signi®cant at the 5% level.
**
Signi®cant at the 1% level.

are estimated and to make the presentation short, only those for lags 2, 4, 8,
and 16, i.e., VR(q), q ˆ 2, 4, 8, and 16, are reported in Table 4. While the
hypothesis that the variance ratio is one cannot be rejected, based on the homoscedasticity assumption, for most lags of the close-to-close returns, it is
rejected for most of the open-to-open returns. Again, it would be an error if
one were to reject the random walk hypothesis based on these results, which
are biased as a result of heteroscedasticity in the returns series. After adjusting
for this violation of homoscedasticity, most of the adjusted Z statistics reported
in Table 4 indicate that the VR(q)s are not di€erent from one. These results
constitute strong evidence that the null hypothesis of unit variance ratio cannot
be rejected.

799

C.I. Lee et al. / Journal of Banking & Finance 24 (2000) 787±807
Table 4
Estimate of variance-ratio VR(q) and variance-ratio test statistics Z(q) and Z (q) a
Open-to-open

Close-to-close

2

4

8

16

2

4

8

16

CAC
VR(q) a
Z(q) b
Z (q) c

0.93
)3.12
)2.24

0.89
)2.70
)1.67

0.86
)2.25
)1.10

0.84
)1.64
)0.61

0.99
)0.67
)0.53

0.96
)1.07
)0.71

0.93
)1.13
)0.57

0.91
)0.92
)0.34

ECU
VR(q)
Z(q)
Z (q)

0.94
)2.29
)1.34

0.92
)1.76
)0.97

0.95
)0.75
)0.37

1.00
0.02
0.01

1.04
1.64
0.85

1.08
1.80
0.87

1.08
1.11
0.45

1.12
1.13
0.38

NNN
VR(q)
Z(q)
Z (q)

0.83
)9.04
)3.91

0.81
)5.40
)1.90

0.76
)4.39
)1.21

0.73
)3.29
)0.70

0.87
)6.80
)2.55

0.92
)2.28
)0.73

0.88
)2.16
)0.54

PIB
VR(q)
Z(q)
Z (q)

0.93
)3.17
)1.42

0.90
)2.50
)1.03

0.87
)1.53
)0.30

0.83
0.75
1.05
1.06
1.01
0.93
)2.74
)2.59
2.16
1.43
0.20
)0.72
)0.93
)0.69
1.20
0.70
0.07
)0.20
P r
P
P r
a
rc …q† is an unbiased estimator
VR(q), variance ratio, is calculated as
rc …q†= r2a …q†, where
P 2
of 1/q of the variance of the qth di€erence of prices and
ra …q† is an unbiased estimator of the
variance of the ®rst di€erence of price. Z(q): Standard-normal-distributed homoscedastic test
statistic. Z (q): Standard-normal-distributed heteroscedasticity-adjusted test statistic.
*
Signi®cant at the 5% level.
**
Signi®cant at the 1% level.

As a further robustness check, we also perform the multivariate variance
ratio test (Chow and Denning, 1993). The results remain the same.
4.5. Close-to-open and open-to-close tests
The close-to-open and open-to-close results are presented in Table 5. First,
with regard to the unit root tests, Panel A.1 in Table 5 shows that the null
hypothesis of one unit root cannot be rejected for the CAC, ECU, NNN, and
PIB contracts. The KPSS stationarity results are reported in Panel A.2 in Table
5. All results show that the null hypothesis of no unit root is strongly rejected
for all four contracts. These results con®rm the results reported in Table 3, and
provide further indication that these contracts traded on the MATIF are
ecient.
Panel B, Table 5 reports the results for the variance ratio tests. The results
are similar to those reported in Table 4. That is, when the statistics are adjusted
for heteroscedasticity, then most of the VR(q)s are not signi®cantly di€erent
from zero. These results indicate that the null hypothesis of unit variance ratio

800

CAC
Panel A: Unit root tests
1. ADF test a
Close-to-open returns
Test statistics
Lags in ADF
Open-to-close returns
Test statistics
Lags in ADF2
2. KPSS test b

ECU

NNN

Test statistic is the t-statistic on g2 from the regression Dpt ˆ g0 ‡ g1 T ‡ g2 ptÿ1 ‡

PIB
P

ci DptÿI ‡ lt

)2.2830
1

)2.2417
1

)0.7446
1

)0.8069
1

)1.8489
1

)2.4901
1

)1.8746
1

)1.5896
1

P
P 2 2
ˆ et ; t ˆ 1; 2; . . . ; T , and
St =S …L†, where StP
The test statistic
is T 2 P
P
S 2 …L† ˆ T ÿ1 e2t ‡ 2T ÿ1 …1 ÿ S=…L ‡ 1†† et etÿs .
The et s are the residuals from a regression of the series being tested on a constant and trend

Close-to-open returns
Test statistics2 ; L ˆ 0
Test statistic: L ˆ 9
Test statistic: L ˆ 29

27.2487
2.7759
0.9620

13.3560
1.3517
0.4649

27.6436
2.7932
0.9530

22.4307
2.2623
0.7686

Open-to-close returns
Test statistic: L ˆ 0
Test statistic: L ˆ 9
Test statistic: L ˆ 29

35.2575
3.5768
1.2222

12.6867
1.2906
0.4476

24.6157
2.49758
0.8525

23.1102
2.3268
0.7865

C.I. Lee et al. / Journal of Banking & Finance 24 (2000) 787±807

Table 5
Close-to-open and open-to-close results

Panel B. Variance ratio test: Estimate of variance-ratio VR(q) and variance-ratio test statistics Z(q) and
Z (q) c
Close-to-open returns
Open-to-close returns
2

8

16

2

4

8

16

0.94
)2.89
)1.80

0.84
)3.82
)1.99

0.77
)3.59
)1.44

0.75
)2.60
)0.80

0.92
)3.86
)2.99

0.90
)2.55
)1.69

0.93
)1.10
)0.57

0.93
)0.77
)0.30

ECU
VR(q)
Z(q)
Z (q)

1.46
18.43
0.97

1.71
15.21
0.80

1.82
11.11
0.59

1.88
7.99
0.42

1.62
24.94
1.40

2.22
26.26
1.37

2.55
21.13
1.04

2.79
16.33
0.78

NNN
VR(q)
Z(q)
Z (q)

0.77
)12.26
)4.19

0.71
)8.23
)2.46

0.65
)6.39
)1.56

0.60
)4.88
)0.95

0.94
)3.21
)1.64

1.00
0.00
0.00

1.00
)0.07
)0.02

1.02
)0.30
)0.08

PIB
VR(q)
Z(q)
Z (q)

0.99
)0.45
)0.29

0.99
)0.29
)0.17

0.96
)0.56
)0.28

0.95
)0.22
)0.22

0.99
)0.45
)0.29

0.99
)0.29
)0.17

0.96
)0.56
)0.28

0.95
)0.55
)0.22

Critical values are )3.13, )3.41, and )3.96 at the 10%, 5%, and 1% levels, respectively. The null hypothesis that the series is I(1), i.e., non-stationary, is
rejected if the test statistic is greater than the critical value.
b
Critical values are 0.119, 0.146, and 0.216 at the 10%, 5%, and 1% levels, respectively. The null hypothesis of stationarity is rejected if the test statistic
exceeds the critical values.
P r
P
P r
c
VR(q), variance ratio, is calculated as
rc …q†= r2a …q†, where
rc …q† is an unbiased estimator of 1/q of the variance of the qth di€erence of prices
P 2
and
ra …q† is an unbiased estimator of the variance of the ®rst di€erence of price. Z (q): Standard-normal-distributed homoscedasticity test statistic.
Z (q): Standard-normal-distributed heteroscedasticity-adjusted test statistic.
*
Signi®cant at 5% level.
**
Signi®cant at 1% level.

C.I. Lee et al. / Journal of Banking & Finance 24 (2000) 787±807

a

4

CAC
VR(q)
Z(q)
Z (q)

801

802

Table 6
GLOBEX sub-period results
CAC
Pret

ECU
Post

Pre

NNN
Post

Pre

PIB
Post

Pre

Post

Open-to-open returns
Test statistics
)3.1432
Lags in ADF
1
Close-to-close returns
Test statistics
)3.1399
Lags in ADF2
1
2. KPSS test b

Open-to-open returns
Test statistics2 :
Lˆ0
Test statistic:
Lˆ9
Test statistic:
L ˆ 29
Close-to-close returns
Test statistic:
L ˆ 04
Test statistic:
Lˆ9
Test statistic:
L ˆ 29

)1.1555
1

)2.1577
1

)1.0606
1

)1.7726
1

)0.9426
1

)2.9744
1

)1.1815

)2.1031
1

)1.1363

)1.4839
1

)1.0414

)3.0037
1

)3.0353
1
)3.1490

P
P
P
P
The test statistic is T ÿ2 St2 =S 2 …L†, where St ˆ et; t ˆ 1; 2; . . . ; T , and S 2 …L† ˆ T ÿ1 e2t ‡ 2T ÿ1 …1 ÿ S=…L ‡ 1††
P
et etÿs . The etÿs are the residuals from a regression of the series being tested on a constant and trend.
4.4293

17.1708

6.8059

19.7358

19.6982

18.4303

10.0345

11.5632

0.4662

1.7698

0.7132

1.9963

2.0191

1.8649

1.07851

1.2218

0.1732

0.6229

0.2617

0.6826

0.7036

0.6375

0.4035

0.4456

4.4603

17.2832

6.7939

19.7964

19.7192

18.4771

9.9081

11.5353

0.4684

1.7819

0.7093

2.0034

2.0173

1.8696

1.0675

1.2131

0.1738

0.6269

0.2617

0.6854

0.7029

0.6392

0.4014

0.4423

C.I. Lee et al. / Journal of Banking & Finance 24 (2000) 787±807

Panel A: Unit root tests
P
1. ADF test a
Test statistic is the t-statistic on g2 from the regression Dpt ˆ g0 ‡ g1 T ‡ g2 ptÿ1 ‡ ci DptÿI ‡ lt

Panel B. Variance ratio test: estimate of variance-ratio VR(q) and variance-ratio test statistics Z(q) and Z (q) c
Open-to-open returns
Close-to-close returns
2

a

8

Post

Pre

0.94
)1.86
)1.27

0.91
0.90
)2.77 )1.87
)2.61 )1.11

0.93
)1.57
)0.99

0.94
)1.81
)1.23

0.85
)4.75
)1.75

2

4

8

16

Pre

Post

Pre

Post

Pre

Post

Pre

Post

Pre

Post

Pre

Post

0.89
)1.90
)1.51

0.86
)1.56
)0.73

0.86
)1.49
)0.90

0.89
)0.81
)0.30

0.76
)1.70
)0.76

1.00
)0.15
)0.11

0.97
)0.95
)0.95

0.96
)0.71
)0.45

0.95
)0.78
)0.65

0.94
)0.64
)0.31

0.92
)0.89
)0.56

0.99
)0.10
)0.04

0.80
)1.40
)0.66

0.85
0.92
)1.96 )1.32
)1.09 )0.84

0.88
)0.97
)0.44

0.95
)0.55
)0.31

0.91
)0.49
)0.17

1.01
0.07
0.04

1.02
0.54
0.43

1.04
1.36
0.84

1.05
0.63
0.43

1.09
1.50
0.86

1.15
1.23
0.64

1.08
0.85
0.41

1.21
1.17
0.44

1.12
0.85
0.34

0.83
)7.44
)2.68

1.02
0.66
0.55

0.87
)3.09
)0.96

1.11
1.77
1.23

0.81
)2.72
)0.66

1.12
1.24
0.67

0.80
)1.95
)0.37

1.15
1.04
0.41

1.04
1.25
0.70

1.06
1.99
1.09

1.08
1.39
0.68

1.03
0.48
0.23

1.00
)0.01
0.00

0.95
)0.49
)0.20

0.82
0.87
0.78
0.92
)7.75 )3.25 )5.09 )1.74
)3.25 )3.85 )1.74 )0.91
1.02
0.64
0.47

16

Post

1.04
0.73
0.45

0.71
0.93
)4.26 )1.14
)1.14 )0.34

0.77
0.92
)4.00 )0.85
)1.38 )0.34

0.67
)3.56
)1.11

0.67
0.97
)3.27 )0.69
)0.69 )0.08
0.66
0.61
)2.60 )2.80
)0.70 )0.75

0.71
0.90
)2.21  )0.72
)0.58 )0.23

Critical values are )3.13, )3.41, and )3.96 at the 10%, 5%, and 1% levels, respectively. The null hypothesis that the series is I(1), i.e., non-stationary, is
rejected if the test statistic exceeds the critical value. * Signi®cant at the 10% level.
b
Critical values are 0.146 and 0.216 at the 5%, and 1% levels, respectively. The null hypothesis of stationarity is rejected if the test statistic exceeds the
critical values.
P r
P
P
c
rc …q† is an unbiased estimator of 1/q of the variance of the qth di€erence of prices
VR(q),
ratio, is calculated as rrc …q†= r2a …q†, where
P variance
2
and
ra …q† is an unbiased estimator of the variance of the ®rst di€erence of price. Z(q): Standard-normal-distributed heteroscedasticity test statistic.
Z*(q): Standard-normal-distributed heteroscedasticity adjusted test statistic.  Signi®cant at the 5% level.  Signi®cant at the 1% level.

C.I. Lee et al. / Journal of Banking & Finance 24 (2000) 787±807

CAC
VR(q)
Z(q)
Z (q)
ECU
VR(q)
Z(q)
Z (q)
NNN
VR(q)
Z(q)
Z (q)
PIB
VR(q)
Z(q)
Z (q)

4

Pre

803

804

C.I. Lee et al. / Journal of Banking & Finance 24 (2000) 787±807

cannot be rejected for these four contracts when close-to-open and open-toclose returns series are used.
4.6. Pre- and post-GLOBEX tests
MATIF, in partnership with the CME and Reuters, jointly developed
GLOBEX in 1993. Trading on GLOBEX started on June 4, 1993. MATIF
products were eligible to be traded on GLOBEX. Thus, it is possible that the
advent of GLOBEX may have in¯uenced the eciency of the contracts examined in this paper. Thus, the analyses are replicated for the pre-and postGLOBEX subperiods and reported in Table 6.
Panel A.1 in Table 6 reports the results for the ADF test. The results show
that the open-to-open and close-to-close returns for the pre-GLOBEX for
CAC are stationary. Similarly, the close-to-close post-GLOBEX PIB returns
are stationary. Panel A.2 in Table 6 reports the KPSS test results. The null
hypothesis of stationarity is rejected for all pre- and post-GLOBEX subperiods
for all open-to-open and close-to-close returns. These results provide evidence
that the eciency of the four MATIF contracts being examined was not affected by the formation of GLOBEX.
The results for the variance ratio tests are reported in Panel B, Table 6, for
the two pre- and post-GLOBEX subperiods. As was the case with the full
sample, for the close-to-close returns for all contracts for both the pre- and
post-GLOBEX periods, there are no heteroscedasticity consistent test statistics
that are statistically signi®cant. For the open-to-open returns for both subperiods, most of the Z (q) are not signi®cant. These results are similar to the
ones for the full sample, with a similar interpretation.

5. Conclusion
Due to the global importance of MATIF, the eciency of four ®nancial
futures contracts traded on it is examined in this paper. Using serial correlation, stationarity, and variance ratio tests, it is shown that the open-to-open
and close-to-close returns series for the contracts do not depart from a random
walk, thereby con®rming the pricing eciency of these contracts.
The results do not necessarily con®rm the possibility that all MATIF traded
contracts are ecient. For example, Esposito and Giraldi (1994) examined the
introduction of trading on futures contracts on the Italian Treasury Bonds
(BTP) on both the LIFFE and MATIF. While BTP futures trading thrived on
the LIFFE, it failed on the MATIF. Esposito and Giraldi advance the plausible argument that the presence of other similar contracts on the LIFFE made
it much easier for international traders to trade BTP contracts in London
rather than in Paris. This paper, however, attests more to the problems asso-

C.I. Lee et al. / Journal of Banking & Finance 24 (2000) 787±807

805

ciated with introducing an inappropriate product, rather than a failure of ef®ciency on MATIF.
Another paper by Chow et al. (1996) examines the trading of the same
contracts on MATIF and on GLOBEX. Their results suggest that traders
prefer to trade on the ¯oor rather than GLOBEX during the time period when
they have a choice of trading with either mechanism. Liquidity is advanced as a
reason for the preference of the ¯oor over GLOBEX. These results also point
to eciency on the MATIF. Also, Geman and Schneeweis (1993) present evidence to show that the NNN traded on MATIF is well suited for use in risk
management strategies.
Lee and Mathur (1999) show that the ®nancial futures contracts trading on
the Spanish futures markets, MEFF, are ecient. MEFF is the fourth largest
futures market in Europe and shares with MATIF the distinction of attracting
foreign traders. The results suggest that exchanges that can structure products
so that they are attractive to foreign traders may experience eciency in the
pricing of their contracts.
Finally, the results from pre- and post-GLOBEX subperiods suggest that
introduction of trading on GLOBEX did not in¯uence the eciency of the
traded contracts. Furthermore, these contracts trade on GLOBEX after hours.
While contracts are traded through an open outcry system on MATIF, there is
an automated continuous auction system on GLOBEX. Thus, the results of
this study imply that the speci®c trading mechanisms involved do not in¯uence
the conclusions drawn in this study.

Acknowledgements
We thank two anonymous referees of this journal for their helpful comments, and Christina Sayles for her assistance with the preparation of the
manuscript.

Appendix A
The variance ratio of the q-di€erenced series is given by
P 2
r …q†
;
VR…q† ˆ P 2c
ra …q†
P 2
where
rc …q† is an
Punbiased estimator of 1/q of the variance of the qth-differenced series and r2a …q† is an unbiased estimator of the variance of the ®rstdi€erenced series. Or,

806

C.I. Lee et al. / Journal of Banking & Finance 24 (2000) 787±807

X

r2c …q† ˆ

nq‡1
1 X
2
…pt ÿ ptÿ1 ÿ ql† ;
m tˆq‡1

where
m ˆ q…nq ÿ q ‡ 1†…1 ÿ 1=n† and l ˆ

1
…pnq‡1 ÿ p1 †
nq

and
nq‡1

X

r2a …q† ˆ

1 X
2
…pt ÿ ptÿ1 ÿ l† :
nq ÿ 1 tˆ2

The standard Z test statistic is
Z…q† ˆ

VR…q† ÿ 1
1=2

‰uu…q†Š

;

where u…q† ˆ ‰2…2q ÿ 1†…q ÿ 1†Š=‰3q…nq†Š.
A re®ned test statistic, Z (q), which adjusts for heteroscedasticity, is proposed by Lo and MacKinlay (1989):
Z  …q† ˆ

VR…q† ÿ 1
‰u …q†Š

1=2

;

where


u …q† ˆ


qÿ1 
X
2…q ÿ j†
q

jˆ1

d…j†;

and
d…j† ˆ

Pnq‡1

ÿ ptÿ1 ÿ l†2 …ptÿj ÿ ptÿjÿ1 ÿ l†2
:
hP
i2
nq‡1
2
…p
ÿ
p
ÿ
l†
t
tÿ1
tˆ2

tˆj‡2 …pt

Both Z(q) and Z  …q† are asymptotically normally distributed with mean zero
and unit standard deviation.

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