Eciency tests in the French derivatives market
Chun I. Lee
a, Kimberly C. Gleason
b, Ike Mathur
c,*a
Texas Southern University, Houston, TX 77004, USA b
Bentley College, Waltham, MA 02154, USA c
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 Marchea Terme International de France (MA-TIF) or the French International Futures and Options Exchange is one of the major derivatives markets in the world. The eciency of four ®nancial contracts traded on the MATIF-CAC40 Index Futures, ECU Bond Futures, National Bond Futures, and PI-BOR 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.Ó2000 Elsevier Science B.V. All
rights reserved.
JEL classi®cation:G15; C22; G13
Keywords:Market eciency; MATIF; Random walk
1. Introduction
With over 70 million contracts traded in 1997, the Marchea Terme Inter-national de France (MATIF) in Paris is one of the major derivatives markets in www.elsevier.com/locate/econbase
*Corresponding author. Tel.: +1-618-453-1421; fax: +1-618-453-5626. E-mail address:[email protected] (I. Mathur).
the world and has attracted many foreign investors.1Anticipating 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 interna-tionalization by oering products and expanding trading that appeal to global investors. Examples of these eorts include the oering of ECU-denominated products and the GLOBEX-partnership with the Chicago Mercantile Ex-change. 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 eciency.
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 fu-tures 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 fu-tures exchanges only MATIF oers 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 GLO-BEX, 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 eciency of the ®nancial futures traded on it. Thus, the purpose of this paper is to conduct comprehensive eciency 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 eciency in well-established markets, the evidence is mixed. By ex-amining 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 eciency is obtained that can shed additional light on the price behavior of assets.
1In 1996, approximately 40% of MATIF
2. The random walk hypothesis and market eciency
Given that this paper deals with eciency of the French derivatives market MATIF, it is interesting to note that the concept of eciency was originally advanced by the French economist Louis Bachelier (1967). Subsequently, re-searchers such as Working (1934), Cowles and Jones (1937), Kendall (1953) and Fama (1965) examined serial correlation coecients 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 eciency. 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 eciency 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 eciency 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 ecient.
While the recent papers cited above provide evidence in support of market eciency, it is far from clear that all markets are ecient. For example, a recent paper by Fujihara and Mougoue (1997) provides evidence of depen-dence in petroleum futures. Similarly, Becker et al. (1996) provide evidepen-dence 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 eciency. Thus, eciency in any market should not be assumed without subjecting it to a thorough examination.
3. Data and methodology
3.1. The MATIF
and the Society des Bourses Frantaises (the French Stock Exchange). Devel-oping its global appeal has been one of its major objectives in recent years. Since 1993, with the joint development of GLOBEX with the Chicago Mer-cantile 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 inves-tors, 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 in-clude 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 Oering Rates, the bench-mark 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 ocially recognized by the CFTC. Trading on the MATIF is conducted via the system of open outcry and after-hour 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
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 be-cause, 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 dierence in volatility during trading and non-trading pe-riods, both close-to-close (RC±C) and open-to-open (RO±O) returns are used and calculated as follows:
RC±CtLn PCt=PCtÿ1
and
RO±OtLn POt=POtÿ1:
Serial correlations, unit root tests, and variance-ratio tests are used to test for the eciency 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 eciency. With a unit root ± anI(1) process ± as the null hypothesis, the following regression on the natural logarithm of prices is estimated:
Dptg0g1Tg2ptÿ1 XL
i1
ciDptÿilt; 1
whereTis the number of observations.
2See http://www.matif.fr for additional statistics.
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
Fig. 1.
powerful against relevant alternative hypotheses. This lack of power in re-jecting 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
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
gsTÿ2 XT
t1
St2=S2 L; 2
whereLis the lag parameter,Stis the cumulative sum of the residuals (et) from a regression of the series on a constant and a linear trend (i.e., St
The null hypothesis of stationarity is rejected in favor of the unit root alter-native 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 eciency. 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 dierent intervals weighted by their length is one. Ifpt is the natural logarithm of price series, then the random walk hypothesis states thatpt follows the following form:
ptWptÿ1et; 4 Additional details are provided in the Appendix A.
4. Empirical evidence
4.1. Basic statistics
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±PierceQstatistics con®rm this ®nding. Before adjusting for hetero-scedasticity, the white noise hypothesis is rejected for all except the close-to-close returns on CAC and ECU, while the adjusted Box±PierceQs 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 eciency 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 Table 1
Basic statistics for returnsa
CAC ECU NNN PIB
O±O C±C O±O C±C O±O C±C O±O C±C
Observations 2110 2110 1630 1630 2839 2839 2156 2156
Meanb 2.58 2.69
)0.20 )0.20 0.81 0.79 0.24 0.25
Std. dev.b 126.02 119.40 77.79 73.82 49.67 45.05 15.52 13.98
T-statistics 0.94 1.0 )0.11 )0.11 0.87 0.93 0.73 0.82
Skewness )0.28 )0.18 24.41 25.70 0.50 0.70 4.70 6.27
Kurtosis 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. b
Expressed in basis points. *
Table 2
Serial correlations of returns
Lag CAC ECU NNN PIB
O±O C±C O±O C±C O±O C±C O±O C±C
1 )0.0680 )0.0142 )0.0577 0.0397 )0.1735 )0.1591 )0.0698 0.0453
(0.0218)a (0.0218) (0.0248) (0.0248) (0.0218) (0.0218) (0.0218) (0.0218)
(0.4494)b (0.2173) (0.7644) (0.6684) (1.7288) (1.8276) (3.6594) (3.2856)
2 0.0105 )0.0063 )0.0019 0.0128 0.0851 0.1659 )0.0036 0.0160
(0.0219) (0.0218) (0.0249) (0.0248) (0.0219) (0.0218) (0.0219) (0.0218) (0.1783) (0.1440) (0.1384) (0.3802) (1.2112) (1.8680) (0.8346) (1.9571) 3 )0.0365 )0.0304 0.0076 0.0157 0.0737 0.1061 0.0084 )0.0594
(0.0219) (0.0218) (0.0249) (0.0248) (0.0219) (0.0218) (0.0219) (0.0218) (0.3290) (0.3183) (0.2785) (0.4207) (1.1277) (1.4921) (1.2673) (3.7578) 4 0.0271 0.0500 0.0134 0.0590 0.0655 0.0625 )0.0741 0.0387
(0.0219) (0.0218) (0.0249) (0.0248) (0.0219) (0.0218) (0.0219) (0.0218) (0.2851) (0.4099) (0.3688) (0.8139) (1.0623) (1.1440) (3.7753) (3.0377) 5 0.0152 )0.0466 0.0507 0.0132 0.1018 0.0949 0.0566 )0.0460
(0.0219) (0.0218) (0.0249) (0.0249) (0.0219) (0.0218) (0.0219) (0.0218) (0.2137) (0.3945) (0.7166) (0.3859) (1.3245) (1.4123) (3.2994) (3.3127) 6 )0.0523 0.0188 )0.0222 0.0203 )0.0056 0.0364 )0.0558 )0.0507
(0.0219) (0.0249) (0.0219) (0.0249) (0.0219) (0.0219) (0.0219) (0.0219) (0.3939) (0.4597) (0.2717) (0.4534) (0.3099) (0.8741) (3.2755) (3.4766) 7 )0.0408 0.0163 )0.0252 )0.0374 0.0359 )0.0503 )0.0116 )0.0048
(0.0220) (0.0249) (0.0219) (0.0249) (0.0220) (0.0219) (0.0220) (0.0219) (0.3479) (0.4290) (0.2897) (0.6150) (0.7860) (1.0283) (1.4964) (1.0739) 8 )0.0027 0.0097 )0.0174 )0.0162 0.0607 0.1380 0.0132 )0.0027
(0.0220) (0.0249) (0.0219) (0.0250) (0.0220) (0.0219) (0.0220) (0.0219) (0.0868) (0.3318) (0.2404) (0.4049) (1.0233) (1.7016) (1.5931) (0.7976) 9 0.0173 )0.0393 0.0182 (0.0242 )0.0867 )0.1015 )0.0008 )0.0328
(0.0220) (0.0249) (0.0219) (0.0250) (0.0220) (0.0219) (0.0220) (0.0219) (0.2281) (0.6644) (0.2482) (0.4970) (1.2211) (1.4607) (0.3902) (2.7976)
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(0.0220) (0.0250) (0.0219) (0.0250) (0.0220) (0.0219) (0.0220) (0.0219) (0.2864) (0.4251) (0.2611) (0.2078) (1.2519) (1.3139) (0.3599) (2.3667) 11 0.0111 0.0142 0.0176 (0.0465 )0.0947 )0.0867 )0.0393 )0.0022
(0.0220) (0.0250) (0.0219) (0.0250) (0.0220) (0.0219) (0.0220) (0.0219) (0.1824) (0.4003) (0.2439) (0.6867) (1.2763) (1.3484) (2.7504) (0.7294) 12 )0.0091 0.0230 0.0131 (0.0294 0.0782 0.0618 )0.0052 0.0098
(0.0220) (0.0250) (0.0220) (0.0250) (0.0220) (0.0220) (0.0220) (0.0220) (0.1629) (0.5087) (0.2102) (0.5468) (1.1610) (1.1400) (0.9971) (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
aStandard deviation of serial correlations.
bHeteroscedasticity-adjusted standard deviation based on Diebold (1986).
*Signi®cant at the 10% level.
**Signi®cant at the 1% level.
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are estimated and to make the presentation short, only those for lags 2, 4, 8, and 16, i.e., VR(q), q2, 4, 8, and 16, are reported in Table 4. While the hypothesis that the variance ratio is one cannot be rejected, based on the ho-moscedasticity 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 dierent from one. These results constitute strong evidence that the null hypothesis of unit variance ratio cannot be rejected.
Table 3 Unit root tests
CAC ECU NNN PIB
Panel A:ADF testa Test statistic is thet-statistic ong
2from the regression Dptg0g1Tg2ptÿ1PciDptÿIlt
Open-to-open returns
Test statistics )3.0406 )1.6363 )1.9352 )2.9071
Lags in ADF 1 1 1 1
Close-to-close returns
Test statistics )3.0242 )1.6919 )1.8209 )2.9607
Lags in ADF2 1 1 1 1
Theets are the residuals from a regression of the series being tested
on a constant and trend Open-to-open returns
hypothesis that the series isI(1), i.e., non-stationary, is rejected if the test statistic exceeds the critical value.
bCritical 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.
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 ecient.
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 dierent from zero. These results indicate that the null hypothesis of unit variance ratio Table 4
Estimate of variance-ratio VR(q) and variance-ratio test statisticsZ(q) andZ(q)a
Open-to-open Close-to-close
aVR(q), variance ratio, is calculated asP rr
of 1/qof the variance of theqth dierence of prices andP r2
a qis an unbiased estimator of the
variance of the ®rst dierence 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. **
Table 5
Close-to-open and open-to-close results
CAC ECU NNN PIB
Panel A:Unit root tests
1. ADF testa Test statistic is the t-statistic ong
2from the regressionDptg0g1Tg2ptÿ1 P
ciDptÿIlt Close-to-open returns
Test statistics )2.2830 )2.2417 )0.7446 )0.8069
Lags in ADF 1 1 1 1
Open-to-close returns
Test statistics )1.8489 )2.4901 )1.8746 )1.5896
Lags in ADF2 1 1 1 1
Theets are the residuals from a regression of the series being tested on a constant and trend Close-to-open returns
Test statistics2;L0 27.2487 13.3560 27.6436 22.4307
Test statistic:L9 2.7759 1.3517 2.7932 2.2623
Test statistic:L29 0.9620 0.4649 0.9530 0.7686
Open-to-close returns
Test statistic:L0 35.2575 12.6867 24.6157 23.1102
Test statistic:L9 3.5768 1.2906 2.49758 2.3268
Test statistic:L29 1.2222 0.4476 0.8525 0.7865
Z(q)c
)3.13,)3.41, and)3.96 at the 10%, 5%, and 1% levels, respectively. The null hypothesis that the series isI(1), i.e., non-stationary, is
rejected if the test statistic is greater than the critical value.
bCritical 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.
cVR(q), variance ratio, is calculated asP
rr
c qis an unbiased estimator of 1/qof the variance of theqth dierence of prices andP
r2
a qis an unbiased estimator of the variance of the ®rst dierence of price.Z(q): Standard-normal-distributed homoscedasticity test statistic. Z(q): Standard-normal-distributed heteroscedasticity-adjusted test statistic.
Table 6
GLOBEX sub-period results
CAC ECU NNN PIB
Pret Post Pre Post Pre Post Pre Post
Panel A:Unit root tests
1. ADF testa Test statistic is the t-statistic ong
Panel B.Variance ratio test: estimate of variance-ratio VR(q)and variance-ratio test statistics Z(q)and Z(q) Open-to-open returns Close-to-close returns
2 4 8 16 2 4 8 16
Pre Post Pre Post Pre Post Pre Post Pre Post Pre Post Pre Post Pre Post
CAC
Critical values are)3.13,)3.41, and)3.96 at the 10%, 5%, and 1% levels, respectively. The null hypothesis that the series isI(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.
cVR(
q), variance ratio, is calculated asP
rr
c qis an unbiased estimator of 1/qof the variance of theqth dierence of prices and P
r2
a qis an unbiased estimator of the variance of the ®rst dierence 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.
cannot be rejected for these four contracts when close-to-open and open-to-close 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 eciency of the contracts ex-amined in this paper. Thus, the analyses are replicated for the pre-and post-GLOBEX 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 eciency of the four MATIF contracts being examined was not af-fected 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 sub-periods, most of theZ(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 eciency of four ®nancial futures contracts traded on it is examined in this paper. Using serial correla-tion, 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 eciency of these contracts.
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 eciency on the MATIF. Also, Geman and Schneeweis (1993) present ev-idence 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 ecient. 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 eciency 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 eciency 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 com-ments, and Christina Sayles for her assistance with the preparation of the manuscript.
Appendix A
The variance ratio of theq-dierenced series is given by
VR q
P
r2 c q P
r2 a q
;
whereP
r2
c q is an unbiased estimator of 1/q of the variance of the q th-dif-ferenced series andP
r2
X
The standardZtest statistic is
Z q VR q ÿ1 uu q1=2;
whereu q 2 2qÿ1 qÿ1=3q nq.
A re®ned test statistic, Z(q), which adjusts for heteroscedasticity, is
pro-posed by Lo and MacKinlay (1989):
Z q VR q ÿ1
BothZ(q) andZ qare asymptotically normally distributed with mean zero and unit standard deviation.
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