The prospects of BRIC countries: Testing weak-form market efficiency

Research in International Business and Finance 30 (2014) 217–232

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Research in International Business and Finance j o ur na l ho me pa ge : w w w . e l s e v i e r . c o m / l o c a t e / r i b a f

The prospects of BRIC countries: Testing weak-form market efficiency Asma Mobarek a,∗, Angelo Fiorante b a b

Stockholm University Business School, Sweden The Centre for European Policy studies at European Credit research Institute, Belgium

a r t i c l e

i n f o

Article history: Received 23 March 2012 Received in revised form 18 March 2013 Accepted 6 June 2013 Available online xxx JEL classification: G14 G01 G15

a b s t r a c t The main purpose of the study is to determine whether the equity markets of Brazil, Russia, India and China (BRIC) may be considered weak-form efficient in recent years. The major findings using daily data and a bias-free statistical technique with a sample spanning from September 1995 to March 2010 indicate that the results from the last sub-periods, including the subprime crisis, support the belief that these markets may have been approaching a state of being fairly weak-form efficient, which reflects the future prospects of BRIC countries. © 2013 Elsevier B.V. All rights reserved.

Keywords: BRIC Weak-form market efficiency Random walk hypothesis Emerging markets

1. Introduction The updated literature on market efficiency has shifted from the efficient market hypothesis (EMH), which states that the level of market efficiency remains unchanged in a complete sense during the estimation period to advocating the possibility of time-varying efficiency or inefficiency. The latter approach has recently been gaining attention (see, for example, Lo, 2004, 2005; Yen and Lee, 2008; Ito and Sugiyama, 2009; Lim and Brooks, 2011). However, Lo (2004, 2005) suggest that the new paradigm

∗ Corresponding author. Tel.: +46 164645; fax: +46 08 674 74 40. E-mail address: [email protected] (A. Mobarek). 0275-5319/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ribaf.2013.06.004

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of adaptive markets hypothesis (AMH), according to which the EMH may persist together with behavioral finance in a logically consistent way. According to this new hypothesis, market efficiency is not an unconditionally fixed phenomenon but is a characteristic that varies continuously over time and across markets (Lim and Brooks, 2011). The issues of whether the equity markets of the BRIC may be considered weak-form efficient remain still highly debatable with no general agreement, given mixed evidence. The intention of this paper is to present a more clear and homogeneous picture of these four significant markets using updated data including the recent ongoing period of turmoil in the financial world as well as a robust time-varying efficiency test methodology that facilitates statistical triangulation (Hung et al., 2009; Chianga et al., ´ 2009; Ito and Sugiyama, 2009; Al-Saleh and Al-Ajmi, 2012). 2010; Charles and Darne, This paper contributes to the existing literature in two ways. First, there is no contemporaneous study on market efficiency and anomalies in the quickly growing economies and transition markets of Brazil, Russia, India and China, also known as the BRIC countries. Second, this study includes the current subprime financial crisis, which represents a developmental stage in the BRIC transition during chaos in the developed market. However, due to major changes in the BRIC economies in the past thirty years, the data have been divided into three sub-periods to observe whether these markets exhibit a trend toward increased weak-form market efficiency. The major findings reveal that the BRIC stock markets appear to exhibit a trend toward increased weak-form efficiency and the disappearance of the day of the week effect, which may lead to the realization of the BRICs’ dream in 2050 (Goldman Sachs Global Economics Group, 2007), although maintaining a well-functioning capital market is always a challenge. The rest of the paper is organized in the following way: Section 2 presents the literature review; Section 3 presents the selected data and the adopted methodology used for the study; Section 4 presents and analyses the empirical findings in detailed; and Section 5 summarizes and concludes the study. 2. Literature review Under weak-form market efficiency claims that future stock prices cannot be anticipated by using past stock price information, as past price information is already incorporated into the current stock price (Fama, 1970). Because weak-form market efficiency is a prerequisite for higher types of efficiency, rejecting it implies that the rejection of the semi-strong and strong forms as well (Campbell et al., 1997). However, Yen and Lee (2008) have recently provided an intensive review of empirical evidence on the EMH over the last five decades. Their survey clearly exhibits that the EMH no longer enjoys the level of support it received during the 1960s and in fact was criticized by behavioral finance in the 1990s. Lo (2004) proposes a new paradigm, adaptive markets hypothesis (AMH), in which the EMH may co-exist alongside behavioral finance in an intellectually consistent manner. According to this new hypothesis, market efficiency is not an unconditional phenomenon but a criterion that varies continuously over time and across markets. Studies on the weak form of market efficiency in emerging markets have shown controversial results. Keane (1983) noted that developed markets have far more advanced systems of information disclosure and processing compared to developing markets. This characteristic may be one of many reasons why a substantial number of emerging markets are less efficient. An extensive paper by Worthington and Higgs (2005) examined the weak-form market efficiency of Asian equity markets. Daily returns were used for ten emerging markets (China, India, Indonesia, Korea, Malaysia, Pakistan, the Philippines, Sri Lanka, Taiwan and Thailand) and five developed markets (Australia, Hong Kong, Japan, New Zealand and Singapore). Various statistical tests suggested weak-form efficiency in all markets. However, when applying the more stringent variance ratio tests, the results were mixed, suggesting that only the developed markets in Hong Kong, New Zealand and Japan could be considered weak-form efficient. Lock (2007) applied the Lo and MacKinlay (1988) variance ratio test on the weekly returns from the Taiwanese stock market from 1990 to 2006 obtaining strong results that not only does the Taiwanese composite stock index move in a random walk fashion, returns for the individual stocks do as well. Gupta and Basu (2007) concluded that the two major equity markets in India do not follow a random walk, as evidence in autocorrelation was detected for the period 1991–2006.

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Mobarek et al. (2008) examined the presence of weak-form efficiency of the Dhaka Stock Exchange in Bangladesh using a non-parametric test as well as parametric and reported weak-form inefficiency. Studies on BRIC countries differ in terms of segmentation and testing procedures. Abrosimova et al. (2007) tested the Russian stock market using daily, weekly and monthly data, reporting that weakform efficiency may only be accepted when using monthly data. Moreover, insufficient evidence was provided by the tests involving trading strategies’ profiting from inefficiencies after transaction costs and risk are considered. McGowan and Ibraham (2009) investigated the Russian stock index in the period 1995–2003 and confirmed a day-of-the-week effect, rejecting weak-form market efficiency. McGowan (2011) later investigated the efficiency of the Russian market, concluding that the market was efficient in the later stage, after 2000. However, Terence et al. (2009), using technical trading analysis, reported that the Russian market is the most inefficient among BRICs and that Brazil is the most efficient market. Similarly, a recent study by Chen and Metghalchi (2012), using technical trading analysis, suggests Brazil to be a highly efficient market. However, there are more studies relating to market efficiency in the Indian and Chinese stock markets among the BRICs. For example, Poshakwale (1996) provided evidence of a day-of-the week effect in the Bombay Stock Exchange over the period 1987–1994. Both Gupta and Yang (2011) applied a random walk test to the major equity markets, BSE and NSE, for the period 1997–2011, finding mixed results regarding market efficiency. For example, for quarterly data, all three methods ADF, PP and KPSS tests support weak-form efficiency for the later sample period, 2007–2011, but there exists slightly conflict evidence for the earlier period, 1997–2007, as only the PP test shows weak-form inefficiency; for monthly data, all three test methods are consistent for weak-form efficiency for the period 2007–2011 and are not efficient for the earlier period, 1997–2007. Similarly, Lim et al. (2009) mitigated the confounding effect of thin trading on return autocorrelation to examine both the Shanghai and Shenzhen Stock Exchanges and rejected the weak-form market efficiency in certain time periods. In addition, Liu (2011) employed a unit root test and the autocorrelation function to examine the period over 2000 to 2008, rejecting weak-form efficiency in the Chinese stock market. However, Fifield and Jettey (2008), applying parametric and non-parametric variance ratio tests to the daily data of 370 stocks over the period 1996–2005, concluded that the efficiency of both markets has improved following regulatory changes. Overall, the results suggest that the Chinese stock markets are characterized by information asymmetry, although timely access to high-quality information that domestic investors enjoy has improved the efficiency of the B-share market. Ever since booming economies began showing remarkable growth potential in the late 20th century, emerging stock markets have captured the attention of researchers and investors, and an understanding of the great necessity of evaluating the soundness of these markets has grown ever since these new economies began their developing and liberalization processes. Driving this increase in exposure is that over the past twenty years, many emerging countries, especially the BRICs, have experienced several types of reform processes to ensure the soundness of their markets while opening their economies to receive foreign capital inflows, spurring market integration between developed and emerging markets. This phenomenon has led to an increase in interest in BRIC markets, which offer new sources of investment possibilities, as reflected in their growth potential. In summary, we may say that we must address the controversial recent findings regarding the weak-form efficiency of the BRICs with a robust technique mitigating the problem of the non-normal distribution of stylized facts of financial data with recent trends.

3. Research methodology and data The study adopts both classical and dynamic frameworks to assess weak-form market efficiency. It tests the random walk properties of stock prices by applying a battery of tests, such as the serial correlation test, the Runs test, two types of variance ratio tests, single (Lo and MacKinlay, 1988), and multiple (Chow and Denning, 1993), and Wright’s (2000) Ranks and Sign test. To assess the robustness of regular weak-form efficiency, the study also considers the well-known stock market anomaly, the day of the week effect, as we have daily data for our observation. We use a bias-free statistical

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technique, GARCH modeling (see for example, Connolly (1989), Easton and Faff (1994)) to assess the day of the week effect in the BRIC stock market. 3.1. Methodology for testing the random walk hypothesis Testing the random walk properties of stock price series using variance ratio tests has been proven successful, since they tend to yield more powerful and accurate results compared to other tests such as the unit root test, various ARIMA and auto-regressive models (e.g., Lo and MacKinaly, 1989; Liu and He, 1991). We present only the dynamic test of variance ratio in details as other test are very common in existing literatures. 3.1.1. Variance ratio test Variance ratio tests are designed to test for type-1 random walk (RW1), which assumes homoskedastic increments as well as type-3 random walk (RW3) if the increments are assumed to be subject to heteroskedasticity, (Campbell et al., 1997). The single variance ratio test proposed by Lo and MacKinlay (1988) uses the fact that if a series of stock prices follows a random walk, then the increments are said to be serially uncorrelated and that the variance of those increments should increase linearly in the sampling intervals. Pt = Pt−1 +  + εt ,

εt ∼IID N(0,  2 )

The variance of the qth difference should be equal to q times the variance of the first differences, e.g., the variance of a weekly series should be five times the variance of a daily series (Karamera et al., 1999). If the random walk model describes the process that generates the stock price, one qth of the variance of (pt − pt−q ) is expected to be equal to the variance of (pt − pt−1 ): Var(pt − pt−q ) = qVar(pt − pt−1 ) where, q is any positive integer. The variance ratio proposed by Lo and MacKinlay (1988) is then given by the following: VR(q) =

(1/q)(Var(pt − Pt−q ))  2 (q) = 2 Var(pt − Pt−1 )  (1)

where, the single variance ratio tests the null hypothesis that: H0 : VR(q) = 1 Lo and MacKinlay (1988) also generated the asymptotic distribution of the estimated variance ratios, proposing two test statistics, Z (q) and Z*(q), under the null hypothesis of homoskedastic increments according to a random walk and heteroskedastic increments according to a random walk, respectively. Assuming homoskedastic increments, the test statistic is as follows: Z(q) =

VR(q) − 1 ∼N(0, 1) ϕ(q)

where ϕ(q) =

 2(2q − 1)(q − 1) 1/2 3q(nq)

Assuming heteroskedastic increments, the test statistic is as follows: Z ∗ (q) =

VR(q) − 1 ∼N(0, 1) ϕ∗ (q)

A. Mobarek, A. Fiorante / Research in International Business and Finance 30 (2014) 217–232

 where ϕ∗ (q) and ıt =

=

q−1  

4

t=1

nq

t 1− q



1/2 ıt 2

j=t+1

ˆ (Pj−1 − Pj−t−1 − ) ˆ (Pj − Pj−1 − )



nq (P j=1 j

221

ˆ − Pj−1 − )

2

2

2

The single variance ratio test compares the test statistics, Z (q) and Z*(q) with the critical values of the standard normal table. The nature of the single variance ratio may not be completely adequate for testing the random walk hypothesis, as the approach is useful for testing only the individual variance ratios for a specific interval q, (e.g., Worthington and Higgs, 2005; Karamera et al., 1999). The random walk hypothesis requires more support, that is, that the variance ratio of all observation intervals, q’s, should simultaneously be equal to 1: VR(q) = 1∀q Chow and Denning (1993) developed the multiple variance ratio tests that provide a multiple comparison of the variance ratios and may be written as follows: Mt (q) = VR(q) − 1 = 0, And considers a set of m tests, {Mt (qi )|i = 1, 2, . . ., m} corresponding to a selected value of observation intervals {qi |i = 1, 2, . . ., m} . Given the proper approach to testing the random walk hypothesis, the multiple variance ratio tests will have several sub-hypotheses that will be tested jointly: H0i : Mt (qi ) = 0 for i = 1, 2, . . ., m / 0 for i = 1, 2, . . ., m H1i : Mt (qi ) = The rejection of any one or more H0i values will reject the random walk hypothesis. The multiple variance ratio approach is based on the Studentized Maximum Modulus (SMM) distribution and uses these critical values, rather than the critical values of a standard normal distribution, to test the null hypotheses: PR{max(|Z(q1 )|, . . ., |Z(qm )|) ≤ SMM(˛; m; T )}≥1 − ˛ where SMM(a; m; T) is the upper ˛ point of the Studentized Maximum Modulus (SMM) distribution with parameters m (number of variance ratios) and T (sample size) degrees of freedom. When the degree of freedom approaches infinity asymptotically (i.e., T = ∞): lim SMM(˛; m; ∞) = Z˛∗ /2 , where T →∞

Z˛∗ /2 = standard normal distribution and ˛* = 1 − (1 − ˛)1/m . Finally, Wright (2000) proposed the use of signs and ranks of a time-varying dynamic test of inefficiency. There are two main reasons to use this test over other single and multiple variance ratio tests: first, it is very likely able to calculate the exact distribution, and second, it is more powerful than other tests when the distribution is not normal (see for example, Hung et al., 2009; Luger, 2003). The variance ratio developed by Wright (2000) assumes that given T observations of asset returns {y1 , . . .., yT }, R1 and R2 are defined as follows:



(Tk)

R1 (k) =

T

(r + · · · + r1t−k+1 )2 t=k 1t T

 R2 (k) =

−1

(Tk)

−1

T −1

r2 t=1 1t

T t=k

T

(r2t + · · · + r2t−k+1 )2

T −1

r2 t=1 2t



−1

−1

 2(2k − 1)(k − 1) −(1/2) 3kt

 2(2k − 1)(k − 1) −(1/2) 3kt

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where r1t =

r(yt ) − ((T + 1)/2)

((T − 1)(T + 1))/12

r2t = −1

;

r(yt ) ; T +1

r (yt ) is the rank of yt among y1 , . . ., yT , and −1 is the inverse of the standard normal cumulative distribution function. The test is based on the sign of the rate of return (S1 ), which is given by the following:



S1 (k) =

(Tk)

−1

T t=k

(St + St−1 + · · · + St−k+1 )2 T

T −1

S2 t=1 t

where St = 2(yt , 0), St = 2 ␮ (yt , ␮), and (rt , q) =



 2(2k − 1)(k − 1) −(1/2) 3kt



+0.5 if rt > q . −0.5 otherwise

3.2. Data and sample Daily price index data have been collected using Thomson Reuter’s Data-stream and include closing prices from Monday to Friday with the currency base denominated in US Dollars for all indices. The indices selected have been chosen with the criteria regarding the size, relevance, trading frequency as well as frequency of their use by domestic and foreign investors for measuring performance. A benchmark is used that includes the equity markets of Japan, UK and the US for comparing results and efficiency. These markets are chosen due to their size and relevance for measuring the possibility of BRICs’ becoming as large as they are in the near future. The statistical tests are applied independently to the selected countries’ most significant stock indices. The daily stock index return, rt , is expressed in percentage terms and calculated using the continuously compounded formula: rt = ln

 P  t Pt−1

× 100

where Pt and Pt−1 represent the closing price of an index at time t and t − 1, respectively, and ln is the natural logarithm. Furthermore, the data are further divided into three sub-groups for extending the analysis, as the market efficiency may have changed during the individual periods due to plausible structural changes as well as shifting market environments. The data used in the first sub-period are subject to consequences of the Asian crisis that began in 1997, which had a direct impact on Japan (which has also experienced a previous crisis in 1995) and most of the Southeast Asian countries. However, the markets of China, India, the US and the UK may have also been affected indirectly due to integrated market economies. Soon after, in 1998, Russia suffered a crisis triggered by the Asian crisis, and Brazil was struck by a currency crisis between 1998 and 1999. During the second subperiod was the “dotcom bubble,” which reached its climax in March 2000 and affected the stock markets of all major industrialized counties. The last sub-period is unique for this study and includes data subject to the recent ongoing worldwide financial crisis, which has not been tested in previous studies. Table 1 presents a summary of the descriptive statistics of the daily return series for the full sample period of the eight markets as well as for the sub-periods. On average, the equity markets of the BRIC have higher mean returns and standard deviation than the markets of the benchmarks, highlighting the risk involved related to the investments in emerging markets. These results are in line with the notion that investments in developed markets are associated with lower risk and lower mean returns compared to more “risky markets,” which offer higher returns for offsetting the higher risk that an investor must assume. However, the returns of the BRIC tend to show higher volatility, especially in the case of Brazil and Russia, having a range between +20% and −20% compared to the benchmark

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Table 1 Descriptive statistics of the daily returns of the BRIC and the benchmark markets. Jarque–Beraa

Maximum

Minimum

Std. Dev.

Skewness

Kurtosis

Full period: 1995:09–2010:03 BRIC 0.0549 0.1043 Brazil Russia 0.0716 0.0395 India 0.0383 0.0572 China 0.0433 0.0011

18.0182 20.2039 18.5558 9.4815

−17.9631 −21.1994 −11.9922 −10.4423

2.6254 2.8152 1.8370 1.7674

−0.2563 −0.4419 −0.1465 −0.2095

9.1966 10.5163 9.0947 7.9430

6121.167*** 9068.677*** 5894.948*** 3896.354***

Benchmark −0.0118 Japan UK 0.0127 US (S&P) 0.0191 US (DJ) 0.0223

−0.0122 0.0390 0.0280 0.0220

12.5711 11.7912 10.9572 10.0891

−11.1857 −10.2701 −9.4695 −8.6950

1.6406 1.2860 1.2793 1.1780

0.0719 −0.1757 −0.1958 −0.2234

7.1704 13.5420 11.1986 10.5589

2757.069*** 17,615.85*** 10,666.94*** 9078.231***

Sub period 1: 1995:09–1999:12 BRIC 0.0628 0.1003 Brazil Russia 0.0497 0.0000 India 0.0199 0.0000 China 0.0582 0.0000

18.0182 15.5569 8.7358 9.4815

−17.2301 −21.1025 −7.9364 −10.4423

2.7970 3.6448 1.6054 1.9948

−0.2146 −0.3749 0.2177 0.4092

10.4716 7.6357 5.9532 8.0298

Benchmark Japan −0.0005 UK 0.0588 US (S&P) 0.0848 US (DJ) 0.0635

−0.0254 0.0607 0.0701 0.0413

12.5711 3.3805 4.9887 4.3511

−6.6665 −3.1012 −7.1127 −6.8999

1.6742 0.8422 1.0432 0.9011

0.5966 −0.1074 −0.4783 −0.5253

7.4068 4.2391 8.1278 7.9906

981.3703*** 74.46798*** 1281.111*** 1224.622***

Sub period 2: 2000:01–2005:12 BRIC 0.0260 0.0654 Brazil Russia 0.1188 0.1238 India 0.0384 0.1265 China −0.0094 0.0000

12.7280 9.6186 8.0190 9.4025

−11.7855 −11.5316 −11.8250 −6.5075

2.3162 2.1100 1.6430 1.3021

−0.1751 −0.4818 −0.7188 0.8226

4.8240 6.0559 7.5745 9.8219

224.9375*** 669.495*** 1499.336*** 3211.164***

−0.0193 0.0070 0.0000 0.0000

6.6987 4.7625 5.5732 5.3455

−7.5164 −4.7424 −6.0052 −8.1497

1.5294 1.0815 1.1705 1.0836

−0.0977 −0.2056 0.1182 −0.2116

4.7031 5.2862 5.4274 7.0668

191.6292*** 351.8537*** 387.8613*** 1090.15***

Subperiod 3: 2006:01–2010:03 BRIC Brazil 0.0876 0.1975 Russia 0.0272 0.0820 India 0.0569 0.0822 China 0.1026 0.1820

16.8570 20.2039 18.5558 9.0178

−17.9631 −21.1994 −11.9922 −9.1062

2.8489 2.7155 2.2696 2.0665

−0.3637 −0.3983 0.0279 −0.4302

9.9156 13.3192 8.9682 5.3933

2226.318*** 4932.017*** 1640.125*** 297.7906***

Benchmark −0.0126 Japan UK −0.0104 US (S&P) −0.0061 US (DJ) 0.0007

11.6443 11.7912 10.9572 10.0891

−11.1857 −10.2701 −9.4695 −8.6950

1.7554 1.8180 1.6035 1.5095

0.2385 −0.1064 −0.2368 −0.1061

8.7134 10.5275 11.9514 9.7847

1513.402*** 2610.936*** 3699.519*** 2121.497***

Market

Mean

Benchmark Japan −0.0194 UK −0.0043 US (S&P) −0.0104 US (DJ) 0.0079

Median

0.0067 0.0779 0.0685 0.0285

2637.08*** 1038.298*** 419.5607*** 1222.707***

a For the Jarque–Bera test of normality, the null hypothesis is rejected for all indices and sub periods at 1%, indicating that the return series are not normally. *** Significant at the 1% level.

countries, which have a moving range between +10% and −10%. It is noteworthy that the mean return of the BRIC countries is far higher than the benchmark countries and that sub-period 3 presents the maximum discrepancy among the two types of return series. All the return series have periods characterized by less or more volatility, but the BRICs’ return series tend to have greater outliers. The distribution properties for all return series appears to be non-normal, which has been tested using

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the Jarque–Bera test of normality, where the null hypothesis is rejected for all return series. The kurtosis values range from 4.2391 to 13.5420 and indicate how strongly the distribution is centered. In general, the Chinese return series demonstrate values more consistent with the return series of the benchmarks compared to Brazil, Russia and India, which tend to be more volatile markets. Nevertheless, the study uses the statistical tests assuming that the non-normal distribution is justified from the distribution. 4. Empirical results and analysis The following section presents and analyzes the empirical findings from the serial correlation tests, the runs test, the variance ratio tests used to assess the random walk hypothesis, and it provides the robustness check of the results from regression estimates obtained from the GARCH(1,1)model, which is used to examine the day-of-the-week effect. The results are divided into three sub-periods to easily present how the equity markets of the BRICs have evolved in terms of their market efficiency. 4.1. Serial correlation test The results (Table 2) for the first sub-period (1995:09–1999:12) reveal that the BRIC suffers from positive autocorrelation, whereas the US markets and Japan show little evidence of significant autocorrelation. For the second sub-period (2000:01–2005:12), the Ljung–Box Q-statistics present evidence that the equity markets of China, Japan and the US have no autocorrelation in their return series up to the 12th lag. In addition, Russia has improved, having less significant autocorrelation compared to the previous period. Brazil and India have several autocorrelation coefficients that are significantly different from zero, thus rejecting the null hypothesis. The third sub-period (2006:01–2010:03) yields evidence that some of the BRICs’ return series are less auto correlated compared to other benchmark countries. Markets based in Japan and the US (S&P and Dow Jones) show significant negative autocorrelation at the 1st and 2nd lag orders, whereas the UK market shows significant negative autocorrelation from the 2nd to the 8th lag orders.1 However, it is crucial to mention that these results should be interpreted with caution, as they assume that the return series are normally distributed. In fact, the Jarque–Bera test reveals that they are not for all sample periods and indices. Essentially, the results from the serial correlation tests show evidence of an improvement compared to the first sub-period, especially in the case of China and partially for Russia. For the third sub-period, Brazil (0.0366) and China (−0.0126) are the markets with the least significantly autocorrelated values. The evidence of serial correlation for the BRIC markets has shown improving results, which may suggest that the markets have become fairly weak-form efficient, although some predictability in returns may still exist. On the other hand, the equity markets of Japan, UK and US have deteriorated substantially compared to previous periods, suggesting that return predictability exists in these markets for this period. 4.2. Runs test The runs test is used to assess the independence between successive price changes and for the first sub-period, the null hypothesis is rejected for Russia and India, whereas Brazil and China show insignificant Z-values. The results (Table 3) for the first sub-period are roughly in line with the serial correlation tests. For the second sub-period, the null hypothesis is accepted only for the Japanese market. The BRIC region continues to show significant negative Z-values, and the UK shows similar values as well. The US markets present significant and positive Z-values. The results for the second sub-period have deteriorated compared to the first sub-period, suggesting that none of the BRIC, UK or the US countries presents independent price changes. These results conflict with the previous serial correlation tests, which show less evidence of autocorrelation for the return series of China, Japan and

1

Autocorrelation results for benchmark are available on request.

Table 2 Results of autocorrelation.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Russia

Subperiod 2: 2000-01-03–2005-12-31

India

China

AC

Q-Stat AC

Q-Stat AC

Q-Stat AC

0.06 −0.03 −0.02 −0.03 −0.01 −0.05 −0.01 0.06 0.06 0.12 0.07 −0.03 −0.04 −0.06 0.00 −0.06 −0.06 0.00 0.05 0.06 0.03 0.03 0.04 0.01 −0.03 −0.02 −0.02 0.01 −0.03 0.03

4.04 4.82 5.43 6.76 6.91 9.92 10.01 13.50 17.45 32.59 38.11 38.86 40.97 45.43 45.47 49.58 53.13 53.20 56.23 60.86 62.27 63.17 64.86 65.01 65.83 66.19 66.73 66.95 67.90 69.24

29.36 30.44 32.99 33.14 33.88 36.68 39.46 39.49 39.79 45.86 50.30 54.43 59.39 59.45 60.01 60.08 60.56 63.66 63.74 63.99 64.85 66.74 75.26 75.52 78.92 79.12 79.39 79.48 80.08 91.98

15.30 15.33 16.05 16.24 18.78 21.34 23.93 26.32 28.15 32.79 33.25 33.44 33.52 33.57 33.68 34.90 35.21 38.49 39.36 40.69 41.29 41.34 41.46 44.01 44.52 46.87 47.37 53.40 53.63 53.93

0.16 0.03 0.05 −0.01 −0.03 0.05 0.05 0.00 0.02 0.07 0.06 0.06 0.07 0.00 0.02 0.00 −0.02 −0.05 0.00 −0.01 0.03 0.04 0.09 −0.01 0.05 −0.01 0.01 0.00 0.02 0.10

0.12 0.00 0.02 0.01 0.05 −0.05 −0.05 0.05 0.04 0.06 0.02 0.01 0.01 0.00 −0.01 −0.03 0.02 −0.05 −0.03 −0.03 −0.02 0.00 −0.01 0.05 −0.02 −0.04 −0.02 −0.07 −0.01 0.01

Brazil Q-Stat

AC

−0.03 1.19 0.12 0.00 1.20 −0.04 0.12 18.02 0.01 0.01 18.09 0.00 0.04 19.87 −0.03 −0.02 20.40 −0.01 −0.06 24.11 −0.01 −0.04 25.93 −0.02 −0.07 31.80 −0.04 0.00 31.84 0.05 −0.05 34.71 0.03 0.06 38.95 0.00 −0.04 40.74 0.05 0.01 40.85 0.01 0.15 68.05 0.04 −0.02 68.49 0.09 0.05 71.65 0.07 0.00 71.73 −0.01 −0.02 72.50 −0.01 0.02 73.00 −0.01 −0.08 80.93 0.00 0.04 82.65 −0.05 −0.05 85.89 −0.02 −0.04 87.96 −0.04 −0.06 92.48 0.00 −0.03 93.30 0.00 0.01 93.47 0.01 −0.01 93.76 0.05 0.08 101.44 0.01 0.05 104.57 −0.02

Russia

Subperiod 3: 2006-01-02–2010-03-26

India

China

Brazil

Russia

India

China

Q-Stat AC

Q-Stat AC

Q-Stat AC

Q-Stat AC

Q-Stat AC

Q-Stat

AC

Q-Stat AC

24.35 26.64 26.91 26.97 28.27 28.41 28.49 29.39 32.35 36.79 38.11 38.15 42.61 42.88 45.55 57.29 64.36 64.49 64.74 65.04 65.10 68.54 69.30 71.58 71.65 71.72 71.83 75.64 75.82 76.86

3.23 3.28 6.86 9.66 10.34 10.36 11.78 12.55 15.66 17.13 19.95 29.39 32.64 32.71 34.17 35.09 35.13 37.80 37.93 37.98 38.02 38.05 38.34 40.50 41.55 41.69 42.20 43.28 50.58 50.73

18.33 18.63 20.39 27.08 27.88 28.39 29.71 30.28 35.00 42.94 43.53 43.61 43.94 47.79 47.84 50.31 51.13 51.23 51.29 51.36 51.53 51.68 51.72 52.77 53.19 54.83 55.30 56.27 56.57 69.16

0.88 1.14 1.17 1.18 5.57 6.30 6.45 7.90 9.34 10.14 10.16 10.84 10.85 12.18 12.28 12.56 13.35 13.52 20.73 22.68 24.65 25.10 25.18 26.87 27.01 27.04 28.17 28.62 30.26 31.50

1.48 3.27 4.85 4.97 5.10 7.68 7.72 8.28 10.04 10.20 12.11 21.49 22.00 22.12 23.04 25.98 31.43 50.85 50.96 55.18 59.56 59.62 62.25 63.99 64.06 66.39 71.10 71.21 75.55 76.94

18.11 18.53 18.67 19.64 21.23 28.28 33.44 42.71 42.89 44.51 50.11 53.12 54.91 96.52 97.10 97.20 99.62 102.21 103.23 105.47 113.26 114.03 116.20 117.35 117.46 127.25 131.89 151.72 154.02 154.25

0.08 0.00 0.00 0.03 −0.01 −0.06 −0.03 0.04 0.09 0.07 −0.09 −0.01 0.08 0.05 0.02 0.00 0.05 0.00 −0.01 −0.04 −0.04 −0.02 0.03 0.00 −0.02 0.01 0.05 0.04 0.07 0.02

6.84 6.85 6.87 8.04 8.14 11.87 12.84 14.84 23.86 30.03 39.86 40.14 47.14 50.03 50.59 50.64 53.35 53.40 53.55 55.68 57.62 57.97 59.01 59.07 59.53 59.65 63.09 65.17 70.33 70.71

0.05 −0.01 −0.05 0.04 0.02 0.00 −0.03 −0.02 0.04 0.03 −0.04 −0.08 0.05 −0.01 0.03 −0.02 0.00 −0.04 −0.01 0.00 0.00 0.00 0.01 0.04 0.03 0.01 −0.02 0.03 −0.07 0.01

0.11 0.01 0.03 0.07 −0.02 −0.02 0.03 −0.02 0.05 0.07 0.02 −0.01 0.01 0.05 0.00 −0.04 −0.02 0.01 0.00 0.00 −0.01 0.01 0.00 0.03 0.02 −0.03 0.02 0.02 −0.01 −0.09

0.02 −0.01 0.00 0.00 −0.05 −0.02 0.01 0.03 −0.03 0.02 0.00 0.02 0.00 0.03 −0.01 −0.01 0.02 0.01 −0.07 0.03 −0.04 0.02 −0.01 0.03 0.01 0.00 −0.03 0.02 0.03 0.03

0.04 −0.04 −0.04 0.01 −0.01 −0.05 0.00 −0.02 −0.04 0.01 −0.04 0.09 0.02 0.01 0.03 0.05 0.07 −0.13 0.01 0.06 0.06 0.00 −0.05 −0.04 0.00 0.04 0.06 −0.01 0.06 −0.03

0.13 0.02 0.01 −0.03 0.04 −0.08 0.07 −0.09 −0.01 −0.04 −0.07 0.05 0.04 0.19 0.02 0.00 0.05 −0.05 0.03 −0.04 0.08 0.02 −0.04 −0.03 0.00 0.09 0.06 0.13 0.04 0.01

−0.01 −0.01 0.05 0.08 −0.01 −0.03 0.02 −0.02 0.00 0.00 0.01 0.02 0.06 −0.06 0.05 0.05 0.00 −0.01 −0.01 0.07 −0.05 0.01 0.06 −0.01 −0.01 0.04 0.01 −0.03 0.07 −0.06

Q-Stat 0.18 0.34 3.47 10.59 10.81 12.08 12.45 13.01 13.02 13.06 13.28 13.81 17.91 21.45 24.54 27.81 27.85 28.00 28.19 33.32 36.29 36.41 40.36 40.62 40.70 42.59 42.74 43.53 48.87 52.60

A. Mobarek, A. Fiorante / Research in International Business and Finance 30 (2014) 217–232

Subperiod 1: 1995-09-01–1999-12-31 Lags Brazil

Note: Q statistics; Chi square statistics with 30 df is 43.77.

225

226

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the US. For the third sub-period, the null hypothesis is accepted for the markets of Russia, India, China and the UK. Brazil shows significantly negative Z-values, rejecting the null hypothesis at 5%, whereas for Japan and the US (S&P), the null hypothesis is rejected at 1%, followed by the US (DJ), for which it is rejected at 10% due to significantly positive Z-values. The evidence here is mixed, in contrast to the findings of the previous serial correlation tests. These results diverge, especially in the case of Brazil, which showed little evidence of autocorrelation in the previous tests. Moreover, Russia and India present significant Ljung–Box Q-statistics, implying that the return series are autocorrelated at several lags, whereas the runs test suggests the opposite. 4.2.1. Variance ratio tests The results from the first sub-period (Table 4) show that the null hypothesis is accepted for Brazil, China, UK, US-S&P and US-Dow Jones, whereas it is rejected for Russia and India. Also in this case, the single variance ratio produces biased results for Brazil and the UK, rejecting random walk under homoskedasticity at q = 2. The multiple variance ratios accept random walk under heteroskedasticity for the Japanese equity market. Overall, the first sub-period indicates that the Table 3 Results of run test (3 sub-periods). Market

Cases < Mean

Actual Runs [R]

Expected Runs [m]

Z-statistics

Full period: 1995:09–2010:03 Brazil 3800 1851 Russia 3800 1924 India 3800 1882 3800 1989 China 1900 Nikkei 3800 FTSE 3800 1855 3800 1887 S&P 500 Dow Jones 3800 1900

1949 1876 1918 1811 1900 1945 1913 1900

1792 1738 1698 1809 1984 1878 2010 1966

1900 1901 1901 1897 1901 1900 1901 1901

−3.49*** −5.28*** −6.58*** −2.85*** 2.69*** −0.71 3.53*** 2.10**

Subperiod 1: 1995:09–1999:12 1130 560 Brazil 1130 607 Russia 1130 590 India China 1130 605 1130 578 Nikkei 1130 564 FTSE 1130 572 S&P 500 1130 588 Dow Jones

570 523 540 525 552 566 558 542

540 488 475 554 586 566 558 556

566 563 565 563 566 566 566 565

−1.54 −4.48*** −5.36*** −0.54 1.20 0.00 −0.47 −0.54

Subperiod 2: 2000:01–2005:12 1564 765 Brazil Russia 1564 778 1564 736 India China 1564 718 1564 782 Nikkei 1564 755 FTSE S&P 500 1564 732 Dow Jones 1564 791

799 786 828 846 782 809 832 773

736 726 691 728 785 749 829 839

783 783 780 778 783 782 780 783

−2.36** −2.88*** −4.53*** −2.52** 0.10 −1.674* 2.49** 2.83***

Subperiod 3: 2006:01–2010:03 Brazil 1104 534 1104 536 Russia 1104 543 India 1104 534 China 1104 540 Nikkei FTSE 1104 512 1104 483 S&P 500 Dow Jones 1104 537

570 568 561 570 564 592 621 567

516 530 537 536 617 564 601 583

552 553 553 552 553 550 544 553

−2.19** −0.81 −0.95 −0.98 3.87*** 0.84 3.46*** 1.83*

* ** ***

Total case

Significant at the 10% level. Significant at the 5% level. Significant at the 1% level.

Cases < Mean

Table 4 Results of variance ratio test (single and multiple variance ratio test). q

Brazil

VR(q) Z(q) Z* (q)

1.06 1.99* 1.03

1.05 0.90 0.46

Russia

VR(q) Z(q) Z* (q)

1.15 5.13* 3.14*

1.28 5.08* 3.31*

India

VR(q) Z(q) Z* (q)

1.12 3.90* 3.16*

China

VR(q) Z(q)

Japan

VR(q) Z(q) Z* (q)

UK

VR(q) Z(q) Z* (q)

US (S&P)

VR(q) Z(q) Z* (q)

US (DJ)

VR(q) Z(q) Z* (q)

Sub-period 1: 1995–1999

2

*

4

Sub-period 2: 2000–2005

8

16

2

4

8

16

2

4

8

16

0.99 −0.12 −0.07

0.93 −0.80 −0.44

0.85 −1.13 −0.61

1.06 0.46 0.26

1.12 4.75* 3.84*

1.15 3.16* 2.51*

1.15 2.01* 1.60

1.16 1.44 1.18

1.04 1.20 0.79

1.38 4.31* 3.02*

1.60 4.59* 3.39*

1.05 1.80 1.26

1.04 0.80 0.56

1.06 0.81 0.58

1.05 0.41 0.31

1.13 4.24* 2.33*

1.22 3.83* 2.08*

1.24 2.69* 1.45

1.18 1.39 0.75

1.19 3.38* 2.74*

1.25 2.82* 2.36*

1.37 2.78* 2.41*

1.11 4.22* 2.16*

1.19 4.05* 2.22*

1.30 3.95* 2.36*

1.46 4.16* 2.70*

1.08 2.59* 1.89

1.12 2.08* 1.54

1.12 1.40 1.03

1.23 1.74 1.28

0.97 −1.10

1.01 0.14

1.10 1.12

1.00 0.01

1.02 0.86

1.02 0.37

0.96 −0.54

0.96 −0.38

0.99 −0.42

0.99 −0.09

1.08 0.91

1.13 0.95

0.96 −1.47 −1.20

0.87 −2.3692 −1.87

0.77 −2.63* −2.03*

0.78 −1.65 −1.29

0.97 −1.10 −1.02

0.93 −1.49 −1.30

0.92 −1.12 −0.95

0.90 −0.90 −0.76

0.87 −4.17* −2.84*

0.72 −5.04* −2.90*

0.69 −3.43* −1.91

0.67 −2.50* −1.41

1.04 0.79 0.64

0.87 −1.45 −1.19

0.79 −1.60 −1.32

1.01 0.42 0.30

0.92 −1.63 −1.13

0.83 −2.30* −1.59

0.83 −1.55 −1.08

0.97 −0.98 −0.61

0.87 −2.30* −1.36

0.81 −2.14* −1.20

0.76 −1.83 −1.00

0.99 −0.19 −0.12

0.97 −0.62 −0.41

0.85 −1.68 −1.20

0.77 −1.78 −1.34

0.97 −1.30 −0.99

0.90 −2.09* −1.56

0.82 −2.34* −1.73

0.78 −1.95 −1.46

0.87 −4.45* −2.53*

0.74 −4.64* −2.42*

0.68 −3.64* −1.86

0.66 −2.54* −1.26

1.04 1.35 0.92

1.02 0.35 0.25

0.97 −0.39 −0.29

0.89 −0.81 −0.62

0.99 −0.42 −0.29

0.97 −0.54 −0.37

0.94 −0.85 −0.59

0.91 −0.82 −0.58

0.89 −3.69* −2.35*

0.78 −3.91* −2.23*

0.73 −3.01* −1.65

0.71 −2.17* −1.17

1.07 2.34* 1.89

0.96 −0.45 −0.24

Sub-period 3: 2006–2010

A. Mobarek, A. Fiorante / Research in International Business and Finance 30 (2014) 217–232

Market

Denotes for critical value at 5%; ± 1.96, H0: VR = 1.

227

228

A. Mobarek, A. Fiorante / Research in International Business and Finance 30 (2014) 217–232

benchmark presents more consistent results compared to the BRICs, whereas Russia and India suffer from positive autocorrelation (persistence) in the returns. The Chinese equity market continues to show consistent results for the second sub-period, accepting the joint hypothesis of the multiple variance ratios and confirming that the stock price series exhibits a random walk process. The Russian equity market has improved results compared to the previous sub-period, indicating that the market now follows a random walk process. In contrast, the Indian equity market continues to suffer from positive autocorrelation (persistence), as the null hypothesis is rejected under both homoskedastic and heteroskedasic random walks. The Brazilian equity market shows deteriorated results compared to the previous sub-period, where positive autocorrelation (persistence) is present in the returns. The equity markets of the benchmark show homogeneous results, where all markets accept the joint hypothesis of the multiple variance ratios while avoiding the inferential error produced by the single variance ratio. Therefore, these developed equity markets are said to follow a random walk process for the second sub-period. Finally, the overall results from the third sub-period support that the BRICs’ equity markets follow a random walk process. For this sub-period, there has been a clear improvement compared to previous results, where the Brazilian and the Chinese equity market follow random walks under the assumption of homoskedastic increments, whereas Russia and India follow random walks under the assumption of heteroskedasic increments. These results may be signaling that these transition markets have been evolving over time, indicating that successive price changes are currently more difficult to predict with past price information, compared to 10–15 years ago. On the other hand, the equity markets of the benchmark show deteriorated results compared to previous sub-periods. The null hypothesis of the multiple variance ratios is rejected for the Japanese and US-S&P markets, implying that these markets suffer from negative autocorrelation in their return series. However, the null hypothesis is accepted for the US-Dow Jones market under heteroskedasticity, whereas the UK market seems to follow a random walk process if the results from the single variance ratio are neglected. It appears that the BRIC countries have not been as heavily affected by the recent crisis period compared with the more developed benchmark countries in terms of market efficiency, which shows deteriorated results compared to previous sub-periods. The results from the single variance ratio (Lo and MacKinlay, 1988) and the multiple variance ratio tests (Chow and Denning, 1993) indicate that the variance ratio is statistically different from 1.0 at the 5% level (1.94) under the single variance ratio test but not significantly different from 1.0 under the multiple variance ratio test. Therefore, an inferential error is suggested, highlighting the critique of the use of the single variance ratio for testing the random walk hypothesis on stock price series where the joint nature of the test is ignored, (i.e., VR(q) = 1 ∀ q), which may lead to biased interpretation, (e.g., Ojah and Karamera (1999) highlights this problematic more carefully in their paper). Furthermore, the rejection of the random walk assuming homoskedastic increments may be due to heteroskedasticity and/or autocorrelation in the stock price series. If the random walk assuming heteroskedatic increments is rejected, then one may say that there is evidence of autocorrelation in the stock price series (Worthington and Higgs, 2003). However, we use Wright’s (2000) R1, R2 and S1 values to overcome the problems inherent in single and multiple variance ratio tests (see for reference Hung et al., 2009; Azad, 2009). We present Wright’s (2000) variance ratio test with a comparative analysis of different levels of efficiency in different sub-periods in Table 5. The results shows remarkable differences when the tests are performed on the sub-periods, revealing how these markets have evolved in terms of efficiency. The result for all sub-periods depicts that the random walk hypothesis is rejected by R1, R2 and S1 for most of the markets at every lag, regardless of whether it was developed or emerging. Comparative analysis of R1, R2 and S1 reflects that the benchmark countries (UK, US) as well as China and Brazil are more weak-form efficient than the other BRIC stock markets. Russia, India and Japan are less efficient during the first sub-period. This finding may be due to the Asian and Russian crises during this period. We observe that the 2nd sub-period shows improvement for most markets except for Brazil and the US. These findings may be due to the dot com bubble and 9/11 attacks in the US. Finally, during the recent subprime crisis, the BRIC countries are more weak-form efficient in terms of R1, R2 and S1 at different lags, especially for Brazil, China and India. On the contrary, for the benchmark countries, especially the US and Japan, R1, R2 and S1 fail to reject the random walk hypothesis, mostly in sub-period 3.

Table 5 Results of variance ratio test (Wright, 2000). Countries

Z

R1

R2

S1

5

10

15

20

25

2

5

10

15

20

25

2

5

10

15

20

25

2.858s 4.441s 2.537s

1.085s 1.112s 1.076s

1.069 1.141s 1.024

1.021 1.099 0.884

1.118 1.146 0.837

1.131 1.248s 0.848

1.184 1.319s 0.873

1.082s 1.122s 1.059

1.061 1.154s 1.008

0.996 1.11 0.875

1.097 1.144 0.818

1.096 1.254s 0.828

1.146 1.318s 0.855

1.041 1.063s 1.068

1.029 1.063 1.043

1.076 1.054 0.981

1.189 1.084 1.004

1.266 1.135 1.049

1.359 1.195 1.079

Russia Sub-period 1 Sub-period 2 Sub-period 3

6.509s 2.967s 2.025

1.194s 1.075s 1.061s

1.422s 1.062 1.115s

1.567s 1.109 1.118

1.737s 1.139 1.168

1.838s 1.155 1.244

1.893s 1.167 1.297

1.189s 1.066s 1.086s

1.405s 1.061 1.161s

1.536s 1.102 1.163

1.706s 1.14 1.193

1.813s 1.159 1.279

1.878s 1.162 1.344s

1.136s 1.062s 1.044

1.291s 1.105s 1.117

1.368s 1.216s 1.178

1.443s 1.312s 1.299s

1.463s 1.387s 1.367s

1.434s 1.446s 1.375s

India Sub-period 1 Sub-period 2 Sub-period 3

6.121s 5.853s 2.018

1.182s 1.119 1.061s

1.369s 1.324 1.128s

1.433s 1.487 1.122

1.482s 1.62 1.159

1.484s 1.705 1.211

1.465s 1.763 1.23

1.153s 1.111 1.064s

1.303s 1.277 1.114s

1.374s 1.382 1.098

1.458s 1.496 1.131

1.479s 1.559 1.189

1.456s 1.604 1.201

1.159s 1.114 1.041

1.375s 1.308 1.13

1.41s 1.547 1.184

1.364s 1.741 1.238

1.291s 1.89 1.335s

1.257 2.015 1.412s

China Sub-period 1 Sub-period 2 Sub-period 3

2.201s 1.896 3.374s

0.966 1.019 1.005

1.031 1.086 1.066

1.106 1.083 1.149

1.155 1.139 1.282s

1.279s 1.211s 1.436s

1.367 1.268s 1.568s

0.963 1.021 0.99

1.032 1.068 1.03

1.092 1.042 1.078

1.097 1.07 1.15

1.2 1.111 1.248

1.26 1.137 1.335s

0.991 1.016 1.017

1.002 1.063 1.125

0.985 1.038 1.301s

0.98 1.1 1.526s

0.999 1.194 1.757s

1.018 1.268s 1.939s

Japan Sub-period 1 Sub-period 2 Sub-period 3

2.344s 1.407 5.323s

0.932s 0.981 0.84s

0.851s 0.922 0.728s

0.765s 0.917 0.686s

0.772s 0.91 0.686s

0.768 0.916 0.675s

0.779 0.925 0.689s

0.942s 0.975 0.847s

0.842s 0.915 0.724s

0.763s 0.913 0.693s

0.79 0.901 0.691s

0.798 0.902 0.686s

0.804 0.898 0.691s

0.968 1.003 0.898s

0.906 0.99 0.792s

0.809s 0.973 0.75s

0.754s 0.983 0.757s

0.723s 0.976 0.759

0.717s 0.975 0.774

US (S&P) Sub-period 1 Sub-period 2 Sub-period 3

2.019 2.988s 3.753s

1.04 0.949s 0.887s

0.949 0.835s 0.812s

0.797s 0.766s 0.736s

0.777s 0.758s 0.683s

0.748s 0.795 0.652s

0.727s 0.798 0.652s

1.029 0.963 0.875s

0.944 0.864s 0.789s

0.791s 0.786s 0.723s

0.766s 0.773s 0.682s

0.737s 0.804 0.652s

0.715s 0.793 0.648s

1.041 0.941s 0.887s

0.968 0.856s 0.809s

0.87 0.854s 0.749s

0.826 0.886 0.729s

0.787 0.949 0.727s

0.763 0.966 0.761

US (DJ) Sub-period 1 Sub-period 2 Sub-period 3

2.207 2.027 2.002

1.066 0.963 0.939s

1.001 0.888s 0.892s

0.902 0.842s 0.825v

0.887 0.819s 0.776s

0.852 0.846 0.733s

0.826 0.846 0.724s

1.064s 0.981 0.916s

0.996 0.927 0.849s

0.901 0.888 0.791s

0.88 0.873 0.753s

0.845 0.896 0.712s

0.823 0.885 0.698s

1.03 0.933s 0.945s

0.995 0.889s 0.912

0.969 0.864 0.915

0.995 0.867 0.898

0.982 0.905 0.884

0.97 0.925 0.893

UK Sub-period 1 Sub-period 2 Sub-period 3

2.002 1.392 1.708

1.059s 1.021 0.958

1.006 0.946 0.892s

0.814s 0.881 0.827s

0.796 0.876 0.784s

0.773 0.877 0.779

0.746 0.853 0.795

1.066s 1.015 0.96

1.005 0.914 0.876s

0.799s 0.847s 0.807s

0.775s 0.827 0.756s

0.753s 0.823 0.752s

0.726s 0.794 0.771

1.009 1.034 0.972

0.971 0.988 0.951

0.909 0.928 0.936

0.967 0.92 0.924

1 0.928 0.942

0.999 0.908 0.974 229

Note: Sub-period 1, refers 1995–1999; Sub-period 2, refers 2000–2005; Sub-period 3, refers 2006–2009; S denotes significant up to 5% level.

A. Mobarek, A. Fiorante / Research in International Business and Finance 30 (2014) 217–232

2 Brazil Sub-period 1 Sub-period 2 Sub-period 3

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4.3. Robustness check of the regular weak-form efficiency test We then tested the day of the week effect to assess the robustness of the weak-form efficiency test reported earlier. The day-of-the-week effect2 was found to be present in the earlier sub-periods, but it was also found to have been slowly disappearing during the last five to ten years; the markets assessed with this type of imperfection have been found to be inconsistent with efficient markets. The examination of the day-of-the-week effect for the sub-periods reports interesting findings concerning the intensity and persistency of this type of stock market anomaly. For the BRICs, it is clear that the day-of-the-week effect has been disappearing or strongly reduced across the sub-periods, where the last sub-period shows practically no signs of this type of market imperfection. It is further proven that the stock markets of the benchmarks experience negligible signs of the dayof-the-week effect across the sub-periods. Basher and Sadorsky (2006) tested the day-of-the-week effect in 21 emerging markets and found no significant effect in the Brazilian market for the period 1992–2003, a finding roughly in line with the findings of this study. The Indian market from 1987–1994 was examined by Poshakwale (1996), who found, despite significant day of the week patterns in the benchmarks, an insignificant day-of-the-week effect, indicating that these types of stock market anomalies are not present in the developed markets included in this sample. The findings concerning seasonal anomalies in developed countries are in line with those of several studies, e.g., Agarawal (1994), Kohers et al. (2004). The result from the first sub-period is in line with the finding indicating that the Indian market continued to suffer from these effects until 1999. However, the following two sub-periods reveal the absence of the day-of-the-week effect in the Indian market. Chukwuogor-Ndu (2006) studied the Russian market from 1997 to 2004, presenting comparable results to our own, and found significant day of the week patterns. The author argues that the Russian market achieved astronomical growth during the period 1999–2000, which may have been the cause of this market imperfection. However, this study’s findings indicate that the day-of-the-week effect disappears in the third sub-period. Abrosimova et al. (2007) studied the Russian market for the period 1995–2001, concluding that it is weak-form efficient only when monthly data are used. The evidence regarding the daily data is in line, showing that for the same time period, all tests reject the null hypothesis of the random walk. The newer data indicate that the Russian market has become more efficient according to the results from the runs test and variance ratio test for the third sub-period. Previous studies on the Indian market have achieved results much in line with this study, e.g., Gupta and Basu (2007) and Poshakwale (1996), using data from 1991 to 2006 and 1987 to 1994, respectively. The general conclusion from previous studies is that the Indian stock market does not follow a random walk, given evidence of autocorrelation, an assessment consistent with the results of this study. However, for the third sub-period, there is an indication of improvement according to the results from the runs test and variance ratio, indicating that the Indian market is weak-form efficient. The Chinese markets have been tested in several studies, e.g., Niblock and Sloan (2007) and Worthington and Higgs (2005), which used daily data from 2002 to 2005 and 1992 to 2003, respectively. Both these studies concluded that the Chinese market does not follow a random walk, with the prior study indicating that the Chinese market appears to have experienced a relative decline in efficiency. Evidentially, this study is in line with parts of the previous findings, as the results differ between the tests and sub-periods examined. However, China has shown the most consistent and stable results of all the BRICs; in this case, the random walk hypothesis is accepted with greater confidence for a number of tests and sub-periods. 5. Conclusion The results provide evidence and a more comprehensive picture regarding the market efficiency of the BRIC countries. The empirical findings differ to some extent depending on the statistical tests used, with variance ratio and run test provide better results than the serial correlation, considering the bias in the data distribution. Nevertheless, the overall representation of the findings and contributions

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The results of the day of the week effect are also available on request.

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of this study emphasizes that the equity markets of the BRICs appear to be evolving in the right direction, especially during the last five to ten years. However, during the earlier sub-periods, these markets experienced significant positive autocorrelation (persistence) in returns. Another notable finding concerns how these emerging markets have been affected by the impact of the current financial crisis, which has paralyzed many developed economies and left great devastation. The last sub-period results for the BRICs clearly provide support that these markets may have been approaching a state of being fairly weak-form efficient. The important implication of this study is that it highlights the relative increase in efficiency, which is an important ingredient for these four transition markets if they wish to foster their growth and welfare. If the several long- and medium-term forecasts and predictions of these four markets are ever realized within a reasonable time frame, each of the BRICs faces significant and individual challenges to keep their development on track. Future research on the BRIC countries remains an important topic because these markets may have a significant influence on our world economy in the near future. In addition to the approach used in our study, other data types may be used, such as individual stocks or other significant indices, and different data frequencies may be relevant for testing market efficiency. Because these markets are facing many challenges and problems, which may be traced to political issues, infrastructure, market microstructures, the causes of efficiency and inefficiency, co-movement with other markets and environmental issues, there is considerable room for other types of economic or political studies that explore these factors. 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