Jun 3, 2016 - ... Str, Peristeri, Athens,. Greece, 12131. E-mail:
... más que un fenómeno universal
RESEARCH ARTICLE
AESTIMATIO, THE IEB INTERNATIONAL JOURNAL OF FINANCE, 2017. 14: 2-31 © 2017 AESTIMATIO, THE IEB INTERNATIONAL JOURNAL OF FINANCE
DOI:10.5605/IEB.14.2
Evaluating the weak-form efficiency of emerging markets ETFs
Rompotis, Gerasismos 왘 RECEIVED : 왘 ACCEPTED :
23
APRIL
2016
3 JUNE 2016
Abstract This paper examines the weak-form efficiency of emerging markets ETFs and to that end several parametric and non-parametric empirical tests are applied. In particular, the autocorrelation and the serial correlation in ETF returns are tested and the randomness in the series of ETF returns is then evaluated by applying runs tests. Finally, three alternative types of variance ratio tests are used to evaluate whether the prices of ETFs follow a random walk, that is, whether the market in question is efficient in the weak form. Overall, the results of the tests reveal that weak-form efficiency is a fundspecific rather than a universal phenomenon. The majority of serial correlation tests used demonstrate that the pricing of most ETFs in the sample is efficient. On the other hand, the autocorrelation, runs and variance ratio tests provide evidence of inefficiency for some of the ETFs examined. Keywords: ETFs, Market efficiency, Weak-form, Emerging markets. JEL classification: G14.
Rompotis, G. Department of Economics, National and Kapodistrian University of Athens, Greece. 25 Ypsilantou Str, Peristeri, Athens, Greece, 12131. E-mail:
[email protected]
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AESTIMATIO, THE IEB INTERNATIONAL JOURNAL OF FINANCE, 2017. 14: 2-31 © 2017 AESTIMATIO, THE IEB INTERNATIONAL JOURNAL OF FINANCE
Evaluación de la eficiencia débil de los fondos cotizados de mercados emergentes
Rompotis, Gerasismos
Resumen El objetivo de este artículo es el análisis de la eficiencia débil de los fondos cotizados de mercados emergentes. Para ello se utiliza una serie de contrastes empíricos de carácter tanto paramétrico como no paramétrico. En concreto, se aborda la cuestión de la autocorrelación y correlación serial de los rendimientos de los fondos cotizados objeto de este artículo. Posteriormente se contrasta la hipótesis de aleatoriedad en los rendimientos de dichos fondos mediante contrastes de rachas. Finalmente, se utilizan tres tipos alternativos de contrastes de ratio de varianza para determinar si los precios de los fondos cotizados de mercados emergentes siguen un paseo aleatorio o, en otros términos, para contrastar la hipótesis de eficiencia débil. En general, los resultados de los contrastes realizados revelan que la eficiencia, en su forma débil, en los fondos cotizados de mercados emergentes, es una cuestión específica de determinados fondos más que un fenómeno universal. En cuanto a resultados particulares, de los contrastes de correlación serial se deduce que la valoración de la mayoría de los fondos cotizados considerados en este artículo es eficiente, mientras que los contrastes de autocorrelación, rachas y ratio de varianzas proporcionan evidencia de ineficiencia en algunos de los fondos examinados. Palabras clave: Fondos cotizados, eficiencia de mercado, forma débil, mercados emergentes.
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n 1. Introduction Given the international investment community’s increasing interest in investing in stock markets of emerging economies in recent years, this paper aims to provide reliable empirical answers to the key question raised by Exchange Traded Funds (ETFs) investors about the pricing efficiency of these markets and the potential for gaining any substantial abnormal returns by exploiting any possible pricing inefficiencies.
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Evaluating the weak-form efficiency of emerging markets ETFs. Rompotis, G.
When it comes to the efficiency of small and emerging markets, the relevant literature demonstrates that these markets can be easily controlled and suffer from thin trading; they are thus basically informationally inefficient. Numerous studies, such as those of Barnes (1986), Buttler and Malaikah (1992), Dickinson and Muragu (1994), and Omran and Farrar (2006), attest to the inefficiency in developing markets. LagoardeSegot and Lucey (2008) reveal heterogeneous levels of efficiency in the Middle Eastern and North African stock markets. The efficiency in these markets is affected by market depth and corporate governance factors but not by economic liberalization. Other explanations for the informational inefficiency of emerging markets include the illiquidity which affects the market’s capacity to accommodate orders (Chordia et al., 2005), the low degree of competition and the dominance of a few key players who can cause stock prices to deviate from their intrinsic value (Mobarek and Keasey, 2000), the lack of market transparency and the scarce corporate information, the limited auditing experience and weak regulation (Blavy, 2002), and the fragmentation of capital markets and the presence of political and economic uncertainties (El-Erian and Kumar, 1995).
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This paper is an extension to our previous work on the pricing efficiency of developed markets ETFs. In particular, Rompotis (2011) examined the validity of weak-form market efficiency using data from US-listed ETFs, which mainly track indices from developed economies as well as some indices from emerging markets, such as Hong Kong, Taiwan and Singapore. In this paper, we exclusively focus on emerging markets using a sample of US-listed ETFs, which cover a wide range of country and regional emerging economies from South Africa, Asia, the Americas and Europe. Another difference from our previous work relates to the techniques used to assess market efficiency. From a methodological perspective, the main difference concerns the use of the runs test and variance ratio tests rather than the Augmented Dickey-Fuller (ADF) and the Phillips-Peron (PP) unit root tests. Overall, the results of the tests reveal that weak-form efficiency is a fund-specific rather than a universal phenomenon. In particular, the majority of serial correlation AESTI
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tests used demonstrate that the pricing of most ETFs in the sample is efficient. On the other hand, the autocorrelation, runs and variance ratio tests provide evidence of inefficiency for some of the ETFs examined. In essence, these results are weaker than those in Rompotis (2011), who revealed that weak-form efficiency is a valid hypothesis when analysing developed markets ETFs. The rest of the paper is organized as follows: Section 2 describes the methodology employed to test the weak-form efficiency of emerging markets ETFs. Section 3 describes the sample used in our study and Section 4 discusses the results of the tests applied to examine the efficiency of the sample of ETFs under study. Lastly, a summary and conclusions are presented in Section 5.
n 2. Methodology This study seeks to assess the weak-form informational efficiency of trading for USlisted ETFs investing in emerging markets. The null hypothesis is that the prices of ETFs follow a random walk and, thus, the ETF market is efficient in the weak form. We examine efficiency using various types of parametric and non-parametric tests, which have been extensively used in the literature.
The next method we use to examine the weak form of market efficiency is the socalled “Wald-Wolfowitz Runs Test”. This is a non-parametric test which checks a AESTI
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We then perform serial correlation testing. A common finding in time series regression analysis is that the residuals are correlated with their own lagged values. For the purposes of our investigation, the existence of statistically significant estimates of serial correlation implies that the daily returns of ETFs are not independent of their lagged values and, therefore, this market cannot be considered efficient in the weak form. The lack of significant serial correlation coefficients indicates that the null hypothesis of the random walk is valid and therefore that the market is efficient.
Evaluating the weak-form efficiency of emerging markets ETFs. Rompotis, G.
First, we perform a similar autocorrelation test to that described in Rompotis (2011). Autocorrelation is a non-parametric test for serial dependence in the time series of returns. Statistically, the absence of significance in autocorrelation coefficients in returns implies that the price series follow a random walk, which in turn means that the market is efficient in the weak form. The null hypothesis is that the autocorrelation coefficients are equal to zero (the market is efficient) whereas the alternative is that they deviate from zero (the market is inefficient). Following the approach of Awad and Daraghma (2009), we estimate autocorrelation for n1,2,3 lagged return estimates.
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randomness hypothesis for a two-valued data sequence. More specifically, it is used to test whether the elements of the sequence are serially independent. In other words, the runs test examines whether the value of one observation influences the values taken by later observations. If there is no impact, the return generating process is random and, thus, the observations are independent.1 As a final step, we apply three alternative types of variance ratio testing in order to establish whether or not the returns of emerging markets ETFs are predictable. If returns can be predicted, market is inefficient in the weak form. The three types of variance ratio tests are used to examine the Random Walk Hypothesis (RWH) in ETF prices. These tests are the Lo and MacKinlay (1988) variance ratio test, the ranksbased and signs-based variance ratio of Wright (2000) and the Chow and Denning (1993) variance ratio test.2
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Evaluating the weak-form efficiency of emerging markets ETFs. Rompotis, G.
n 3.The sample
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This paper employs a sample of 40 iShares ETFs which are listed on the New York Stock Exchange but track country or regional indices from the Americas, Europe, Asia and South Africa. Table 1 presents the profiles of the sample with the symbol, name and benchmark name for each ETF. Moreover, each ETF’s inception date is provided along with its expense ratio, average daily trading volume, assets (in $000s) as of 30th April 2015, average intraday volatility calculated as the percentage difference between the highest and the lowest trading price on day t divided by the closing price on the same day, and trading frequency calculated as the number of trading days with non-zero volume as a percentage of total trading history (in days) for each fund. Nasdaq.com and us.iShares.com provided us with the necessary information. Another feature of the table (and of the tables to follow) is that it displays the data with ETFs grouped geographically. More specifically, four groups of emerging markets are considered. The first group, the South African one, contains only one fund. The second group, the Asian one, contains the most funds with 27 ETFs.3
1 2 3
More information on runs test can be found on: www.itl.nist.gov/div898/handbook/eda/section3/eda35d.htm.
The methodology applied in performing these three tests has been based on information found in Chen (2008).
It should be noted that the Asian group includes some ETFs which are not solely invested in stocks listed in Asian stock exchanges. An example is the iShares MSCI BRIC ETF (BKF), which invests in the MSCI BRIC Index, an index which covers stocks from Brazil, Russia, India and China. For this ETF, however, the exposure to Asia (i.e. India, China and Kong Kong) counts for almost the 59% of the total portfolio (according to information provided on the us.ishares.com). In this as well as other similar obscure cases where the total exposure to Asia dominates, we classify ETFs within the Asian group. A similar approach has been followed for the iShares MSCI Emerging Markets EMEA ETF (EEME), which covers several countries such as South Africa, Russia, Poland,Turkey, Greece and Hungary. The portion of European stocks in the portfolio is more than 58% and, therefore, this ETF has been included in the European group.
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The third group, which is the European one, contains five funds. The last group, the Americas, includes seven ETFs. With respect to ETF inception dates, Table 1 displays a wide range of “ages”. The oldest ETFs are those invested in the MSCI indices of Malaysia and Mexico. These funds, initially known as WEBs (World Equity Benchmark Shares), were created in March 1993 by Barclays Global Investors. The second-oldest ETFs are also invested in single country indices, namely the MSCI indices of Taiwan, Thailand and Brazil. On the other extreme, the youngest funds in the sample were created sometime in 2012. The majority of the new listings invest in indices which cover emerging Asian markets. The increasing interest in Asian stocks reflected in the listing of new ETFs is probably due to the robust growth prospects of these economies, at least at the time when the ETFs in question were listed. This is presumably also the case for the iShares MSCI Emerging Markets Latin America ETF (EEML), which is heavily invested (more than 55%) in Brazilian stocks.
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Going further, Table 1 presents an average daily volume of 2.4 million shares for the ETFs in the sample. The average volume of the South African ETF amounts to 298,000 shares, the average Asian volume is 2.95 million shares, the average European ETF is the least traded with a volume of 162,000 shares and, finally, the group of American ETFs has an average volume of 2.4 million shares per day. The above listed figures are very striking but they somehow misrepresent the actual outlook of these emerging markets ETFs’ trading activity. More specifically, if we exclude the three ETFs whose average daily volume exceeds 10 million shares and are sample outliers, and calculate the average volume of the rest of the sample, we obtain a figure of 553,000 shares per day (not clearly reported in the table). This figure is much lower than the average volume of the total sample and the mean of two out of the four groups. Consequently,
Evaluating the weak-form efficiency of emerging markets ETFs. Rompotis, G.
Regarding expenses, Table 1 reports an average sample expense ratio of 0.60%. The group means are also around 60 basis points (bps). In particular, the expense ratio of the South African ETF is 0.61% while for Asian and European ETFs it is equal to 0.61% and 0.60%, respectively. The average fee for the Americas ETFs is 0.55%. It should be noted here that there is a modest dispersion in the expense ratios of the European and the American groups but the corresponding variation in the Asian group is more marked. Specifically, the lowest expense ratio in the group is 0.18%, comparable to many US-listed ETFs tracking domestic indices. On the other hand, the highest expense ratio is almost 1% (0.93%), which is extremely high for an ETF. One last comment on expenses is that, on average and unsurprisingly, the expense ratios charged by emerging markets ETFs are much greater than those charged by domestically invested ETFs. Investors, especially those who are expense-averse, should take this into consideration when deciding on which ETFs to go with.
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iShares MSCI Emerg Markets Financials ETF
iShares MSCI Emerging Markets Materials
iShares MSCI Emer Markets Consumer Discr
iShares Emerging Markets Infrastructure ETF
iShares Emerging Markets Dividend ETF
iShares MSCI China ETF
iShares FTSE China ETF
iShares China Large-Cap ETF
iShares MSCI China Small-Cap ETF
iShares MSCI India ETF
EMFN
EMMT
EMDI
EMIF
DVYE
MCHI
FCHI
FXI
ECNS
INDA
MSCI BRIC Index
iShares MSCI BRIC ETF
iShares MSCI Emerging Markets Energy Cap
iShares MSCI Emerging Markets Asia ETF
EEMA
BKF
iShares MSCI Emerging Markets Small-Cap E
EEMS
EMEY
MSCI Emerging Markets Asia Index
iShares MSCI Emerging Markets Value ETF
EVAL
MSCI India Total Return Index(SM)
MSCI China Small Cap Index
FTSE China 25 Index
FTSE China (HK Listed) Index
MSCI China Index
Dow Jones Emerging Markets Select Dividend
S&P Emerging Markets Infrastructure Index
MSCI Emerging Markets Consumer Discretion
MSCI Emerging Markets Materials Index
MSCI Emerging Markets Financials Index
MSCI EM Energy 25-50 Index
MSCI Emerging Markets Small Cap Index
MSCI Emerging Markets Value Index
MSCI Emerging Markets Growth Index
iShares MSCI Emerging Markets Growth ETF
EGRW
MSCI Emerging Markets Index(SM)
MSCI Emerging Markets Minimum Volatility
iShares MSCI Emerging Markets ETF
iShares MSCI Emerging Markets Minim Vol.
EEMV
MSCI Emerging Markets Investable Market In
MSCI South Africa Index
Benchmark
EEM
iShares Core MSCI Emerging Markets ETF
iShares MSCI South Africa ETF
Name
IEMG
ASIA
EZA
Symbol
2/2/2012
28/9/2010
5/10/2004
24/6/2008
29/3/2011
23/2/2012
16/6/2009
8/2/2012
20/1/2010
20/1/2010
8/2/2012
12/11/2007
8/2/2012
16/8/2011
8/2/2012
8/2/2012
7/4/2003
18/10/2011
18/10/2012
3/2/2003
Inception Date
0.67%
0.61%
0.74%
0.74%
0.61%
0.49%
0.75%
0.67%
0.67%
0.67%
0.67%
0.67%
0.49%
0.67%
0.49%
0.49%
0.67%
0.25%
0.18%
0.61%
Expense Ratio
402,307
8,683
16,585,437
6,887
380,610
38,946
18,242
1,322
3,175
3,051
4,000
145,202
27,602
9,241
2,034
944
47,965,097
298,843
1,123,609
298,260
Volume
3,594,896
46,852
7,591,369
38,858
2,460,854
212,419
82,470
5,666
6,960
5,604
3,238
307,732
169,612
81,447
23,355
5,837
33,309,982
2,569,281
7,850,084
467,241
Assets ($000s)
1.022%
1.032%
1.769%
1.291%
1.015%
1.044%
1.204%
0.270%
0.859%
0.695%
0.399%
2.004%
0.742%
1.021%
1.288%
0.392%
1.745%
0.885%
0.927%
1.955%
Intraday Volatility
96.93%
98.44%
100.00%
96.58%
99.32%
99.88%
100.00%
45.56%
89.63%
72.81%
47.78%
100.00%
93.33%
92.26%
86.79%
50.99%
100.00%
99.55%
100.00%
99.89%
Trading Frequen.
This table presents the profiles of emerging markets ETFs, with their symbol, name, benchmark, inception date, expense ratio, average volume (in shares), assets as of 30th April 2015, average intraday volatility calculated as the percentage difference between the intraday highest minus the intraday lowest price divided by the closing price on day t, and the percentage trading frequency calculated as the days with non-zero volume as a percentage of the total trading history of each ETF.
l Table 1. Profiles of ETFs
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iShares MSCI Thailand Capped ETF
iShares MSCI Turkey ETF
TUR
iShares MSCI Mexico Capped ETF
iShares MSCI All Peru Capped ETF
EWW
EPU
Grand Mean
Mean
iShares MSCI Brazil Small-Cap ETF
iShares MSCI Chile Capped ETF
iShares MSCI Brazil Capped ETF
EWZ
EWZS
iShares Latin America 40 ETF
ILF
ECH
iShares MSCI Emerg Markets Latin America
EEML
AMERICA
Mean
iShares MSCI Poland Capped ETF
iShares MSCI Russia Capped ETF
ERUS
iShares MSCI Emerging Markets EMEA ETF
EEME
EPOL
iShares MSCI Emerg Markets Eastern Europ
ESR
EUROPE
Mean
THD
MSCI Korea 25/50 Index
iShares MSCI South Korea Capped ETF
iShares MSCI Taiwan ETF
EWY
MSCI Philippines Investable Market Index
EWT
MSCI Malaysia Index
iShares MSCI Malaysia ETF
iShares MSCI Philippines ETF
EWM
EPHE
28/9/2010 12/11/2007 12/3/1996 19/6/2009
MSCI Brazil Small Cap Index MSCI Chile IMI 25/50 Index MSCI Mexico IMI 25/50 Index MSCI All Peru Capped Index
10/7/2000
MSCI Brazil 25/50 Index
25/10/2001
18/1/2012
MSCI Emerging Markets Latin America Index S&P Latin America 40 Index
26/3/2008
9/11/2010
25/5/2010
18/1/2012
30/9/2009
26/3/2008
20/6/2000
9/5/2000
28/9/2010
12/3/1996
5/5/2010
8/2/2012
18/11/2009
MSCI Turkey Investable Market Index
MSCI Russia 25 / 50 Index
MSCI Poland IMI 25/50 Index
MSCI Emerging Markets EMEA
MSCI Emerging Markets Eastern Europe Index
MSCI Thailand IMI 25/50 Index
MSCI Taiwan Index(SM)
MSCI India Small Cap Index MSCI Indonesia Investable Market Index
iShares MSCI India Small-Cap
iShares MSCI Indonesia ETF
SMIN
EIDO
CNX Nifty Index
iShares India 50 ETF
INDY
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Evaluating the weak-form efficiency of emerging markets ETFs. Rompotis, G.
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191,414 2,420,585 2,442,726
0.51%
0.60%
2,467,357
189,489
28,166
12,704,833
1,360,691
2,146
0.55%
0.49%
0.61%
0.61%
0.61%
0.50%
0.49%
277,180 161,564
0.61%
336,593
168,481
1,901
23,665
2,950,329
212,079
7,600,647
2,339,314
205,673
1,712,395
391,807
8,691
163,041
0.60%
0.61%
0.61%
0.49%
0.67%
0.61%
0.61%
0.61%
0.61%
0.61%
0.49%
0.61%
0.74%
0.93%
1,952,344
931,280
188,563
1,893,493
274,660
47,096
3,347,980
756,273
10,893
201,948
469,594
294,720
207,335
9,291
28,801
2,596,215
429,336
4,370,345
4,408,973
517,168
459,335
518,126
54,888
973,114
1.327%
1.790%
1.781%
2.048%
2.023%
1.511%
2.539%
2.054%
0.577%
1.500%
2.196%
1.709%
1.520%
0.737%
1.336%
1.151%
1.573%
1.595%
1.642%
1.240%
1.405%
1.584%
1.260%
1.180%
92.69%
96.99%
100.00%
100.00%
100.00%
100.00%
100.00%
100.00%
78.91%
94.93%
100.00%
100.00%
100.00%
75.88%
98.79%
90.90%
100.00%
100.00%
100.00%
100.00%
100.00%
99.76%
84.69%
100.00%
we can infer that the high average volume figures are skewed by the trading intensity of specific ETFs such as that of the iShares MSCI Emerging Markets ETF (EEM), which has an average volume of 48 million shares, and the iShares China Large-Cap ETF (FXI), which has an average daily volume of 16.6 million shares. The next trading variable concerned is ETF assets as of 30th April 2015. The sample average is $1.95 billion, while the group means are $467.2 million, $2.60 billion, $201.9 million and $931.3 million for the South African, Asian, European and Americas group, respectively. As is the case with volumes, the averages do not tell the whole truth about the assets held by the ETFs examined in this study. In particular, the median of the entire sample is $284.7 million (not reported in the table) and shows that, as is the case with trading activity, the assets invested in emerging markets ETFs are mainly channeled to the specific funds mentioned above, which dominate the trading activity in the field.
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On the question of intraday volatility, Table 1 provides an average figure for the whole sample of 1.327%. With respect to the individual groups, the South African ETF shows higher intraday volatility than the average of the entire sample, the Asian ETF group is slightly less volatile whereas the corresponding European and American ETF groups are more volatile than the sample average. A general comment on intraday volatility is that there is no specific trend within each individual group. For instance, in the case of Asian ETFs, there are funds which present modest or even low volatility while there are also funds showing a highly volatile intraday behaviour. This is undoubtedly linked to the special features of each underlying market and it is therefore hard to form particular expectations about volatility for a specific region or market.
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When it comes to trading frequency, the average term presented in Table 1 is 92.69%. The group mean values are 99.89%, 90.90%, 94.93% and 96.99% for the South African, Asian, European and Americas group, respectively. These percentages indicate that, on average, there are just a few days on which investors do not trade with emerging markets ETFs. Nevertheless, by scanning through the individual ETFs, we observe that there are funds whose trading frequency is lower than 50%, while other funds present an absolute trading activity with no zero volume days. The descriptive statistics of ETF and index returns for the sample of ETFs examined in this study are provided in Table 2. This table presents the average daily return of each ETF and benchmark, the risk of each fund and index expressed in terms of the standard deviation of the returns, the extreme scores, and the coefficients of skewness and kurtosis over a period ending 30th April, 2015.4 4
Returns have been calculated in percentage terms with daily closing price data found on Bloomberg.
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l Table 2. Descriptive statistics of returns
This table presents the descriptive statistics of emerging markets ETFs and benchmarks’ daily returns (average return), standard deviation, minimum and maximum return records, skewness and kurtosis. ETF returns are calculated with closing trade prices. Symbol
Average ETF Index
EZA
0.058
0.065
IEMG
0.014
EEMV
0.032
EEM EGRW
Standard deviation
Minimum
ETF Index
ETF Index
Maximum ETF Index
2.253
1.895 -20.082 -12.686
0.020
0.997
0.736
-4.360
0.041
0.948
0.678
-4.895
0.050
0.048
2.045
1.324 -16.166
-9.484
0.021
0.023
1.425
0.833
-7.286
-4.099
EVAL
0.001
0.001
1.573
0.831
-6.044
-3.948
7.118
3.522
EEMS
0.012
0.021
1.200
0.811
-5.235
-5.085
5.803
3.934
-4.765
-3.416
Skewness ETF Index 0.122
-0.114
Kurtosis ETF Index
22.922
13.148
11.225
4.337
-3.920
4.341
2.868
-0.142
-0.185
1.145
1.474
-3.494
5.124
2.720
-0.017
-0.021
3.065
1.704
22.770 10.598
0.708
-0.380
16.270
8.672
0.175
-0.010
7.381
1.386
0.289
0.024
3.160
1.346
-0.092
-0.745
2.711
4.270
0.046
2.671
1.201
-0.002 10.946
10.819
ASIA
8.093
3.292
EEMA
0.027
0.033
1.071
0.845
5.187
3.540
0.298
BKF
0.006
0.006
2.252
1.731 -14.216 -11.230 20.630
14.477
0.381
EMEY
-0.042
-0.038
1.676
1.150 -13.692
-4.634 12.054
4.643
-0.393
0.078
14.566
1.816
EMFN
0.020
0.019
1.767
1.209
-6.579
7.767
5.759
-0.103
-0.206
3.097
2.538
EMMT
-0.016
-0.010
1.678
1.320 -10.968
-7.035
7.436
5.833
-0.268
-0.213
3.476
2.336
EMDI
0.022
0.023
1.211
0.921
-6.523
-4.058
7.003
3.428
0.297
-0.048
8.424
0.522
0.035
0.044
1.293
1.027
-8.271
-6.232
7.174
5.605
-0.133
-0.272
3.456
3.270
-0.019 -0.004
0.994
0.726
-4.161
-3.775
4.359
2.527
0.034
-0.099
0.834
1.252
1.489
1.337
-8.211
-6.106
9.368
6.765
0.183
0.097
4.070
3.133
EMIF DVYE
0.040
-8.808
MCHI
0.029
FCHI
0.041
0.045
2.291
1.885 -15.529 -12.332 20.393
15.146
0.725
0.447
13.623
9.151
FXI
0.067
0.069
2.341
1.943 -14.845 -17.919 20.270 15.450
0.589
0.082 10.240
10.124
ECNS
0.025
0.030
1.399
1.153
-7.932
-5.217
7.295
7.294
-0.030
-0.200
2.706
3.907
INDA
0.023
0.028
1.501
1.272
-6.253
-5.521
6.465
5.998
-0.020
0.024
1.327
2.232
INDY
0.026
0.026
1.667
1.376
-6.709
-5.905
13.452
6.630
0.274
0.084
4.126
1.612
SMIN
0.048
0.049
1.696
1.358
-5.237
-4.466
6.764
5.208
0.112
-0.305
1.120
1.112
EIDO
0.027
0.027
1.863
1.505 -11.958
-9.123
9.708
8.255
-0.083
-0.241
4.183
4.868
EWM
0.035
0.045
1.355
0.992 -11.622 -10.654
8.988
5.954
-0.149
-0.499
6.254
8.449
EPHE
0.051
0.055
1.387
1.220
-7.511
7.198
6.484
-0.234
-0.532
3.405
4.232
EWY
0.052
0.054
2.166
1.928 -13.823 -18.675
22.422
28.385
0.909
0.369 16.300
23.479
-8.046
0.034
1.815
1.454 -11.067
-7.881
14.155
8.580
0.294
-0.155
7.207
0.046
0.050
2.035
1.631 -11.657 -13.259
15.458
9.650
-0.041
-0.443
5.808
3.709 6.713
Mean
0.024
0.029
1.598
1.229 -9.196
-7.465 10.622
7.502
0.132 -0.122
5.984
4.642 3.070
EUROPE ESR
0.005
0.012
1.971
1.740
-9.884
-9.816
10.732
8.032
-0.242
-0.262
3.082
EEME
0.002
0.008
1.479
1.233
-8.650
-5.840
6.714
5.051
-0.251
-0.032
4.115
1.784
EPOL
0.021
0.031
1.922
1.687 -10.965 -10.281
9.013
7.407
-0.341
-0.362
3.571
3.437
ERUS
-0.021
-0.010
2.170
1.952 -12.006 -12.212
9.917
14.581
-0.427
-0.174
3.367
6.657
TUR
0.034
0.034
2.656
2.255 -14.950 -13.618 20.586 16.924
0.161
-0.018
6.582
5.748
Mean
0.008
0.015
2.040
1.773 -11.291 -10.353 11.392 10.399 -0.220 -0.170
4.144
4.139
-0.039
-0.028
1.394
1.262
5.002
-0.063
0.078
3.182
1.186
0.059
0.066
2.175
2.053 -19.467 -16.800 26.246 24.025
0.313
0.243
14.817
13.703
0.058
0.069
2.438
2.252 -19.628 -16.742
25.581
18.079
0.094
0.007
9.543
7.940
-0.052
-0.042
1.633
1.524
-8.406
6.747
6.799
-0.279
-0.158
2.209
2.303
AMERICA EEML ILF EWZ EWZS
-7.252
-8.880
-5.101
6.676
ECH
0.007
0.011
1.732
1.522 -12.072 -11.071
15.686
16.764
-0.025
0.060
EWW
0.057
0.058
1.840
1.674 -10.986 -10.194
21.473
16.176
0.500
0.124
11.201
8.116
EPU
0.025
0.036
1.421
1.292 -13.784 -14.110
6.532
7.165
-0.650
-0.971
7.329
12.152
Mean
0.016
0.025
1.805
1.654 -13.153 -11.775 15.563 13.430 -0.016 -0.088
8.307
8.459
Grand Mean
0.022
0.027
1.706
1.388 -10.422
6.292
5.239
AESTI
-8.711 11.890
M AT I O
9.042
0.062 -0.122
9.867 13.809
AESTIMATIO, THE IEB INTERNATIONAL JOURNAL OF FINANCE, 2017 14: 2-31
0.027
THD
Evaluating the weak-form efficiency of emerging markets ETFs. Rompotis, G.
EWT
11
The average daily ETF return of the sample is 0.022%, while the corresponding return for the benchmarks is slightly better at 0.029%. Moreover, the South African ETF performed better than the sample average (average return of 5.8 bps), the group of Asian ETFs slightly outperformed the sample average (2.4 bps average return), while the European and Americas groups performed slightly worse than the sample average. The same pattern applies to the corresponding benchmarks. When it comes to risk, Table 2 reports an average sample variance of 1.706 whereas the average risk figure of the tracking indices is 1.388. At the group mean level, the South African ETF is more volatile than the sample average, as are the European and American ETFs. On the other hand, the average Asian ETF is less volatile than the sample average. The same behaviour is displayed by the ETF benchmarks.5 Going further, the extreme scores in Table 2, i.e., the minimum and maximum returns, are indicative of the great volatility involved in trading with ETFs covering emerging markets. Finally, the table shows that the return series do not suffer from any skewness bias but they are subject to a kurtosis impact. In particular, the series seem to be leptokurtic.
n 4. Empirical results
AESTIMATIO, THE IEB INTERNATIONAL JOURNAL OF FINANCE, 2017 14: 2-31
Evaluating the weak-form efficiency of emerging markets ETFs. Rompotis, G.
4.1. Autocorrelation tests
12
Table 3 reports the results of the time series autocorrelation tests used to examine the efficiency of US-listed emerging markets ETFs. Presented in the table are the autocorrelation coefficient of each ETF in the sample, the corresponding Ljung-Box-Q statistics and the p-values which indicate the significance of autocorrelations. Autocorrelations are calculated by successively taking into account one, two and three lagged return observations. In regards to the 1st-order autocorrelation, the average coefficient of the entire sample is 0.086. Moreover, the Asian ETFs have a higher 1st-order autocorrelation than the sample average whereas the South African, the European and the American ETFs present lower autocorrelation estimates than the sample average. Going further, the autocorrelation for the majority of the individual ETFs is significant at 1% or better but the European ETFs present non-significant 1st-order autocorrelation (with the exception of one fund). Finally, with just a few exceptions, the individual autocorrelations are positive. Based on these results, we may conclude that the pricing of the majority of the examined ETFs is not efficient in the weak form, when the 1st-order autocorrelation is taken into consideration. In other words, the ETF returns as a whole cannot be 5
It should be noted that the comparison performed in return and risk among groups is just for information purposes without being absolutely valid given that the trading history of the various ETFs examined is not similar to each other and, thus, a reliable comparison of the groups’ performance and risk cannot be performed.
AESTI
M AT I O
l Table 3. Autocorrelation of ETF daily returns
This table presents the calculations of autocorrelations in ETFs’ daily returns along with the relevant q-statistics and the probabilities (p-values) indicating of the statistical significance of calculations. Symbol EZA
Autocorrelation (1 lag) Coef.
Q-Stat
Autocorrelation (2 lags)
p-value 0.090
Coef. -0.042
Q-Stat
p-value
7.678
0.022
0.032
2.883
IEMG
0.225
32.204
0.000
0.017
35.027
EEMV
0.163
23.508
0.000
0.054
29.054
EEM
0.152
65.182
0.000
-0.054
67.730
EGRW
0.160
20.689
0.000
0.039
EVAL
0.183
27.142
0.000
EEMS
0.149
20.701
EEMA
0.071
4.115
BKF
0.154
EMEY EMFN
Autocorrelation (3 lags) Coef.
Q-Stat
p-value
-0.033
11.210
0.011
0.000
-0.027
35.056
0.000
0.000
-0.033
29.163
0.000
0.000
0.014
67.732
0.000
23.996
0.000
-0.063
25.655
0.000
0.047
32.221
0.000
-0.051
32.808
0.000
0.000
0.070
28.306
0.000
-0.001
28.767
0.000
0.042
0.056
7.089
0.029
-0.061
9.305
0.025
44.599
0.000
-0.064
47.430
0.000
-0.012
48.916
0.000
0.190
29.233
0.000
0.039
33.620
0.000
-0.035
33.756
0.000
0.183
33.297
0.000
-0.008
33.977
0.000
-0.057
36.676
0.000
EMMT
0.185
33.975
0.000
-0.017
34.274
0.000
-0.037
35.521
0.000
EMDI
0.116
10.871
0.001
0.024
11.986
0.002
-0.068
14.964
0.002
EMIF
0.172
43.917
0.000
0.008
45.992
0.000
-0.046
48.027
0.000
DVYE
0.154
18.932
0.000
0.044
22.498
0.000
-0.010
22.531
0.000
MCHI
0.025
0.667
0.414
0.051
3.368
0.186
-0.047
5.372
0.146
FCHI
0.003
0.014
0.908
0.028
1.383
0.501
-0.069
9.457
0.024
ASIA
FXI
0.669
0.414
0.008
0.831
0.660
-0.031
3.446
0.328
0.098
11.145
0.001
0.091
22.597
0.000
-0.014
22.613
0.000
INDA
0.062
3.088
0.079
-0.028
3.572
0.168
0.005
3.574
0.311
INDY
0.083
9.372
0.002
-0.004
9.388
0.009
0.005
9.423
0.024
SMIN
0.133
14.294
0.000
0.000
14.547
0.001
0.057
17.305
0.001
EIDO
0.039
1.902
0.168
0.026
2.871
0.238
-0.093
13.116
0.004
EWM
0.099
27.672
0.000
0.006
28.378
0.000
0.005
28.512
0.000
EPHE
0.078
7.111
0.008
0.017
7.748
0.021
-0.073
13.281
0.004
EWY
-0.206
120.490
0.000
-0.029
121.120
0.000
-0.028
122.730
0.000
EWT
0.030
2.561
0.110
0.020
3.772
0.152
-0.030
6.057
0.109
THD
0.024
1.036
0.309
0.047
5.050
0.080
0.023
6.214
0.102
Mean
0.100
22.533
0.091
0.018
25.105
0.076
-0.029
27.036
0.040
ESR
0.033
1.554
0.213
0.012
1.804
0.406
-0.028
2.867
0.413
EEME
0.029
0.678
0.410
-0.020
0.976
0.614
-0.013
1.132
0.769
EPOL
0.017
0.379
0.538
-0.004
0.395
0.821
-0.018
0.810
0.847
ERUS
0.089
8.914
0.003
0.006
9.133
0.010
-0.048
11.479
0.009
TUR
0.038
2.571
0.109
0.032
4.554
0.103
0.023
5.704
0.127
Mean
0.041
2.819
0.255
0.005
3.373
0.391
-0.017
4.398
0.433
AMERICA EEML
0.073
4.443
0.035
0.033
5.673
0.059
-0.017
5.780
0.123
ILF
0.006
0.099
0.753
-0.074
15.543
0.000
0.016
16.202
0.001
EWZ
0.005
0.075
0.785
-0.051
7.299
0.026
0.011
7.618
0.055
EWZS
0.079
7.166
0.007
0.072
14.119
0.001
-0.013
14.123
0.003
ECH
0.125
29.443
0.000
-0.016
29.443
0.000
-0.023
30.563
0.000
EWW
0.102
29.394
0.000
-0.029
30.394
0.000
-0.024
32.745
0.000
EPU
0.084
10.490
0.001
-0.028
11.105
0.004
-0.013
11.554
0.009
Mean
0.068
11.587
0.226
-0.013
16.225
0.013
-0.009
16.941
0.027
Grand Mean
0.086
17.662
0.135
0.009
20.399
0.103
-0.024
22.044
0.086
AESTI
M AT I O
AESTIMATIO, THE IEB INTERNATIONAL JOURNAL OF FINANCE, 2017 14: 2-31
EUROPE
Evaluating the weak-form efficiency of emerging markets ETFs. Rompotis, G.
-0.016
ECNS
13
considered independent of their lagged values and, thus, the random walk hypothesis tends to be rejected. This finding implies that past returns do affect future returns, mostly in a positive fashion as indicated by the majority of 1st-order autocorrelation. As to the question of the 2nd-order autocorrelation, Table 3 reports an average autocorrelation coefficient of 0.009. The average estimated p-value is 0.103 while there are 28 ETFs with significant 2nd-order autocorrelations at 5% or better, indicating that the efficiency hypothesis is rejected for the majority of the ETFs in the sample. When it comes to the behaviour of individual groups, it is similar to that shown in the case of the 1st-order autocorrelation, namely the Asian ETFs are more serially dependent than the average fund of the sample while the remaining groups are less dependent, with the European ETFs being the most efficient group given that the returns of all but one European ETFs present non-significant 2nd-order autocorrelation. In essence, the results concerning the 3rd-order autocorrelation are similar to those of the 1st- and 2nd-orders. Specifically, the relevant average autocorrelation coefficient is equal to -0.024 while the corresponding average p-value is 0.086. In addition, there are 29 ETFs with significant 3rd-order autocorrelations at the 5% level or better. These estimates indicate that the null hypothesis, which assumes that the returns of ETFs are not affected by their lagged values, is a fund-specific phenomenon. As with the previous autocorrelation orders, the European ETFs are the most informationally efficient group among the various groups examined.
AESTIMATIO, THE IEB INTERNATIONAL JOURNAL OF FINANCE, 2017 14: 2-31
Evaluating the weak-form efficiency of emerging markets ETFs. Rompotis, G.
4.2. Serial correlation testing
14
The results of serial correlation testing are described in this section. Table 4 reports the results of the relevant correlogram prepared. The table contains the correlation coefficients, the corresponding Q-statistics for the statistical significance of the estimates and the p-values, which indicate the significance of estimates. Following the presentation of autocorrelations in Table 3, the correlogram estimates are presented for the 1st-, 2nd- and 3rd-order serial correlation and for the four ETF groups examined in this paper. Regarding the correlogram and the relevant Q-statistics estimates, the main inference that can be drawn from the results in Table 4 is that no matter what the order of the serial correlation may be, all 1st-, 2nd-and 3rd- order serial correlation estimates are insignificant at any acceptable level (the relevant p-values of the estimated Q-statistics of all funds are greater than 0.95, approximating unity) whereas the average serial correlations do not materially differ from zero. This is also the case for all the individual estimates. No meaningful differences are to be noted among the individual groups. Based on the results in Table 4, we can reach the conclusion that the ETF market under examination is efficient in the weak form. AESTI
M AT I O
l Table 4. Serial correlation of ETF daily returns (Q-statistics)
This table presents the calculations of serial correlations in ETF daily returns along with the relevant q-statistics and the probabilities (Ps) of the statistical significance of calculations. Symbol
Autocorrelation (1 lag)
Autocorrelation (2 lags)
Coef.
Q-Stat
p-value
Coef.
Q-Stat
p-value
0.000
0.000
0.994
-0.002
0.010
0.995
IEMG
0.000
0.000
0.999
-0.001
0.001
EEMV
-0.002
0.003
0.960
-0.001
0.003
EZA
Autocorrelation (3 lags) Coef.
Q-Stat
p-value
-0.003
0.035
0.998
1.000
0.010
0.070
0.995
0.998
-0.003
0.012
1.000
ASIA
0.000
0.000
0.984
-0.001
0.002
0.999
0.003
0.026
0.999
EGRW
-0.003
0.009
0.923
-0.004
0.020
0.990
0.021
0.375
0.945
EVAL
-0.001
0.001
0.972
-0.004
0.017
0.992
0.020
0.345
0.951
EEMS
0.002
0.005
0.943
0.005
0.024
0.988
0.003
0.030
0.999
EEMA
EEM
-0.003
0.008
0.928
-0.001
0.010
0.995
0.013
0.139
0.987
BKF
0.000
0.000
0.987
-0.001
0.002
0.999
-0.002
0.007
1.000
EMEY
0.000
0.000
0.996
-0.003
0.009
0.996
0.013
0.145
0.986
EMFN
0.001
0.001
0.978
-0.003
0.010
0.995
-0.003
0.021
0.999
EMMT
-0.001
0.000
0.987
-0.005
0.028
0.986
-0.002
0.033
0.998
EMDI
-0.003
0.008
0.928
-0.005
0.025
0.987
0.015
0.205
0.977
EMIF
-0.002
0.005
0.944
-0.004
0.029
0.985
0.007
0.111
0.991
DVYE
0.001
0.000
0.988
0.001
0.002
0.999
0.005
0.022
0.999
MCHI
-0.003
0.008
0.928
0.001
0.009
0.995
0.002
0.016
0.999
FCHI
-0.004
0.025
0.874
0.002
0.035
0.983
-0.006
0.093
0.993
FXI
-0.001
0.004
0.948
-0.001
0.006
0.997
-0.002
0.015
1.000
ECNS
0.000
0.000
0.992
-0.001
0.001
0.999
0.003
0.013
1.000
INDA
0.000
0.000
0.995
0.001
0.001
1.000
-0.002
0.004
1.000
INDY
0.002
0.004
0.949
-0.002
0.012
0.994
0.000
0.012
1.000 0.996
0.001
0.001
0.976
-0.003
0.008
0.996
0.008
0.059
EIDO
-0.009
0.095
0.758
0.005
0.122
0.941
0.000
0.122
0.989
EWM
0.000
0.000
1.000
0.001
0.001
0.999
0.003
0.026
0.999
EPHE
-0.002
0.004
0.950
-0.005
0.031
0.985
0.005
0.057
0.996
EWY
-0.001
0.001
0.976
-0.001
0.004
0.998
-0.004
0.057
0.996
EWT
-0.002
0.012
0.914
0.001
0.015
0.992
0.001
0.021
0.999
THD
0.000
0.000
0.993
0.001
0.001
0.999
0.003
0.013
1.000
Mean
-0.001
0.007
0.954
-0.001
0.016
0.992
0.004
0.076
0.992
ESR
0.000
0.000
0.986
-0.003
0.015
0.993
-0.002
0.019
0.999
-0.001
0.000
0.988
0.002
0.003
0.999
-0.004
0.018
0.999
EPOL
0.000
0.000
0.994
0.000
0.000
1.000
-0.004
0.018
0.999
ERUS
-0.001
0.001
0.980
-0.003
0.011
0.995
0.002
0.014
1.000
TUR
0.001
0.001
0.972
0.001
0.003
0.999
-0.004
0.029
0.999
Mean
0.000
0.000
0.984
-0.001
0.006
0.997
-0.002
0.020
0.999
-0.001
0.000
0.986
0.002
0.002
0.999
0.003
0.010
1.000
0.001
0.005
0.944
-0.003
0.039
0.981
0.000
0.039
0.998
EEME
AMERICA EEML ILF EWZ
0.001
0.003
0.956
-0.002
0.010
0.995
0.000
0.010
1.000
EWZS
0.000
0.000
0.992
0.001
0.001
0.999
0.004
0.017
0.999
ECH
0.001
0.002
0.965
-0.002
0.011
0.995
-0.004
0.041
0.998
EWW
0.000
0.000
0.996
-0.002
0.009
0.995
0.002
0.024
0.999
EPU
0.001
0.003
0.957
0.001
0.004
0.998
-0.006
0.053
0.997
Mean
0.000
0.002
0.971
-0.001
0.011
0.995
0.000
0.028
0.999
-0.001
0.005
0.962
-0.001
0.014
0.993
0.002
0.059
0.994
Grand Mean
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EUROPE
Evaluating the weak-form efficiency of emerging markets ETFs. Rompotis, G.
SMIN
15
l Table 5. Breusch-Godfrey serial correlation LM Test
This table presents the calculations of the Breusch-Godfrey serial correlation LM Test statistics along with the relevant probabilities (p-values) of the statistical significance of calculations. In addition, the F-statistic for the significance of the estimated AR(3) model is presented along with the corresponding p-values. Symbol
1st Order serial correlation
2nd Order serial correlation
3rd Order serial correlation
LM statistic
p-value
LM statistic
p-value
LM statistic
p-value
F-statistic
p-value
0.036
0.849
5.896
0.052
8.654
0.034
2.628
0.112
IEMG
0.001
0.971
0.669
0.716
6.340
0.096
1.437
0.302
EEMV
1.788
0.181
1.810
0.405
5.305
0.151
8.671
0.000
EEM
1.850
0.174
6.688
0.035
8.023
0.046
25.222
0.000
EGRW
1.992
0.158
7.620
0.022
9.736
0.021
8.949
0.000
EVAL
0.320
0.572
6.513
0.039
8.166
0.043
11.239
0.000
EEMS
0.827
0.363
3.335
0.189
3.573
0.311
8.991
0.000
EEMA
2.110
0.146
6.060
0.048
8.199
0.042
2.258
0.210
BKF
0.079
0.778
0.234
0.890
1.037
0.792
18.311
0.000
EMEY
0.006
0.937
2.066
0.356
3.101
0.376
11.673
0.000
EMFN
0.211
0.646
2.204
0.332
2.602
0.457
12.379
0.000
EMMT
0.197
0.658
6.517
0.038
7.048
0.070
12.112
0.000
EMDI
1.588
0.208
5.482
0.064
6.986
0.072
0.429
0.898
EMIF
1.106
0.293
8.222
0.016
8.296
0.040
16.261
0.000
DVYE
0.096
0.756
0.258
0.879
1.362
0.714
6.958
0.000
MCHI
3.738
0.053
5.189
0.075
5.201
0.158
1.829
0.140
FCHI
5.213
0.022
5.342
0.069
15.499
0.001
3.009
0.123
FXI
3.453
0.063
4.626
0.099
8.772
0.032
1.134
0.334
ECNS
0.096
0.757
0.144
0.931
1.512
0.680
6.973
0.000
INDA
0.038
0.845
0.406
0.816
0.461
0.927
1.275
0.282
INDY
9.718
0.002
15.114
0.001
19.415
0.000
2.185
0.231
SMIN
0.242
0.623
2.060
0.357
6.062
0.109
5.645
0.001
EIDO
10.518
0.001
10.836
0.004
10.843
0.013
4.705
0.003
EWM
0.000
0.994
1.468
0.480
3.002
0.391
9.391
0.000
EPHE
0.450
0.502
3.919
0.141
4.815
0.186
4.552
0.004
EWY
1.155
0.283
2.025
0.363
2.418
0.490
43.384
0.000
EWT
13.332
0.000
13.569
0.001
15.469
0.001
2.048
0.105
THD
0.153
0.695
0.374
0.829
4.258
0.235
1.981
0.115
Mean
2.233
0.433
4.546
0.304
6.574
0.239
8.630
0.102
ESR
0.308
0.579
3.770
0.152
7.297
0.063
0.981
0.401
EEME
0.322
0.571
0.903
0.637
5.956
0.114
0.397
0.755
EPOL
0.030
0.863
0.050
0.975
9.851
0.020
0.270
0.847
ERUS
0.265
0.607
4.481
0.106
4.493
0.213
2.828
0.119
TUR
0.834
0.361
1.314
0.518
3.160
0.368
1.857
0.135
Mean
0.352
0.596
2.104
0.478
6.151
0.155
1.267
0.451
EZA
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Evaluating the weak-form efficiency of emerging markets ETFs. Rompotis, G.
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16
EUROPE
AMERICA EEML
0.457
0.499
0.858
0.651
1.774
0.621
1.872
0.133
ILF
7.743
0.005
8.886
0.012
9.109
0.028
5.436
0.001
EWZ
3.841
0.050
4.807
0.090
4.915
0.178
2.097
0.158
EWZS
0.178
0.673
2.183
0.336
4.448
0.217
4.468
0.004
ECH
1.201
0.273
10.887
0.004
10.894
0.012
10.173
0.000
EWW
0.021
0.885
5.283
0.071
5.634
0.131
11.280
0.000
EPU
1.275
0.259
1.301
0.522
131.807
0.000
3.791
0.010
Mean
2.102
0.378
4.886
0.241
24.083
0.170
5.588
0.044
Grand Mean
1.920
0.454
4.334
0.308
9.637
0.211
7.027
0.136
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The results of the Breusch-Godfrey Lagrange Multiplier serial correlation test used are shown in Table 5. This table presents the coefficients of LM test and the corresponding p-values indicating of the statistical significance of the estimated Breusch-Godfrey statistics. Furthermore, the table presents the 1st-, 2nd- and 3rd-order serial correlations. With respect to the serial correlation of first order, the average estimate is 1.920 while the corresponding average p-value is 0.454. The average term implies that, on average, there is no 1st-order serial correlation in residuals. The 2nd- and 3rd-order serial correlations behave similarly to the 1st-order serial correlation. The average LM statistics of the entire sample are equal to 4.334 and 9.637, respectively, and the corresponding average p-values are 0.308 and 0.211. There are, however, 11 and 14 out of 40 single serial correlations of 2nd- and 3rd-order respectively that are statistically significant at the 5% level or better. Finally, the estimates of the F-statistic which assesses the hypothesis that coefficients of the relevant autoregressive AR(3) model used are jointly equal to zero are also presented in Table 5. We should recall here that a rejection of the null hypothesis is indicative of serial correlation in ETF returns and consequently the efficient market hypothesis should be rejected. According to the results in Table 5, the hypothesis of no serial correlation in returns is rejected for a sufficient number of ETFs. More specifically, in 22 cases, the estimated F-statistics are statistically significant and, thus, informational efficiency is not the case for the respective ETFs. 4.3. Wald-Wolfowitz runs test
Overall, the results of the runs tests suggest that the returns of a significant number of funds in the sample are affected by their lagged values. In other words, for the 23 ETFs AESTI
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AESTIMATIO, THE IEB INTERNATIONAL JOURNAL OF FINANCE, 2017 14: 2-31
We attempt to answer the key question about the randomness of the ETF return-generating process by applying the runs test, and the relevant z-statistics reveal that the returns of the majority of funds are not the outcome of a random process. In particular, there are 23 ETFs which present a statistically significant z-statistic at the 5% level or better. The majority of these significant z-statistics are found in the Asian group while the European group seems to be the most efficient based on the outcomes of the runs tests. These findings resemble those obtained by analysing the estimations of autocorrelation in Table 3.
Evaluating the weak-form efficiency of emerging markets ETFs. Rompotis, G.
The results of the Wald-Wolfowitz runs test, which assesses whether the returns of emerging markets ETFs are the result of a random process, are presented in Table 6. The table reports the test-statistic value, which is the median return for each ETF in the sample, the number of return observations (cases) which are lower than the test value, the number of cases which are greater than the test value, the number of runs, the estimated z-statistics and the relevant p-values corresponding to the z-statistics.
17
in question, the lagged prices can convey some information about the trends in concurrent returns of these ETFs, and, consequently, the pricing of these ETFs seems to be inefficient in the weak form.
l Table 6. Wald-Wolfowitz runs test
This table presents the calculations of the Wald-Wolfowitz Runs Test which is used to determine whether or not the time series of ETF returns are related to a random process. Symbol EZA
Test Value (median return)
Cases< Test Value
Cases>= Test Value
Total cases
No of runs
z-stat
p-value
0.140
1,415
1,415
2,830
1,410
-0.226
0.890 0.000
ASIA IEMG
0.031
316
316
632
254
-5.016
EEMV
0.037
443
442
885
402
-2.792
0.003
EEM
0.096
1,415
1,415
2,830
1,205
-7.934
0.000
EGRW
0.041
405
404
809
352
-3.764
0.000
EVAL
0.003
405
404
809
344
-4.327
0.000 0.000
EEMS
0.063
465
464
929
400
-4.300
EEMA
-0.015
405
404
809
371
-2.427
0.008
0.025
937
937
1,874
785
-7.071
0.000
AESTIMATIO, THE IEB INTERNATIONAL JOURNAL OF FINANCE, 2017 14: 2-31
Evaluating the weak-form efficiency of emerging markets ETFs. Rompotis, G.
BKF
18
EMEY
-0.037
405
404
809
357
-3.412
0.000
EMFN
0.067
496
496
992
440
-3.621
0.000
EMMT
-0.047
496
496
992
427
-4.447
0.000
EMDI
0.061
405
404
809
385
-1.442
0.074
EMIF
0.058
738
737
1,475
663
-3.933
0.000 0.001
DVYE
0.004
400
399
799
356
-3.151
MCHI
-0.004
512
513
1,025
522
0.531
0.760
FCHI
-0.002
862
861
1,723
865
0.121
0.943
FXI
0.014
1,329
1,328
2,657
1,328
-0.058
0.978
ECNS
0.062
577
576
1,153
523
-3.211
0.001
INDA
0.000
407
406
813
403
-0.316
0.931
INDY
0.047
684
683
1,367
642
-2.300
0.010
SMIN
0.082
405
404
809
372
-2.357
0.011
EIDO
0.043
627
626
1,253
632
0.254
0.902
EWM
0.004
1,415
1,415
2,830
1,315
-3.798
0.000
EPHE
0.022
577
576
1,153
546
-1.856
0.028
EWY
0.042
1,415
1,415
2,830
1,413
-0.113
0.947
EWT
0.009
1,415
1,415
2,830
1,425
0.338
0.942
THD
0.004
893
892
1,785
871
-1.065
0.147
Mean
0.026
698
697
1,396
652
-2.647
0.248
ESR
0.013
701
701
1,402
690
-0.641
0.683
EEME
0.000
412
412
824
408
-0.349
0.929
EPOL
0.005
620
620
1,240
646
1.420
0.071
ERUS
-0.040
562
561
1,123
547
-0.925
0.089
EUROPE
TUR
0.118
893
892
1,785
871
-1.065
0.147
Mean
0.019
638
637
1,275
632
-0.312
0.384
AMERICA EEML
-0.031
412
412
824
405
-0.558
0.755
ILF
0.090
1,415
1,415
2,830
1,312
-3.911
0.000
EWZ
0.092
1,415
1,415
2,830
1,364
-1.955
0.025
EWZS
0.012
577
576
1,153
548
-1.738
0.038
ECH
0.001
937
937
1,874
831
-4.945
0.000
EWW
0.109
1,415
1,415
2,830
1,317
-3.723
0.000
EPU
0.062
737
737
1,474
683
-2.866
0.002
Mean
0.048
987
987
1,974
923
-2.814
0.117
Grand Mean
0.032
759
759
1,518
716
-2.324
0.258
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4.4. Variance ratio tests 4.4.1 Lo and MacKinlay (1988) variance ratio test The results of the Lo and MacKinlay (1988) variance ratio test on whether the ETF prices follow a random walk are presented in Table 7. The table has two panels: Panel A contains the results from the first version of the variance ratio, which assesses the random walk hypothesis by assuming homoskedasticity-consistent standard errors; and Panel B reports on the second version of the ratio, which examines the random walk hypothesis by assuming heteroskedasticity-consistent standard errors. Table 7 lists the variance ratios and the z-statistics, and indicates their significance level. The test periods used are q1=2, q2=4, q3=8 and q4=16. As far as the first version of the test is concerned, i.e., the homoskedastic one, the results in Table 7 indicate that the individual statistics for the majority of ETFs reject the null hypothesis that the variance ratio is not statistically different from 1 at any q considered. There is a stronger rejection of the null hypothesis at the low test periods, namely at q1=2 and q2=4, for which 25 and 23 variance ratio estimates, respectively, are statistically significant at 5% or better. The rejection of the null hypothesis weakens as we move to the next test periods, that is, to q3=8 and q4=16. In these cases, the statistically significant variance ratios are equal to 16 and 11, respectively.
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Overall, the main conclusion that can be drawn from the analysis of the results of the Lo and MacKinlay (1988) conventional variance ratio is that the pricing of about half of the US-listed ETFs tracking stock indices from emerging economies considered is not a random walk and, consequently, for those specific funds the market cannot be considered efficient in the weak form. These results are in line with the results of the Wald-Wolfowitz Runs Test in the previous section, which also showed that informational efficiency is not universal in the ETF market examined but rather is a fund-specific phenomenon.
Evaluating the weak-form efficiency of emerging markets ETFs. Rompotis, G.
The results of the second version of the Lo and MacKinlay (1988) variance ratio in Panel B, i.e., the heteroskedastic one, resemble the results in Panel A. This means that the null hypothesis of a random walk is rejected for the majority of the funds as the variance ratios calculated are statistically different from unity in 23, 21, 12 and 8 cases at q1=2, q2=4, q3=8 and q4=16, respectively. A minor difference in results between the homoskedastic and heteroskedastic versions of the variance ratio is that the second one produces slightly less statistically significant estimates than the first one.
19
20
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1.108a
1.146
1.023
EMDI
EMIF
DVYE
MCHI
1.265
5.709
1.181
EMMT
a
1.287
4.120
a
1.275
3.755
1.111
ECNS
a
a
1.004
0.946
0.239
-1.802
1.006
0.965
FXI
1.066
FCHI
0.738
1.277a
6.604
1.172a
a
1.171b
3.069
a
1.277a
5.708
1.181a
EMFN
1.213a
1.288a
1.147a
EMEY
7.087
4.193
1.164a
1.138b
2.047
BKF
1.303
4.184
1.137
1.072b
EEMA
a
a
EEMS
1.315a
4.739
1.167a
EVAL
1.272a
4.363
1.153a
1.217a
7.972
EGRW
1.297
4.705
1.158
1.150a
EEMV
a
EEM
1.387a
5.428
0.968
Var. Ratio
a
0.797
z-stat
1.216a
1.015
Var. Ratio
z-stat
4.987
-1.499
0.086
1.131
4.340
5.691
2.595
4.459
4.663
4.371
4.939
2.095
4.941
4.788
4.131
6.160
4.724
5.196
-0.923
q2=4
1.360
a
0.917
0.936
1.013
1.331 a
1.245a
1.098
1.162
1.221b
1.279b
1.197b
1.062
1.409 a
1.297b
1.193
1.199a
1.260 b
1.396a
0.887 b
Var. Ratio
4.136
-1.454
-0.904
0.145
3.161
3.185
0.943
1.720
2.358
2.680
2.890
0.599
4.215
2.852
1.852
3.574
2.618
3.366
0.819
-2.041
1.570
a
0.935
0.924
1.081
1.428
b
1.278b
1.118
1.164
1.239
1.403b
1.182
1.101
1.594 a
1.416b
1.213
1.216b
1.355 b
1.537a
b
Var. Ratio
0.591
2.750
2.422
0.761
1.176
1.714
2.604
1.787
0.652
4.113
2.686
1.377
2.606
2.401
3.070
-2.184
z-stat
4.394
-0.763
-0.717
q4=16 z-stat
q3=8
Panel A: Homoskedastic random walk hypothesis
IEMG
ASIA
EZA
Symbol
q1=2
1.140
0.228
0.661
4.282
5.711
3.025
5.071
5.183
3.971
5.059
2.330
3.020
4.868
4.648
5.512
4.644
5.717
0.700
z-stat
1.113
b
2.517
0.966 -0.785
1.007
1.025
1.149
a
1.174a
1.111a
1.184
a
1.184a
1.150a
1.165a
1.075b
a
1.170a
1.156a
1.151a
1.161 a
1.220a
1.016
Var. Ratio
q1=2
1.312
1.281
a
0.948
1.007
1.072
1.297
a
1.282a
1.179b
1.273
a
1.285a
1.297a
1.217a
1.146b
a
1.325a
1.281a
1.219a
1.306
a
1.400a
0.970
Var. Ratio
z-stat
3.330
-0.664
0.121
1.016
4.513
4.806
2.619
3.772
4.189
4.203
3.294
2.256
3.480
4.864
4.269
4.014
4.505
5.287
-0.706
q2=4
1.281
1.377
b
0.921
0.943
1.027
1.354
a
1.257b
1.117
1.178
1.239b
1.301b
1.206
1.081
1.431
a
1.319a
1.214
1.205b
b
1.427a
0.891
Var. Ratio
z-stat
2.793
-0.648
-0.569
0.233
3.288
2.743
1.072
1.504
2.145
2.673
1.879
0.749
2.986
2.924
1.967
2.289
2.504
3.463
-1.584
q3=8
1.611
a
0.946
0.940
1.114
1.483
b
1.304b
1.160
1.200
1.278
1.457b
1.201
1.143
1.647
a
1.470b
1.259
1.229
1.402
b
1.613a
0.828
Var. Ratio
3.161
-0.320
-0.404
0.648
2.915
2.221
0.985
1.132
1.663
2.695
1.201
0.865
3.032
2.823
1.562
1.681
2.359
3.257
-1.671
z-stat
q4=16
Panel B: Heteroskedastic random walk hypothesis
This table presents the variance ratio estimates and test z-statistics of the Random Walk Hypothesis (RWH) based on the conventional variance ratio of Lo and MacKinlay (1988). Two versions of the test are applied. The first version assesses the homoskedastic random walk hypothesis, which assumes homoskedasticity-consistent standard errors while the second version assesses the heteroskedastic random walk hypothesis, which assumes heteroskedasticity-consistent standard errors. The test periods used are q1=2, q2=4, q3=8 and q4=16. a and b reflect statistical significance at 1 and 5% level, respectively.
l Table 7. Lo-MacKinlay variance ratio test
AESTIMATIO, THE IEB INTERNATIONAL JOURNAL OF FINANCE, 2017 14: 2-31
Evaluating the weak-form efficiency of emerging markets ETFs. Rompotis, G.
1.134
1.239a
3.042
3.799
1.367
3.422
a
1.082
1.134a
1.037
1.060
0.999
1.027
1.032
1.103
INDY
SMIN
EIDO
EWM
EPHE
EWY
EWT
THD
Mean
1.029
1.038
TUR
Mean
1.037
0.957
-0.208
3.233
2.614
0.996
b
1.078
1.142a
1.091a
1.084a
1.064
1.086
EWZS
ECH
EWW
EPU
Mean
Grand Mean
4.858
2.953
1.109a
6.158
1.142
1.086
1.076
1.180
1.209a
2.643
a
0.954
EWZ
-0.065
1.058
0.999
1.115
1.056
1.096b
1.126b
1.016
0.992
1.051
1.180
1.070
ILF
1.679
1.328
1.213
2.901
0.830
0.465
1.230
1.421
EEML
AMERICA
1.024
1.087a
ERUS
1.016
EEME
EPOL
1.033
ESR
EUROPE
1.093
2.022
b
0.994
1.141a
4.577
1.086a
-0.042
1.045
1.312
b
1.098
2.042
1.072b
INDA
1.761
2.532
1.714
1.562
3.106
4.840
3.263
-1.232
-1.306 -1.719 1.959 1.857 0.559 1.140 0.296 1.181
0.904 1.171 1.127 1.031 1.088 1.036 1.112
1.141
1.038
1.141
1.025
1.151
1.200
0.874
1.038 0.834b
0.548 -2.271
1.056
1.021
1.149
1.122
0.963
0.899
0.973
1.202
1.134
0.966
0.934
1.092
1.156
0.873
1.263
1.204
1.066
0.874b
0.375
1.652
1.004
-0.003
-0.694
-0.086
1.679
1.166
-0.521
-0.966
0.225
2.555
-1.274
2.513
2.373
1.322
1.025
1.116
2.157
1.122
1.089
1.000
0.928
0.993
1.156
1.082
0.971
0.946
1.020
1.142b
0.894
1.261b
1.190 b
1.137
2.253
0.306
-0.126
1.021
3.133
1.574
1.063
-0.175
1.680
4.022
0.859
3.636
2.639
1.488
AESTIMATIO, THE IEB INTERNATIONAL JOURNAL OF FINANCE, 2017 14: 2-31
M AT I O
Evaluating the weak-form efficiency of emerging markets ETFs. Rompotis, G.
AESTI
21
0.984
0.183
1.234
0.300
1.481
1.542
-1.520
-2.002
0.248
0.233
1.427
0.925
-0.299
-0.657
-0.230
1.449
1.282
-0.415
-0.796
0.711
1.887
-1.019
1.698
1.712
0.427
1.534
3.316
0.977
3.466
3.011
2.041
1.291
1.693
1.107
0.994
2.342
0.722
0.521
0.959
3.056
1.226
1.139
1.186
1.088
1.065
1.086
1.092a
2.543
1.854
1.735
3.652
3.650
1.148
1.090
1.081
1.112b
1.213a
b
2.376 1.143a
1.080
b
0.959
0.956
1.123
1.061
1.099
1.132
1.021
0.999
1.056
1.186
1.073
1.040
0.996
1.098
1.144b
1.050
1.248a
b
1.106
0.997 -0.111
0.999 -0.017
1.061
1.039
1.030
1.088b
1.025
1.019
1.034
1.105
1.034
1.027
1.000 -0.003
1.061
1.087a
1.039
1.136a
1.084 a
1.074b
2.182
1.300
0.818
2.257
2.974
2.689
-0.711
-0.718
1.791
0.954
1.761
1.863
0.323
-0.014
0.837
2.745
1.316
0.928
-0.085
1.176
2.824
0.677
3.303
2.604
1.489
1.125
1.045
1.098
1.036
1.135
1.185
0.909
0.878
1.075
1.037
1.124
1.102
1.011
0.944
1.003
1.171
1.090
0.976
0.951
1.032
1.148
0.904
1.283b
1.202 b
1.157
1.106
0.358
0.654
0.453
1.240
1.675
-0.965
-1.225
0.675
0.388
1.391
0.928
0.106
-0.517
0.031
1.532
0.982
-0.344
-0.625
0.236
1.841
-0.821
2.369
2.368
1.365
1.171
1.058
1.165
1.036
1.169
1.232
0.884
0.843
1.077
1.047
1.168
1.152
0.986
0.933
0.994
1.236
1.153
0.976
0.944
1.121
1.169
0.895
1.311
1.231
1.106
0.997
0.325
0.833
0.300
1.088
1.442
-0.814
-1.037
0.462
0.339
1.287
0.947
-0.086
-0.415
-0.039
1.391
1.123
-0.230
-0.469
0.604
1.478
-0.613
1.789
1.796
0.613
22
AESTI
M AT I O
1.261
1.267a
4.368
9.243
1.147
1.174a
1.160a
1.177a
1.079
EEMV
EEM
EGRW
EVAL
EEMS
EEMA
1.098b
1.171a
1.150a
0.998
1.008
1.010
1.094a
EMDI
EMIF
DVYE
MCHI
FCHI
FXI
ECNS
1.294
6.025
1.191
a
EMMT
1.291a
5.674
1.180a
1.281a
4.248
1.011
1.201a
3.182
1.018
0.498
0.323
1.010
1.271a
-0.051
1.151b
2.789
6.566
a
1.324a
EMFN
1.310a
8.314
4.827
1.192a
1.170a
1.130
2.234
b
BKF
1.350a
5.083
1.167a
EMEY
1.329a
5.021
1.279a
a
4.564
1.395a
5.695
0.973
Var. Ratio
a
0.808
z-stat
1.227a
1.015
Var. Ratio
3.641
0.311
0.395
0.169
4.250
5.558
2.294
4.952
4.901
4.925
7.184
1.979
5.699
4.997
4.239
7.584
4.150
5.306
-0.769
z-stat
1.210b
0.983
0.993
0.970
1.324a
1.252a
1.084
1.259 b
1.306a
1.364a
1.333a
1.062
1.472a
1.353a
1.231b
1.256a
1.266b
1.440a
0.890
Var. Ratio
z-stat
2.408
-0.298
-0.098
-0.326
3.099
3.267
0.808
2.757
3.260
3.501
4.871
0.597
4.859
3.397
2.224
4.611
2.680
3.742
-1.975
q3=8
Panel A: Ranks test
q2=4
IEMG
ASIA
EZA
Symbol
q1=2
1.319b
1.005
0.996
1.045
1.400b
1.275b
1.063
1.239
1.318b
1.458a
1.320a
1.070
1.602a
1.472a
1.204
1.252a
1.319 b
1.535a
0.805 b
Var. Ratio
2.153
0.329
2.567
2.397
0.410
1.710
2.276
2.957
3.151
0.450
4.169
3.047
1.318
3.048
2.457
0.064
1.153
1.099a
1.005
1.006
1.012
1.150a
1.171a
1.105a
1.191
a
1.183a
1.162a
1.187a
1.074
b
1.159a
1.171a
1.158a
1.165a
a
1.222a
1.014
-2.355
3.054
Var. Ratio
q1=2 z-stat
-0.039
q4=16
3.347
0.247
0.268
0.400
4.248
6.566
2.974
6.019
5.762
4.615
8.090
2.110
4.861
4.853
4.504
8.803
4.559
5.590
0.736
z-stat
1.217a
1.006
1.013
1.039
1.281a
1.271a
1.163b
1.283
a
1.285a
1.309a
1.276a
1.132
b
1.336a
1.320a
1.275a
1.247a
1.279
a
1.391a
0.964
Var. Ratio
z-stat
3.931
0.178
0.294
0.665
4.250
5.558
2.478
4.771
4.798
4.696
6.387
2.002
5.478
4.862
4.187
7.023
4.439
5.258
-1.030
q2=4
1.247b
0.972
0.973
0.991
1.324a
1.252a
1.096
1.209b
1.250b
1.323a
1.276a
1.057
1.452a
1.322a
1.208b
1.231a
1.265
b
1.415a
0.872
b
Var. Ratio
z-stat
2.840
-0.489
-0.379
-0.101
3.099
3.267
0.922
2.227
2.663
3.103
4.045
0.548
4.659
3.098
2.005
4.161
2.666
3.524
-2.306
q3=8
Panel B: Rank scores test
1.389a
0.995
0.977
1.063
1.400
1.275b
1.111
1.196
1.248
1.440b
1.264b
1.086
1.596a
1.449b
1.213
1.237b
1.346
b
1.535a
0.786
b
Var. Ratio
2.999
-0.063
-0.214
0.457
2.567
2.397
0.717
1.403
1.775
2.840
2.596
0.556
4.125
2.901
1.379
2.869
2.337
3.055
-2.589
z-stat
q4=16
This table presents the ranks-based and the signs-based variance ratio estimates and test z-statistics of the Random Walk Hypothesis (RWH) based on Wright’s (2000) non-parametric variance ratio. In general, the Wright (2000) variance ratio assesses the homoskedastic random walk hypothesis, which assumes homoskedasticity-consistent standard errors. Three versions of the test are applied, namely the ranks-based, the rank scores-based and the signs-based version of the test. The test periods used are q1=2, q2=4, q3=8 and q4=16. a, b and c reflect statistical significance at 1, 5 and 10% level, respectively.
l Table 8. Wright’s non-parametric variance ratio test
AESTIMATIO, THE IEB INTERNATIONAL JOURNAL OF FINANCE, 2017 14: 2-31
Evaluating the weak-form efficiency of emerging markets ETFs. Rompotis, G.
1.179
3.506
1.095
1.165a
INDY
SMIN
1.186
3.682
0.990
1.013
1.028
1.110
EWT
THD
1.056
1.035
1.032
TUR
Mean
1.032
1.167
2.081
2.711
4.611
3.563
1.039b
b
1.080
1.158a
1.095a
1.120a
1.084
1.093
EWZS
ECH
EWW
EPU
Mean
Grand Mean
3.269
5.046
6.842
1.153
1.122
1.175a
1.100b
1.243a
a
1.039
EWZ
2.063
1.055
1.039b
1.101
1.041
1.078
1.072
1.003
1.011
1.042
1.189
1.080
1.011
ILF
1.588
1.121
1.459
1.871
0.307
0.921
1.049
0.666
EEML
AMERICA
1.009
ERUS
1.032
EEME
EPOL
1.028
ESR
EUROPE
Mean
1.069
1.069
EPHE
EWY
1.006
2.351
b
-0.508
0.994
1.183a
1.026
6.001
1.029
1.113a
EWM
1.302a
EIDO
4.700
a
a
1.097
1.877
1.066
INDA
2.820
2.666
3.595
2.852
5.616
3.035
0.897
1.111
1.555
0.823
1.772
1.282
0.051
0.166
0.844
3.362
1.797
0.304
0.174
1.255
5.215
-0.107
4.591
3.537
1.473
AESTIMATIO, THE IEB INTERNATIONAL JOURNAL OF FINANCE, 2017 14: 2-31
M AT I O
1.257
1.949 3.036 0.486 2.339 1.098 1.573
1.170
1.027 1.180b 1.088 1.140
-0.357
0.980
1.207a
0.827 -0.591
1.085 0.967
0.265
1.272
0.567
-0.412
-0.304
0.201
2.069
1.666
-0.562
-0.338
-0.501
3.577
-1.344
3.590
3.214
1.201
1.018
1.089
1.050
0.965
0.969
1.016
1.186
1.117
0.969
0.981
0.956
1.199a
0.888
1.373a
a
1.125
Evaluating the weak-form efficiency of emerging markets ETFs. Rompotis, G.
AESTI
23
1.257
1.156
1.094
1.243b
1.013
1.235b
1.202
0.957
0.930
1.078
0.992
1.106
1.048
0.865
0.947
0.993
1.216
1.189
0.963
1.001
0.919
1.277a
0.877
1.423b
b
1.034
1.164
0.757
2.119
0.162
2.312
1.561
-0.518
-0.846
0.506
-0.021
1.019
0.363
-1.083
-0.349
-0.057
1.620
1.810
-0.453
0.009
-0.627
3.353
-0.992
2.736
2.161
0.218
2.413
5.798
1.176
4.378
3.257
2.090
1.167
1.093
1.083
1.120a
1.096a
3.255
3.503
4.600
5.084
7.035
2.711 1.163a
1.080
1.151
1.119
1.167a
1.103a
1.240a
a
1.007
1.373
1.039
1.109
1.048
1.089
b
2.063
1.657
1.281
1.554
1.012 1.096
0.526
1.004
1.040
1.185
1.071
1.014
2.466
0.731
1.127
3.650
1.205
0.870
0.999
1.074
1.179a
1.009
1.274a
1.150 a
1.103
1.026
1.039b
1.058
1.036
1.037
1.074b
1.015
1.025
1.030
1.109
1.029
1.016
0.992 -0.451
1.071 b
1.109a
1.033
1.154a
1.088 a
1.073b
2.757
2.561
3.428
2.917
5.565
3.035
0.196
1.111
1.678
0.965
2.018
1.716
0.218
0.065
0.809
3.279
1.594
0.410
-0.041
1.350
5.077
0.177
4.169
2.972
1.568 1.211
1.124
1.074
1.168b
1.018
1.176b
1.170
0.954
0.967
1.068
1.014
1.094
1.053
0.984
0.945
0.992
1.167
1.085
0.951
0.956
0.954
1.175a
0.870
1.317a
b
1.134
1.363
0.895
2.181
0.331
2.573
1.949
-0.836
-0.591
0.658
0.224
1.348
0.605
-0.195
-0.534
-0.106
1.832
1.213
-0.881
-0.784
-0.524
3.150
-1.550
3.044
2.638
1.290
1.142
1.074
1.218a
0.996
1.187a
1.202
0.925
0.930
1.058
0.989
1.104
1.059
0.899
0.916
0.966
1.202
1.126
0.930
0.944
0.944
1.222b
0.841
1.356b
1.215
1.047
1.022
0.555
1.903
-0.047
1.843
1.561
-0.903
-0.846
0.377
-0.037
1.003
0.453
-0.807
-0.546
-0.287
1.472
1.206
-0.847
-0.682
-0.432
2.688
-1.283
2.300
1.803
0.306
Panel C: Signs test q1=2 Symbol EZA
q2=4
q3=8
q4=16
Var. Ratio z-stat Var. Ratio z-stat Var. Ratio z-stat Var. Ratio z-stat 0.989 -0.564
0.969 -0.884
0.952 -0.871
0.944 -0.672
IEMG
1.193a
4.853
1.364a
4.890
1.448a
3.806
1.523a
EEMV
1.114a
3.395
1.235a
3.737
1.246b
2.477
1.231
1.560
EEM
1.145a
7.707
1.261a
7.425
1.321a
5.767
1.388a
4.693
EGRW
1.117a
3.340
1.214a
3.251
1.159
1.527
1.039
0.250
EVAL
a
1.152
4.324
1.277a
4.210
1.358a
3.447
1.448b
2.893
EEMS
1.132a
4.035
1.281a
4.577
1.379a
3.904
1.426a
2.952
EEMA
1.088b
2.496
1.167b
2.537
1.166
1.599
1.201
1.300
BKF
1.164a
7.115
1.289a
6.680
1.335a
4.908
1.358a
3.519
EMEY
a
1.122
3.481
a
1.201
3.063
b
1.219
2.110
1.293
1.891
EMFN
1.125a
3.937
1.232a
3.903
1.327a
3.478
1.361b
2.586
EMMT
1.131a
4.128
1.233a
3.920
1.198b
2.109
1.093
0.665
EMDI
1.048
1.371
1.078
1.184
0.981 -0.178
0.925 -0.487
EMIF
1.096a
3.671
1.144a
2.964
1.179b
2.319
1.264b
2.303
DVYE
1.089b
2.512
1.185b
2.799
1.210b
2.009
1.128
0.824
AESTIMATIO, THE IEB INTERNATIONAL JOURNAL OF FINANCE, 2017 14: 2-31
Evaluating the weak-form efficiency of emerging markets ETFs. Rompotis, G.
ASIA
24
2.984
MCHI
0.971 -0.937
0.984 -0.267
0.962 -0.406
1.026
0.188
FCHI
1.001
1.014
1.001
0.016
1.016
0.149
0.999 -0.021
1.003
0.056
1.024
0.279
1.300a
1.371a
4.261
1.555a
4.282
0.024
0.309
FXI
0.997 -0.136
ECNS
1.134a
4.565
INDA
1.009
0.246
0.974 -0.394
0.950 -0.486
INDY
1.058b
2.137
1.127b
2.516
1.196b
2.450
1.231
1.939
SMIN
1.105
2.988
1.173
2.631
1.214b
2.062
1.270
1.743
EIDO
0.998 -0.085
EWM
1.068a
EPHE
1.060
b
EWY
1.004
0.226
0.458
1.119
1.434
EWT
0.989 -0.602
0.982 -0.512
0.986 -0.254
1.053
0.635
THD
1.020
1.080
1.797
1.170b
2.428
1.319a
3.065
Mean
1.079 2.639
1.147 2.631
1.167
1.918
1.201 1.630
1.035
0.447
a
b
5.447
0.865 -0.876
0.980 -0.378
0.967 -0.396
1.050 0.403
3.609
1.093b
2.633
1.137b
1.266a
2.032
1.070
1.275
0.987 -0.149
1.030
0.854
0.828
1.025
2.466
3.218
0.949 -0.393
EUROPE ESR
1.010
0.374
1.026
EEME
1.007
0.209
0.962 -0.577
0.528
0.942 -0.559
EPOL
0.955 -1.590
0.916 -1.579
0.831b -2.016
ERUS
1.019
0.627
1.049
0.877
1.067
0.757
1.039
0.298
TUR
1.044
1.870
1.100b
2.265
1.145b
2.064
1.144
1.383
Mean
1.007 0.298
1.011 0.303
1.004 0.138
1.039
0.328
0.945 -0.356 0.762 -1.905
0.986 -0.050
AMERICA 1.058
1.657
1.109
1.678
1.068
0.658
1.058
ILF
EEML
1.066a
3.496
1.088b
2.512
1.055
0.985
1.084
1.011
EWZ
1.047b
2.519
1.057
1.608
1.037
0.661
1.022
0.265
EWZS
1.063b
2.150
1.101
1.826
1.114
1.309
1.134
1.035
ECH
1.107a
4.620
1.189a
4.371
1.195b
2.850
1.228b
2.241
EWW
1.083a
4.436
1.097b
2.763
1.086
1.551
1.147
1.780
EPU
1.068b
2.605
1.129b
2.645
1.165b
2.140
1.194
1.689
Mean
1.070 3.069
1.110 2.486
1.103
1.451
1.124 1.200
Grand Mean
1.066 2.342
1.119 2.227
1.130 1.544
1.154 1.287
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0.377
4.4.2 Wright (2000) ranks and signs variance ratio test The results of the non-parametric Wright (2000) ranks and signs variance ratio test are presented in Table 8. The table has three panels. The first panel contains the results of the test which are based on the ranks-based version of Wright’s variance ratio test. The second panel relates to the results obtained from the rank scoresbased version of the test. Finally, the third panel presents the results of the signs-based test. All the alternative versions of Wright’s variance ratio test are assumed to be homoskedasticity-consistent in contrast to the Lo and MacKinlay (1988) variance ratio test, which assumes both a homoskedasticity — and a heteroskedasticity-consistent test. Given that the homoskedasticity — and heteroskedasticity-consistent Lo and MacKinlay versions of variance ratio are similar, any heteroskedasticity there may be is minimal. Reported in the table are the variance ratios and the relevant z-statistics on the significance of estimates. As with the approach in the previous section, the test periods used are q1=2, q2=4, q3=8 and q4=16. ETFs at q1=2, q2=4, q3=8 and q4=16, respectively. Based on these estimates, we can conclude that market efficiency is not a valid hypothesis for the ETFs, which present Wright’s variance ratios that statistically differ from unity. By comparing these results to the Lo and MacKinlay (1988) variance ratios in the previous section, it is evident that the rejection of the null hypothesis by both tests becomes weaker as we move from the low to the high test periods, that is from q1=2 to q4=16.
The rejection of the efficient market hypothesis for a number of ETFs means that for these funds the past information which is incorporated in their historical returns AESTI
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Overall, the main inference that can be drawn from analysing the results of Wright’s (2000) non-parametric variance ratio is that the pricing of a significant number of emerging markets ETFs is not a random walk and, consequently, the weak-form efficiency hypothesis can be rejected for those specific funds. We should recall that a similar conclusion was drawn in the previous section when the results of the conventional Lo and MacKinlay (1988) test were broken down.
Evaluating the weak-form efficiency of emerging markets ETFs. Rompotis, G.
The rank scores-based version of Wright’s test does not convey any new information about the validity of the random walk hypothesis with respect to the ETFs examined. This means that the results are quite similar to the ranks-based type of the test, both as far as the number of statistically significant estimates and the power of the RWH test as we move from the low to the high test periods are concerned. This is also the case for the signs-based version of the test, and so this too leads to the rejection of the random walk hypothesis for a sufficient number of ETFs in the sample.
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may be valuable to investors seeking abnormal profits via trading with ETFs. However, such opportunities are rather fund-specific and, in any case, abnormal profits are not ensured and should be assessed against the costs of monitoring the whole ETF market to spot those funds whose pricing is not a random walk and may offer some chace of above-average market returns. 4.4.3 Chow and Denning (1993) multiple variance ratio test The results of the Chow and Denning (1993) multiple variance ratio test are displayed in Table 9. In particular, the table presents five alternative estimates of the Chow-Denning joint variance ratio test, two of which are based on the framework of the homoskedasticity-consistent and the heteroskedasticity-consistent Lo and MacKinlay (1988) variance ratio test, whereas the other three are based on the ranks-based, rank scores-based and signs-based versions of the Wright (2000) homoskedastic variance ratio test. Reported in the table are the relevant maximum absolute z-statistics and the corresponding p-values of the test statistics.
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Evaluating the weak-form efficiency of emerging markets ETFs. Rompotis, G.
The results in Table 9 verify the inference about the rejection of the random walk hypothesis for a sufficient number of ETFs in the sample drawn by analysing the Lo and MacKinlay (1988) and the Wright (2000) variance ratio tests. For about half of the ETFs the RWH is rejected. More specifically, in 22, 20, 22 and 23 cases the alternative types of the Chow-Denning joint variance ratio test statistics are significant at 5% or better, thus failing to verify the weak-form efficient market hypothesis which assumes that the ETF prices follow a random walk.
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As is the case with the results in the previous two sections, the statistical significance of a significant number of the Chow and Denning (1993) multiple variance ratio tests indicate that investors stand some chance of making a profit based on the historical prices of ETFs covering emerging stock markets, but these opportunities are fund-specific rather than abundant and universal.
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l Table 9. Chow-Denning variance ratio test
This table presents the maximum test |z|-statistics and the respective p-values of the Random Walk Hypothesis (RWH) based on the methodology of the multiple variance ratio test developed by Chow and Denning (1993). Five versions of the test are applied, which are successively based on the Lo-MacKinlay (1988) homoskedastic variance ratio test, the Lo-MacKinlay (1988) heteroskedastic variance ratio test, the Wright (2000) ranks-based variance ratio test, the Wright (2000) rank scores-based variance ratio test and the Wright (2000) signs-based variance ratio test. Lo-MacKinlay (1988)-based test Symbol EZA
Wright (2000)-based test
homoskedastic RWH heteroskedastic RWH homoskedastic RWH
homoskedastic RWH
homoskedastic RWH
Max |z|
P-value
Max |z|
P-value
Max |z|
P-value
Max |z|
P-value
Max |z|
P-value
0.694
0.931
1.761
0.278
0.395
0.956
0.379
0.965
2.645
0.028
ASIA IEMG
2.184
0.111
1.671
0.328
0.329
0.982
0.807
0.729
0.279
0.990
EEMV
5.428
0.000
5.717
0.000
1.083
0.544
2.589
0.026
0.876
0.694
EEM
7.972
0.000
4.644
0.000
2.355
0.055
5.590
0.000
0.403
0.962
EGRW
4.363
0.000
5.512
0.000
1.810
0.178
4.559
0.000
1.434
0.340
EVAL
1.230
0.627
4.648
0.000
5.695
0.000
8.803
0.000
0.635
0.847
EEMS
7.087
0.000
4.868
0.000
4.368
0.000
4.504
0.000
3.065
0.007
EEMA
5.708
0.000
2.330
0.077
9.243
0.000
2.110
0.071
7.707
0.000
BKF
1.802
0.257
5.071
0.000
0.921
0.656
5.762
0.000
3.481
0.001
EMEY
2.042
0.155
3.025
0.010
1.588
0.249
6.019
0.000
3.937
0.000
EMFN
3.042
0.009
5.711
0.000
2.063
0.122
2.974
0.007
4.128
0.000
EMMT
3.799
0.001
3.650
0.001
8.314
0.000
6.566
0.000
1.371
0.362
EMDI
1.312
0.569
0.785
0.896
5.674
0.000
1.373
0.343
3.671
0.002
EMIF
4.577
0.000
2.041
0.155
6.025
0.000
7.035
0.000
2.519
0.041
DVYE
4.858
0.000
3.011
0.010
2.789
0.011
2.090
0.085
2.150
0.070
MCHI
2.901
0.015
3.652
0.001
0.498
0.920
5.084
0.000
3.609
0.000
FCHI
1.421
0.491
1.735
0.292
1.877
0.146
4.600
0.000
4.436
0.001
FXI
4.724
0.000
1.534
0.414
4.700
0.000
2.413
0.054
2.032
0.099 0.000
ECNS
4.788
0.000
0.722
0.921
6.001
0.000
2.466
0.025
4.890
INDA
4.941
0.000
2.342
0.075
5.046
0.000
4.862
0.000
3.737
0.001
INDY
2.095
0.137
1.291
0.584
4.611
0.000
5.478
0.000
4.577
0.000
0.278
3.480
0.002
2.351
0.043
1.678
0.234
2.537
0.034
4.371
0.000
1.791
0.263
1.871
0.140
4.696
0.000
0.528
0.898
EWM
4.340
0.000
4.203
0.000
0.508
0.910
4.250
0.000
0.577
0.867
EPHE
4.987
0.000
1.016
0.773
4.925
0.000
3.931
0.000
0.309
0.982
EWY
2.271
0.089
1.225
0.631
3.641
0.001
0.489
0.927
0.877
0.677
EWT
1.719
0.301
0.965
0.804
3.537
0.001
1.550
0.283
0.884
0.741
THD
0.904
0.838
0.569
0.966
1.772
0.176
0.784
0.756
2.265
0.064
Mean
3.579
0.144
2.860
0.267
3.466
0.190
3.817
0.131
2.478
0.321
EUROPE ESR
5.709
0.000
0.959
0.807
4.564
0.000
1.127
0.534
3.340
0.000
EEME
3.069
0.009
0.521
0.975
5.021
0.000
0.731
0.786
4.324
0.000
EPOL
1.574
0.388
3.330
0.004
4.250
0.000
1.594
0.258
5.447
0.000
ERUS
2.157
0.118
1.316
0.566
3.035
0.007
2.018
0.125
2.516
0.023
TUR
0.966
0.803
0.625
0.952
1.344
0.371
0.881
0.673
2.016
0.109
Mean
2.695
0.264
1.350
0.661
3.643
0.076
1.270
0.475
3.529
0.026
AMERICA EEML
6.604
0.000
5.059
0.000
2.234
0.069
2.063
0.091
3.496
0.004
ILF
6.158
0.000
5.183
0.000
1.049
0.568
8.090
0.000
7.115
0.000
EWZ
3.233
0.005
3.466
0.002
6.566
0.000
3.257
0.006
4.620
0.000
EWZS
2.022
0.162
0.977
0.797
2.081
0.084
4.378
0.001
0.937
0.640
ECH
0.830
0.876
3.316
0.004
6.842
0.000
5.798
0.000
2.988
0.006
EWW
3.263
0.004
4.513
0.000
0.666
0.837
3.035
0.010
1.678
0.212
EPU
1.131
0.697
2.689
0.028
5.699
0.000
0.665
0.827
2.799
0.012
Mean
3.320
0.249
3.600
0.119
3.591
0.223
3.898
0.134
3.376
0.125
Grand Mean
3.351
0.197
2.773
0.290
3.433
0.201
3.427
0.195
2.771
0.243
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1.761
EIDO
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n 5. Conclusion This paper expands the existing literature on the efficient capital markets framework by investigating weak-form efficiency of ETF returns. More specifically, we use historical daily return data for a sample of 40 US-listed ETFs invested in emerging market indices. The data used covers the period from the inception of each ETF till 30th April 2015. In this study, we use a series of parametric and non-parametric tests provided by the finance literature and statistical economics to assess whether all the previously publiclyavailable information is reflected in the prices of ETFs or, alternatively, whether an ETF investor is likely to obtain above-market returns based on the released information. First, we apply various types of serial correlation testing. The estimated autocorrelations provide evidence for the rejection of the efficient market hypothesis. The efficient market hypothesis is likewise rejected for several funds in the sample via the other serial correlation tests used. Therefore, we could say that the serial correlation testing suggests that the efficiency of emerging markets ETFs is fund-specific rather than universal.
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Another non-parametric test used in this study is the Wald-Wolfowitz Runs test. This tests assesses whether the ETF returns are the result of a random process. The findings obtained from this test indicate that the returns of a significant number of funds in the sample are affected by their lagged values. In other words, the lagged returns can convey some information about the trends in concurrent returns for the ETFs in question, and, consequently, the pricing of these ETFs seems to be inefficient in the weak form.
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In the next step, we apply three alternative and supplementary variance ratio tests. The first method, a parametric one, is the well-known Lo and MacKinlay (1988) variance ratio test, the results of which demonstrate that there is a significant number of ETFs whose pricing is not a random walk. This pattern implies that for those particular funds the pricing is not efficient in the weak form. The second test applied is the Wright (2000) non-parametric variance ratio test. This tests provides similar results to the Lo and MacKinlay (1988) test. The last test applied to test the random walk hypothesis is the Chow and Denning (1993) multiple variance ratio test. The results of this test are in line with the results of the previous two tests. Overall, the results of the tests reveal that weak-form efficiency is a fund-specific rather than a universal phenomenon. In particular, the majority of serial correlation tests used demonstrate that the pricing of most ETFs in the sample is efficient. On the other hand, the autocorrelation, runs and variance ratio tests provide evidence of inefficiency for some of the ETFs examined. AESTI
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As a concluding note we would add that along with informational efficiency there may be other forms of efficiency applicable in the case of ETFs. One obvious such example would be the tracking efficiency of ETFs, namely, their ability to perfectly replicate the performance of their underlying benchmarks. Another form of efficiency may concern the tracking ability of ETFs in comparison to the respective ability of their immediate index funds counterparts. A final type of efficiency, which probably relates more to the concept of the current study, concerns the efficient arbitrage execution on behalf of large institutional investors. Efficient arbitrage means that any gaps between the trading and net asset values of ETFs are just temporary and rapidly eliminated. On the contrary, non-efficient arbitrage execution implies that there are opportunities for informed investors to gain sufficient above-average returns in violation of the efficient capital market hypothesis. These issues could be dealt with in future research.
n References n Awad, I. and Daraghma, Z. (2009). Testing the Weak-Form Efficiency of the Palestinian Securities Market, International Research Journal of Finance and Economics, 32, pp. 7-17. n Barnes P. (1986). Thin Trading and Stock Market Efficiency: A Case of the Kuala Lumpur Stock Exchange, Journal of Business Finance and Accounting, 13(4), pp. 609-617. n Blavy, R. (2002). Changing Volatility in Emerging Markets: A Case Study of Two Middle Eastern Stock Exchanges, Revue Entente Cordiale Autumn-Winter, pp. 1-35. n Butler, K.C. and Malaikah, S.J. (1992). Efficiency and Inefficiency in Thinly Traded Stock Markets: Kuwait and Saudi
Business and Economics Research Journal, 7(12), pp. 97-106. n Chordia, T., Roll, R. and Subrahmanyam, A. (2005). Evidence on the Speed of Convergence to Market Efficiency, Journal of Financial Economics, 76, pp. 271-292. n Chow, K.V. and Denning, K.C. (1993). A Simple Multiple Variance Ratio Test, Journal of Econometrics, 58(3), pp. 385-401. n Dickinson, J.P. and Muragu, K. (1994). Market Efficiency in Developing Countries: A Case Study of the Nairobi Stock Exchange, Journal of Business Finance and Accounting, 21(1), pp. 133-150. n El-Erian, M.A. and Kumar, M.S. (1995). Emerging Equity Markets in Middle Eastern Countries, International Monetary Fund Staff Paper, 42, pp. 313-343. n Lagoarde-Segot, T. and Lucey, B. (2008). Efficiency in Emerging Markets-Evidence from the MENA Region, International Financial Markets, Institutions and Money, 18, pp. 94-105.
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n Lo, A.W. and MacKinlay, A.C. (1988). Stock Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification Test, Review of Financial Studies, 1(1), pp. 41-66. n Mobarek, A. and Keasey, K. (2000). Weak Form Efficiency of an Emerging Market: Evidence from Dhaka Stock Market of Bangladesh, Working Paper presented at the ENBS Conference held on Oslo, May 2000. n Omran, M. and Farrar, S. (2006). Tests of Weak Form Efficiency in the Middle East Emerging Markets, Studies in Economics and Finance, 23, pp. 13-26. n Rompotis, G.G. (2011). Testing Weak-Form Efficiency of Exchange Traded Funds Market, The IEB International Journal of Finance, 2, pp. 2-23.1 n Wright, J.H. (2000). Alternative Variance-Ratio Tests Using Ranks and Signs, Journal of Business & Economic
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