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1. Introduction

The Efficient Market Hypothesis (EMH) was introduced by Cootner [1] and Samuelson [2]. Recently, Fama [3] developed three states of efficiency:

  • Strong form efficiency states all information in a market, whether public or private, is contained in the stock price.
  • Semi-strong efficiency means that all public information is calculated into a stock’s current share price.
  • Weak form efficiency implies that all past prices of a stock are reflected in today’s stock price.

When markets are fully efficient, neither technical analysis, fundamental analysis nor insider information enable an investor to obtain returns greater than those that could be obtained by holding random portfolios or individual stocks with the same risk.

Today, many financial economists and investors accept that the presence of the first two scenarios are almost impossible even in high capitalized markets (Campbell et al. [4] and Grossman and Stiglitz [5]); this is why the weak-form version of market efficiency is the most tested criterion in the financial literature. To test the level of market efficiency has been a quite popular topic in financial literature because, if a market is not efficient, this means that future stock prices are somewhat predictable based on past stock price which enable investors to earn excess risk adjusted rates of return.

One of the most interesting works is the one by Markiel and Fama [6], where authors considered that the weak and the semi strong forms of efficiency were strongly supported by their results. After this work, some researchers have tested whether technical analysis is able to provide abnormal returns to the investors (see, for example, Fama and Blume [7], Fama and French [8], Olson [9], Rosillo et al. [10], Shynkevich [11], Metghalchi et al. [12] or Bobo and Dinica [13]).

Other researchers decided to analyze price adjustments after market events (see, for example, Pettit [14], Asquith and Mullins [15] and Michaely, Thaler and Womack [16], Aharony and Swary [17] and Kalay and Loewenstein [18], among others).

Another part of the financial literature has tested the EMH based on the statistical implication of this hypothesis: that stock returns follow a random walk. Interesting contributions are Lo and MacKinlay [19], Lima and Tabak [20], Fifield and Jetty [21], Charles and Darné [22], Al-Ajmi and Kim [23] or Mlambo and Biekpe [24] between others.

Recent contributions have come from some mathematicians and physicians that have focused their attention on Mandelbrot’s critics to the EMH [25]. Mandelbrot proposed that stock prices follow a fractional Brownian motion and not a random walk. One of the implications of this assumption is that stock prices exhibit long memory, which is against the EMH. On this basis, to explore the presence of market memory is an alternative method to test the market efficiency. Relevant contributions are Beben and Orłowski [26], DiMatteo et al. [27], Zunino et al. [28], Cajueiro [29], Kristoufek [30], Ferreira et al. [31], Kristoufek [32] and Dimitrova et al. [33].

This paper goes along a similar line, and it is based on the recent novel approach introduced by Sanchez et al. [34], where the authors analyzed the relationship between market efficiency and a statistical arbitrage technique based on Hurst exponent [35]. We propose to extend the analysis to the 50 largest capitalized companies in 39 so-called advanced and emerging countries to see if a Pairs Trading strategy based on Hurst Exponent, which is a market memory indicator, can obtain a significant profit during different periods.

Our results will show that emerging markets are not efficient while the developed ones are, for most of the period, under study. We will prove that the method used is robust by studying the return of the trades with each pair, considering the estimated Hurst exponent of the pair selection. We will show that, as expected, the lower the Hurst exponent of the pair series, the higher the return of the pair in the Pairs Trading strategy. The paper is structured as follows: Section 2 introduces the Pairs Trading technique based on Hurst exponent. In this section, we present the fundamentals of the Pairs Trading technique as well as the main contributions done by the financial literature. This section also introduces some relevant questions about Hurst Exponent and the Pairs Trading strategy. Section 3 contains the results of the different strategies developed. Finally, Section 4 presents the conclusions.

2. A Pairs Trading Technique Based on Hurst Exponent 2.1. Fundamentals of Pairs Trading The strategy of statistical arbitrage arose in the 1980s. Since its birth, there have been different studies in this area.

The pioneer in investigating this strategy was Gatev et al. [36] who found statistically significant results using US market values during the period 1962–1997. Gatev et al. [37] carried out the study again extending the period until 2002 and obtaining average annualized higher returns of up to 11%. The authors concluded that these higher returns from this strategy are due to a reward for the application of the Law of One Price.

Elliott et al. [38] used a Gaussian Markov chain model to measure dispersion, while Do et al. [39] employed theoretical pricing methods. The cointegration approach was used by Vidyamurthy [40], Burgess [41], and Haque and Haque [42].

Perlin [43] used a Pairs Trading strategy in the Brazilian market, concluding that it works significantly, pointing out that positive superior returns are significant.

Do and Faff ([44,45]) used the distance method introduced by Gatev et al. during the period 2000–2009 and concluded that the Pairs Trading strategy was still profitable, but the profitability decreases over the time. This decline was attributed to a worsening of arbitrage risks and an increase in market efficiency. This is the first contribution where transaction costs are considered, showing that, from 2002 onwards, it generated losses.

Bowen et al. [46] developed their study taking intraday values and concluded that this strategy may be affected by transaction costs and speed of execution. They showed that the highest profitability is achieved at the first and last minute. Similar results are obtained by Liu et al. [47], where authors introduced an intraday trading strategy based on a conditional modeling to model spreads between pairs of stocks. The authors found remarkable returns including transaction costs during specific periods.

Huck [48] introduced a forecasting methodology using a combination of Neural Networks techniques and multi-criteria decision-making methods; Xie and Wu [49] proposed an alternative approach using the copula technique that is able to capture the structure of dependence of co-movement between two assets. Göncü and Akyildirim [50] supported the strategy of statistical arbitrage by assuming that the dispersion of two assets follows an Ornstein–Uhlenbeck process around a long-term equilibrium level.

Avellaneda et al. [51] studied the strategy of statistical arbitrage employing US actions. To do this, they used Principal Component Analysis and sectorial ETFs. In both cases, they detected opposite trading signals, considering the waste the returns of the shares and modeling the investment process.

Krauss [52] examined the literature on pairs trading strategy. It did so by dividing it into five groups; firstly, it studied the distance method; secondly, it used the co-integration method, it used the stochastic approach to identify the optimal portfolio trends, and, finally, it selected other approaches with some limitations in the literature.

Rad et al. [53] studied the performance of Pairs Trading based on the distance, cointegration, and copula methods on the entire US equity market from 1962 to 2014 including trading costs. The authors found that all strategies show positive results and mainly during periods of significant volatility.

Ramos-Requena et al. [35] introduced the Hurst exponent as a selection method in Pairs Trading. The authors found that this new methodology gives better results than the classical methodologies such as the distance or the correlation method. In a recent contribution [54], these authors proposed an alternative method to correlation and cointegration called the HP method.

Finally, all of these contributions are focused on the methodology for pairs selection. In a different line, Ramos-Requena et al. [55] introduced different models to calculate the amount of money that must be allocated to each stock. The authors showed these new alternatives perform better than the usual Equal Weight method.

2.2. Notes on Hurst Exponent

The hypothesis that price variations are well-described by means of a fractional Brownian motion was introduced by Mandelbrot [25]. This process is a long memory generalization of the Brownian motion process with a self-similarity exponent (called Hurst exponent) different to 0.5. Thus, when the process is a Brownian motion, the Hurst exponent (H) is equal to 0.5; when it is persistent, H will be greater than 0.5, and, finally, when it is anti-persistent, then H will be less than 0.5.

The Hurst exponent was introduced by Hurst in 1951 [56] to deal with the problem of reservoir control near the Nile River Dam, but, in recent decades, its application has been widely extended in economics in general and in finance in particular (see López-García and Ramos-Requena [57] for a literature and methodological review). There is also some novel applications, like Trinidad-Segovia et al. [58] and Nikolova et al. [59], where it was used to study volatility clusters.

Ramos-Requena et al. [35] used the Hurst exponent as a management tool for statistical arbitrage strategies based on the concept of reversion to the mean.

Since the first method introduced by Hurst [56], the R/S analysis, different methodologies have been proposed. In this paper, we use the Generalized Hurst exponent (GHE ) introduced by Barabasi and Vicsek [60].

This algorithm is calculated as follows:

Kq(τ)=<|X(t+τ)−X(t)|q><|X(t)|q>

where X is the series (in this paper, X will be the pair series as defined in Section 2.3),τcan vary between 1, andτmax,τmaxis usually chosen as a quarter of the length of the series, and<·>denotes the sample average over the time window.

Therefore, the GHE is defined on the basis of the behavior on the scale of the statistic given in (1), given by the power law:

Kq(τ)∝τqH(q)·

whereH(q)is the Hurst exponent, which characterizes the power law scaling.

The GHE is calculated by linear regression after taking logarithms in Equation (2), for different values ofτ [27,61].

2.3. Methodology Our trading methodology is developed as follows:

Firstly, we normalize the stock prices. If we consider shares A and B, and their share prices arePAandPB, respectively, the pair series is defined as:

log(PA)−b∗log(PB)

where b is a constant, and it is used to normalize the stock prices.

To calculate the value of b, we will use the method described by Ramos-Requena et al. [55], called minimizing distance.

The functionf(b)=∑t xA(t)−bxB(t)will be minimized, looking for the value of b, such thatxAandbxBhave the minimal distance, wherexA(t)=logPA(t)−logPA(0)andxB(t)=logPB(t)−logPB(0).

Now, the pairs will be selected, using the Hurst exponent approach as developed in Section 2.2. Here, we look for pairs such that the Hurst exponent of their pair series is as low as possible.

Finally, the trading strategy will be developed. If s is the pair series, m the average of the series s, andσthe standard deviation ofm−s [62], then:

  • Ifm+2σ>s>m+σ, the pair will be sold ats0. The position will be closed whens<mors>s0+σ.

  • Ifm−2σ<s<m−σ, the pair will be bought ats0. The position will be closed whens>mors<s0−σ.

3. Experimental Results

This section shows the main results obtained by applying the Pairs Trading strategy. This will be done by taking the 50 largest capitalized companies in 39 countries. Three sub-periods (From 1 January 2000 to 31 December 2007, the second period is from 1 January 2007 to 31 December 2014 and the last period is from 1 January 2014 to 10 April 2020) and different portfolios (of 30, 40, and 50 pairs) are also considered. In this study, we considered transaction costs of 0.01%. Table A1 includes the classification of the countries studied between emerging and advanced.

Table A2, Table A3 and Table A4 show the results obtained for the period 2000–2007 for the portfolios composed of 30, 40, and 50 pairs. It can be seen that the highest profits after transaction costs are obtained for emerging countries, especially in South Africa (71.21%, 65.84%, and 65.68%), Japan (32.61%, 28.99%, and 28.87%) and Israel (28.99%, 23.54%, 25.76%). Japan is not an emerging country, but the long-lasting negative bias in its stock market has caused many investors to forget about it. Regarding Israel, the country cannot be considered an emerging country, but its stock market posseses a very low capitalization, even below emerging countries such as South Africa or Indonesia. For the same period, developed markets, especially the United States, show significantly negative returns after transaction costs (−12.87%, −11.61%, and −10.05%) as well as other European countries such as Norway, Russia, and Portugal.

If we look at the Sharpe ratio values, we can see that a value above 1 is obtained for countries such as South Africa (1.98, 1.6 and 1.45), Lebanon (1.11), Namibia (1.1), Israel, and Japan. Against these values, we find Norway with a negative Sharpe ratio (−0.74), and the United States (−0.35, −0.31, and −0.26).

Table A5, Table A6 and Table A7 show results obtained for the period 2007–2014. During this period, we are faced with the subprime crisis, which led to a large drop in the values of the main world stock market indexes as a consequence of the volatility increase. Despite this, it can be seen that the greatest benefits are obtained for emerging countries such as Israel (54.25%, 51.59% and 47.32%) and South Africa (33.80%, 32.73% and 29.88%). In this ranking, we find some European countries with significant benefits, such as Portugal (36.82%, 24.75% and 10.91%), Netherlands (26.26%, 31.27% and 27.94%), and Greece (19.85%, 19.88% and 19.89%). It is not like in the previous period, when it is clear that the developed countries are at a disadvantage in this strategy; for example, the United States is making positive gains in this period (1.30%, 4.13%, and 4.66%). The positive results could be attributed to the high volatility and correlation during financial crisis. These results are congruent with previous finding of Ramos Requena et al. [35] and Lopez García et al. [63].

The Sharpe ratio will indicate that the best investment options will be in countries such as Lebanon (2.53), Israel (1.44, 1.35, and 1.23), and South Africa (1.31, 1.28, and 1.08).

Finally, Table A8, Table A9 and Table A10 present the main results obtained for the period 2014–2020 for the portfolios composed of 30, 40, and 50 pairs. In this period, the highest profitability after transaction costs is for Greece (59.71%, 47.70%, 42.39%). Two other emerging countries (Colombia and South Africa) are among the most profitable to apply the Pairs Trading strategy during this period. France, Spain, or Dubai are the least profitable to invest in, with negative returns during this period.

If we look at the risk, the values of the Sharpe ratio indicate that Lebanon (3.85) and Colombia (2.11, 1.9 and 1.84) are the most appropriate countries. However, according to this ratio, it is not advisable to invest in countries such as Mexico or Dubai with a negative Sharpe ratio value.

One of the main features of Pairs Trading’s strategy is its market neutrality. As presented by Ramos-Requena et al. [35], to comply with this property, investors must consider pairs with a value of the Hurst exponent (H) below 0.5.

Figure 1, Figure 2 and Figure 3 show the relationship between the H value and the average return obtained for each of the periods studied (2000–07, 2007–14, 2014–20), in which all the countries considered in this paper are included. It can be seen that, as the value of H decreases, the average profitability increases for the three periods studied, it being significant that pairs with a value of 0.5 give negative average profitability. Therefore, those countries that select their pairs with an H close to 0 get a higher average return.

It is also important to note that the selection of the pairs based on the Hurst exponent is refreshed each six months with data from the previous year; therefore, the selected pairs are used for the next six months, without refreshing the calculation of the Hurst exponent. Consequently, these results are a kind of robustness check of the pair selection method, since we can see that the pairs with the lowest Hurst exponent in the past are the one for which the mean reversion strategy best work in the future.

Figure 4 gives the relationship between the value of H and the average return for the period 2000–2007, for Brazil, Colombia, Israel, and Saudi Arabia. We can see that, in all cases, if only pairs with small values of H are selected, they would obtain their highest returns. The case of Brazil (a) is significant, as pairs with values between 0.1 and 0.2 would obtain an average return of around 1%. In the case of Brazil (a), Colombia (b), and Saudi Arabia (d), when the value of H of a pair is between 0.4 and 0.5, the strategy get negative returns.

Figure 5 shows the comparison between average returns and the value of H, for the countries Brazil (a), Israel (b), Mexico (c), and South Africa (d) for the period 2007–2014. As in the previous period, as the value of H decreases, the average return increases. It is significant in the case of Brazil and South Africa that, for all the values of H, it obtains a positive profitability.

Finally, Figure 6 shows for Colombia (a), Pakistan (b), Thailand (c), and Hong Kong (d) the average profitability vs. the H value of the pair series for the period 2014–2020. As we have been seeing, as the value of the Hurst exponent (H) decreases, the average return increases. If we observe what happens in the case of Thailand, we would only obtain a positive average return if the value if H is between 0.2 and 0.3.

Therefore, we can also conclude that it is interesting to form the pairs of shares that make up the portfolios with the lowest possible value of the Hurst exponent of the pair series, as this would mean an increase in the profitability of the strategy. 4. Conclusions According with the EMH, arbitrage strategies cannot over perform random portfolios with the same class of risk. In this paper, we look at market efficiency by comparing the performance of an arbitrage technique based on the Hurst exponent in emerging and developed markets.

We found that our statistical arbitrage strategy is consistent in emerging markets and it can obtain a significant profit during the period considered. This is the case of South Africa, Colombia, or Lebanon where the strategy obtains important results. However, in the case of the developed markets, only during high volatility periods, such as after the financial crisis, does the strategy performance properly. After the financial crisis, there are several markets where the Pairs Trading give significant results. The cases of Portugal and Greece are interesting, which are countries seriously affected by the financial crisis in Europe. These results are consistent with the previous findings of Ramos-Requena [35].

These results are also consistent with previous works of DiMatteo et al. [27], Zunino et al. [28], and Kristoufek [30], and they are a clear proof of the degree of inefficiency of emerging markets. Again, we consider that the performance of arbitrage methods in developed markets during specific periods could be considered a proof of the Adaptative Markets hypothesis [64].

On the other hand, we have studied the degree of incidence that the value of the Hurst exponent of the pair series has on the strategy performance, as proposed by Ramos-Requena et al. [35]. We have proved that the main characteristics of the Pairs Trading strategy, the mean reversion, are achieved with a low H. Another interesting result is that, when the value of H is around 0.1 or 0.2, the performance of the strategy is greater.

To conclude, we would like to remark that the selection methodology shows that the strategy is robust because the pairs with the lowest Hurst exponent in the past are the one for which the mean reversion strategy best works in the future. Next, we highlight some possible limitations of this study (we thank the anonymous referees for pointing these out). The main issue is that the inefficiency of some markets may be due to various market frictions. For example, short selling banning on some countries is not taken into consideration for the difficulties to short sell some stocks in some countries. We have considered transaction fees, but we have not considered any cost or revenue incurring by the short selling positions, as well as any revenue for interest on cash not used. We have used daily closing prices to open or close positions. Though we have considered the most capitalized stocks in each country, it is still possible that the scale of the strategy may impact those prices. Therefore, the real implementation of this strategy may suffer some difficulties and the profitability of the strategy may be lower due to market frictions. However, we are mainly interested in the inefficiency of the markets, and it is beyond the scope of this paper (though very interesting) to determine the origin of this inefficiency. .

Figure 1. Comparison between the value of H and the mean return of the portfolios for the period 2000-2007.

Figure 2. Comparison between the value of H and the mean return of the portfolios for the period 2007-2014.

Figure 3. Comparison between the value of H and the mean return of the portfolios for the period 2014-2020.

Figure 4. Comparison between the value of H and the mean return between countries for the period 2000-2007.

Figure 5. Comparison between the value of H and the mean return between countries for the period 2007-2014.

Figure 6. Comparison between the value of H and the mean return between countries for the period 2014-2020.

Author Contributions

Conceptualization, K.B., J.P.R.-R., J.E.T.-S., and M.A.S.-G.; Methodology, K.B., J.P.R.-R., J.E.T.-S., and M.A.S.-G.; Software, K.B., J.P.R.-R., J.E.T.-S., and M.A.S.-G.; Validation, K.B., J.P.R.-R., J.E.T.-S., and M.A.S.-G.; Formal Analysis, K.B., J.P.R.-R., J.E.T.-S., and M.A.S.-G.; Investigation, K.B., J.P.R.-R., J.E.T.-S., and M.A.S.-G.; Resources, K.B., J.P.R.-R., J.E.T.-S., and M.A.S.-G.; Data Curation, K.B., J.P.R.-R., J.E.T.-S., and M.A.S.-G.; Writing-Original Draft Preparation, K.B., J.P.R.-R., J.E.T.-S., and M.A.S.-G.; Writing-Review and Editing, K.B., J.P.R.-R., J.E.T.-S., and M.A.S.-G.; Visualization, K.B., J.P.R.-R., J.E.T.-S., and M.A.S.-G.; Supervision, K.B., J.P.R.-R., J.E.T.-S., and M.A.S.-G.; Project Administration, K.B., J.P.R.-R., J.E.T.-S., and M.A.S.-G.; Funding Acquisition, J.E.T.-S. and M.A.S.-G. All authors have read and agreed to the published version of the manuscript.

Funding

Juan Evangelista Trinidad-Segovia is supported by grant PGC2018-101555-B-I00 (Ministerio Español de Ciencia, Innovación y Universidades and FEDER) and UAL18-FQM-B038-A (UAL/CECEU/FEDER). Miguel Ángel Sánchez-Granero acknowledges the support of grants PGC2018-101555-B-I00 (Ministerio Español de Ciencia, Innovación y Universidades and FEDER) and UAL18-FQM-B038-A (UAL/CECEU/FEDER) and CDTIME.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Publicly available datasets were analyzed in this study. This data can be found here: Investing.com.

Conflicts of Interest

The authors declare no conflict of interest.

Appendix A. Classification of Emerging and Advanced Countries

Table

Table A1.Classification of emerging and advanced countries (following MSCI).

Table A1.Classification of emerging and advanced countries (following MSCI).

Country Classification
ArgentinaEmerging
BahrainEmerging
BelgiumAdvanced
BrazilEmerging
ColombiaEmerging
Czech RepublicEmerging
DenmarkAdvanced
DubaiEmerging
FinlandAdvanced
FranceAdvanced
GreeceEmerging
Hong KongAdvanced
IndiaEmerging
IsraelAdvanced
ItalyAdvanced
JapanAdvanced
JordanEmerging
KuwaitEmerging
LebanonEmerging
MauritiusEmerging
MexicoEmerging
MoroccoEmerging
NamibiaEmerging
NetherlandsAdvanced
NorwayAdvanced
OmanEmerging
PakistanEmerging
PalestineEmerging
PolandEmerging
PortugalAdvanced
RomaniaEmerging
RussiaEmerging
Saudi ArabiaEmerging
South AfricaEmerging
SpainAdvanced
SwedenAdvanced
SwitzerlandAdvanced
ThailandEmerging
United StatesAdvanced

Appendix B. Results

Below is a comparison between the main results obtained.

Appendix B.1. Period 2000-2007

Table

Table A2.Results obtained for the period 2000-2007 (30 Pairs), where N is the number of pairs; AAV Average annualized return; and Profit is the profitability for the full period with transaction costs.

Table A2.Results obtained for the period 2000-2007 (30 Pairs), where N is the number of pairs; AAV Average annualized return; and Profit is the profitability for the full period with transaction costs.

Country N Operations AAV Sharpe Ratio Profits
Argentina3016660.80%0.314.14%
Bahrain306-0.10%-0.53-0.20%
Belgium3036171.50%0.5710.99%
Brazil3031271.10%0.267.06%
Colombia301612-0.80%-0.25-4.34%
Czech Republic301224-0.40%-0.26-3.31%
Denmark302710-0.30%-0.11-2.60%
Dubai30509-0.50%-0.30-2.67%
Finland3025912.00%0.7214.64%
France3032841.50%0.5411.71%
Greece3026440.20%0.050.32%
Hong Kong30630.20%0.781.28%
India3031160.80%0.225.46%
Israel3036283.60%0.9628.99%
Italy3032491.80%0.6813.22%
Japan3029834.00%1.0432.61%
Jordan3019800.50%0.162.14%
Kuwait3024520.20%0.070.58%
Lebanon301710.60%1.112.64%
Mauritius301855-0.50%-0.23-3.92%
Mexico3023621.40%0.487.91%
Morocco308820.60%0.353.91%
Namibia3015903.00%1.0612.07%
Netherlands3033223.20%0.8027.59%
Norway30679-1.10%-0.74-8.63%
Oman30740-0.10%-0.08-0.85%
Pakistan3021161.90%0.5114.19%
Palestine302640.50%0.422.51%
Poland3040.90%1.370.20%
Portugal302772-0.50%-0.16-4.72%
Romania3034-0.30%-0.71-1.21%
Russia302887-0.90%-0.27-7.86%
Saudi Arabia3025300.30%0.121.86%
South Africa3046826.90%1.4565.84%
Spain303040.00%-0.07-0.40%
Sweden3040570.00%-0.01-1.55%
Switzerland3035520.60%0.193.32%
Thailand3027790.80%0.214.77%
United States302736-1.50%-0.26-11.61%

Table

Table A3.Results obtained for the period 2000-2007 (40 Pairs), where N is the number of pairs; AAV Average annualized return; and Profit is the profitability for the full period with transaction costs.

Table A3.Results obtained for the period 2000-2007 (40 Pairs), where N is the number of pairs; AAV Average annualized return; and Profit is the profitability for the full period with transaction costs.

Country N Operations AAV Sharpe Ratio Profits
Argentina4017760.50%0.272.66%
Bahrain406-0.10%-0.53-0.20%
Belgium4047141.40%0.6110.12%
Brazil4039230.40%0.122.32%
Colombia401851-0.50%-0.18-2.76%
Czech Republic401224-0.30%-0.26-2.51%
Denmark403477-0.20%-0.10-2.27%
Dubai40509-0.40%-0.30-2.03%
Finland4033932.10%0.7815.15%
France4041581.70%0.6712.96%
Greece403499-0.20%-0.04-1.87%
Hong Kong40630.10%0.780.98%
India4040840.90%0.256.18%
Israel4046583.00%0.9123.54%
Italy4041241.80%0.7713.47%
Japan4037953.60%1.0229.45%
Jordan402539-0.10%-0.03-1.13%
Kuwait4032040.20%0.091.00%
Lebanon401710.40%1.112.06%
Mauritius402335-0.50%-0.28-4.08%
Mexico4030320.50%0.192.24%
Morocco4010180.40%0.323.15%
Namibia4017062.50%1.1010.17%
Netherlands4044863.40%0.9528.78%
Norway40679-0.80%-0.74-6.47%
Oman408090.10%0.070.20%
Pakistan4026202.00%0.6515.54%
Palestine402640.40%0.421.83%
Poland4040.70%1.370.10%
Portugal403710-0.30%-0.11-3.43%
Romania4034-0.20%-0.71-0.91%
Russia403503-1.00%-0.33-8.58%
Saudi Arabia4033200.00%0.00-0.73%
South Africa4060736.90%1.6065.68%
Spain403040.00%-0.07-0.28%
Sweden405049-0.40%-0.16-4.26%
Switzerland4047340.30%0.121.32%
Thailand4035890.00%0.00-0.90%
United States403461-1.70%-0.35-12.87%

Table

Table A4.Results obtained for the period 2000-2007 (50 Pairs), where N is the number of pairs; AAV Average annualized return; and Profit is the profitability for the full period with transaction costs.

Table A4.Results obtained for the period 2000-2007 (50 Pairs), where N is the number of pairs; AAV Average annualized return; and Profit is the profitability for the full period with transaction costs.

Country N Operations AAV Sharpe Ratio Profits
Argentina5017760.40%0.272.14%
Bahrain506-0.10%-0.53-0.10%
Belgium5057351.40%0.6610.25%
Brazil5047470.90%0.245.65%
Colombia502080-0.50%-0.20-2.72%
Czech Republic501224-0.20%-0.26-2.04%
Denmark504307-0.20%-0.09-2.06%
Dubai50509-0.30%-0.30-1.60%
Finland5042131.90%0.7613.96%
France5049871.80%0.7713.80%
Greece504315-0.40%-0.14-3.66%
Hong Kong50630.10%0.780.79%
India5048700.90%0.286.23%
Israel5057103.30%1.0925.76%
Italy5049731.60%0.7512.21%
Japan5046373.60%1.0828.87%
Jordan5030710.20%0.080.59%
Kuwait5039040.20%0.090.82%
Lebanon501710.30%1.111.57%
Mauritius502782-0.50%-0.34-4.16%
Mexico5035730.50%0.232.59%
Morocco5011440.40%0.282.47%
Namibia5017062.00%1.108.16%
Netherlands5055863.10%0.9626.08%
Norway50679-0.70%-0.74-5.24%
Oman508280.00%0.03-0.07%
Pakistan5029891.90%0.6914.50%
Palestine502640.30%0.421.55%
Poland5040.50%1.370.10%
Portugal504643-0.60%-0.23-5.43%
Romania5034-0.20%-0.71-0.71%
Russia504114-0.60%-0.21-5.52%
Saudi Arabia5040750.00%-0.01-1.12%
South Africa5074587.40%1.9871.21%
Spain503040.00%-0.07-0.26%
Sweden505989-0.50%-0.21-4.90%
Switzerland5058470.50%0.192.63%
Thailand5041790.10%0.050.16%
United States504180-1.30%-0.31-10.04%

Appendix B.2. Period 2007-2014

Table

Table A5.Results obtained for the period 2007-2014 (30 Pairs), where N is the number of pairs; AAV Average annualized return; and Profit is the profitability for the full period with transaction costs.

Table A5.Results obtained for the period 2007-2014 (30 Pairs), where N is the number of pairs; AAV Average annualized return; and Profit is the profitability for the full period with transaction costs.

Country N Operations AAV Sharpe Ratio Profits
Argentina3028770.10%0.03-0.06%
Bahrain301860.90%1.044.94%
Belgium3040762.90%0.9223.64%
Brazil3037562.00%0.5314.55%
Colombia3038441.00%0.416.62%
Czech Republic305061.30%0.529.93%
Denmark3030241.70%0.4012.69%
Dubai302836-2.00%-0.56-15.25%
Finland3041032.00%0.4815.03%
France3034701.50%0.4810.94%
Greece3037392.50%0.4819.85%
Hong Kong3014251.70%0.555.72%
India3040513.20%0.5125.75%
Israel3037356.10%1.2354.25%
Italy3038171.80%0.5213.83%
Japan3030103.70%0.8430.30%
Jordan3023590.60%0.153.41%
Kuwait302862-0.10%-0.03-1.85%
Lebanon303180.70%2.535.39%
Mauritius3011530.40%0.282.72%
Mexico3025351.00%0.347.35%
Morocco3026350.60%0.233.82%
Namibia3025371.60%0.5011.95%
Netherlands3034153.10%0.7126.26%
Norway302091-0.90%-0.41-7.50%
Oman301816-1.30%-0.57-10.11%
Pakistan3028050.80%0.165.06%
Palestine30492-0.60%-0.69-4.56%
Poland3018861.80%0.8813.37%
Portugal3038364.20%0.7336.82%
Romania307232.50%0.8319.76%
Russia3030810.70%0.154.27%
Saudi Arabia3035080.50%0.142.33%
South Africa3045573.60%1.0829.88%
Spain3020870.20%0.070.80%
Sweden3040722.50%0.5519.14%
Switzerland3040332.90%0.7922.86%
Thailand303217-1.10%-0.27-8.67%
United States3029960.30%0.111.30%

Table

Table A6.Results obtained for the period 2007-2014 (40 Pairs), where N is the number of pairs; AAV Average annualized return; and Profit is the profitability for the full period with transaction costs.

Table A6.Results obtained for the period 2007-2014 (40 Pairs), where N is the number of pairs; AAV Average annualized return; and Profit is the profitability for the full period with transaction costs.

Country N Operations AAV Sharpe Ratio Profits
Argentina4036600.20%0.050.48%
Bahrain401860.70%1.043.65%
Belgium4052432.50%0.8720.29%
Brazil4047962.20%0.6716.60%
Colombia4048460.70%0.324.19%
Czech Republic405061.00%0.527.37%
Denmark4040080.90%0.236.20%
Dubai403524-1.40%-0.43-11.28%
Finland4053081.80%0.4613.47%
France4045511.20%0.428.56%
Greece4048732.50%0.5319.88%
Hong Kong4018311.00%0.353.34%
India4052873.60%0.6329.78%
Israel4048585.90%1.3551.59%
Italy4048412.30%0.7718.49%
Japan4039193.00%0.7223.12%
Jordan4030230.70%0.184.14%
Kuwait403839-0.10%-0.02-1.36%
Lebanon403180.50%2.534.02%
Mauritius4013170.30%0.201.67%
Mexico4032830.70%0.254.48%
Morocco4033070.60%0.273.97%
Namibia4030041.50%0.5710.95%
Netherlands4045173.60%0.9131.27%
Norway402536-0.80%-0.40-6.43%
Oman402395-1.10%-0.52-8.50%
Pakistan4036071.40%0.319.70%
Palestine40492-0.50%-0.69-3.42%
Poland4024351.60%0.8211.59%
Portugal4049813.00%0.6224.75%
Romania408892.10%0.9016.88%
Russia4039961.20%0.308.70%
Saudi Arabia4045940.80%0.274.85%
South Africa4060044.00%1.2833.80%
Spain4026780.50%0.203.33%
Sweden4051262.00%0.4915.12%
Switzerland4051751.70%0.5512.71%
Thailand404267-0.90%-0.27-7.87%
United States4038820.70%0.284.13%

Table

Table A7.Results obtained for the period 2007-2014 (50 Pairs), where N is the number of pairs; AAV Average annualized return; and Profit is the profitability for the full period with transaction costs.

Table A7.Results obtained for the period 2007-2014 (50 Pairs), where N is the number of pairs; AAV Average annualized return; and Profit is the profitability for the full period with transaction costs.

Country N Operations AAV Sharpe Ratio Profits
Argentina504279-0.20%-0.06-2.16%
Bahrain501860.50%1.042.96%
Belgium5064963.10%1.1425.60%
Brazil5058542.40%0.7918.43%
Colombia5057620.70%0.344.05%
Czech Republic505060.80%0.525.90%
Denmark5048840.90%0.256.32%
Dubai504144-1.20%-0.40-10.03%
Finland5064711.80%0.5113.51%
France5055271.30%0.499.89%
Greece5060492.50%0.5719.89%
Hong Kong5022181.10%0.413.76%
India5065293.20%0.6025.79%
Israel5059175.50%1.4447.32%
Italy5059872.80%0.9923.10%
Japan5048132.50%0.6418.94%
Jordan5037030.60%0.224.06%
Kuwait5046980.60%0.234.16%
Lebanon503180.40%2.533.14%
Mauritius5014930.20%0.141.10%
Mexico5039210.60%0.233.72%
Morocco5039650.40%0.202.31%
Namibia5033951.30%0.599.62%
Netherlands5057983.30%0.9227.94%
Norway502941-0.80%-0.48-6.59%
Oman502805-1.00%-0.49-7.46%
Pakistan5043951.40%0.379.92%
Palestine50492-0.40%-0.69-2.80%
Poland5029351.50%0.8410.91%
Portugal5061083.00%0.7024.88%
Romania5010451.80%0.8814.09%
Russia5049981.20%0.338.40%
Saudi Arabia5056110.90%0.346.08%
South Africa5073463.90%1.3132.73%
Spain5031000.30%0.151.98%
Sweden5062632.30%0.6217.45%
Switzerland5062942.00%0.7315.54%
Thailand505249-1.40%-0.45-11.05%
United States5047230.70%0.324.66%

Appendix B.3. Period 2014-2020

Table

Table A8.Results obtained for the period 2014-2020 (30 Pairs), where N is the number of pairs; AAV Average annualized return; and Profit is the profitability for the full period with transaction costs.

Table A8.Results obtained for the period 2014-2020 (30 Pairs), where N is the number of pairs; AAV Average annualized return; and Profit is the profitability for the full period with transaction costs.

Country N Operations AAV Sharpe Ratio Profits
Argentina3025140.00%0.00-0.94%
Bahrain3050.00%0.160.00%
Belgium3030483.90%1.8224.98%
Brazil3023752.40%0.7013.61%
Colombia3035435.00%2.1131.02%
Czech Republic301009-0.70%-0.48-4.44%
Denmark3020891.30%0.567.10%
Dubai302307-1.30%-0.35-7.87%
Finland3030010.90%0.304.30%
France302411-0.60%-0.31-4.20%
Greece3029788.60%1.3559.71%
Hong Kong3019972.20%0.5711.43%
India3027602.50%0.4714.38%
Israel3025901.40%0.717.64%
Italy3026871.40%0.557.60%
Japan3021081.90%0.6010.60%
Jordan301682-0.30%-0.17-2.46%
Kuwait3028342.70%0.8515.36%
Lebanon301821.30%3.857.04%
Mauritius302330.00%0.080.12%
Mexico301808-1.40%-0.67-8.90%
Morocco3016060.20%0.120.76%
Namibia3022602.00%0.7111.55%
Netherlands3024671.70%0.599.58%
Norway3023810.80%0.294.41%
Oman301005-0.20%-0.12-1.44%
Pakistan3021491.00%0.255.28%
Palestine303580.00%0.04-0.02%
Poland3028042.00%0.6511.47%
Portugal3022430.00%0.01-0.55%
Romania3020360.50%0.152.22%
Russia3020950.00%-0.01-0.90%
Saudi Arabia3027802.60%0.8214.77%
South Africa3030363.90%1.2723.79%
Spain302321-0.80%-0.28-5.37%
Sweden3026532.60%1.0515.82%
Switzerland3022590.80%0.324.35%
Thailand3018690.00%0.01-0.52%
United States3020900.80%0.414.20%

Table

Table A9.Results obtained for the period 2014-2020 (40 Pairs), where N is the number of pairs; AAV Average annualized return; and Profit is the profitability for the full period with transaction costs.

Table A9.Results obtained for the period 2014-2020 (40 Pairs), where N is the number of pairs; AAV Average annualized return; and Profit is the profitability for the full period with transaction costs.

Country N Operations AAV Sharpe Ratio Profits
Argentina403177-0.40%-0.10-3.19%
Bahrain4050.00%0.160.00%
Belgium4038603.70%1.8823.03%
Brazil4030621.70%0.569.63%
Colombia4045054.00%1.8424.47%
Czech Republic401087-0.60%-0.48-3.47%
Denmark4026341.00%0.495.64%
Dubai403107-1.60%-0.48-9.68%
Finland4037740.30%0.110.76%
France403017-0.10%-0.04-1.15%
Greece4040087.10%1.2847.70%
Hong Kong4025931.70%0.468.65%
India4034362.40%0.5113.84%
Israel4032761.30%0.716.88%
Italy4034411.20%0.516.44%
Japan4026772.30%0.8313.63%
Jordan402276-0.20%-0.14-1.97%
Kuwait4037533.20%1.1418.86%
Lebanon401820.90%3.855.15%
Mauritius402330.00%0.080.04%
Mexico402230-1.10%-0.60-7.16%
Morocco402078-0.10%-0.06-1.12%
Namibia4028472.00%0.7411.39%
Netherlands4032451.20%0.516.79%
Norway4030310.40%0.161.74%
Oman401088-0.10%-0.05-0.67%
Pakistan4028510.90%0.274.89%
Palestine403580.00%0.040.01%
Poland4036691.50%0.517.78%
Portugal4029610.30%0.091.06%
Romania4026640.10%0.03-0.27%
Russia4027470.30%0.091.11%
Saudi Arabia4035712.40%0.8413.51%
South Africa4038183.40%1.1820.05%
Spain402901-0.70%-0.30-5.03%
Sweden4032392.10%0.9812.69%
Switzerland4028781.10%0.486.08%
Thailand402525-0.70%-0.32-4.53%
United States4026430.90%0.514.64%

Table

Table A10.Results obtained for the period 2014-2020 (50 Pairs), where N is the number of pairs; AAV Average annualized return; and Profit is the profitability for the full period with transaction costs.

Table A10.Results obtained for the period 2014-2020 (50 Pairs), where N is the number of pairs; AAV Average annualized return; and Profit is the profitability for the full period with transaction costs.

Country N Operations AAV Sharpe Ratio Profits
Argentina503799-1.40%-0.38-8.56%
Bahrain5050.00%0.160.00%
Belgium5046873.30%1.8320.36%
Brazil5038171.20%0.436.64%
Colombia5053543.80%1.9022.83%
Czech Republic501112-0.40%-0.47-2.82%
Denmark5031281.00%0.485.27%
Dubai503821-1.70%-0.57-10.36%
Finland5044850.40%0.151.40%
France503692-0.20%-0.12-1.84%
Greece5050266.50%1.2842.39%
Hong Kong5032211.90%0.489.66%
India5040852.00%0.4811.38%
Israel5039621.50%0.898.21%
Italy5042960.90%0.404.64%
Japan5032242.30%0.8513.46%
Jordan5027570.20%0.120.55%
Kuwait5045973.30%1.2919.38%
Lebanon501820.70%3.854.16%
Mauritius502330.00%0.080.05%
Mexico502731-0.90%-0.54-6.05%
Morocco5024960.20%0.150.90%
Namibia5033861.70%0.729.72%
Netherlands5038711.40%0.657.73%
Norway5036400.50%0.232.47%
Oman5011720.00%0.02-0.13%
Pakistan5035831.80%0.559.88%
Palestine503580.00%0.040.03%
Poland5043551.30%0.506.83%
Portugal5036360.30%0.080.87%
Romania503263-0.10%-0.04-1.15%
Russia503452-0.10%-0.04-1.29%
Saudi Arabia5043581.90%0.7510.83%
South Africa5045872.50%0.9014.38%
Spain503468-0.50%-0.23-3.59%
Sweden5039351.80%0.8510.51%
Switzerland5035111.00%0.505.60%
Thailand503215-0.40%-0.22-3.14%
United States5031020.60%0.382.98%

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Karen Balladares

1,

José Pedro Ramos-Requena

2,

Juan Evangelista Trinidad-Segovia

2,* and

Miguel Angel Sánchez-Granero

3

1Facultad de Ciencias Administrativas, Universidad de Guayaquil, 090514 Guayaquil, Ecuador

2Departamento de Economía y Empresa, Universidad de Almería, Carretera Sacramento s/n, La Cañada de San Urbano, 04120 Almería, Spain

3Departamento de Matemáticas, Universidad de Almería, Carretera Sacramento s/n, La Cañada de San Urbano, 04120 Almería, Spain

*Author to whom correspondence should be addressed.

Word count: 6380

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© 2021. This work is licensed under http://creativecommons.org/licenses/by/3.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.

Abstract

In this paper, we use a statistical arbitrage method in different developed and emerging countries to show that the profitability of the strategy is based on the degree of market efficiency. We will show that our strategy is more profitable in emerging ones and in periods with greater uncertainty. Our method consists of a Pairs Trading strategy based on the concept of mean reversion by selecting pair series that have the lower Hurst exponent. We also show that the pair selection with the lowest Hurst exponent has sense, and the lower the Hurst exponent of the pair series, the better the profitability that is obtained. The sample is composed by the 50 largest capitalized companies of 39 countries, and the performance of the strategy is analyzed during the period from 1 January 2000 to 10 April 2020. For a deeper analysis, this period is divided into three different subperiods and different portfolios are also considered.

Details

Title
Statistical Arbitrage in Emerging Markets: A Global Test of Efficiency
First page
179
Publication year
2021
Publication date
2021
Publisher
MDPI AG
e-ISSN
22277390
Source type
Scholarly Journal
Language of publication
English
DOI
https://doi.org/10.3390/math9020179
ProQuest document ID
2479917128
Copyright
© 2021. This work is licensed under http://creativecommons.org/licenses/by/3.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.