Finance Research Letters 13 (2015) 74–80
Contents lists available at ScienceDirect
Finance Research Letters
journal homepage: www.elsevier.com/locate/frl
Are emerging MENA stock markets mean
reverting? A Monte Carlo simulation
Simon Neaime ⇑
Department of Economics, Institute of Financial Economics, American University of Beirut, Beirut, Lebanon
a r t i c l e
i n f o
Article history:
Received 26 February 2015
Accepted 2 March 2015
Available online 9 March 2015
JEL classification:
G15
G14
C22
C15
a b s t r a c t
We provide further empirical evidence on the mean reversion
hypothesis for ten frontier stock markets in the Middle East and
North Africa (MENA) using a battery of panel and time series
econometric tests including Monte Carlo simulations. Standard
unit root and panel unit root tests indicate that stock prices in
the MENA region are not mean reverting which is consistent with
the weak form efficient market hypothesis. However, Monte Carlo
simulations depict mean reversion in the stock markets of Saudi
Arabia, Jordan and Bahrain.
Ó 2015 Elsevier Inc. All rights reserved.
Keywords:
MENA stock markets
Mean reversion
Panel and time series tests
1. Introduction
There has been a considerable research in the finance literature devoted to the predictability of
stock returns. However, many studies [for example, Campbell and Perron (1991), Ferson et al.
(2003)] have cast serious doubt on the predictive power of variables believed to forecast stock returns
in long horizon regressions. Finance practitioners and academics have always questioned the long-run
time-series properties of equity prices while paying attention to whether the motion of stock prices
can be characterized as a random walk or as a mean reverting process. If the dynamics of stock prices
overtime are mean reverting, then there exists a tendency for the price level to return to its trend path
over time and investors may be able to forecast future returns using information on past returns. On
the other hand, a random walk process implies that any shock to stock prices is permanent and that
⇑ Tel.: +961 3 829944; fax: +961 1 744484.
E-mail address: [email protected]
http://dx.doi.org/10.1016/j.frl.2015.03.001
1544-6123/Ó 2015 Elsevier Inc. All rights reserved.
S. Neaime / Finance Research Letters 13 (2015) 74–80
75
there is no tendency for the price level to revisit a specific trend or path over time. In other words,
historical observations become totally irrelevant for the purpose of forecasting future returns. The
random walk property also implies that the volatility of stock prices can grow without a bound in
the long run. Aside from being an interest by themselves, these time-series properties have important
implications for asset pricing.
The evidence of mean reversion was first documented for the United States (US) market. Using US
individual firm-level data, DeBondt and Thaler (1985) first report that past losing stocks over the
previous 3–5 years significantly outperform past winning stocks over a 3–5 years holding period.
Their results indicate that stock prices do not follow a random walk, but contain a strong mean reverting component. Fama and French (1988) also report mean reversion in US equity market using longhorizon regressions, and Poterba and Summers (1988) document evidence of mean reversion using
the variance ratio test. Subsequently, researchers have also tested for mean reversion in equity prices
using international data. For example, Richards (1997) reports evidence of long-term winner–loser
reversals for equity indices for sixteen countries. Balvers et al. (2000) find significant evidence of mean
reversion across eighteen developed equity markets and demonstrate that one can exploit the property of mean reversion to predict equity returns using a parametric contrarian investment strategy.
Other researchers, however, report conflicting results against mean reversion. For example, Lo and
MacKinlay (1988) report some evidence against mean reversion in weekly US data. Kim et al.
(1991) show that mean reversion exists only in pre-war US data, while Richardson and Stock
(1989) and Richardson (1993) argue that the results from Fama and French (1988) and Poterba and
Summers (1988) are not robust because of small-sample biases. Chaudhuri and Wu (2003) test for
mean reversion for emerging market stock prices and find that the null hypothesis of no mean
reversion cannot be rejected in general using the standard unit-root test. They argue, however, that
emerging markets may be subject to structural changes, and if a structural break is explicitly taken
into account in the regression, mean reversion can be detected in 14 out of 17 countries. While the
existing literature on the MENA region has analyzed extensively issues of stock markets interdependence, spillovers, and contagion vulnerability (see Neaime, 2002, 2005, 2012; Guyot et al., 2014;
Lagoarde-Segot and Lucey, 2006 among others), studies on mean reversion and efficient market
hypotheses remain scarce. For instance, Hakim and Neaime (2003) indicate evidence of mean reversion in the more mature stock markets of Egypt, Jordan, Turkey and Morocco but the sample period
was relatively short (at most five years in some countries).
Much of the controversy on the issue of mean reversion arises because the speed of reversion may
be slow and standard econometric tests do not have sufficient power to discriminate a mean reversion
process from a random walk process. In this paper, we test for mean reversion of stock price indices in
ten frontier MENA stock markets using daily data from January 2005 through July 2014. Our results
provide useful information from this relatively large sample, and complement the existing literature
on stock market efficiency in MENA. To overcome the power deficiency problem, we conduct the mean
reversion test in a panel framework. We pool data of ten MENA stock markets and utilize the information on the cross-sectional variations in equity returns to increase the power of the test, so that mean
reversion can be more easily detected. Following Levin, Lin, and Chu’s (LLC, 2002) methodology, we
subtract the cross-sectional averages from the respective series to mitigate the impact of crosssectional dependence.
The remainder of the paper is organized as follows. Section 2 lays down the empirical methodology
and results, and Section 3 concludes the paper.
2. Empirical methodology and results
Our primary interest in this study is to test whether MENA stock prices follow random walk or
mean-reverting processes. Let pit be the natural logarithm of country i’s stock-price index with dividends reinvested at time t, and Rit ¼ pit pit1 be its continuously compounded return. Let T = 3436
observations be the sample size. Consider the following process:
i
pit ¼ ci þ k pit1 þ v it
ð1Þ
76
S. Neaime / Finance Research Letters 13 (2015) 74–80
where ci is a constant parameter and v it is a stationary process which is allowed to be serially correlated, i = 1, 2,. . ., 10; t = 1, 2,. . ., T. If ki = 1, the equity price follows a random walk; while if ki < 1, the
equity price is mean reverting.
The most popular tests for the random walk hypothesis are the Augmented Dickey and Fuller
(1979, 1981, ADF) tests and the Phillips and Perron (1988, PP) tests. For the ADF tests, one subtracts
pit1 from both sides of Eq. (1) to obtain:
i
pit pit1 ¼ Rit ¼ ci þ ðk 1Þpit1 þ v it
ð2Þ
To conduct the tests, it is common to add lagged terms of the dependent variable and obtain the
following equation:
i
i i
i
Rit ¼ ci þ b pit1 þ Rm
j¼1 cj Rtj þ v t
ð3Þ
where bi (ki 1). Eq. (3) tests for the null hypothesis of a random walk against a mean stationary
alternative. The m extra regressors Ritj are added to eliminate possible nuisance-parameter dependencies in the asymptotic distributions of the test statistics caused by serial correlation in the error terms.
For a given sample, if the estimate of ki is not significantly different from unity, then the null hypothesis of a random walk cannot be rejected. On the other hand, if one finds that ki < 1, then the alternative
hypothesis of mean reversion is supported. The PP tests work in a similar way except that the extra
regressors Ritj are not included in the regressions, but the serial correlation of the residuals is
corrected via a non-parametric approach.
One significant drawback of the popular ADF and PP tests is that they have low power against the
alternative of slow-speed mean reversion in small samples (see Campbell and Perron (1991), Cochrane
(1991), and DeJong et al. (1992), among others). Therefore, failure to reject the null hypothesis may
not be interpreted as decisive evidence against mean reversion. Because of this inherent problem,
researchers have advocated pooling data and testing the hypothesis in a panel framework to gain test
power. Our study employs panel unit root tests in order to achieve more robust conclusions on mean
reversion in MENA stock market indices.
Our dataset is retrieved from the Thomson Reuters database and covers ten MENA stock markets
each represented by its major stock market index in brackets: Bahrain (BHSEASI), Egypt (EGX 30),
Jordan (ASE), Morocco (CFG 25), Tunisia (TUNINDEX), Kuwait (KWSEIDX), Saudi Arabia (SASEIDX),
United Arab Emirates (UAE) (DFMGI), Oman (MMS 30) and Qatar (DSM). Our data consist of daily closing price indices up from January 2005 to July 2014. Table 1 reports the descriptive statistics of the
daily returns of the ten stock markets in the sample. Most distributions exhibit some degree of skewness but with significant variability in kurtosis.1 Clearly, most markets exhibit substantial departures
from normality. We formally tested for normality of the return distributions using the Jarque Bera
Statistic (JB).2
Table 1 indicates that the mean returns in all ten MENA stock markets are fairly close to zero. It is
also clear that MENA returns are in general not normal. Table 2 reports the daily cross-correlation in
returns among the ten stock markets. The entire cross correlations are positive and indeed some of
them are as high as 41% (e.g., Oman with Qatar). These relatively high cross-sectional correlations
motivate demeaning the data in our estimation technique. It appears that Oman shows the highest
correlations, with an average of 33.3% with its neighbors. It is followed by Qatar, Kuwait and then
Saudi Arabia. Lower correlations are noted for the non-oil producing MENA countries of Egypt,
Jordan, Morocco and Tunisia.
We start the empirical analysis by plotting the MENA stock market indices and then apply the
Fisher test on our panel daily dataset covering the period 2005–2014 (Fig. 1).
Levin et al. (2002) argued that standard unit root tests have limited power against the alternative
hypothesis with highly persistent deviations from equilibrium. Moreover, panel unit root tests are
PN
PN
3
4
ðRi RÞ
ðRi RÞ
represent the return
The skewness (S) and kurtosis (K) are computed as follows: S ¼ i¼1Nr3
and K ¼ i¼1Nr4
, where Ri ; R
in day i and the average return for the series respectively. For a normal distribution, S and K are respectively 0 and 3.
2
Under
the null ihypothesis of normality, JB is distributed v2 with 2 degrees of freedom. JB is defined as follows:
h
JB ¼ T6 S2 þ 14 ðK 3Þ2 , where S and K represent the Skewness and Kurtosis.
1
77
S. Neaime / Finance Research Letters 13 (2015) 74–80
Table 1
Descriptive statistics of MENA stock market returns, 2005–2014 .
Egypt
Jordan
Morocco
Tunisia
Saudi Arabia
Kuwait
Oman
Qatar
UAE
Bahrain
Mean
Maximum
Minimum
Std. dev.
Skewness
Kurtosis
Jarque–Bera
Probability
0.0003
0.073
0.180
0.015
1.15
15.32
22,491
0.00
0.001
0.077
0.045
0.008
0.14
11.15
9532
0.00
0.0002
0.048
0.055
0.007
0.44
12.37
12,686
0.00
0.0004
0.041
0.050
0.005
0.55
21.85
51,053
0.00
0.0001
0.094
0.103
0.014
1.12
15.94
24,683
0.00
0.00
0.082
0.062
0.007
0.28
18.58
34,787
0.00
0.002
0.080
0.087
0.009
1.21
26.69
81,214
0.00
0.0002
0.094
0.094
0.013
0.42
14.01
17,464
0.00
0.002
0.083
0.087
0.011
0.08
16.73
26,999
0.00
0.0001
0.036
0.049
0.005
0.62
13.21
15,128
0.00
# of obs.
3436
3436
3436
3436
3436
3436
3436
3436
3436
3436
Source: Author’s estimates.
Table 2
Cross correlation of MENA stock market returns, 2005–2014.
Saudi Arabia
Kuwait
Oman
Qatar
UAE
Bahrain
Saudi Arabia
Kuwait
Oman
Qatar
UAE
Bahrain
1
0.12
0.13
0.12
0.18
0.07
1
0.24
0.28
0.29
0.31
1
0.41
0.35
0.24
1
0.40
0.22
1
0.22
1
Jordan
Morocco
Tunisia
Egypt
Jordan
Morocco
Tunisia
Egypt
1
0.23
0.10
0.04
1
0.07
0.09
1
0.03
1
Bahrain
Egypt
Jordan
KSA
Kuwait
Morocco
Oman
Qatar
Tunisia
UAE
20000 40000
0
20000 40000
0
1000 2000 3000 4000
0
1000 2000 3000 4000
0
Index
0
20000 40000
Source: Author’s estimates.
0
1000 2000 3000 4000 0
1000 2000 3000 4000
Time
Graphs by Country
Fig. 1. MENA stock market indices, 2005–2014. Source: Thomson Reuters database.
78
S. Neaime / Finance Research Letters 13 (2015) 74–80
Table 3
Fischer test for panel data in MENA stock market indices, 2005–2014.
MENA indices
Inverse chi-squared (20)
Inverse normal
Inverse logit t (54)
Modified inv. chi-squared
P
Z
L
Pm
Statistics
P-value
23.33
0.73
0.72
0.53
0.27
0.23
0.24
0.30
Source: Author’s estimates.
Notes: Ho: (1) all panels contain unit roots; HA: at least one panel is stationary; (2) the Fischer type unit-root test is based on the
Augmented Dickey–Fuller unit root test; (3) the P statistics requires the number of panels to be finite; (4) other statistics are
suitable for finite or infinite number of panels.
Table 4
Unit root and Monte Carlo simulations in MENA stock market indices, 2005–2014.
KSA
RWADF
RW PP
0.30
0.31
Jordan
0.66
0.58
Bahrain
0.60
0.58
Egypt
0.30
0.30
Kuwait
0.11
0.21
Morocco
0.36
0.38
Oman
0.37
0.38
Qatar
0.84
0.90
Tunisia
1.49
1.51
UAE
0.6
0.6
Mackinnon’s
CVs
5%
1%
1.95
1.95
2.56
2.64
Monte Carlo
CVs
RW ADF
0.3⁄
0.6⁄⁄
0.59⁄⁄
0.30
0.11
0.36
0.37
0.84
1.49
0.6
5%
1%
0.17
0.18
Source: Author’s estimates.
Notes: KSA refers to Kingdom of Saudi Arabia; RW refers to Random Walk. A ⁄ and ⁄⁄ corresponds to significance level at 5% and
1% respectively. Monte Carlo Critical Values (CVs) are based on simulation of 2000 samples generated from a uniform
distribution.
more robust than standard unit root tests applied on each cross-section. Im, Persaran, and Shin (IPS,
2003) type test relaxes the LLC’s restrictive assumption that all panels are stationary under the
alternative hypothesis. However, Fisher’s panel unit root test, also known as the combined p-value
test, is of higher power. Unlike LLC and IPS tests, Fisher’s test does not require a balanced panel data
and is more informative under the alternative i.e., at least one panel is stationary. Choi (2001) proposed three other test statistics besides the Fisher’s inverse chi-square test statistic (P). The first is
the inverse normal test Z, the second is the Logit test L, and the third is the modified inv-chi square
(Pm). Choi (2001) applied different versions of the Fisher and IPS tests to panel data on monthly US
real exchange rates from 1970 to 1996. The Fisher test provides evidence in favor of the Purchasing
Power Parity (PPP) hypothesis, whereas the IPS test did not. Maddala and Wu (1999) provide evidence
that the Fisher test is superior to the IPS test, which in turn is more powerful than the LLC test.
Nevertheless, and using the above robust unit root tests, the null hypothesis of the existence of a unit
root across our 10 MENA stock market indices could not be rejected (see Table 3).
Failure to reject the null hypothesis in a panel framework does not always constitute enough
empirical evidence against mean reversion. Specifically, under panel unit root tests, it may be the case
that while one of the stock markets (panels/clusters) is stationary, the overall test may indicate
otherwise when the whole cluster is taken into consideration. To eliminate this likelihood, we apply
the unit root tests on each individual MENA stock market index (Table 4).
Again, individual country ADF and PP unit root tests could not reject the null hypothesis of a unit
root in favor of mean reversion. Interestingly, however, Saudi Arabia, Jordan and Bahrain’s unit root
test statistics are now not far off from rejecting the null hypothesis. We therefore assert that if the
series index is generated from a uniform distribution, then the critical values generated from
Monte Carlo simulations may save the mean reversion hypothesis in some MENA stock markets.
Indeed, Saudi Arabia, Jordan, and Bahrain’s stock market indices become mean reverting under the
S. Neaime / Finance Research Letters 13 (2015) 74–80
79
assumption that indices are generated from a uniform distribution form which the Monte Carlo CVs
are obtained. The Monte Carlo’s CVs outlined in Table 4 confirm our conjecture. The Saudi and
Bahraini stock markets, for instance, still lack informational and financial transparency and efficiency,
and the Saudi government’s ownership in most listed companies dominates by far the private sector’s
share. Consequently, portfolio managers can now forecast future movements in stock prices based on
past behavior and develop trading strategies to earn abnormal returns in each of Saudi Arabia, Jordan
and Bahrain.
3. Conclusion
An important area of research in the financial economics literature has centered on the issue of
mean reversion in stock prices. Despite the plethora of studies dating back to the 1960s, the extant
literature has not reached a crisp consensus on whether or not stock prices follow a unit root process.
This information is crucial for investors, for if stock prices follow a random walk then shocks to prices
have a permanent effect. Prices will attain a new equilibrium and future returns cannot be predicted
based on historical movements in stock prices. Moreover, this also opens up the possibility that
volatility in stock markets will increase in the long run without bound. On the other hand, if stock
prices are mean reverting then shocks to prices will be transitory. This ensures that investors can forecast future movements in stock prices based on past behavior and develop trading strategies to earn
abnormal returns.
This paper studied mean reversion in ten MENA countries’ stock price indices by applying panel
and time series unit root tests on daily stock market data over the period 2005–2014. We used three
different categories of unit root tests, namely the Fisher test within the context of panel data, ADF and
PP on individual stock markets to corroborate the panel unit root type test, and Monte Carlo
simulations. By assuming that stock market indices follow a uniform distribution through Monte
Carlo Simulations, the null hypothesis is rejected in favor of mean reversion in each Saudi Arabia,
Jordan, and Bahrain, but could not be rejected for the remaining seven indices. Issues of informational
efficiency in the three stock markets remain a problem despite recent efforts aimed at opening up
those stock markets, and at enhancing their informational and operational efficiencies. Trading strategies based upon historical information may, however, prove to earn higher than average returns in the
stock markets of Saudi Arabia, Jordan, and Bahrain.
Acknowledgments
Financial assistance from the Institute of Financial Economics at the American University of Beirut
is gratefully acknowledged (Grant #2014-002). An earlier version of this paper was presented during
the Institute of Financial Economics Seminar Series, January 2015. The author is grateful to useful
comments and suggestions received from the seminar’s participants and to Nasser Badra for superb
research assistance.
References
Balvers, R., Wu, Y., Gilliland, E., 2000. Mean reversion across national stock markets and parametric contrarian investment
strategies. J. Finance 55 (2), 745–772.
Campbell, J.Y., Perron, P., 1991. Pitfalls and Opportunities: What Macroeconomists Should Know about Unit Roots. National
Bureau of Economic Research Macroeconomics Annual. MIT Press, Cambridge.
Chaudhuri, K., Wu, Y., 2003. Random walk versus breaking trend in stock prices: evidence from emerging markets. J. Bank.
Finance 27 (4), 575–592.
Choi, I., 2001. Unit root tests for panel data. J. Int. Money Finance 20, 249–272.
Cochrane, J.H., 1991. A critique of the application of unit root tests. J. Econ. Dyn. Control 15 (2), 275–284.
DeBondt, W., Thaler, R., 1985. Does the stock market overreact? J. Finance 40 (3), 793–805.
DeJong, D.N. et al, 1992. The power problems of unit root tests in time series with autoregressive errors. J. Econometrics 53
(1–3), 323–343.
Dickey, D.A., Fuller, W., 1979. Distribution of the estimators in autoregressive time series with a unit root. J. Am. Stat. Assoc. 74
(366), 427–431.
Dickey, D.A., Fuller, W., 1981. Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica 49 (4),
1057–1082.
80
S. Neaime / Finance Research Letters 13 (2015) 74–80
Fama, E.F., French, K.R., 1988. Permanent and temporary components of stock prices. J. Political Economy 96 (2), 246–273.
Ferson, W.E., Sarkissian, S., Simin, T.T., 2003. Spurious regression in financial economics. J. Finance 58 (4), 1393–1413.
Guyot, A., L.-Segot, T., Neaime, S., 2014. Foreign shocks and international cost of equity destabilization: evidence from the MENA
region. Emerg. Markets Rev. 18, 101–122.
Hakim, S., Neaime, S., 2003. Mean reversion across MENA stock markets: implications for derivative pricing. Int. J. Bus. 8 (3),
345–356.
Im, K.S., Pesaran, M.H., Shin, Y., 2003. Testing for unit roots in heterogeneous panels. J. Econometrics 115, 53–74.
Kim, M.J., Nelson, C.R., Startz, R., 1991. Mean reversion of stock prices: a reappraisal of the empirical evidence. Rev. Econ. Stud.
58 (3), 5151–5280.
Lagoarde-Segot, T., Lucey, B.M., 2006. Financial vulnerability in emerging markets. Evidence from the Middle East and North
Africa. Institute for International Integration Studies Discussion Paper Series, iiisdp114.
Levin, A., Lin, C.-F., Chu, J., 2002. Unit root tests in panel data: asymptotic and finite-sample-sample properties. J. Econometrics
108, 1–24.
Lo, A.W., MacKinlay, A.C., 1988. Stock market prices do not follow random walks: evidence from a simple specification test. Rev.
Financial Stud. 1 (1), 41–66.
Maddala, G.S., Wu, S., 1999. A comparative study of unit root tests with panel data. Oxford Bull. Econ. Stat. 61, 631–652.
Neaime, S., 2002. Liberalization and financial integration of MENA stock markets. In: Regional Trade, Finance and Labor Markets,
Proceedings of the Economic Research Forum (ERF) Ninth Annual Conference, Al Sharjah, UAE, October 26–28.
Neaime, S., 2005. Financial market integration and macroeconomic volatility in the MENA region: an empirical investigation.
Review of Middle East Economics and Finance, vol. 3 (3). Springer, pp. 231–253.
Neaime, S., 2012. The global financial crisis, financial linkages and correlations in returns and volatilities in emerging MENA
stock markets. Emerg. Markets Rev. 13 (2), 268–282.
Phillips, P., Perron, P., 1988. Testing for a unit root in time series regression. Biometrika 75 (2), 335–346.
Poterba, J.M., Summers, L.H., 1988. Mean reversion in stock prices: evidence and implications J. Financial Econ. 22 (1), 27–59.
Richards, A.J., 1997. Winner–loser reversals in national stock market indexes: Can they be explained? J. Finance 52 (5),
2129–2144.
Richardson, M., 1993. Temporary components of stock prices: a skeptic’s view. J. Bus. Econ. Stat. 11 (2), 199–207.
Richardson, M., Stock, J.H., 1989. Drawing inferences from statistics based on multiyear asset returns. J. Financial Econ. 25 (2),
323–348.