Description
A stock market or equity market is a public entity (a loose network of economic transactions, not a physical facility or discrete entity) for the trading of company stock (shares) and derivatives at an agreed price; these are securities listed on a stock exchange as well as those only traded privately.
Case Study of Weak-Form Efficiency: Saudi Stock
Market
Abstract
The purpose of the paper is to test the weak-form market efficiency in Saudi Arabia's stock market, Tadawul which is
expected to follow a random walk. All share index and sectoral indices for daily closing prices in Tadawul between
October 15, 2006 and November 15, 2012 are collected. Unit root Dickey-Fuller test, Pearson Correlation test, Durbin-
Watson test and Wald-Wolfowitz runs-test are used as basic stochastic tests for a non- stationarity of the daily prices
for all the listed companies in the market, both overall and sector-wise. The four tests confirmed the weak-form market
efficiency in the Saudi stock market for All share prices and 11 individual sectors. The findings are necessary for all
investors in Saudi Arabia and the member states of the GulfCooperation Council (GCC). Listed firms could also
benefit from the findings by seeing the true picture of their stock price. The finding is used as a basis for testing the
market efficiency in the semi-strong form, which has not yet been tested by any researcher. Accordingly, investors in
the Saudi market are not expected to generate abnormal returns simply by depending on past information and technical
analysis. This paper will add value to the literature of market efficiency in the emerging market and the GCC since it
covers all the listed companies, tests sector-wise, and covers an extended period of time. To confirm the weak-form
efficiency in Saudi, the study uses four tests and covers a long period of time during and after the financial crisis.
Keywords: Weak-form market efficiency, random walk hypothesis, unit root test, auto correlation, run test,
Kingdom of Saudi Arabia.
1. Introduction
Many studies have tested market efficiency in the developed markets. In the last two decades, studies in the emerging
markets started to follow suit. Most of these studies have tried to answer a simple question: Are share prices moving
randomly? However, empirical testing came up with mixed findings and different conclusions in both developed and
emerging markets. One view in support of the random walk hypothesis (RWH) is that stock returns are following a
random walk process and thus, it is not possible to predict their future movements based on past information. The
second view, in contrast, states that there is indeed a trend path in the stock returns and that it is possible to predict the
future price movements based on the history of prices. The dissimilar results could depend on: (1) the tests that are
used; (2) the markets under examination; (3) the type of sector and industry examined, and (4) the time-frame for the
study. The RWH which has been tested heavily on the weak- form efficiency has obviously failed to prove the
performance of equity markets worldwide. However, developed markets have shown a higher degree of informational
efficiency than emerging markets.
The market is said to be efficient when prices of securities reflect all relevant information (Fama, 1991). Investors are
freely obtaining new information which makes them, due to competition, immediately discount this information into the
price. In other words, there is no chance for an arbitrage opportunity that can be used to make excess abnormal profits
(Fama 1965). Efficient market hypothesis (EMH) was earlier developed by Fama (1970) and Fama and French (1989)
and later revised to identify three levels of efficiency, which differ in terms of the type of information set reflected in
the market. The weak form efficiency, which is the first level of EMH, assumes the absence of predictability of time-
series of security prices. This leads to the random walk theory which claims that the prices are independent of each
other and past movements or trends cannot be used to predict future movements. Therefore, serial independence (i.e.
no autocorrelation) for the set of share price changes is a fundamental requirement for the market to follow a random
walk. As Fama (1970) stated that all types of "new" news, by definition, have to be "new and unpredictable", resulting
in the unpredictability of future stock prices. Both Samuelson (1965) and Fama (1970) indicated that the EMH
supposes that the share price adjusts instantaneously to new information. Hence, current prices should fully discount
and reflect all available information and ought to follow a random walk process, meaning that the successive returns
are independently and identically distributed. The second level is the semi-strong form efficiency where prices reflect
all past prices and the public information. The third level is the strong form efficiency where the share price reflects all
past, public and insider information.
35
EMH deals with the question of whether stock prices fully reflect the entire historical price. The simplest random
walk model, as shown in the following equation, states that the actual price equals the previous price
plus the realization of a random variable:
P
it
=P
it-1
E(R)
it
c
it
where:
P
i
t = Current stock price for firm i
P
i
t-1 = Last closing price to current time
t-1
E(R)
i
t
= Expected return (price change) at time t, also called drift
c
i
t = Random Error
Furthermore, according to the above equation, the expected return on a security is based on the available
information set at time t (|
t
), as argued by (Solnik, 1996): E (R
it
| |
t
). The paper investigates informational
efficiency in the Saudi stock market for the period January 1, 2007 until October 30, 2012 at the general market
and sector levels. Its main purpose is to test the weak-form market efficiency through the random walk model.
Accordingly, if the question is answered, it can be decided whether the usage of technical analysis to forecast and
predict future price changes is of material benefit. The rationale for this study is that little research has targeted
countries from the Middle East and the stock exchanges in the GCC.
1
The knowledge of how efficient a stock market is
and how it discounts and reflects the set of information into the market prices of the securities is of central importance
to users of the capital markets. Taking into account the economic growth, trade liberalization, introduction of
electronic trading, globalization and emergence of global markets; once the behavior of the prices is determined, the
easier it is to understand the market and the economy. Another contribution of this study to the literature is the
sectoral analysis of the Saudi Arabia, which has been limited to only a few papers.
2. The Saudi Arabia Stock Exchange (TADAWUL)
The Saudi Stock Exchange (Tadawul) is the only stock exchange in the Kingdom of Saudi Arabia. Its trading hours are
11:00AM to 3:30PM, Saturday to Wednesday and it is supervised by the Capital Market Authority (CMA). Saudi joint
stock companies had their beginnings in the mid-1930s, when the Arab Automobile was established as the country's
first joint stock company. The Saudi Stock Exchange emerged in the late 1970s where the number of joint stock
companies was increasing as a result of nationalization of foreign companies, including banks. By 1975 there were
about 14 public companies. The rapid economic expansion, beside the nationalization of part of the foreign banks
capital in the 1970s led to the establishment of a number of large corporations and joint stock banks. The market
remained informal until the early 1980s when the Saudi government created a national stock market. In 1984, a
Ministerial Committee composed of the Ministry of Finance and National Economy, Ministry of Commerce and Saudi
Arabian Monetary Agency (SAMA) was formed to regulate and develop the market. SAMA was the government
body charged with regulating and monitoring market activities until the CMA was established in July 2003 under the
Capital Market Law (CML) by Royal Decree No. (M/30). The CMA is the sole regulator and supervisor of the capital
market, it issues the required rules and regulations to protect investors and ensure fairness and efficiency in the market.
The Council of Ministers approved on March 19, 2007, the formation of the Saudi Stock Exchange (Tadawul)
Company. This was in accordance with Article 20 of the Capital Market Law establishing Tadawul as a joint stock
company. Tadawul is organized into 15 sectors, each consisting of companies that have a common business line and
operate in the same industry. The market capitalization on October 4, 2011 was $315,521 million. In addition, Tadawul
All Share Index consists of all listed companies, as shown in table 1.
3. Previous Studies
Bachelier (1900) was the first to point out that security prices and prices of other speculative commodities follow a
random walk; this was later confirmed by Pearson (1905) and Working (1934). Kendall (1953) was the first researcher
to use the term "random walk" in the finance literature. Until the early 1950s, it was accepted that technical analysis,
could be used to examine the behavior of past prices and beat the market. Malkiel (1992) McQueen et al (1996), Fama
and French (1989), Al-Loughani and Chappell (1997), Seiler and Rom (1997), and Abrosimova et al (2002) supported
the assumption that price changes are random and past prices were not useful in predicting future price.
Alexander (1964) and Fama and Blume (1966) used a filter rule, which gives a rule for buying and selling stocks
1
The Gulf Cooperation Council countries are Bahrain, Kuwait, Oman, Qatar, Saudi Arabia and the Uunited
Arab Emerats.
36
depending on past price movements but found that such rule could not generate trading profits. Jensen (1968)
performed risk-adjusted measures and found that mutual funds do not outperform the market from 1945-1964. Conrad
and Kaul (1988) and Lo and MacKinlay (1988) examined the weekly returns of the NYSE stock and both studies
found that a positive serial correlation over short horizons, but one that is negligible and insignificant. Lo and
MacKinlay (1988) provide evidence that random walk model was strongly rejected in NYSE-AMEX between 1962
and1985. However, Huber (1995) studied the Vienna Stock Market and rejected the RWH. Kvedaras and Basdevant
(2004) concluded that the Estonian, Latvian and Lithuanian Stock Exchange Market, with some turbulence, approaching
the weak form of efficiency.
Keim and Stambaugh (1986) found significant predictability in stock prices using forecasts based on certain
predetermined variables. Fama and French (1988) show that long holding-period returns are significantly negatively
serially correlated, implying that 25-40% of the variation of longer-horizon returns is predictable from past returns.
Balaban (1995) rejected the random walk on Istanbul Securities Exchange. Kompa and Matuszewska-Janica (2009)
examined the Warsaw Stock Exchange from 2000 to 2006 for the log daily returns. The weak-form efficiency was
found in the main market indexes as well as companies in the following sectors: telecommunication, gas and oil, and
metals. Medium-size company index was found to achieve abnormal returns. Reviewing the Arab markets and the GCC,
most of the studies used run test and serial correlation to examine the RWH. Gandhi et al (1980) used monthly data for
the period 1975-1978 for the Kuwait Stock Exchange and found that RWH for the All Share and Industrial indices was
rejected. Testing United Arab Emirates (UAE) market, Ebid (1990) found that it is considered to be weak-form
efficient. Butler and Malaikah (1992) analyzed the behavior of the Kuwait and Saudi Arabia stock markets between
1985 and 1989 and they provided evidence of weak-form inefficiency in both of the markets. However, they could not
conclude if the Saudi market is informationally inefficient. Civelek (1991) and El-Erian and Kumar (1995) studied the
Amman Financial Market and both got relatively frequent positive dependence. Al-Loughani (1995) used the weekly
data for the Kuwait Stock Exchange for 1986-1990 and found that autocorrelation and runs test were consistent with
the RWH. Khababa (1998) concluded that Saudi market is not weak-form efficient. Dahel and Laabas (1999) examined
the behavior of the daily stock prices over the period 1994-1998 in the Gulf markets: Bahrain, Kuwait, Saudi Arabia and
Oman. They concluded that Kuwait Stock Market is the only efficient market and is strongly in support of the concepts
of the RWH. Abraham et al (2002) used weekly data for All Share indices of Saudi Arabia, Kuwait and Bahrain for
1992-1998. Variance ratio tests rejected the RWH for all three stock markets. By applying the Beveridge and Nelson
(1981) decomposition of index returns and after removing the effects of infrequent trading, a RWH was not rejected for
the Saudi and Bahraini markets. Taking into considerations market imperfections such as thinly and infrequent trading,
Hassan et al (2003) examined Kuwait Stock Exchange over the period 1995-2000 by using EGARCH and GARCH-M
and found that the market is weak-form inefficient.
Rao and Shankaraiah (2003) studied the weak form efficiency of the Bahrain Stock Market over the period 1996-2000
and confirmed the weak-form efficiency. Smith (2007) studied the RWH in the Middle Eastern stock markets and found
that Israeli, Jordanian, and Lebanese markets were weak-form efficient while the Kuwait and Oman markets were not.
For the Tel-Aviv, Amman and Beirut stock market and non-Kuwaiti companies that traded on the Kuwait stock
market, stock price indices follow a random walk. Moustafa (2004) examined the behavior of the prices in the UAE
stock market and concluded that most firms are weak-form efficient and prices follow a random walk. Babaker (2004)
investigated the market efficiency of all Arab Stock Exchanges and the results showed that emerging markets are less
efficient than developed markets. In addition, at different time periods, stock markets vary in efficiency. Asiri (2000,
2004, 2007) examined Kuwait's stock market for the daily stock prices for 1999-2001, 1991-2002 and 2000-2002.
Using unit root test, ARIMA (AR1); exponential smoothing and autocorrelation tests confirmed the weak-form
efficiency. Sector analysis also gives robust support to the findings. The results confirmed the randomness for all share
prices and each sector. Studying all companies listed on the Bahrain Stock Exchange, Asiri (2008) confirmed that all
daily prices and each sector follow a random walk with no drift and trend and supporting the weak-form market
efficiency. Using daily sectoral indices between 2000 and 2005, Squalli (2006) explored the efficiency in the different
sectors of the Dubai Financial Market (DFM) and Abu Dhabi Securities Market (ADSM). Variance ratio tests rejected
the randomness in all of the sectors in UAE except in the banking sector in DFM. In comparison, using runs test, the
insurance sector of the ADSM gave evidence of weak-form efficiency in the UAE. Al-Khazali et al (2007) re-
examined the empirical validity of the weak-form in emerging markets of the MENA region: Bahrain, Egypt, Jordan,
Kuwait, Morocco, Oman, Saudi Arabia and Tunisia. In their study, they utilized the Lo and MacKinlay (1988, 1989),
Wright's (2000) rank and sign VR and the runs tests. Once the returns from the indices were adjusted to reconcile
distortions from thinly and infrequently traded stocks, the study found random walk and weak-form efficiency in all of
the markets examined.
37
Using multiple variance tests on different sectors, Benjelloun and Squalli (2008) tested the markets of Jordan, Qatar,
Saudi Arabia and the UAE and found that there is no consistency in their results among the different sectors and the
different markets. Randomness was rejected in Jordan, Abu Dhabi and Dubai when using the general index. However,
if the sectoral indexes were used, they failed to reject the randomness in some sectors. Using the runs test, randomness
was rejected in all of the stock market if general indexes were used, with the exception to Dubai. However, using the
sectoral indexes, they have failed to reject the weak-form efficiency in some sectors.
Elango and Hussein (2008) examined the market efficiency across seven stock markets in the GCC countries
2
for the
daily indices over the period 2001-2006. Kolmogorov-Smirnov test shows that all of the seven markets reject the RWH
and using the runs test for randomness, they found that the successive price changes were not random. Marashdeh and
Shrestha (2008) investigated if the stock price index in the UAE follows random by using unit root, Augmented Dickey
Fuller and Philip-Perron tests along with Perron's Innovational Outliner and Additive Outliner models. The results show
that the data has a unit root and follows a random walk. Awad and Daraghma (2009) examined the efficiency of the
Palestine Security Exchange for 35 stocks listed in the market using the daily indices and concluded that daily returns
are inefficient in the weak-form. AlKhazali (2011) has conducted a study examining the market efficiency in the Gulf
countries and concluded that the RWH is not rejected in all the GCC markets. Al-Jafari (2011) and Al-Jafari and
Altaee (2011) found that both Bahrain and Kuwait stock markets are informationally inefficient at the weak-form
level. Salameh et al (2011) explored the weak form market efficiency for Saudi Arabia, Amman, Kuwait, Dubai, Abu
Dhabi, Egypt, Morocco, Tunisia, Qatar, Oman, Bahrain and Palestine markets. In general, Saudi Market was the only
market that behaved randomly under both the serial autocorrelation tests and the runs test. However, under both the
Augmented Dickey-Fuller and Phillips-Perron unit root tests, it was found that all of the markets do not behave
randomly. Testing the daily closing prices for the eleven high-volume trading banks listed on the Karachi Stock
Exchange, Bashir et al (2011-a) rejected the weak-form efficiency in the banking sector and (2011-b) rejected in the
textile sector in Pakistan.
4. Data and Methodology
The Data. All Share Index and sectoral indices for daily closing prices in Tadawul over the period October 30, 2006
through November 15, 2012 are collected. The data set consists of the daily closing values of 16 indices, the All-Share
Index (TASI), and 15 other sectoral indices. The data collected is for two periods: during and after the financial crisis.
Random walk is tested for the whole market and then for each sector and each period. The
actual returns on the market are calculated as follows:
R
it
=[(I
it
- I
it-1
) / I
it-1
] x 100
where:
R
it
= the daily return on day t for sector i
I
i
t = stock index closing value for sector i
I
i
t-1 = stock index closing value for sector i on day t-1
The daily return is computed either as a percentage or logarithmic price change. Osborne (1959) suggested that
the lognormal probability distribution of price change is better explained in random walk. Jaradat and Al-Zeaud (2011)
justified this measure by arguing that mathematically, logarithm of relative price is producing a time series of
continuously compounded returns. Using the same approach of Srinivasan (2010), stock market returns are defined as
continuously compounded or log returns at time t. Furthermore, as per Lauterbach and Ungar (1995), continuously
compounded returns are additive and their distribution follows the normal distribution more closely than arithmetic
returns. Therefore, stock returns are calculated by the log difference change in the price index.
Dickey-Fuller Unit Root Test with Drift. Most researchers used the unit root test in order to test for the non-
stationary which is the necessary condition for the presence of random walk. Equation (1) presents the simple form of
unit root, where current price is expected to be totally explained by lagged price by one period (slope coefficient = 1).
If this is not true, then the current price is explained by a constant (drift) which is o, and a coefficient for the lagged
price to be less than 1. The null hypothesis in this case is: Ho: |=1 against Ha: |<1.
P
it
= o + |P
it-1
+ c
it
(1 )
where:
2
Each GCC country has one market and the UAE has two markets: the Abu Dhabi Secruities Market and Dubai
Financial Market.
38
o = Expected price change or drift
| = Expected to be unity
P
it
= Current daily share price for firm i
P
it-
1 = Lagged one period current daily share price for firm i
c
it
= Independently and identically distributed with mean 0 and constant
variance o
2
, IID (0, o
2
).
The independence in the error (c
it
) implies that increments are uncorrelated and that any non-linear function of
the increments is also uncorrelated. In addition, the model is assuming that increments are identically distributed
and the error term (c) is assumed to be white noise.
Formulating the above equation in the first difference, as considered by Dickey and Fuller, P
it-1
is subtracted
from both sides and the model is:
?P
it
= o + µ P
it-1
+ c
it
(2 )
where:
?P
it
= First difference in share price for firm i
o = Expected price change or drift
µ = (Slope - 1)
P
it-
1 = Lagged one period current daily share price for firm i
Since the actual price is changed to the first difference, the hypothesis testing would change to Ho: µ = 0 against
Ha: µ< 0. Model (1) is testing for a coefficient of 1, while model 2 is testing for a coefficient of 0. The more negative the µ, the better the t-
value would be to reject the null hypothesis and conclude that prices are stationary and do not follow random walks.
Pearson Product-Moment Correlation Coefficient. Applying the same method used by Kendall (1953), the
correlation coefficient between the current return on an index and the one period lag-return should indicate if there is a
serial correlation. A positive coefficient indicates a tendency towards a possible continuation momentum of abnormal
returns on the next day, while a negative sign is a tendency towards a possible reversal of returns. If the sign is
significant, then that is a hint of possible market inefficiencies, and today's returns can be used to predict future
expected returns. However, if serial correlation coefficients are small, there is no 'systematic' correlation but rather a
'negligible' relation between one price change and the subsequent ones, and would be consistent with the weak-form
efficiency.
Autocorrelation test via the Durbin-Watson (D-W) Statistic. Gupta (2010) argued that Durbin-Watson test is
the best test to detect autocorrelation as such:
n
d=
¿ (e t
t=2
n
÷ e
t
÷
1
)
2
(3 )
¿e 2
t
t=1
where:
d = Durbin-Watson Statistics
e
t
= the residuals from a regression for time period t
e
t-
1 = the residuals from a regression fro time period t-1
To test for positive autocorrelation at significance o, the test statistic d is compared to lower and upper critical
values (d
L
and d
U
):
If d < d
L
= error terms are positively autocorrelated
If d > d
U
= error terms are not positively autocorrelated
If d
L
< d < d
U
= the test is inconclusive
Statistically, the absence of statistical significance in autocorrelation test implies that the series follow a random
walk, which means that the market is efficient at the weak-form. The assumption of normally distributed random
errors is needed to derive the probability distribution of the test statistic used in the D-W test. This method has also
been used extensively by: Kendall (1953), Fama (1965), Fama and French (1989), Worthington and Higgs (2006),
Squalli (2006), Sharma and Mahendru (2009), Rao and Shankaraiah (2003), Awad and Daraghma (2009), and Omran
and Farrar (2006).
Wald-Wolfowitz Runs Test. Fama (1965) argued that this test examines the serial dependence in share price
movements. If no influence exists, then it can be said that the observations are independent. The runs test is a
nonparametric test, which can be used to test for independence between successive series without requiring normality
of the distribution. After observing the number of 'runs' in a sequence of price changes, randomness is
39
tested at 5% significance level with an absolute Z value greater than 1.96 and 1% significance level with an absolute Z
value greater than 2.58 indicating non-randomness.
=
where:
Z
R
M
= standard normal variable
= number of runs
= 1 +
(
( × )
)
= mean number of runs
$
(4 )
o = (
(
)
)!
- -
-"
#!= standard deviation
nu, nd = number of ups and down in observations in each category
5. The Findings
Table 2 presents a summary of the descriptive statistics of the daily returns for All Share indices and sectors, measured
in log. Figure 1 clearly shows the simple pattern of randomness in All Share prices. Figure 2
highlights the normality of the returns for All Share index which is one of the conditions for the unit root test.
The Dickey-Fuller (DF) Test. Table 3 summarizes the main statistics derived from running the OLS for the current
closing index for All Share as a function of the lagged one period index. At the 1% level of significance, the most
important statistic, which is the t-value on |, is providing evidence that the slope | is insignificantly different from 1 (t-value -2 <
-2.862). T-test for the intercept (o = 0, i.e. no drift) indicates that the t-value is insignificant to reject the null hypothesis. In
other words, the model is a random walk without drift. Therefore, it is concluded that prices in the KSA Stock
Exchange are following a random walk. The best prediction of the current price is the last price. R
2
indicates that
99.30% of the variation in the current price is explained by the lagged share price. Figure 3 supports the above
findings, and it clearly shows that the current share price (index) could not generate any excess return in the next
period, with the exception of few unusual observation.
Changing the dependent variable to the "first difference of the closing price" (?P
t
) as a function of lagged
closing price and the white noise, is providing an alternative test to stationarity. The hypothesis to be tested is
Ho: | = 0 against the alternative Ha: |< 0. Table 3 presents the summary results for the unit root tests (actual closing price and first
difference in price) which provide evidence that share prices in Tadawul are following random walk. The coefficient
for lagged price is close to zero (|=-0.003) and t-value (-1.609) suggests that there is not enough evidence to reject the null
hypothesis that the slope coefficient is not significantly different from zero. If this is the case, then the series exhibits a
unit root and is non-stationary. D-W of 2.054 rejects the problem of autocorrelation in the model. Testing individual
indices for the 15 sectors, it is found that only Banks and Financial Services do not follow random walk (t-value = -4.67).
Pearson Correlation Coefficient. It is found that out of 16 indices in Tadawul tested (All Share Index and 15 sectoral
indices), none of them showed any strong or even moderate relationship between the daily returns and the lagged
return with correlation of coefficient varying between 0.203 for the Energy and Utilities and 0.028 for the Media and
Publishing sector. Thus, the current daily prices change of the indices is independent from the previous day's change.
Table 4 summarizes the coefficients for all sectors which are found to be very weak.
Autocorrelation test (D-W Statistic). No positive autocorrelation is found in the All Share Indexes or their sectoral
indices. All of the d-statistics are very close to 2, which lead to the conclusion that there is no positive autocorrelation
in the Saudi Market, and hence the market is weak-form efficient. From the 16 indices tested, we could not find a
positive serial correlation between the residuals in any index, and thus all of the indices tested have met the criteria of
an efficient market hypothesis at the weak-form (Table 4).
Runs-Test. From this test, it is found that at 5% level of significance, the All Share "TASI" returns from the market
index follow random walk, and from the 15 sectors, 11 exhibited daily returns that followed random walks. The four
that do not follow random walk are Banks and Financial Services (Z= -2.442), Energy and Utilities (Z= 2.414),
Insurance (Z= -2.855), and Building and Construction (Z= -2.733). Testing at 1% level of significance, only two
sectors are not following random walks: Insurance and Building and Constructions. These results are shown in table 4.
Comparing the results of the four tests on each sector, we find some contradictory results, and thus we have
controversial findings and cannot reach to a final conclusion whether the daily returns of these indices are
informationally efficient in the weak-form. In general, sector-wise, the market of Saudi Arabia's Tadawul is found to
be closer to the properties of the weak-form efficiency of EMH. Accordingly, it is not expected that there will be
investors in the market of Saudi Arabia whom can generate excessive returns by simply depending on past information
and technical analysis to formulate trading decision beating the market on a continuous and
40
systematical basis. In addition, All Share Index has met the properties of the weak-form efficiency in all the models
tested along with 11 out of the 15 sectors. Table 4 summarizes the findings of the four tests used for the different
indices in the Saudi Arabia.
Testing the random walk for share prices during and post financial crisis confirmed the main findings for All Share
index in most of the tests conducted (see Table 5). Furthermore, figure 4 compares the random walks during these two
periods.
6. Conclusion
The purpose of this study is to explore and test the random walk and weak-form informational market efficiency in the
Saudi Arabia. In order to examine the behavior of the daily returns of the stock markets, both overall and sector-wise,
four tests are applied: Dicky-Fuller unit root, Pearson correlation coefficient, Durbin-Watson (autocorrelation), and
Wald-Wolfowitz runs-tests. The findings show empirical evidence that Saudi stock prices exhibit unit root for the All
Share index and for the individual sectors with the exception of Banking and Financial Services sector. In addition,
All Share indices showed no significant correlation between the daily returns, and the remaining indices did not show
any strong or even moderate relationship between the daily returns. Using the Durbin-Watson statistic, none of the
indices exhibit a positive autocorrelation during the period of the study. However, using the runs-test for testing
randomness, at 5% level of significance, only four indices out of the total 16 indices, did not qualify to behave
similar to a RWM. While at 1% level of significance, only two sectors did not follow random walk. As a result, a
final conclusion cannot be reached whether or not the daily returns of these indices follow a random walk and are
informationally efficient in the weak-form for the whole market. However, by using four tests, most of the results
provide evidence to conclude that in general, sector-wise, the market of Saudi Arabia's Tadawul is weak-form
efficient. Moreover, with confidence, we can say that the All Share general market index of Saudi Arabia and 11
indices have met the properties of the weak-form efficiency of EMH using all of the models tested.
Consequently, it is not expected that there will be investors in the market of Saudi Arabia who can generate excessive
returns by simply depending on past information and technical analysis to formulate trading decision beating the
market on a continuous and systematical basis. The findings of this study are considered to be an added value to the
literature concerning the random walk and testing the weak-form market efficiency in the emerging markets, especially
in the MENA region and GCC countries. These results can be a starting point for further studies testing the semi-strong
form of EMH in Saudi Arabia.
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14,000
12,000 10,000
8,000 6,000 4,000
2,000
0
Figure 1: Closing Indices for Tadawul All-Share "TASI"
500
400
300
200
100
0
Figure 2: Distribution of returns for Tadawul All-Share Index "TASI"
Figure 3: Closing prices against Lag prices for All-Share "TASI"
44
During Crisis
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
After Crisis
9,000
8,000 7,000
6,000 5,000
4,000 3,000
2,000 1,000
0
Figure 4: Financial crisis and random walk in TASI
45
4
1
9
3
9
7
3
7
5
3
5
3
3
3
1
3
0
9
2
8
7
2
6
5
2
4
3
2
2
1
1
9
9
1
7
7
1
5
5
1
3
3
1
1
1
8 9
6 7
4 5
2 3
1
9
8
9
9
3
7
8
8
5
8
3
3
7
8
1
7
2
9
6
7
7
6
2
5
5
7
3
5
2
1
4
6
9
4
1
7
3
6
5
3
1
3
2
6
1
2
0
9
1
5
7
1
0
5
5 3
1
Table 1: Tadawul Market Structure
Sector code
TASI
TBFSI
TPISI
TCESI
TRESI
TEUSI
TAFSI
TTISI
TINSI
TMISI
TIVSI
TBCSI
TRDSI
TTRSI
TMPSI
THTSI
Sector Name
Tadawul All Share Index
Banks & Financial Services Sector
Petrochemical Industries Sector
Cement Sector
Retail Sector
Energy & Utilities Sector
Agriculture & Food Industries Sector
Telecom & Information Technology Sector
Insurance Sector
Multi-Investment Sector
Industrial Investment Sector
Building & Construction Sector
Real Estate Development Sector
Transport Sector
Media and Publishing Sector
Hotel & Tourism Sector
No. of companies in the index
150
11
14 10
10 2
15 5
31 7
13 15
8432
Table 2: Summary Statistics for Tadawul
Daily Returns Min M ax M ean Std. Dev. Skewness Kurtosis
All Share TASI -.0998 .2 4 8 9 -.000106 .0206400 -.247 6 .5 0 0
TAFSI -.0963 .0 9 5 3 .000130 .0188385 -.429 5 .9 6 8
TBCSI -.0991 .0 9 8 7 -.000226 .0221368 -.607 4 .8 6 1
TBFSI -.0978 .0 9 1 3 -.000244 .0175964 .0 1 4 6 .1 9 7
TCESI -.0986 .0 9 7 5 -.000043 .0152281 -.249 10.400
TEUSI -.0982 .0 9 5 6 .000089 .0181705 .1 7 8 6 .1 5 4
THTSI -.0993 .2 4 8 9 .000302 .0261277 .5 8 7 9 .6 6 8
TINSI -.0956 .0 9 7 4 -.000131 .0226482 -.541 3 .1 7 7
TIVSI -.0981 .0 9 7 9 .000250 .0213593 -.646 4 .5 5 6
TMISI -.0979 .1 2 0 7 -.000475 .0230984 -.487 4 .9 3 5
TMPSI -.0996 .1 0 0 3 -.000646 .0216263 -.150 4 .8 5 1
TPISI -.0992 .0 9 8 9 .000441 .0233343 -.476 4 .4 0 5
TRDSI -.0995 .0 9 9 0 -.000492 .0189798 -.326 6 .2 5 3
TRESI -.0987 .0 9 9 1 .000214 .0181629 -.457 7 .4 3 2
TTISI -.0998 .0 9 9 0 -.000368 .0174865 -.285 6 .9 8 8
TTRSI -.0991 .0 9 7 7 -.000392 .0221046 -.146 5 .1 4 9
46
Table 3: Summary results for the unit root test
Dependent Variable: Price
Expected | = 1
Dependent Variable:
change in price
3
Sectors Index Expected | = 0
Slope: Se | T
Drift: o R
2
Slope: | Drift: o
| ( DF )
All-Share TASI 0 .9 9 6 2 3 .6 5 .0 0 2 -2 0 .9 9 3 -.003 23.267
1 TBFSI 0 .9 8 6 * 279* .0 0 3 - 4 .6 7 0 .9 7 7 -.004 66.525
2 TPISI 0 .9 9 7 1 4 7 .9 .0 0 2 -1.5 0 .9 6 9 -.003 21.613
3 TCESI 0 .9 9 7 1 2 .9 4 .0 0 2 -1.5 0 .9 9 6 -.002 10.833
4 TRESI 0 .9 9 1 43.87** .0 0 4 -2.25 0 .9 8 0 -.009** 42.980**
5 TEUSI 0 .9 8 9 5 0 .6 3 * .0 0 4 -2.75 0 .9 8 0 -.010** 46.556**
6 TAFSI 0 .9 8 9 5 4 .8 2 * .0 0 4 -2.75 0 .9 7 8 -.011** 53.020**
7 TTISI 0 .9 9 5 4 6 .9 1 * .0 0 2 -2.5 0 .9 8 2 -.005** 9 .2 8 6
8 TINSI 0 .9 9 8 2 .0 1 .0 0 2 -1 0 .9 9 6 -.002 1 .6 5 3
9 TMISI 0 .9 9 8 21.66*** .0 0 2 -1 0 .9 9 0 -.002 4 .8 8 8
10 TIVSI 0 .9 9 2 9 6 .4 7 * .0 0 4 -2 0 .9 7 3 -.008** 40.800**
11 TBCSI 0 .9 9 8 7 .6 1 .0 0 2 -1 0 .9 9 5 -.002 7 .6 1 6
12 TRDSI 0 .9 9 8 1 3 .5 6 .0 0 2 -1 0 .9 9 2 -.002 6 .1 8 9
13 TTRSI 0 .9 9 5 32.69** .0 0 3 -1.67 0 .9 8 3 -.005 15.354
14 TMPSI 0 .9 9 5 1 0 .4 8 .0 0 2 -2.5 0 .9 9 1 -.004** 7 .6 8 9
15 THTSI 0 .9 8 6 159* .0 0 5 -2.2 0 .9 5 9 -.014** 75.222*
* significant at 1% ** significant at 5% *** significant at 10%
3
Since returns on index is calculated as "change in index", using first difference or returns as a variable provided
similar results.
47
Table 4: Summary results for the four tests
Sample size = 23,488 observations
Correlation
Sectors
Index
DF Unit Root
Ho: Unit root
H o : No
correlation
Durbin-Watson Ho:
No autocorrelation
Runs-Test
Ho: Random Series
B Unit
Value Ranalom statdstics Ranalom staZstic Ranalom
All-
Share
1
2
3
4
5
6
7
8
9
10
11
TASI
TBFSI
TPISI
TCESI
TRESI
TEUSI
TAFSI
TTISI
TINSI
TMISI
TIVSI
TBCSI
0 .9 9 6
0 .9 8 6
0 .9 9 7
0 .9 9 7
0 .9 9 1
0 .9 8 9
0 .9 8 9
0 .9 9 5
0 .9 9 8
0 .9 9 8
0 .9 9 2
0 .9 9 8
ro o t
Don't
Reject
Re j e c t
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
0 .0 8 4
0 .1 0 9
0 .0 4 6
0 .0 6 0
0 .0 3 4
0 .2 0 3
0 .0 8 1
0 .0 6 1
0 .1 1 4
0 .0 9 4
0 .0 3 5
0 .1 3 0
d
Wk
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
i
2 .0 0 8
2 .0 0 3
2 .0 0 6
2 .0 0 3
1 .9 9 8
2 .0 0 3
2 .0 0 3
2 .0 0 3
2 .0 0 8
1 .9 9 8
2 .0 0 5
2 .0 0 8
d
Wk
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
ti
-1.438
-2.442
-0.698
-0.638
0 .5 8 2
2 .4 1 4
-1.511
-1.341
-2.855
1 .0 1 4
0 .9 3 0
-2.733
d
Wk
Don't
Reject
Re j e c t
Don't
Reject
Don't
Reject
Don't
Reject
Re j e c t
Don't
Reject
Don't
Reject
Re j e c t
Don't
Reject
Don't
Reject
Re j e c t
12
13
14
TRDSI 0.998
0 .9 9 5
TTRSI
TMPSI 0.995
Don't
Reject
Don't
Reject
Don't
Reject
Don't
0 .0 6 7
0 .0 4 3
0 .0 2 8
Don't
Reject
Don't
Reject
Don't
Reject
Don't
2 .0 0 3
1 .9 9 6
1 .9 9 8
Don't
Reject
Don't
Reject
Don't
Reject
Don't
0 .5 8 2
0 .5 8 4
1 .2 2 1
Don't
Reject
Don't
Reject
Don't
Reject
Don't
15 THTSI 0 .9 8 6
Reject
0 .0 3 7
Reject
2 .0 0 2
Reject
0 .0 0 1
Reject
Table 5: Financial crisis and the randomness of share prices for TASI
Correlation Runs-Test
States
df
DF Unit Root
Ho: Unit root
H o : No
correlation
Durbin-Watson Ho:
No autocorrelation
Ho: Random
Series
B
Unit
ro o t
Value
Random
Wa l k
Don't
d
statistics
Random
Wa l k
Don't
Z
statistic
Random
Wa l k
Don't
During-crisis 439
Don't 0.146
0.992 Reject
Reject
1 .9 7 7
Reject
-2.339
Reject*
Post crisis
1023 0.990 Reojn'tt 0.053 D
ec
Don't
Reject
1 .9 0 3
Don't
Reject
-0.469
Don't
Reject
* at 1% level of significance
48
doc_462611657.docx
A stock market or equity market is a public entity (a loose network of economic transactions, not a physical facility or discrete entity) for the trading of company stock (shares) and derivatives at an agreed price; these are securities listed on a stock exchange as well as those only traded privately.
Case Study of Weak-Form Efficiency: Saudi Stock
Market
Abstract
The purpose of the paper is to test the weak-form market efficiency in Saudi Arabia's stock market, Tadawul which is
expected to follow a random walk. All share index and sectoral indices for daily closing prices in Tadawul between
October 15, 2006 and November 15, 2012 are collected. Unit root Dickey-Fuller test, Pearson Correlation test, Durbin-
Watson test and Wald-Wolfowitz runs-test are used as basic stochastic tests for a non- stationarity of the daily prices
for all the listed companies in the market, both overall and sector-wise. The four tests confirmed the weak-form market
efficiency in the Saudi stock market for All share prices and 11 individual sectors. The findings are necessary for all
investors in Saudi Arabia and the member states of the GulfCooperation Council (GCC). Listed firms could also
benefit from the findings by seeing the true picture of their stock price. The finding is used as a basis for testing the
market efficiency in the semi-strong form, which has not yet been tested by any researcher. Accordingly, investors in
the Saudi market are not expected to generate abnormal returns simply by depending on past information and technical
analysis. This paper will add value to the literature of market efficiency in the emerging market and the GCC since it
covers all the listed companies, tests sector-wise, and covers an extended period of time. To confirm the weak-form
efficiency in Saudi, the study uses four tests and covers a long period of time during and after the financial crisis.
Keywords: Weak-form market efficiency, random walk hypothesis, unit root test, auto correlation, run test,
Kingdom of Saudi Arabia.
1. Introduction
Many studies have tested market efficiency in the developed markets. In the last two decades, studies in the emerging
markets started to follow suit. Most of these studies have tried to answer a simple question: Are share prices moving
randomly? However, empirical testing came up with mixed findings and different conclusions in both developed and
emerging markets. One view in support of the random walk hypothesis (RWH) is that stock returns are following a
random walk process and thus, it is not possible to predict their future movements based on past information. The
second view, in contrast, states that there is indeed a trend path in the stock returns and that it is possible to predict the
future price movements based on the history of prices. The dissimilar results could depend on: (1) the tests that are
used; (2) the markets under examination; (3) the type of sector and industry examined, and (4) the time-frame for the
study. The RWH which has been tested heavily on the weak- form efficiency has obviously failed to prove the
performance of equity markets worldwide. However, developed markets have shown a higher degree of informational
efficiency than emerging markets.
The market is said to be efficient when prices of securities reflect all relevant information (Fama, 1991). Investors are
freely obtaining new information which makes them, due to competition, immediately discount this information into the
price. In other words, there is no chance for an arbitrage opportunity that can be used to make excess abnormal profits
(Fama 1965). Efficient market hypothesis (EMH) was earlier developed by Fama (1970) and Fama and French (1989)
and later revised to identify three levels of efficiency, which differ in terms of the type of information set reflected in
the market. The weak form efficiency, which is the first level of EMH, assumes the absence of predictability of time-
series of security prices. This leads to the random walk theory which claims that the prices are independent of each
other and past movements or trends cannot be used to predict future movements. Therefore, serial independence (i.e.
no autocorrelation) for the set of share price changes is a fundamental requirement for the market to follow a random
walk. As Fama (1970) stated that all types of "new" news, by definition, have to be "new and unpredictable", resulting
in the unpredictability of future stock prices. Both Samuelson (1965) and Fama (1970) indicated that the EMH
supposes that the share price adjusts instantaneously to new information. Hence, current prices should fully discount
and reflect all available information and ought to follow a random walk process, meaning that the successive returns
are independently and identically distributed. The second level is the semi-strong form efficiency where prices reflect
all past prices and the public information. The third level is the strong form efficiency where the share price reflects all
past, public and insider information.
35
EMH deals with the question of whether stock prices fully reflect the entire historical price. The simplest random
walk model, as shown in the following equation, states that the actual price equals the previous price
plus the realization of a random variable:
P
it
=P
it-1
E(R)
it
c
it
where:
P
i
t = Current stock price for firm i
P
i
t-1 = Last closing price to current time
t-1
E(R)
i
t
= Expected return (price change) at time t, also called drift
c
i
t = Random Error
Furthermore, according to the above equation, the expected return on a security is based on the available
information set at time t (|
t
), as argued by (Solnik, 1996): E (R
it
| |
t
). The paper investigates informational
efficiency in the Saudi stock market for the period January 1, 2007 until October 30, 2012 at the general market
and sector levels. Its main purpose is to test the weak-form market efficiency through the random walk model.
Accordingly, if the question is answered, it can be decided whether the usage of technical analysis to forecast and
predict future price changes is of material benefit. The rationale for this study is that little research has targeted
countries from the Middle East and the stock exchanges in the GCC.
1
The knowledge of how efficient a stock market is
and how it discounts and reflects the set of information into the market prices of the securities is of central importance
to users of the capital markets. Taking into account the economic growth, trade liberalization, introduction of
electronic trading, globalization and emergence of global markets; once the behavior of the prices is determined, the
easier it is to understand the market and the economy. Another contribution of this study to the literature is the
sectoral analysis of the Saudi Arabia, which has been limited to only a few papers.
2. The Saudi Arabia Stock Exchange (TADAWUL)
The Saudi Stock Exchange (Tadawul) is the only stock exchange in the Kingdom of Saudi Arabia. Its trading hours are
11:00AM to 3:30PM, Saturday to Wednesday and it is supervised by the Capital Market Authority (CMA). Saudi joint
stock companies had their beginnings in the mid-1930s, when the Arab Automobile was established as the country's
first joint stock company. The Saudi Stock Exchange emerged in the late 1970s where the number of joint stock
companies was increasing as a result of nationalization of foreign companies, including banks. By 1975 there were
about 14 public companies. The rapid economic expansion, beside the nationalization of part of the foreign banks
capital in the 1970s led to the establishment of a number of large corporations and joint stock banks. The market
remained informal until the early 1980s when the Saudi government created a national stock market. In 1984, a
Ministerial Committee composed of the Ministry of Finance and National Economy, Ministry of Commerce and Saudi
Arabian Monetary Agency (SAMA) was formed to regulate and develop the market. SAMA was the government
body charged with regulating and monitoring market activities until the CMA was established in July 2003 under the
Capital Market Law (CML) by Royal Decree No. (M/30). The CMA is the sole regulator and supervisor of the capital
market, it issues the required rules and regulations to protect investors and ensure fairness and efficiency in the market.
The Council of Ministers approved on March 19, 2007, the formation of the Saudi Stock Exchange (Tadawul)
Company. This was in accordance with Article 20 of the Capital Market Law establishing Tadawul as a joint stock
company. Tadawul is organized into 15 sectors, each consisting of companies that have a common business line and
operate in the same industry. The market capitalization on October 4, 2011 was $315,521 million. In addition, Tadawul
All Share Index consists of all listed companies, as shown in table 1.
3. Previous Studies
Bachelier (1900) was the first to point out that security prices and prices of other speculative commodities follow a
random walk; this was later confirmed by Pearson (1905) and Working (1934). Kendall (1953) was the first researcher
to use the term "random walk" in the finance literature. Until the early 1950s, it was accepted that technical analysis,
could be used to examine the behavior of past prices and beat the market. Malkiel (1992) McQueen et al (1996), Fama
and French (1989), Al-Loughani and Chappell (1997), Seiler and Rom (1997), and Abrosimova et al (2002) supported
the assumption that price changes are random and past prices were not useful in predicting future price.
Alexander (1964) and Fama and Blume (1966) used a filter rule, which gives a rule for buying and selling stocks
1
The Gulf Cooperation Council countries are Bahrain, Kuwait, Oman, Qatar, Saudi Arabia and the Uunited
Arab Emerats.
36
depending on past price movements but found that such rule could not generate trading profits. Jensen (1968)
performed risk-adjusted measures and found that mutual funds do not outperform the market from 1945-1964. Conrad
and Kaul (1988) and Lo and MacKinlay (1988) examined the weekly returns of the NYSE stock and both studies
found that a positive serial correlation over short horizons, but one that is negligible and insignificant. Lo and
MacKinlay (1988) provide evidence that random walk model was strongly rejected in NYSE-AMEX between 1962
and1985. However, Huber (1995) studied the Vienna Stock Market and rejected the RWH. Kvedaras and Basdevant
(2004) concluded that the Estonian, Latvian and Lithuanian Stock Exchange Market, with some turbulence, approaching
the weak form of efficiency.
Keim and Stambaugh (1986) found significant predictability in stock prices using forecasts based on certain
predetermined variables. Fama and French (1988) show that long holding-period returns are significantly negatively
serially correlated, implying that 25-40% of the variation of longer-horizon returns is predictable from past returns.
Balaban (1995) rejected the random walk on Istanbul Securities Exchange. Kompa and Matuszewska-Janica (2009)
examined the Warsaw Stock Exchange from 2000 to 2006 for the log daily returns. The weak-form efficiency was
found in the main market indexes as well as companies in the following sectors: telecommunication, gas and oil, and
metals. Medium-size company index was found to achieve abnormal returns. Reviewing the Arab markets and the GCC,
most of the studies used run test and serial correlation to examine the RWH. Gandhi et al (1980) used monthly data for
the period 1975-1978 for the Kuwait Stock Exchange and found that RWH for the All Share and Industrial indices was
rejected. Testing United Arab Emirates (UAE) market, Ebid (1990) found that it is considered to be weak-form
efficient. Butler and Malaikah (1992) analyzed the behavior of the Kuwait and Saudi Arabia stock markets between
1985 and 1989 and they provided evidence of weak-form inefficiency in both of the markets. However, they could not
conclude if the Saudi market is informationally inefficient. Civelek (1991) and El-Erian and Kumar (1995) studied the
Amman Financial Market and both got relatively frequent positive dependence. Al-Loughani (1995) used the weekly
data for the Kuwait Stock Exchange for 1986-1990 and found that autocorrelation and runs test were consistent with
the RWH. Khababa (1998) concluded that Saudi market is not weak-form efficient. Dahel and Laabas (1999) examined
the behavior of the daily stock prices over the period 1994-1998 in the Gulf markets: Bahrain, Kuwait, Saudi Arabia and
Oman. They concluded that Kuwait Stock Market is the only efficient market and is strongly in support of the concepts
of the RWH. Abraham et al (2002) used weekly data for All Share indices of Saudi Arabia, Kuwait and Bahrain for
1992-1998. Variance ratio tests rejected the RWH for all three stock markets. By applying the Beveridge and Nelson
(1981) decomposition of index returns and after removing the effects of infrequent trading, a RWH was not rejected for
the Saudi and Bahraini markets. Taking into considerations market imperfections such as thinly and infrequent trading,
Hassan et al (2003) examined Kuwait Stock Exchange over the period 1995-2000 by using EGARCH and GARCH-M
and found that the market is weak-form inefficient.
Rao and Shankaraiah (2003) studied the weak form efficiency of the Bahrain Stock Market over the period 1996-2000
and confirmed the weak-form efficiency. Smith (2007) studied the RWH in the Middle Eastern stock markets and found
that Israeli, Jordanian, and Lebanese markets were weak-form efficient while the Kuwait and Oman markets were not.
For the Tel-Aviv, Amman and Beirut stock market and non-Kuwaiti companies that traded on the Kuwait stock
market, stock price indices follow a random walk. Moustafa (2004) examined the behavior of the prices in the UAE
stock market and concluded that most firms are weak-form efficient and prices follow a random walk. Babaker (2004)
investigated the market efficiency of all Arab Stock Exchanges and the results showed that emerging markets are less
efficient than developed markets. In addition, at different time periods, stock markets vary in efficiency. Asiri (2000,
2004, 2007) examined Kuwait's stock market for the daily stock prices for 1999-2001, 1991-2002 and 2000-2002.
Using unit root test, ARIMA (AR1); exponential smoothing and autocorrelation tests confirmed the weak-form
efficiency. Sector analysis also gives robust support to the findings. The results confirmed the randomness for all share
prices and each sector. Studying all companies listed on the Bahrain Stock Exchange, Asiri (2008) confirmed that all
daily prices and each sector follow a random walk with no drift and trend and supporting the weak-form market
efficiency. Using daily sectoral indices between 2000 and 2005, Squalli (2006) explored the efficiency in the different
sectors of the Dubai Financial Market (DFM) and Abu Dhabi Securities Market (ADSM). Variance ratio tests rejected
the randomness in all of the sectors in UAE except in the banking sector in DFM. In comparison, using runs test, the
insurance sector of the ADSM gave evidence of weak-form efficiency in the UAE. Al-Khazali et al (2007) re-
examined the empirical validity of the weak-form in emerging markets of the MENA region: Bahrain, Egypt, Jordan,
Kuwait, Morocco, Oman, Saudi Arabia and Tunisia. In their study, they utilized the Lo and MacKinlay (1988, 1989),
Wright's (2000) rank and sign VR and the runs tests. Once the returns from the indices were adjusted to reconcile
distortions from thinly and infrequently traded stocks, the study found random walk and weak-form efficiency in all of
the markets examined.
37
Using multiple variance tests on different sectors, Benjelloun and Squalli (2008) tested the markets of Jordan, Qatar,
Saudi Arabia and the UAE and found that there is no consistency in their results among the different sectors and the
different markets. Randomness was rejected in Jordan, Abu Dhabi and Dubai when using the general index. However,
if the sectoral indexes were used, they failed to reject the randomness in some sectors. Using the runs test, randomness
was rejected in all of the stock market if general indexes were used, with the exception to Dubai. However, using the
sectoral indexes, they have failed to reject the weak-form efficiency in some sectors.
Elango and Hussein (2008) examined the market efficiency across seven stock markets in the GCC countries
2
for the
daily indices over the period 2001-2006. Kolmogorov-Smirnov test shows that all of the seven markets reject the RWH
and using the runs test for randomness, they found that the successive price changes were not random. Marashdeh and
Shrestha (2008) investigated if the stock price index in the UAE follows random by using unit root, Augmented Dickey
Fuller and Philip-Perron tests along with Perron's Innovational Outliner and Additive Outliner models. The results show
that the data has a unit root and follows a random walk. Awad and Daraghma (2009) examined the efficiency of the
Palestine Security Exchange for 35 stocks listed in the market using the daily indices and concluded that daily returns
are inefficient in the weak-form. AlKhazali (2011) has conducted a study examining the market efficiency in the Gulf
countries and concluded that the RWH is not rejected in all the GCC markets. Al-Jafari (2011) and Al-Jafari and
Altaee (2011) found that both Bahrain and Kuwait stock markets are informationally inefficient at the weak-form
level. Salameh et al (2011) explored the weak form market efficiency for Saudi Arabia, Amman, Kuwait, Dubai, Abu
Dhabi, Egypt, Morocco, Tunisia, Qatar, Oman, Bahrain and Palestine markets. In general, Saudi Market was the only
market that behaved randomly under both the serial autocorrelation tests and the runs test. However, under both the
Augmented Dickey-Fuller and Phillips-Perron unit root tests, it was found that all of the markets do not behave
randomly. Testing the daily closing prices for the eleven high-volume trading banks listed on the Karachi Stock
Exchange, Bashir et al (2011-a) rejected the weak-form efficiency in the banking sector and (2011-b) rejected in the
textile sector in Pakistan.
4. Data and Methodology
The Data. All Share Index and sectoral indices for daily closing prices in Tadawul over the period October 30, 2006
through November 15, 2012 are collected. The data set consists of the daily closing values of 16 indices, the All-Share
Index (TASI), and 15 other sectoral indices. The data collected is for two periods: during and after the financial crisis.
Random walk is tested for the whole market and then for each sector and each period. The
actual returns on the market are calculated as follows:
R
it
=[(I
it
- I
it-1
) / I
it-1
] x 100
where:
R
it
= the daily return on day t for sector i
I
i
t = stock index closing value for sector i
I
i
t-1 = stock index closing value for sector i on day t-1
The daily return is computed either as a percentage or logarithmic price change. Osborne (1959) suggested that
the lognormal probability distribution of price change is better explained in random walk. Jaradat and Al-Zeaud (2011)
justified this measure by arguing that mathematically, logarithm of relative price is producing a time series of
continuously compounded returns. Using the same approach of Srinivasan (2010), stock market returns are defined as
continuously compounded or log returns at time t. Furthermore, as per Lauterbach and Ungar (1995), continuously
compounded returns are additive and their distribution follows the normal distribution more closely than arithmetic
returns. Therefore, stock returns are calculated by the log difference change in the price index.
Dickey-Fuller Unit Root Test with Drift. Most researchers used the unit root test in order to test for the non-
stationary which is the necessary condition for the presence of random walk. Equation (1) presents the simple form of
unit root, where current price is expected to be totally explained by lagged price by one period (slope coefficient = 1).
If this is not true, then the current price is explained by a constant (drift) which is o, and a coefficient for the lagged
price to be less than 1. The null hypothesis in this case is: Ho: |=1 against Ha: |<1.
P
it
= o + |P
it-1
+ c
it
(1 )
where:
2
Each GCC country has one market and the UAE has two markets: the Abu Dhabi Secruities Market and Dubai
Financial Market.
38
o = Expected price change or drift
| = Expected to be unity
P
it
= Current daily share price for firm i
P
it-
1 = Lagged one period current daily share price for firm i
c
it
= Independently and identically distributed with mean 0 and constant
variance o
2
, IID (0, o
2
).
The independence in the error (c
it
) implies that increments are uncorrelated and that any non-linear function of
the increments is also uncorrelated. In addition, the model is assuming that increments are identically distributed
and the error term (c) is assumed to be white noise.
Formulating the above equation in the first difference, as considered by Dickey and Fuller, P
it-1
is subtracted
from both sides and the model is:
?P
it
= o + µ P
it-1
+ c
it
(2 )
where:
?P
it
= First difference in share price for firm i
o = Expected price change or drift
µ = (Slope - 1)
P
it-
1 = Lagged one period current daily share price for firm i
Since the actual price is changed to the first difference, the hypothesis testing would change to Ho: µ = 0 against
Ha: µ< 0. Model (1) is testing for a coefficient of 1, while model 2 is testing for a coefficient of 0. The more negative the µ, the better the t-
value would be to reject the null hypothesis and conclude that prices are stationary and do not follow random walks.
Pearson Product-Moment Correlation Coefficient. Applying the same method used by Kendall (1953), the
correlation coefficient between the current return on an index and the one period lag-return should indicate if there is a
serial correlation. A positive coefficient indicates a tendency towards a possible continuation momentum of abnormal
returns on the next day, while a negative sign is a tendency towards a possible reversal of returns. If the sign is
significant, then that is a hint of possible market inefficiencies, and today's returns can be used to predict future
expected returns. However, if serial correlation coefficients are small, there is no 'systematic' correlation but rather a
'negligible' relation between one price change and the subsequent ones, and would be consistent with the weak-form
efficiency.
Autocorrelation test via the Durbin-Watson (D-W) Statistic. Gupta (2010) argued that Durbin-Watson test is
the best test to detect autocorrelation as such:
n
d=
¿ (e t
t=2
n
÷ e
t
÷
1
)
2
(3 )
¿e 2
t
t=1
where:
d = Durbin-Watson Statistics
e
t
= the residuals from a regression for time period t
e
t-
1 = the residuals from a regression fro time period t-1
To test for positive autocorrelation at significance o, the test statistic d is compared to lower and upper critical
values (d
L
and d
U
):
If d < d
L
= error terms are positively autocorrelated
If d > d
U
= error terms are not positively autocorrelated
If d
L
< d < d
U
= the test is inconclusive
Statistically, the absence of statistical significance in autocorrelation test implies that the series follow a random
walk, which means that the market is efficient at the weak-form. The assumption of normally distributed random
errors is needed to derive the probability distribution of the test statistic used in the D-W test. This method has also
been used extensively by: Kendall (1953), Fama (1965), Fama and French (1989), Worthington and Higgs (2006),
Squalli (2006), Sharma and Mahendru (2009), Rao and Shankaraiah (2003), Awad and Daraghma (2009), and Omran
and Farrar (2006).
Wald-Wolfowitz Runs Test. Fama (1965) argued that this test examines the serial dependence in share price
movements. If no influence exists, then it can be said that the observations are independent. The runs test is a
nonparametric test, which can be used to test for independence between successive series without requiring normality
of the distribution. After observing the number of 'runs' in a sequence of price changes, randomness is
39
tested at 5% significance level with an absolute Z value greater than 1.96 and 1% significance level with an absolute Z
value greater than 2.58 indicating non-randomness.
=
where:
Z
R
M
= standard normal variable
= number of runs
= 1 +
(
( × )
)
= mean number of runs
$
(4 )
o = (
(
)
)!
- -
-"
#!= standard deviation
nu, nd = number of ups and down in observations in each category
5. The Findings
Table 2 presents a summary of the descriptive statistics of the daily returns for All Share indices and sectors, measured
in log. Figure 1 clearly shows the simple pattern of randomness in All Share prices. Figure 2
highlights the normality of the returns for All Share index which is one of the conditions for the unit root test.
The Dickey-Fuller (DF) Test. Table 3 summarizes the main statistics derived from running the OLS for the current
closing index for All Share as a function of the lagged one period index. At the 1% level of significance, the most
important statistic, which is the t-value on |, is providing evidence that the slope | is insignificantly different from 1 (t-value -2 <
-2.862). T-test for the intercept (o = 0, i.e. no drift) indicates that the t-value is insignificant to reject the null hypothesis. In
other words, the model is a random walk without drift. Therefore, it is concluded that prices in the KSA Stock
Exchange are following a random walk. The best prediction of the current price is the last price. R
2
indicates that
99.30% of the variation in the current price is explained by the lagged share price. Figure 3 supports the above
findings, and it clearly shows that the current share price (index) could not generate any excess return in the next
period, with the exception of few unusual observation.
Changing the dependent variable to the "first difference of the closing price" (?P
t
) as a function of lagged
closing price and the white noise, is providing an alternative test to stationarity. The hypothesis to be tested is
Ho: | = 0 against the alternative Ha: |< 0. Table 3 presents the summary results for the unit root tests (actual closing price and first
difference in price) which provide evidence that share prices in Tadawul are following random walk. The coefficient
for lagged price is close to zero (|=-0.003) and t-value (-1.609) suggests that there is not enough evidence to reject the null
hypothesis that the slope coefficient is not significantly different from zero. If this is the case, then the series exhibits a
unit root and is non-stationary. D-W of 2.054 rejects the problem of autocorrelation in the model. Testing individual
indices for the 15 sectors, it is found that only Banks and Financial Services do not follow random walk (t-value = -4.67).
Pearson Correlation Coefficient. It is found that out of 16 indices in Tadawul tested (All Share Index and 15 sectoral
indices), none of them showed any strong or even moderate relationship between the daily returns and the lagged
return with correlation of coefficient varying between 0.203 for the Energy and Utilities and 0.028 for the Media and
Publishing sector. Thus, the current daily prices change of the indices is independent from the previous day's change.
Table 4 summarizes the coefficients for all sectors which are found to be very weak.
Autocorrelation test (D-W Statistic). No positive autocorrelation is found in the All Share Indexes or their sectoral
indices. All of the d-statistics are very close to 2, which lead to the conclusion that there is no positive autocorrelation
in the Saudi Market, and hence the market is weak-form efficient. From the 16 indices tested, we could not find a
positive serial correlation between the residuals in any index, and thus all of the indices tested have met the criteria of
an efficient market hypothesis at the weak-form (Table 4).
Runs-Test. From this test, it is found that at 5% level of significance, the All Share "TASI" returns from the market
index follow random walk, and from the 15 sectors, 11 exhibited daily returns that followed random walks. The four
that do not follow random walk are Banks and Financial Services (Z= -2.442), Energy and Utilities (Z= 2.414),
Insurance (Z= -2.855), and Building and Construction (Z= -2.733). Testing at 1% level of significance, only two
sectors are not following random walks: Insurance and Building and Constructions. These results are shown in table 4.
Comparing the results of the four tests on each sector, we find some contradictory results, and thus we have
controversial findings and cannot reach to a final conclusion whether the daily returns of these indices are
informationally efficient in the weak-form. In general, sector-wise, the market of Saudi Arabia's Tadawul is found to
be closer to the properties of the weak-form efficiency of EMH. Accordingly, it is not expected that there will be
investors in the market of Saudi Arabia whom can generate excessive returns by simply depending on past information
and technical analysis to formulate trading decision beating the market on a continuous and
40
systematical basis. In addition, All Share Index has met the properties of the weak-form efficiency in all the models
tested along with 11 out of the 15 sectors. Table 4 summarizes the findings of the four tests used for the different
indices in the Saudi Arabia.
Testing the random walk for share prices during and post financial crisis confirmed the main findings for All Share
index in most of the tests conducted (see Table 5). Furthermore, figure 4 compares the random walks during these two
periods.
6. Conclusion
The purpose of this study is to explore and test the random walk and weak-form informational market efficiency in the
Saudi Arabia. In order to examine the behavior of the daily returns of the stock markets, both overall and sector-wise,
four tests are applied: Dicky-Fuller unit root, Pearson correlation coefficient, Durbin-Watson (autocorrelation), and
Wald-Wolfowitz runs-tests. The findings show empirical evidence that Saudi stock prices exhibit unit root for the All
Share index and for the individual sectors with the exception of Banking and Financial Services sector. In addition,
All Share indices showed no significant correlation between the daily returns, and the remaining indices did not show
any strong or even moderate relationship between the daily returns. Using the Durbin-Watson statistic, none of the
indices exhibit a positive autocorrelation during the period of the study. However, using the runs-test for testing
randomness, at 5% level of significance, only four indices out of the total 16 indices, did not qualify to behave
similar to a RWM. While at 1% level of significance, only two sectors did not follow random walk. As a result, a
final conclusion cannot be reached whether or not the daily returns of these indices follow a random walk and are
informationally efficient in the weak-form for the whole market. However, by using four tests, most of the results
provide evidence to conclude that in general, sector-wise, the market of Saudi Arabia's Tadawul is weak-form
efficient. Moreover, with confidence, we can say that the All Share general market index of Saudi Arabia and 11
indices have met the properties of the weak-form efficiency of EMH using all of the models tested.
Consequently, it is not expected that there will be investors in the market of Saudi Arabia who can generate excessive
returns by simply depending on past information and technical analysis to formulate trading decision beating the
market on a continuous and systematical basis. The findings of this study are considered to be an added value to the
literature concerning the random walk and testing the weak-form market efficiency in the emerging markets, especially
in the MENA region and GCC countries. These results can be a starting point for further studies testing the semi-strong
form of EMH in Saudi Arabia.
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14,000
12,000 10,000
8,000 6,000 4,000
2,000
0
Figure 1: Closing Indices for Tadawul All-Share "TASI"
500
400
300
200
100
0
Figure 2: Distribution of returns for Tadawul All-Share Index "TASI"
Figure 3: Closing prices against Lag prices for All-Share "TASI"
44
During Crisis
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
After Crisis
9,000
8,000 7,000
6,000 5,000
4,000 3,000
2,000 1,000
0
Figure 4: Financial crisis and random walk in TASI
45
4
1
9
3
9
7
3
7
5
3
5
3
3
3
1
3
0
9
2
8
7
2
6
5
2
4
3
2
2
1
1
9
9
1
7
7
1
5
5
1
3
3
1
1
1
8 9
6 7
4 5
2 3
1
9
8
9
9
3
7
8
8
5
8
3
3
7
8
1
7
2
9
6
7
7
6
2
5
5
7
3
5
2
1
4
6
9
4
1
7
3
6
5
3
1
3
2
6
1
2
0
9
1
5
7
1
0
5
5 3
1
Table 1: Tadawul Market Structure
Sector code
TASI
TBFSI
TPISI
TCESI
TRESI
TEUSI
TAFSI
TTISI
TINSI
TMISI
TIVSI
TBCSI
TRDSI
TTRSI
TMPSI
THTSI
Sector Name
Tadawul All Share Index
Banks & Financial Services Sector
Petrochemical Industries Sector
Cement Sector
Retail Sector
Energy & Utilities Sector
Agriculture & Food Industries Sector
Telecom & Information Technology Sector
Insurance Sector
Multi-Investment Sector
Industrial Investment Sector
Building & Construction Sector
Real Estate Development Sector
Transport Sector
Media and Publishing Sector
Hotel & Tourism Sector
No. of companies in the index
150
11
14 10
10 2
15 5
31 7
13 15
8432
Table 2: Summary Statistics for Tadawul
Daily Returns Min M ax M ean Std. Dev. Skewness Kurtosis
All Share TASI -.0998 .2 4 8 9 -.000106 .0206400 -.247 6 .5 0 0
TAFSI -.0963 .0 9 5 3 .000130 .0188385 -.429 5 .9 6 8
TBCSI -.0991 .0 9 8 7 -.000226 .0221368 -.607 4 .8 6 1
TBFSI -.0978 .0 9 1 3 -.000244 .0175964 .0 1 4 6 .1 9 7
TCESI -.0986 .0 9 7 5 -.000043 .0152281 -.249 10.400
TEUSI -.0982 .0 9 5 6 .000089 .0181705 .1 7 8 6 .1 5 4
THTSI -.0993 .2 4 8 9 .000302 .0261277 .5 8 7 9 .6 6 8
TINSI -.0956 .0 9 7 4 -.000131 .0226482 -.541 3 .1 7 7
TIVSI -.0981 .0 9 7 9 .000250 .0213593 -.646 4 .5 5 6
TMISI -.0979 .1 2 0 7 -.000475 .0230984 -.487 4 .9 3 5
TMPSI -.0996 .1 0 0 3 -.000646 .0216263 -.150 4 .8 5 1
TPISI -.0992 .0 9 8 9 .000441 .0233343 -.476 4 .4 0 5
TRDSI -.0995 .0 9 9 0 -.000492 .0189798 -.326 6 .2 5 3
TRESI -.0987 .0 9 9 1 .000214 .0181629 -.457 7 .4 3 2
TTISI -.0998 .0 9 9 0 -.000368 .0174865 -.285 6 .9 8 8
TTRSI -.0991 .0 9 7 7 -.000392 .0221046 -.146 5 .1 4 9
46
Table 3: Summary results for the unit root test
Dependent Variable: Price
Expected | = 1
Dependent Variable:
change in price
3
Sectors Index Expected | = 0
Slope: Se | T
Drift: o R
2
Slope: | Drift: o
| ( DF )
All-Share TASI 0 .9 9 6 2 3 .6 5 .0 0 2 -2 0 .9 9 3 -.003 23.267
1 TBFSI 0 .9 8 6 * 279* .0 0 3 - 4 .6 7 0 .9 7 7 -.004 66.525
2 TPISI 0 .9 9 7 1 4 7 .9 .0 0 2 -1.5 0 .9 6 9 -.003 21.613
3 TCESI 0 .9 9 7 1 2 .9 4 .0 0 2 -1.5 0 .9 9 6 -.002 10.833
4 TRESI 0 .9 9 1 43.87** .0 0 4 -2.25 0 .9 8 0 -.009** 42.980**
5 TEUSI 0 .9 8 9 5 0 .6 3 * .0 0 4 -2.75 0 .9 8 0 -.010** 46.556**
6 TAFSI 0 .9 8 9 5 4 .8 2 * .0 0 4 -2.75 0 .9 7 8 -.011** 53.020**
7 TTISI 0 .9 9 5 4 6 .9 1 * .0 0 2 -2.5 0 .9 8 2 -.005** 9 .2 8 6
8 TINSI 0 .9 9 8 2 .0 1 .0 0 2 -1 0 .9 9 6 -.002 1 .6 5 3
9 TMISI 0 .9 9 8 21.66*** .0 0 2 -1 0 .9 9 0 -.002 4 .8 8 8
10 TIVSI 0 .9 9 2 9 6 .4 7 * .0 0 4 -2 0 .9 7 3 -.008** 40.800**
11 TBCSI 0 .9 9 8 7 .6 1 .0 0 2 -1 0 .9 9 5 -.002 7 .6 1 6
12 TRDSI 0 .9 9 8 1 3 .5 6 .0 0 2 -1 0 .9 9 2 -.002 6 .1 8 9
13 TTRSI 0 .9 9 5 32.69** .0 0 3 -1.67 0 .9 8 3 -.005 15.354
14 TMPSI 0 .9 9 5 1 0 .4 8 .0 0 2 -2.5 0 .9 9 1 -.004** 7 .6 8 9
15 THTSI 0 .9 8 6 159* .0 0 5 -2.2 0 .9 5 9 -.014** 75.222*
* significant at 1% ** significant at 5% *** significant at 10%
3
Since returns on index is calculated as "change in index", using first difference or returns as a variable provided
similar results.
47
Table 4: Summary results for the four tests
Sample size = 23,488 observations
Correlation
Sectors
Index
DF Unit Root
Ho: Unit root
H o : No
correlation
Durbin-Watson Ho:
No autocorrelation
Runs-Test
Ho: Random Series
B Unit
Value Ranalom statdstics Ranalom staZstic Ranalom
All-
Share
1
2
3
4
5
6
7
8
9
10
11
TASI
TBFSI
TPISI
TCESI
TRESI
TEUSI
TAFSI
TTISI
TINSI
TMISI
TIVSI
TBCSI
0 .9 9 6
0 .9 8 6
0 .9 9 7
0 .9 9 7
0 .9 9 1
0 .9 8 9
0 .9 8 9
0 .9 9 5
0 .9 9 8
0 .9 9 8
0 .9 9 2
0 .9 9 8
ro o t
Don't
Reject
Re j e c t
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
0 .0 8 4
0 .1 0 9
0 .0 4 6
0 .0 6 0
0 .0 3 4
0 .2 0 3
0 .0 8 1
0 .0 6 1
0 .1 1 4
0 .0 9 4
0 .0 3 5
0 .1 3 0
d
Wk
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
i
2 .0 0 8
2 .0 0 3
2 .0 0 6
2 .0 0 3
1 .9 9 8
2 .0 0 3
2 .0 0 3
2 .0 0 3
2 .0 0 8
1 .9 9 8
2 .0 0 5
2 .0 0 8
d
Wk
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
Don't
Reject
ti
-1.438
-2.442
-0.698
-0.638
0 .5 8 2
2 .4 1 4
-1.511
-1.341
-2.855
1 .0 1 4
0 .9 3 0
-2.733
d
Wk
Don't
Reject
Re j e c t
Don't
Reject
Don't
Reject
Don't
Reject
Re j e c t
Don't
Reject
Don't
Reject
Re j e c t
Don't
Reject
Don't
Reject
Re j e c t
12
13
14
TRDSI 0.998
0 .9 9 5
TTRSI
TMPSI 0.995
Don't
Reject
Don't
Reject
Don't
Reject
Don't
0 .0 6 7
0 .0 4 3
0 .0 2 8
Don't
Reject
Don't
Reject
Don't
Reject
Don't
2 .0 0 3
1 .9 9 6
1 .9 9 8
Don't
Reject
Don't
Reject
Don't
Reject
Don't
0 .5 8 2
0 .5 8 4
1 .2 2 1
Don't
Reject
Don't
Reject
Don't
Reject
Don't
15 THTSI 0 .9 8 6
Reject
0 .0 3 7
Reject
2 .0 0 2
Reject
0 .0 0 1
Reject
Table 5: Financial crisis and the randomness of share prices for TASI
Correlation Runs-Test
States
df
DF Unit Root
Ho: Unit root
H o : No
correlation
Durbin-Watson Ho:
No autocorrelation
Ho: Random
Series
B
Unit
ro o t
Value
Random
Wa l k
Don't
d
statistics
Random
Wa l k
Don't
Z
statistic
Random
Wa l k
Don't
During-crisis 439
Don't 0.146
0.992 Reject
Reject
1 .9 7 7
Reject
-2.339
Reject*
Post crisis
1023 0.990 Reojn'tt 0.053 D
ec
Don't
Reject
1 .9 0 3
Don't
Reject
-0.469
Don't
Reject
* at 1% level of significance
48
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