Testing the efficient market hypothesis on the Nairobi Securities Exchange

This paper tests the weak-form of the efficient market hypothesis (EMH) of the Nairobi Securities Exchange (NSE) using daily and weekly index data from the NSE 20 share index over the period, January 2001 to January 2015 and the NSE All Share Index (ASI) from its initiation, in February 2008 to January 2015. To test weak-form efficiency in this market, this study uses the serial correlation test, unit root tests (ADF and Phillips-Perron) and runs test. Results indicate that we cannot accept the EMH for the NSE using the serial correlation test, unit root tests and the runs test. Overall, the Kenyan market is found to not be weak-form efficient.


Introduction ©
The efficiency of a stock exchange is extremely important as it enables for the prices to fully incorporate information (Antoniu, Ergul and Holmes, 1997). It is only in this case that prices can provide the correct signals for efficient capital allocation. Fama and Litterman (2012) add that market efficiency indicates that prices reflect all available information and, hence, provide accurate signals for allocating resources to their most productive uses. Kim and Singal (2000) emphasize that advantages to the more efficient market are better allocation of capital and an increase in the productivity of capital.
The efficiency of stock markets is considered to have increased compared to the level of efficiency many years ago. This has been attributed to the advancement in technology that has enabled information to quickly reflect on the share prices. In a study conducted by Yang, Kwak, Kaizoji and Kim (2008) that analyzed the time series of the Standard and Poor's 500 Index (S & P 500), the Korean Composite Stock Price Index (KOSPI) and the Nikkei 225 Stock Average (NIKKEI), it was observed that, before the year 2000, information used to get by slowly, hence, resulting in the markets being less efficient. However, information flow is currently faster and more even because of the rapid development of communication through high speed internet, mobile technologies, and worldwide broadcasting systems. The expectation is of the present stock markets to become more efficient than past markets, confirming the EMH (Yang et al., 2008).
Automation of stock exchanges has enhanced information efficiency, as it facilitates the process of market prices quickly reflecting new information. Ciner (2002) investigated the information content of trading volume on the Toronto Stock Exchange before and after the move towards fully electronic trading. The empirical analysis supports more accurate price discovery after electronic trading. The findings of the study indicate that the predictive power of volume for price variability disappears after full automation. Naidu and Rozeff (1994) scrutinize the reasons why automation could influence aspects of trading with one being the market efficiency of the Singapore Stock Exchange after it fully automated in 1989. It suggests that improvements in market efficiency appear in reduced serial correlations of returns.
Since 2000, there have been both regulatory and technological developments. Cognizant of the observation by Yang et al. (2008) that, as a result of technology, market efficiency increased significantly from the year 2000 and that by Lim (2009) on using both linear and non-linear tests to determine market efficiency, it is only proper to re-visit the issue for the NSE.
The purpose of this study is to assess the current level of efficiency of the NSE using daily and weekly index data from the NSE 20 share index, and the NSE ASI. The methods that were used to analyze the daily and weekly index data are the serial correlation test, unit root tests and the runs test. These tests focus on the absolute efficiency approach and will be able to show whether the NSE is efficient or not. The contributions of this paper are, firstly, that the study tested the marketefficiency of the NSE using two indexes, the NSE 20 share index, and the NSE ASI. The latter has not been used as data for any prior study on the NSE. Preceding studies have used either the NSE 20 share index or share prices of individual shares. Secondly, this study also conducted one of the longest studies on the NSE that has ever been conducted, as the sample period was from January 2001 to January 2015 for the NSE 20 share index which is over a period of fourteen years. While for the NSE ASI, the study was from when the index was initiated in February 2008 to January 2015 which is a period of approximately seven years.
The rest of this paper is organized as follows. Section 1 discusses the literature review. Section 2 describes the data. Section 3 discusses the data. Section 4 presents the results and final section summarizes the findings and provides conclusions.

Literature review
The theory of efficient markets is concerned with whether prices at any point in time "fully reflect" available information (Fama, 1970). There is a natural mechanism for financial markets to converge towards an efficient state through price competition among market operators and exploitation of available arbitrage opportunities. As more market operators perform these arbitrage operations to take advantage of the price differential, it forces the share prices to their efficient values. Subsequently, profit opportunities are eliminated as the market moves to equilibrium, at this point, the market is efficient. The convergence mechanism explains the process through which the market learns about new information. The speed of convergence is as quick as the market is liquid and large, and information is freely accessible and costless (Arouri, Jawadi and Nguyen, 2010).
For years, empirical testing has been a subject of major stock markets, the same cannot be said of many emerging markets (Jefferis and Smith, 2004). However, new empirical methods have been developed which provide new opportunity for analysis of efficiency in both developed and emerging markets. Antoniu et al. (1997) are of the opinion that the conventional tests of efficiency have been developed for testing markets which are characterized by high level of liquidity, sophisticated investors with access to high quality and reliable information and few institutional impediments. On the other hand, emerging markets are typically characterized by low liquidity, thin trading, considerable volatility and, possibly, less well informed investors with access to unreliable information. Arouri et al. (2004) report the majority of emerging markets are less efficient than developed markets because of some market imperfections. As a result, recent studies on emerging markets have focused on the weak-form efficiency, whereas literature on developed markets is concerned about all three forms of efficiency. Several factors effectively contribute to prevent emerging markets from being efficient. These are infrequent and discontinuous trading, low market liquidity, low quality and quantity of information disclosure, untimely financial reporting and inappropriate accounting regulations, capital flow restrictions and market regulation, and discriminatory taxation (Arouri et al., 2010).
Ngugi, Murinde and Green (2002) investigate the response of emerging stock markets in Africa to various reforms implemented during the revitalizing process capturing mainly market efficiency and volatility during the period January 1988 to December 1999, specifically, for the NSE. The three main types of reforms implemented in these markets since the 1990s are identified, in other words, revitalization of the regulatory framework, modernization of trading systems and relaxation of restrictions on foreign investors. The authors find that there are benefits of investments to improve market microstructure. Markets with advanced trading technology, tight regulatory system and relaxed foreign investors' participation show greater efficiency and lower market volatility. In general, it is deduced that reforms help to reduce volatility which, in turn, leads to higher efficiency. Mlambo and Biekpe (2003) observe that stock markets around the world are making efforts to improve market efficiency by improving information dissemination, making stock price information accessible to a broader range of investors and introducing electronic or computerbased trading systems. This has enabled market participants to have equal opportunities to access all relevant information. There is a positive correlation between most stock market development indicators and internet access; therefore, stock market liquidity and efficiency can be improved by providing information online and also promoting the infrastructure to improve internet accessibility.
Previous studies that have been conducted on the Kenyan market have been summarized on Table 1 below. Most of these studies have found the NSE to be weak-form efficient other than the study by Ngugi et al. (2002) and Smith, Jefferis and Ryoo (2002).
where γ 1 is the covariance at lag k and γ 0 is the variance. Therefore, when autocorrelations are present, the first order autoregressive process contains values of ε t lagged by just one period, indicating that the disturbance in period t is influenced by the disturbance in the previous period, Serial correlations test is a parametric test, it requires returns to be normally distributed. It is the best test for examining weak-form efficiency, because the relationship between price changes in the current period and its value in the previous period is measured (Abedini, 2009).

Unit root tests. Application of the Augmented
Dickey Fuller (ADF) test is appropriate to determine a unit root. It is based on the following ordinary least squares (OLS) regression (Abedini, 2009): where γ t equals the logarithm of a stock price at time t 1 , ∆ stands for changes, and ∆ is a sequence of independent, normally distributed random variables with a mean of zero and constant variance while k is the number of lagged changes. Buguk and Brorsen (2003) indicate that the ADF test statistic is the ratio of the estimated to its calculated standard error obtained from an OLS regression. The authors add that the null hypothesis is b = 0 against the one-sided (lowertail) alternative hypothesis, b < 0. The null hypothesis is rejected if the pseudo t statistic is larger than the critical value.
The Phillips-Perron test is a non-parametric method to test unit root and is similar to the Dickey-Fuller test (Liu, 2011). It incorporates an alternative (non-parametric) method of controlling for serial correlation when testing for a unit root by estimating the non-augmented Dickey-Fuller test equation and modifying the test statistic so that its asymptotic distribution is unaffected by serial correlation (Worthington and Higgs, 2006). The Z t statistic of Perron (1987, 1988) is a modification of the Dickey-Fuller t statistic which allows for autocorrelation and conditional heteroskedasticity in the error term of the Dickey-Fuller regression. This is based on the estimation of the equation: The equation that shows the random walk relationship is: If the AR 1 regression equals p = 1, the time series γ t has a unit root it is equal to zero (δ = 0). Therefore, if the time series has a unit root, it is non-stationary. The presence of a unit root indicates support for the random walk hypothesis (RWH) implying market efficiency (Lagoarde-Segot and Lucey, 2008).  (6) and the standard normal Z-statistic to test the hypothesis is:

Runs test.
where R = actual number of runs, m = expected number of runs and 0.5 = continuity adjustment. If R m, the Z value is negative which implies a positive serial correlation. The positive serial correlation means that there is a positive dependence of stock price indicating a violation of the RWH (Patel et al., 2012).
Runs test determines whether successive price changes are independent (Abraham, Seyyed and Alsakran, 2002). It is a non-parametric test as it does not require returns to be normally distributed (Urquhart and Hudson, 2013), that is, its validity is not dependent on the shape of the underlying distribution hence a fitting statistical technique to test the weak-form market efficiency (Abedini, 2009). It is considered to be a linear test and it can also detect non-linearity in a returns series, although the results differ from the linear test. Moreover, this test is not affected by any extreme values in the return series, therefore, it does not require constant variance of the data (Mlambo and Biekpe, 2007). It serves as a good complement to the serial correlation test, because, while serial correlation coefficients may be significantly affected by a single outlier, the results from the runs test are not seriously affected by a few outliers.

Data
The data were availed from the NSE and from Bloomberg. The market efficiency of the NSE is analysed using the NSE 20 share index and the NSE ASI using both daily and weekly data respectively. In total, four time series were analyzed. The start of the period for the NSE 20 share index is January 2001 and for the NSE ASI is February 2008 when it was initiated. The end of the period for both indexes is in January 2015. Each of the indexes is traded on the main investment market segment of the exchange. The currency base denominated is in Kenyan Shillings (KES). The data that were analysed consisted of index returns that are transformed to natural logs of both the daily and weekly prices of the index.
The price returns (r t ) are expressed in percentage terms were calculated as the ending index price minus the beginning index price divided by the beginning index price multiplied by 100. The natural logarithm (ln) of the price returns was calculated for each of the time series on MS Excel.
The results of which were transferred to the Eviews software for analysis of the descriptive statistics, serial correlations test and unit root tests. The same results were also transferred to the SPSS software to conduct the runs test.

Data analysis. 3.1.1. Descriptive statistics.
The skewness of all four time series is positive which means that the distribution has a right tail. The kurtosis of all four time series is greater than 3 this means the tail of the graph of the density function is short/fat thus leptokurtic. All four time series have Jarque-Bera statistics that are significantly higher than the 0.05 critical value of 5.99. We reject the null hypothesis of a normal distribution and accept the alternative hypothesis of non-normal distribution. Results of the descriptive statistics are reported in Table 2 below.  Table 4 below.  Table 4 below.