**5. Application: testing the weak form of efficiency of emerging economies**

To put the theory in perspective, we have selected 24 countries which have emerging economies, from around the world, based on the MSCI Emerging Markets Index. These markets were classified into three groups within the Index. These are being Americas (Brazil, Chile, Columbia, Mexico and Peru); Europe, Middle East and Africa (the Czech Republic, Egypt, Greece, Hungary, Poland, Qatar, Russia, South Africa, Turkey and the United Arab Emirates); and, lastly, Asia (China, India, Indonesia, South Korea, Malaysia, Pakistan, the Philippines, Taiwan and Thailand).

To test whether the markets within these countries are weak form efficient or not, stock prices need to be analysed. It needs to be checked whether the prices are independent from each other or contain a unit root. Therefore, monthly stock price data was collected from the stock markets of these countries, from their major indices. Data covered the time period between February 2008 and May 2017, which signifies a time from the major 2008 global financial crisis until the current date. These stock prices were placed in the WinRATS programme to test the following hypothesis:

H0 : contains unit root (efficient market) (i.e. H0 : γ = 0).

Ha : stationary (inefficient market) (i.e. H<sup>a</sup> : γ < 0). If the null hypothesis holds, then it is said that the data contains a unit root and the market is efficient. However, if the null hypothesis is rejected, meaning that the alternative hypothesis holds, then the data is stationary and the market is not efficient.

There are many tests (linear or nonlinear) that can be used to test for the existence of a unit root. Although nonlinear tests being the most recent ones developed and supported by many researchers, in this application we have used the traditional augmented Dickey-Fuller (ADF) test to look for a unit root within our sample [60].

Dickey-Fuller (DF) test was developed particularly to observe the stationarity of the data and whether it contains a unit root. Augmented Dickey-Fuller test was developed after this classic DF test, and it is said to be more powerful and can even solve more complex models. There are three regression models in the DF test, such as

Model 1: *Δy<sup>t</sup>* = *γy<sup>t</sup>* − 1 + ԑ*<sup>t</sup>* Model 2: *Δy<sup>t</sup>* = *a*<sup>0</sup> + *γy<sup>t</sup>* − 1 + ԑ*<sup>t</sup>* Model 3: *Δy<sup>t</sup>* = *a*<sup>0</sup> + *γy<sup>t</sup>* − 1 + *a*2*<sup>t</sup>* + ԑ*<sup>t</sup>* For ADF test, the 'Dickey-Fuller test is augmented by the logs of Δy<sup>t</sup> Model 1: *<sup>Δ</sup> <sup>y</sup><sup>t</sup>* <sup>=</sup> *<sup>γ</sup> <sup>y</sup><sup>t</sup>*-1 <sup>+</sup> <sup>∑</sup>*<sup>i</sup>*=<sup>1</sup> *<sup>k</sup>* <sup>∆</sup> *<sup>y</sup><sup>t</sup>*-*<sup>k</sup>* <sup>+</sup> <sup>ԑ</sup>*<sup>t</sup>* Model 2: *<sup>Δ</sup> <sup>y</sup><sup>t</sup>* <sup>=</sup> *<sup>a</sup>*<sup>0</sup> <sup>+</sup> *<sup>γ</sup> <sup>y</sup><sup>t</sup>*-1 <sup>+</sup> <sup>∑</sup>*<sup>i</sup>*=<sup>1</sup> *<sup>k</sup>* <sup>∆</sup> *<sup>y</sup><sup>t</sup>*-*<sup>k</sup>* <sup>+</sup> <sup>ԑ</sup>*<sup>t</sup>*

Model 3: *<sup>Δ</sup> <sup>y</sup><sup>t</sup>* <sup>=</sup> *<sup>a</sup>*<sup>0</sup> <sup>+</sup> *<sup>γ</sup> <sup>y</sup><sup>t</sup>*-1 <sup>+</sup> *<sup>a</sup>*2*<sup>t</sup>* + ∑*<sup>i</sup>*=<sup>1</sup> *<sup>k</sup>* <sup>∆</sup> *<sup>y</sup><sup>t</sup>*-*<sup>k</sup>* <sup>+</sup> <sup>ԑ</sup>*<sup>t</sup>*

In these models, Model 1 has no constant and no trend, whereas Model 2 has a constant but again no trend. Model 3, however, has both constant and a trend. In this test the error terms are assumed to be homoscedastic and are serially independent from each other [61].

' [61]:

Results obtained from the WinRATS programme is presented in **Table 1** below. These results signify the tau values of the model. There will be higher chance to reject the null hypothesis when this obtained tau value is more negative, because it indicates a unit root at the confidence level [62]. Again, using the work of Dickey and Fuller, the resulting values for each country with a sample size of 112 were compared to the critical values provided by them [60]. The identified critical value at the 10% significance level was observed to be 2.73. Any result, after taking its absolute value, found to be above the critical value of 2.73, indicated the rejection of the null hypothesis, and hence the market observed was not efficient.

As mentioned in the previous sections, there are many contradicting results for market efficiency of countries. The reasons can be due to the time period used within the sample, sample size, type of tests used, etc. The general thought behind emerging markets was that these markets are mainly inefficient and therefore offer many opportunities for investors allowing them to generate above average returns. However, our results indicated that out of these 24 economies, only 7 of them were found to be stationary and hence inefficient at the 10% significance level. These economies were from Brazil, the Czech Republic, Egypt, Hungary, Poland, Russia and Taiwan. The rest of the economies were found to contain a unit root and therefore


If the null hypothesis holds, then it is said that the data contains a unit root and the market is efficient. However, if the null hypothesis is rejected, meaning that the alternative hypothesis

There are many tests (linear or nonlinear) that can be used to test for the existence of a unit root. Although nonlinear tests being the most recent ones developed and supported by many researchers, in this application we have used the traditional augmented Dickey-Fuller (ADF)

Dickey-Fuller (DF) test was developed particularly to observe the stationarity of the data and whether it contains a unit root. Augmented Dickey-Fuller test was developed after this classic DF test, and it is said to be more powerful and can even solve more complex models. There

In these models, Model 1 has no constant and no trend, whereas Model 2 has a constant but again no trend. Model 3, however, has both constant and a trend. In this test the error terms

Results obtained from the WinRATS programme is presented in **Table 1** below. These results signify the tau values of the model. There will be higher chance to reject the null hypothesis when this obtained tau value is more negative, because it indicates a unit root at the confidence level [62]. Again, using the work of Dickey and Fuller, the resulting values for each country with a sample size of 112 were compared to the critical values provided by them [60]. The identified critical value at the 10% significance level was observed to be 2.73. Any result, after taking its absolute value, found to be above the critical value of 2.73, indicated the rejection of

As mentioned in the previous sections, there are many contradicting results for market efficiency of countries. The reasons can be due to the time period used within the sample, sample size, type of tests used, etc. The general thought behind emerging markets was that these markets are mainly inefficient and therefore offer many opportunities for investors allowing them to generate above average returns. However, our results indicated that out of these 24 economies, only 7 of them were found to be stationary and hence inefficient at the 10% significance level. These economies were from Brazil, the Czech Republic, Egypt, Hungary, Poland, Russia and Taiwan. The rest of the economies were found to contain a unit root and therefore

are assumed to be homoscedastic and are serially independent from each other [61].

' [61]:

holds, then the data is stationary and the market is not efficient.

test to look for a unit root within our sample [60].

60 Financial Management from an Emerging Market Perspective

are three regression models in the DF test, such as

= *γy<sup>t</sup>* − 1 + ԑ*<sup>t</sup>*

+ *γy<sup>t</sup>* − 1 + ԑ*<sup>t</sup>*

+ *γy<sup>t</sup>* − 1 + *a*2*<sup>t</sup>*

*<sup>k</sup>* <sup>∆</sup> *<sup>y</sup><sup>t</sup>*-*<sup>k</sup>* <sup>+</sup> <sup>ԑ</sup>*<sup>t</sup>*

*<sup>k</sup>* <sup>∆</sup> *<sup>y</sup><sup>t</sup>*-*<sup>k</sup>* <sup>+</sup> <sup>ԑ</sup>*<sup>t</sup>*

*<sup>k</sup>* <sup>∆</sup> *<sup>y</sup><sup>t</sup>*-*<sup>k</sup>* <sup>+</sup> <sup>ԑ</sup>*<sup>t</sup>*

the null hypothesis, and hence the market observed was not efficient.

+ ∑*<sup>i</sup>*=<sup>1</sup>

+ ԑ*<sup>t</sup>*

For ADF test, the 'Dickey-Fuller test is augmented by the logs of Δy<sup>t</sup>

= *a*<sup>0</sup>

= *a*<sup>0</sup>

Model 1: *<sup>Δ</sup> <sup>y</sup><sup>t</sup>* <sup>=</sup> *<sup>γ</sup> <sup>y</sup><sup>t</sup>*-1 <sup>+</sup> <sup>∑</sup>*<sup>i</sup>*=<sup>1</sup>

Model 2: *<sup>Δ</sup> <sup>y</sup><sup>t</sup>* <sup>=</sup> *<sup>a</sup>*<sup>0</sup> <sup>+</sup> *<sup>γ</sup> <sup>y</sup><sup>t</sup>*-1 <sup>+</sup> <sup>∑</sup>*<sup>i</sup>*=<sup>1</sup>

Model 3: *<sup>Δ</sup> <sup>y</sup><sup>t</sup>* <sup>=</sup> *<sup>a</sup>*<sup>0</sup> <sup>+</sup> *<sup>γ</sup> <sup>y</sup><sup>t</sup>*-1 <sup>+</sup> *<sup>a</sup>*2*<sup>t</sup>*

Model 1: *Δy<sup>t</sup>*

Model 2: *Δy<sup>t</sup>*

Model 3: *Δy<sup>t</sup>*

**Table 1.** ADF test results of the 24 emerging economies. Note: The bold figures represent significance at 10% level.

can be said to be efficient in the weak form of information efficiency. These results provided an interesting ground for comparison to information efficiency literature, especially focusing on the post-crisis period.

There are many studies in the field and many different results. Looking at previous studies, we can see that when some support our evidence, some does not. For example, Zahid et al. tested the Karachi Stock Exchange (Pakistan) for the weak form of efficiency using various parametric and non-parametric tests, including ADF test, from period 13 March 2000 to 31 October 2011. Their results indicated that the market did not follow a random walk and, therefore, was not efficient [63]. However, our result does not support this and shows efficiency in the weak form. This example shows how using different dates and monthly data can cause the outcome to change.

Phiri, on the other hand, looked at the Johannesburg Stock Exchange to observe whether a unit root exits. Weekly data was collected from five indices, from the period between 31 January 2000 and 16 December 2014. Results of the study showed that, when applying the linear tests such as the ADF test, there was evidence showing the existence of weak form of efficiency, which supports our finding. However, when nonlinear tests were used, such as the Enders and Granger Test, then the results indicated a stationarity and showed inefficiency [29]. This example, now, indicates how the new methods for testing unit roots can be more powerful than the conventional linear tests.

Another interesting result obtained is from China. Our results indicate that the Chinese stock market, although it is perceived as highly speculative and driven by market rumours, is weak form efficient. Studies by Laurence et al., Liu et al. and Lima and Tabak show supporting evidence to our findings, whereas studies conducted by Mookerjee and Yu showed opposing results [64–67].

So, how do these results contribute? First of all, these results clearly break the idea that emerging markets are not efficient, even in the weak form. And, secondly, they specifically indicate a time period as of the financial crisis and are good reference point for researchers if they want to analyse the effects of the crisis on the stock markets.
