Efficient Market Hypothesis: Testing Weak Form in GCC Markets

Efficient Market Hypothesis and the Random Walk

The Efficient Market Hypothesis (EMH) in its weak form suggests that share prices should follow a random walk — that is, each change in share price is unpredictable based on past information. Formally, this is expressed in a relationship where the variables are independent and identically distributed random variables representing equity prices at times 1, 2, 3, …, k. In this formulation, X denotes the equity price at a given point in time n, and any change in equity price at a given moment is not explained by the past equity price.

Augmented Dickey-Fuller Test Framework

The Augmented Dickey-Fuller (ADF) test considers a model in which p is the lag order of the process, determinable by examination of autocorrelation and partial autocorrelation plots, and where the remaining factors are determined by regression. The unit root test carries the null hypothesis that a unit root is present; rejection of the null hypothesis implies that the time series is stationary. The variable y refers to the unit root: when the unit root changes over time in a predictable manner, y = 1, which implies a non-stationary process. In a stationary process, the mean and variance do not change in a predictable manner.

Thus, if the null hypothesis holds, the process is non-stationary, meaning that the mean and variance will change over time, following a trend. Those conditions, if they hold, mean that weak form EMH does not hold for the asset or market in question. A rejection of the null hypothesis would imply that weak form EMH does hold in the asset or market in question.

Methodology and Hypotheses

To determine weak form EMH in developed and GCC countries, a series of tests can be applied. If EMH holds, then the markets move in a random walk, which means that movements from one day to the next are not trend-bound and therefore cannot be predicted. The tests focus on establishing the conditions for the random walk.

H₀: GCC stock market returns are normally distributed.

Establishing whether returns are normally distributed is the first step in this type of analysis, because the statistical tests applied at later stages differ depending on whether market returns follow a normal distribution. The null hypothesis is therefore that GCC market returns are normally distributed, since this would support subsequent tests and would reflect random walk conditions (Jamaani & Roca, 2015). The alternate hypothesis is that the returns are not normally distributed.

H₀: Developed and GCC stock market returns are weak form efficient.

This null hypothesis is measured using a number of different tests that examine the degree of independence between market movements in both GCC and developed countries. The alternate hypothesis is that the stock market returns are not weak form efficient — that is, the returns show a trend. It is understood that evidence of semi-strong or strong form efficiency would also constitute evidence of weak form efficiency, but clarifying the alternate hypothesis properly requires this distinction.

Statistical Tests for Market Independence

A number of different statistical tests were undertaken to demonstrate the independence of market movements. These tests were the Augmented Dickey-Fuller (ADF), the Phillips-Perron (PP), the variance ratio (VR), Wright's ranks-and-signs test, the serial correlation test, the stationarity test, and the Hurst exponent analysis. The ADF test examines the unit root to determine whether the time series is stationary. A stationary time series implies that the mean and variance do not change in a predictable manner, which would indicate that weak form EMH holds. The Phillips-Perron (PP) test builds on the ADF test, using a slightly different methodology to test for independence within the data, again to support or reject the null hypothesis that developed and GCC markets demonstrate weak form EMH.

Variance ratio tests are also useful in testing the random walk hypothesis. The VR, Chow-Denning VR, and Wright's ranks-and-signs tests are all variance ratio tests. The maximum absolute value of individual variance ratio test statistics can be used to reject the null hypothesis. Chow-Denning, for example, is used to guard against large Type I errors in the standard variance ratio test (Chen, 2008). Wright's ranks-and-signs test introduces a different technique to evaluate the data, in particular reducing the impact of size distortions on the data set — that is, reducing the influence of massive single-day market moves — thus reducing size distortions within the data series (Wright, 2000).

The serial correlation test is used to detect autocorrelation errors in the original regression model. Stationarity testing seeks to determine whether the time series has a constant mean, variance, and autocovariance that do not change over time. While strict stationarity is unlikely, sufficient stationarity would support the null hypothesis that weak form EMH holds in developed and GCC stock markets.

References

Chen, J. (2008). Variance ratio tests of random walk hypothesis of the euro exchange rate. International Business & Economics Research Journal, 7(12), 97–105.

Jamaani, F., & Roca, E. (2015). Are the regional Gulf stock markets weak-form efficient as single stock markets and as a regional stock market? Research in International Business & Finance, 33, 221–246.

Wright, J. (2000). Alternative variance-ratio tests using ranks and signs. Journal of Business and Economic Statistics, 18, 1–9.