The random walk theory and stock prices: evidence from Johannesburg stock exchange

Abstract

In this paper, we test the Johannesburg Stock Exchange market for the existence of the random walk hypothesis using monthly time series of the All Share Index (ALSI) covering the period 2000 2011. Traditional methods, such as unit root tests and autocorrelation test, were employed first and they all confirmed that during the period under consideration, the JSE price index followed the random walk process. In addition, the ARIMA model was constructed and it was found that the ARIMA (1, 1, 1) was the model that most excellently fitted the data in question. Furthermore, residual tests were performed to determine whether the residuals of the estimated equation followed a random walk process in the series. The authors found that the ALSI resembles a series that follow random walk hypothesis with strong evidence of a wide variance between forecasted and actual values, indicating little or no forecasting strength in the series. To further validate the findings in this research, the variance ratio test was conducted under heteroscedasticity and resulted in non-rejection of the random walk hypothesis. It was concluded that since the returns follow the random walk hypothesis, it can be said that JSE, in terms of efficiency, is on the weak form level and therefore opportunities of making excess returns based on out-performing the market is ruled out and is merely a game of chance.