56 Journal of Economics and Behavioral Studies (ISSN: 2220-6140) Vol. 8, No. 5, pp. 56-67, October 2016 Investigating Chaos on the Johannesburg Stock Exchange Prince Kwasi Sarpong CFP, Mabutho Sibanda, Merle Holden University of KwaZulu-Natal, Durban, South Africa p.k.sarpong@live.com, sibandam@ukzn.ac.za, merleholden@gmail.com Abstract: This study investigates the existence of chaos on the Johannesburg Stock Exchange (JSE) and studies three indices namely the FTSE/JSE All Share, FTSE/JSE Top 40 and FTSE/JSE Small Cap. Building upon the Fractal Market Hypothesis to provide evidence on the behavior of returns time series of the above mentioned indices, the BDS test is applied to test for non-random chaotic dynamics and further applies the rescaled range analysis to ascertain randomness, persistence or mean reversion on the JSE. The BDS test shows that all the indices examined in this study do not exhibit randomness. The FTSE/JSE All Share Index and the FTSE/JSE Top 40 exhibit slight reversion to the mean whereas the FTSE/JSE Small Cap exhibits significant persistence and appears to be less risky relative to the FTSE/JSE All Share and FTSE/JSE Top 40contrary to the assertion that small cap indices are riskier than large cap indices. Keywords: Fractal Market Hypothesis; Efficient Market Hypothesis; Chaos Theory; Rescaled Range Analysis 1. Introduction Financial crises, such as the ones that occurred in 1987, 1998, 2000 and then recently in 2007, have been brushed off as anomalies by proponents of the Efficient Market Hypothesis (EMH) who maintain that markets remain informationally efficient. However, the frequency with which these crises occur cannot be explained by the underlying assumptions of an efficient market. Although a study by Bendel, Smit and Hamman (1996) provides a special impetus on the behaviour of the stock market time series using a variety of indices, results were somehow mixed across indices. However, evidence of long-run persistence in the overall share returns were observed suggesting that future returns are influenced by past returns at least in the long term (Bendel, Smith & Hamman, 1996) which cultivates the need for further interrogation of the behaviour of share returns in modern economies. Classical finance theory is based, inter alia, on the assumptions of investors being rational, of informationally efficient markets and market equilibrium. Equilibrium infers the nonexistence of emotional forces like greed and fear, which trigger the economy to evolve and to adjust to new conditions. Regulating such human tendencies are desirable to minimise their effects, but doing away with them, however, Dzwould take away the life out of the system, including the far from equilibrium conditions that are necessary for developmentdz ȋPeters, 1996: 5). This study applies the BDS test as described by Brock, Dechert and Scheinkman (1996) to test for the null hypothesis that the return series of the selected indices are pure noise or completely random. The BDS test, inter alia, has the ability to identify different kinds of deviations from randomness be it non-linear or linear stochastic processes and deterministic chaos. The BDS test is the most popular test for non-linearity and was originally created to test for the null hypothesis of independent and identical distribution (iid) aimed at identifying non-random chaotic dynamics (Zivot & Wang, 2006). The study further applies the rescaled range analysis developed by Hurst (1951) to detect persistence, mean reversion or randomness on the Johannesburg Stock Exchange (JSE) with the aim of providing more adequate assumptions and consequently more realistic models of financial behaviour on the JSE. Closely related to the rescaled range analysis is the Hurst exponent, which is indicated by H, sometimes referred to as Ǯthe index of dependenceǯ, which measures three kinds of trends in a given time series, namely, mean reversion, persistence and randomness. The rescaled range analysis was widely used in financial analysis when the application of chaos theory in financial analysis was popular in the early 1990s (Voss, 2013).