Investigating Chaos on the Johannesburg Stock Exchange

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.

Investment Implications of the Fractal Market Hypothesis

“…Sarpong et al (2016) found H ¼ 0:46 for the JSE using daily data from 1995 to 2015 (thereby embracing the full period investigated by Chimanga and Mlambo, 2014). In addition, Sarpong et al (2016) used the BDS test (Brock et al, 1996) to verify that JSE price index data exhibit non-random chaotic dynamics rather than pure randomness. These results confirm those obtained by Smith (2008) using four joint variance ratio tests, rejected the random walk hypothesis on the JSE.…”

“…Smith (2008) also found statistically significant results that H < 0:5, but over a shorter horizon and using daily (rather than monthly) data. Sarpong et al (2016) using daily JSE index data spanning 20 years from 1995 to 2015 also found H < 0:5 prior to 2012 and H % 0 after 2012. The South African market was also found to be more "sectorized" or heterogenous with respect to H; different market sectors are characterized by different values of H and these values tend to persist over time.…”

The impact of COVID-19 on the South African stock market: a sectoral-level analysis.

“…Affleck-Graves and Money (1975) subsequently presented findings that contradicted the study mentioned above, providing evidence supporting the weak form of efficiency. According to recent research conducted by Sarpong et al (2016), it has been argued that small-cap companies receive less attention or are completely overlooked by a significant number of analysts and investors. Consequently, the market for small stocks tends to exhibit inefficiencies compared to their large-cap counterparts, resulting in prices deviating from their fair values.…”