Time diversification and holding periods on the Johannesburg Stock Exchange - Panday, Akshay Kumar (Department of Finance and Tax, 2017)
This dissertation investigates the existence of time diversification on the Johannesburg Stock Exchange (JSE), with the goal of providing investor guidance toward their optimal investment horizon on the JSE Focusing on the Random Walk and Mean Reversion Models, a variety of tests were employed to identify serial correlation within the JSE logarithmic total returns. By assessing the possibility of mean reversion or trending behavior in returns, this study aims to determine if short-term variance (as a risk measure) calculation intervals accurately describe the long-term risk on the JSE when scaled. Additionally, the skewness of the logarithmic and arithmetic return distributions on the JSE, as the return interval lengthens, was investigated. The focus was on a composite JSE All Share Index (ALSI) resulting from the merger of the FTSE/JSE All Share Total Return Index (J203T), the JSE Actuaries Index (adjusted for dividends (AJ203)) and early JSE total return data (Firer & McLeod, 1999). The JSE All Bond Index (ALBI) was used in this study as an alternate asset class to JSE Equities. The dataset is comprised of 117 years (01/01/1900 to 31/12/2016) of ALSI and 18 years (31/12/1998 to 31/12/2016) of ALBI price and return series. The frequency of returns analyzed range from monthly to twenty-year total returns. The dataset was further analyzed, into a period before and after 1987 to observe the long and short-term serial correlation dynamics of the JSE, and to investigate how these change over time. This breakpoint (1987) was chosen due to the belief that structural change occurred on the JSE after 1986. Data analysis included; descriptive statistics and tests for normality, the Augmented Dickey Fuller and Phillips-Perron tests for stationarity, the Autocorrelation Function tests for serial correlation, the Quandt-Andrews and Bai-Perron tests for structural breaks, the Variance Ratio Test, and the Runs Test. These parametric and nonparametric methods were performed on both the nominal and real total returns of the ALSI and ALBI. This investigation uncovered significant short-term trending behavior in the ALSI returns, combined with evidence of medium-term mean reversion in this indexes returns. A lack of mean reversion and limited evidence of trending behavior in the ALBI returns were uncovered. ALSI returns have rejected the Random Walk Model over the short and medium-term, while ALBI returns have for the most part, failed to significantly reject the Random Walk Model. The short-term trending behavior in ALSI returns was observed at the monthly, quarterly and semi-annual return frequencies. This behavior suggests that if variances (as risk measures) calculated over these shorter trending periods, are scaled to represent the risk of longer periods, they will underestimate the true period risk on the JSE. Furthermore, the implications of the mean reversion evidence in three yearly returns, suggest that if the variances (as risk measures) are calculated over these three-year periods, and were to be scaled to represent the variance of longer periods, then these longer periods would have their period risk overstated. This paper has documented the change in the logarithmic return distribution of the ALSI, that exhibited negative skewness as the return holding period lengthens. Paradoxically positive skewness is observed as the return holding period increased was observed for the arithmetic distribution of ALSI returns. In the presence of autocorrelation in ALSI returns, portfolio and fund managers should employ the Lo and MacKinlay (1988) variance adjustment to unbias their risk estimates - if they scale short or medium term variances. The existence of Mean Reversion at the three-year frequency in South African Equities, provides evidence to support Time Diversification. As a direct result of this, this study proposes that a five to six-year holding period is optimal to take advantage of these mean reverting returns.