Aggregational Gaussianity Using Sobol Sequencing In the South African Equity Markets: Implications for the Pricing of Risk

Stylized facts of asset returns in the South African market have received extensive attention, with multiple studies published on non-normality of returns, heavy-tailed distributions, gain-loss asymmetry and, particularly, volatility clustering. The one such fact that has received only cursory attention world-wide is that of Aggregational Gaussianity - the widely-accepted/stylized fact that empirical asset returns tend to normality when the period over which the return is computed increases. The aggregational aspect arises from the \(n\)-day log-return being the simple sum of \(n\) one-day log-returns. This fact is usually established using Q-Q-plots over longer and longer intervals, and can be qualitatively confirmed. However, this methodology inevitably uses overlapping data series, especially for longer period returns. When an alternative resampling methodology for dealing with common time-overlapping returns data is used an alternate picture emerges. Here we describe evidence from the South African market for a discernible absence of Aggregational Gaussianity and briefly discuss the implications of these findings for the quantification of risk and to the pricing and hedging of derivative securities.