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Room P3.10, Mathematics Building
David Taylor, Research and Actuarial Science Division, School of Management Studies, University of Cape Town, South Africa
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.