Excluding sum stable distributions as an explanation of second moment condition failure - the Australian evidence

This paper examines the issue of stock return moments in the Australian stock market. The existence of at least second moments is a fundamental assumption of underlying finance theory. We determine, using characteristic exponent point estimates, that the population variance may be infinite but on the same data, we also find that Hill-estimates are above 2 for all stocks, indicating that second moments do exist. This conflicting result is resolved by setting up a simulation experiment in which we show that the empirical combination of the Hill-estimate and the characteristic exponent lies outside the simulated confidence intervals for sum stables. This enhances the evidence for the existence of second moments in Australian stock returns.

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