Small sample power of tests of normality when the alternative is an alpha-stable distribution

This paper is a Monte-Carlo study of the small sample power of six tests of a normality hypotheses when the alternative is an alpha-stable distribution with param- eter values similar to those estimated for monthly total returns on equity indices. In these circumstances a sample size of 2oo is required to detect departures from normality. In most cases only small samples of consistent monthly data on such to- tal returns are available and these are not sufficient to differentiate between normal and alpha-stable distributions.