Abstract
We present a simple but effective procedure for determining whether a reasonably large sample comes from a stable population against the alternative that it comes from a population with finite higher moments. The procedure uses the fact that a stable population sample has moments of the fourth and sixth order whose magnitudes increase very rapidly as the sample size increases. This procedure shows convincingly that stock returns, when taken as a group, do not come from stable populations. Even for individual stocks, our results show that the stable-population- model null hypothesis can be rejected for more than 95% of the stocks.