The search for a distribution which accurately describes the behavior of stock price returns has generated a considerable amount of controversy. While it is well known that the traditionally used assumption of lognormality deviates in systematic ways from the empirically observed—the latter has fatter tails and a larger concentration of mass near zero—none of the alternatives that have been proposed over the years (Stable Paretian—Mandelbrot [5], Poisson mixture of; lognormal distributions—Press [10], scaled T distribution—Praetz [9], lognormal with nonstationary variance—Rosenberg [11], subordinate stochastic process—Clark [2]) has gained general acceptance.