Do Stock Returns Follow A Finite Variance Distribution ? 1

In this paper we propose a test statistic to discriminate between models with nite variance and models with in nite variance. The test statistic is the ratio of the sample standard deviation and the sample interquartile range. Both asymptotic and nite sample properties of the test statistic are discussed. We show that the test has good power properties against in nite-variance distributions and has small size distortions in nite samples. The statistic is applied to compare the competing models for S&P 500 index returns. Our test cannot reject most distributions with nite variance for both a pre-crash sample and a post-crash sample, and hence supports the literature. However, for a sample including crash days, our test suggests that the nite-variance distributions must be rejected.