Do Stock Returns Follow a Finite Variance Distribution?

Qi-Man Shao

In this paper we propose a test statistic to discriminate between models with finite variance and models with infinite variance. The test statistic is the ratio of the sample standard deviation and the sample interquartile range. Both asymptotic and finite sample properties of the test statistic are discussed. We show that the test has good power properties against infinite-variance distributions and has small size distortions in finite samples. The statistic is applied to compare the competing models for S&P 500 index returns. Our test cannot reject most distributions with finite 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 finite-variance distributions must be rejected.