Abstract
This article investigates the types of probability distributions that can best represent equity returns using a large sample of daily S&P500 index returns. The competing models, Stable Paretian and Pearson families, are compared using Bayesian methods. The evidence against Stable Paretian as a model of S&P500 index returns is overwhelming. The distribution that best fits the data is Pearson Type IV, and Student's t fits almost as well. One implication is that a Bayesian decision maker should strongly shift beliefs in favor of a Pearson distribution with finite means and variances as a model of daily changes in the S&P500 stock index.
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