This paper studies expectations formation when the underlying process has fat tails. Using a large sample of firm sales growth expectations, we document three facts: (i) the relationship between forecast revisions and future forecast errors is strongly non-linear, (ii) the distribution of sales growth has fat tails, and (iii) extreme values of sales growth tend to mean-revert. We formally show that these three facts are consistent with a model in which the underlying process is non-Gaussian, but forecasters fail to recognize this fully. We estimate this model and show that it quantitatively explains our three facts. Finally, we show that the model is consistent with evidence from an online forecasting experiment where the underlying process is non-Gaussian and with the non-linearity in the momentum of stock returns.