@cluhmann, this is a very good point. I think this rationale explains what is happening here. Since the median is positive for the synthetic returns I’ve generated, the mean inferred by the StudentT model is influenced by that.
My initial intuition was completely wrong, since my goal is to infer a broader credible interval for the sharpe ratio, when fat tails are observed in the returns. Using the StudentT model seems to do the opposite, given that the credible interval is actually narrower for this case.
In other words, if I have 2 different returns vectors, the credible interval for the sharpe ratio of the fat tailed one should be broader (to account for uncertainty related to extreme events) than the other inferred for a normal returns vector (without fat tails). Any advice on how to accomplish such a model? The normal model does not either seem to exhibit the behavior I would like, although better than the StudentT model.
I’ve uploaded to github (with some modifications) the notebook I used to do the experiment, if anyone wants to reproduce.