There exist a large number of metrics to evaluate the performance-risk trade-off of a portfolio. Although those metrics have proven to be useful tools in practice, most of them require a large amount of data and implicitly assume returns to be normally distributed. Bayesian modeling is a statistical framework that allows great flexibility in modeling financial returns as well as risk metrics. In addition, uncertainty of these metrics can be directly quantified in terms of the posterior distribution.
In this talk I will briefly provide an overview of Bayesian statistics and how Probabilistic Programming frameworks like PyMC can be used to build and estimate complex statistical models. I will then show how several common financial risk metrics like the Sharpe ratio can be expressed as a probabilistic program. Using real-world data from anonymized algorithms running on Quantopian I will demonstrate how the normality assumption can strongly bias the Sharpe ratio and how heavy-tailed distributions can remedy this problem.
Thomas Wiecki received his PhD from Brown University where he developed Bayesian models to help understand brain disorders. He currently works as the data science lead at Quantopian. Among other projects, he is involved in the development of PyMC — a probabilistic programming framework written in Python.