Probabilistic alpha and beta: quantifying an uncertain edge

In finance, the performance of an asset is often quantified by alpha (the excess returns above a benchmark return) and beta (the volatility or risk of the asset relative to a benchmark). In this post, we develop time-varying, probabilistic versions of alpha and beta, and go through the process of using these new metrics to build a dynamic stocks/bonds portfolio to improve on the classic 60/40 portfolio.

Illustration of the S&P500 return distribution and 23 sigma intervals.

The 23-sigma fallacy

This is the first post of a short series of posts on extreme events in financial time series. We will investigate the return distribution of financial assets, use power-law theory to describe its tails, see how estimating higher moments such as kurtosis becomes meaningless, and finally discuss a fundamental flaw in popular models such as … Read more