Most mathematical analyses that I've seen involve running prior sequences of real-returns of various lengths though a monte-carlo simulation. So the distributio

Most mathematical analyses that I've seen involve running prior sequences of real-returns of various lengths though a monte-carlo simulation. So the distributions of prior returns is baked in (via a uniform sampling of historical timeframes). Here is a good example: https://www.portfoliovisualizer.com/monte-carlo-simulation https://www.portfoliovisualizer.com/monte-carlo-simulation Plenty of the white-papers from the big mutual fund firms give the impression they use very similar analysis methods.