MPT and Mean Variance optimisation do not take into account fat tails and many other things like the problema in estimating the co variances etc. Nassim Taleb has been arguing this for a long time, following the ideas by Mandelbrot. They argues stock prices are fractals, but I couldn’t find what they suggest regarding portfolio construction: is there a “fractal” theory for portfolio construction?
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There seems to be some newer papers on this, though maybe not a consensus yet on the approach?
An Optimal Investment Portfolio Constructed with Fractal Analysis and Long Memory Models, by Robert Garafutdinov (Chapter in conference proceedings book, 2021)
https://link.springer.com/chapter/10.1007/978-3-030-89477-1_99
Fractal statistical measure and portfolio model optimization under power-law distribution, by Wu, Zhang, Li, Yan; North American Journal of Economics and Finance, Vol 58, November 2021
https://www.sciencedirect.com/science/article/abs/pii/S1062940821001169
