Fractal Analysis and Alternatives to Mean–Variance Portfolio Construction
Summary
The document questions whether modern portfolio theory and mean–variance optimization adequately address fat-tailed returns and the difficulty of estimating covariances. It asks whether ideas associated with Mandelbrot and Taleb, including fractal descriptions of asset prices, lead to a distinct approach to portfolio construction.
The response points to two 2021 research works as possible starting points: one combines fractal analysis with long-memory models, and another studies portfolio optimization under power-law distributions. These references suggest that researchers have explored alternatives that account for nonstandard return behavior. However, the document does not explain either method, compare its assumptions with mean–variance optimization, or report empirical performance. It also notes that there may not be a settled consensus, so the cited papers are leads for further study rather than evidence that a particular fractal portfolio method is established or superior.
Key ideas
- Mean–variance optimization can be sensitive to covariance estimation and may not represent fat-tailed returns well.
- The question connects fractal descriptions of asset prices with portfolio construction.
- Cited research explores fractal analysis, long-memory models, and power-law distributions.
- The document offers research leads but does not explain or evaluate the proposed methods.
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Full text
# Portfolio construction: If modern portfolio theory is not good than what else? # Portfolio construction: If modern portfolio theory is not good than what else? 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? ## Answer by Mike (score 1) https://quant.stackexchange.com/a/70525 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 ```
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