12. The Normal Distribution Myth
This is the thirteenth video in the open-source fortitudo.tech Python package playlist: https://github.com/fortitudo-tech/for...
The normal return distribution assumption has been made on many occasions in academic finance theories such as CAPM, Black-Litterman, and mean-variance.
However, most people with just a bit of practical investment experience understand that the assumption is incorrect, see the Portfolio Construction and Risk Management book: https://antonvorobets.substack.com/p/...
Some academics keep insisting that the old methods are not that bad, arguing for the existence of something called “Aggregational Gaussianity”, where log-returns should become closer to a normal distribution on longer horizons.
The academic arguments are based on some undefined central limit theorem (CLT), but when we test this against real-world data, it seems that this assumption does not hold.
The Normal Distribution Myth SSRN article (https://ssrn.com/abstract=5283255) performs several formal tests for normality of 10 US equity indices, using 26 years of daily data.
There are also several logical issues with using log-returns to justify the old theories on longer horizons that are carefully presented in the SSRN article.
You can also get a high-level description of the results in this Substack article: https://antonvorobets.substack.com/p/...
For a deep presentation and walkthrough of the next-generation investment framework, you can access the Applied Quantitative Investment Management course: https://antonvorobets.substack.com/t/...