The Informational Content in Lepto-Variance and Its Relation to Higher Moments
Abstract
Lepto-regression is defined as the machine learning process of constructing a Regression Tree of a target feature on itself. It is a novel, model-free method potentially revealing information on important sample structure properties. But it is yet not clear what the informational content of lepto-variance is and how it is related to other well-known statistics of a sample. One significant finding is that 58% of the historical US stock return variability is 1-bit lepto-variance that can not be explained by any financial factor. The central question investigated in this paper is to use small normal N(0, 1) drawn samples to explore how the 1-bit sample lepto-variance and lepto-ratio relate to sample variance, skewness and excess kurtosis. Using a large sample simulation, the lepto ratio of a normal is found to converge to 36.3%. For smaller normally distributed simulated N(0, 1) samples, while lepto-variance itself is highly correlated to sample variance, lepto-variance as a fraction of total variance is highly correlated to excess kurtosis. Both lepto-variance and lepto-ratio are orthogonal to sample skew. Another finding is that while lepto-ratio is strongly correlated to lepto-variance it remains orthogonal to sample variance.
Versions
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BibTeX
@misc{polimenis2026informational,
title = {{The Informational Content in Lepto-Variance and Its Relation to Higher Moments}},
author = {Vassilis Polimenis},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25144},
eprint = {2609.25144},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25144},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Informational Content in Lepto-Variance and Its Relation to Higher Moments
AU - Vassilis Polimenis
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.25144
UR - https://arxiv.org/abs/2609.25144
AB - Lepto-regression is defined as the machine learning process of constructing a Regression Tree of a target feature on itself. It is a novel, model-free method potentially revealing information on important sample structure properties. But it is yet not clear what the informational content of lepto-variance is and how it is related to other well-known statistics of a sample. One significant finding is that 58% of the historical US stock return variability is 1-bit lepto-variance that can not be explained by any financial factor. The central question investigated in this paper is to use small normal N(0, 1) drawn samples to explore how the 1-bit sample lepto-variance and lepto-ratio relate to sample variance, skewness and excess kurtosis. Using a large sample simulation, the lepto ratio of a normal is found to converge to 36.3%. For smaller normally distributed simulated N(0, 1) samples, while lepto-variance itself is highly correlated to sample variance, lepto-variance as a fraction of total variance is highly correlated to excess kurtosis. Both lepto-variance and lepto-ratio are orthogonal to sample skew. Another finding is that while lepto-ratio is strongly correlated to lepto-variance it remains orthogonal to sample variance.
ER -