Journal of Quality Engineering and Management

Regression analysis of low beta anomaly in a stochastic portfolio with real market data

Document Type : Original Article

Authors

Soheila Mirzaei
Shokoufeh Banihashemi

Department of Mathematics and Computer Science, Faculty of Statistics, Allameh Tabatabaei University, Tehran, Iran.

https://doi.org/10.48313/jqem.2025.532332.1562
Abstract
Purpose: This research aims to empirically analyze the low beta anomaly within the framework of random basket theory using linear and quantile regression. This financial anomaly refers to the higher long-term returns of a portfolio of low-beta stocks than of a portfolio of high-beta stocks. This study examines the excess growth rate generated in a random portfolio based on this financial anomaly. The statistical population of this study consists of 8 stocks from the US stock market during the period 2015 to 2023.
Methodology: To achieve the research objectives, a continuous-time dynamic model with analytical solutions is proposed. To find its optimal weights or strategies, the "functionally generated portfolios" approach and the concept of "generating functions" are used. Finally, a regression analysis of US stock market data is conducted to examine the growth rate generated in this model.
Findings: The results show that investors are always trying to increase their investment returns by adopting an appropriate method. In this regard, higher returns from low-beta investment portfolios have been observed over the past few decades, and the use of random portfolios as a reasonable method to examine the portfolio's excess return in this financial anomaly is thus crucial.
Originality/Value: Given the innovative nature of this research in using stochastic portfolio theory to examine the excess growth rate generated based on the low beta anomaly, the results can help investors construct optimal portfolios with higher long-term returns.

Keywords

Portfolio generating functions
Beta risk measure
Low beta anomaly
Stochastic portfolio theory
Subjects
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Journal of Quality Engineering and Management
Volume 15, Issue 3
Autumn 2025
Pages 247-257

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