Download pdf
Do Stock Returns Adhere to the Distribution Stipulated by the Student’s T-distribution?
- 1 Wuhan Britain-China School
- 2 University of Toronto Scarborough
* Author to whom correspondence should be addressed.
Abstract
When people are analyzing data with thicker tails compared to the normal distribution, student’s t-distribution is commonly applied, making it potentially relevant in the financial markets, especially returns of a stock. This research focuses on estimating the parameters of the student’s t-distribution in empirical data, employing the maximum likelihood fitting method in order to determine accurate parameters of estimation. In order to conclude whether the t-distribution is close math or not, we assess the goodness of fit, where synthetic data is generated, and the Kolmogorov-Smirnov (KS) test is applied. Moreover, to determine if the t-distribution is the best fit for the data, a Likelihood ratio test is conducted. It provides a statistical comparison between t-distribution and alternative distributions, allowing us to select the most suitable model. Furthermore, the relationship between volatility and degrees of freedom is examined using a scatterplot. This aims to uncover any potential correlation or patterns between these variables. By undertaking these investigations, we deepened our understanding of the statistical characteristics of stock returns and gained insights for potential applications in financial modeling and risk analysis.
Keywords
Student’s t-distribution, Stock returns, Maximum likelihood estimation, Kolmogorov-Smirnov test, Degree of freedom
[1]. Hayes, A. (n.d.). What is T-distribution in probability? how do you use it?. Investopedia. https://www.investopedia.com/terms/t/tdistribution.asp#:~:text=The%20Bottom%20Line-,The%20t%2Ddistribution%20is%20used%20in%20statistics%20to%20estimate%20the,greater%20chance%20for%20extreme%20values.
[2]. Rossi, Richard J. (2018). Mathematical Statistics: An Introduction to Likelihood Based Inference. New York: John Wiley & Sons. p. 227. ISBN 978-1-118-77104-4.
[3]. What are logarithmic returns and how to calculate them in pandas dataframe. Saturn Cloud Blog. (2023, September 8). https://saturncloud.io/blog/what-are-logarithmic-returns-and-how-to-calculate-them-in-pandas-dataframe/#:~:text=Logarithmic%20returns%2C%20also%20known%20as,the%20value%20of%20an%20asset.
[4]. Clauset, A., Shalizi, C. R., & J., N. M. E. (2009). 3.3. In Power-law distributions in empirical data. essay, Arxiv.
[5]. Huelsenbeck, J. P., Hillis, D. M., & Nielsen, R. (1996). A likelihood-ratio test of monophyly. Systematic Biology, 45(4), 546–558. https://doi.org/10.1093/sysbio/45.4.546
Cite this article
Xiao,N.;Shi,W. (2024). Do Stock Returns Adhere to the Distribution Stipulated by the Student’s T-distribution?. Advances in Economics, Management and Political Sciences,92,233-239.
Data availability
The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
Disclaimer/Publisher's Note
The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of EWA Publishing and/or the editor(s). EWA Publishing and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.
About volume
Volume title: Proceedings of the 2nd International Conference on Financial Technology and Business Analysis
© 2024 by the author(s). Licensee EWA Publishing, Oxford, UK. This article is an open access article distributed under the terms and
conditions of the Creative Commons Attribution (CC BY) license. Authors who
publish this series agree to the following terms:
1. Authors retain copyright and grant the series right of first publication with the work simultaneously licensed under a Creative Commons
Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this
series.
2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the series's published
version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial
publication in this series.
3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and
during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See
Open access policy for details).