Probability Distributions for Modeling Stock Market Returns—An Empirical Inquiry

Jayanta K. Pokharel, Gokarna Aryal, Netra Khanal () and Chris P. Tsokos
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Jayanta K. Pokharel: Department of Business Analytics & Actuarial Science, Siena College, Loudonville, NY 12211, USA
Gokarna Aryal: Department of Mathematics and Statistics, Purdue University Northwest, Hammond, IN 46323, USA
Netra Khanal: Department of Mathematics, The University of Tampa, Tampa, FL 33606, USA
Chris P. Tsokos: Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA

IJFS, 2024, vol. 12, issue 2, 1-27

Abstract: Investing in stocks and shares is a common strategy to pursue potential gains while considering future financial needs, such as retirement and children’s education. Effectively managing investment risk requires thoroughly analyzing stock market returns and making informed predictions. Traditional models often utilize normal variance distributions to describe these returns. However, stock market returns often deviate from normality, exhibiting skewness, higher kurtosis, heavier tails, and a more pronounced center. This paper investigates the Laplace distribution and its generalized forms, including asymmetric Laplace, skewed Laplace, and the Kumaraswamy Laplace distribution, for modeling stock market returns. Our analysis involves a comparative study with the widely-used Variance-Gamma distribution, assessing their fit with the weekly returns of the S&P 500 Index and its eleven business sectors, drawing parallel inferences from international stock market indices like IBOVESPA and KOSPI for emerging and developed economies, as well as the 20+ Years Treasury Bond ETFs and individual stocks across varied time horizons. The empirical findings indicate the superior performance of the Kumaraswamy Laplace distribution, which establishes it as a robust alternative for precise return predictions and efficient risk mitigation in investments.

Keywords: asymmetric Laplace distribution; capital market; exceedance probability; Gaussian distribution; log-likelihood; Nelder–Mead optimization; variance-gamma distribution; skew Laplace distribution; stock index; Kumaraswamy Laplace distribution (search for similar items in EconPapers)
JEL-codes: F2 F3 F41 F42 G1 G2 G3 (search for similar items in EconPapers)
Date: 2024
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