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Probability Distributions for Modeling Stock Market Returns—An Empirical Inquiry

Author

Listed:
  • 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)

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.

Suggested Citation

  • Jayanta K. Pokharel & Gokarna Aryal & Netra Khanal & Chris P. Tsokos, 2024. "Probability Distributions for Modeling Stock Market Returns—An Empirical Inquiry," IJFS, MDPI, vol. 12(2), pages 1-27, May.
    • Handle: RePEc:gam:jijfss:v:12:y:2024:i:2:p:43-:d:1389236
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    References listed on IDEAS

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    1. Tomasz J. Kozubowski & Krzysztof Podgórski, 2000. "A Multivariate and Asymmetric Generalization of Laplace Distribution," Computational Statistics, Springer, vol. 15(4), pages 531-540, December.
    2. Poiraud-Casanova, Sandrine & Thomas-Agnan, Christine, 2000. "About monotone regression quantiles," Statistics & Probability Letters, Elsevier, vol. 48(1), pages 101-104, May.
    3. William McGill, 1962. "Random fluctuations of response rate," Psychometrika, Springer;The Psychometric Society, vol. 27(1), pages 3-17, March.
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