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Do Stock Returns Follow a Finite Variance Distribution?

Author

Listed:
  • Qi-Man Shao

    (Department of Mathematics, University of Oregon Eugene)

  • Hao Yu

    (Department of Statistical and Actuarial Sciences, The University of Western Ontario London)

  • Jun Yu

    (Department of Economics, The University of Auckland)

Abstract

In this paper we propose a test statistic to discriminate between models with finite variance and models with infinite variance. The test statistic is the ratio of the sample standard deviation and the sample interquartile range. Both asymptotic and finite sample properties of the test statistic are discussed. We show that the test has good power properties against infinite-variance distributions and has small size distortions in finite samples. The statistic is applied to compare the competing models for S&P 500 index returns. Our test cannot reject most distributions with finite variance for both a pre-crash sample and a post-crash sample, and hence supports the literature. However, for a sample including crash days, our test suggests that the finite-variance distributions must be rejected.

Suggested Citation

  • Qi-Man Shao & Hao Yu & Jun Yu, 2001. "Do Stock Returns Follow a Finite Variance Distribution?," Annals of Economics and Finance, Society for AEF, vol. 2(2), pages 467-486, November.
    • Handle: RePEc:cuf:journl:y:2001:v:2:i:2:p:467-486
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    Citations

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    Cited by:

    1. Yuya Sasaki & Yulong Wang, 2020. "Testing Finite Moment Conditions for the Consistency and the Root-N Asymptotic Normality of the GMM and M Estimators," Papers 2006.02541, arXiv.org, revised Sep 2020.
    2. Szabolcs Majoros & Andr'as Zempl'eni, 2018. "Multivariate stable distributions and their applications for modelling cryptocurrency-returns," Papers 1810.09521, arXiv.org.
    3. Jacobi, Arie & Tzur, Joseph, 2021. "Wealth Distribution across Countries: Quality of Weibull, Dagum and Burr XII in Estimating Wealth over Time," Finance Research Letters, Elsevier, vol. 43(C).
    4. Naaman, Michael & Sickles, Robin, 2015. "The Volcano Distribution with an Application to Stock Market Returns," Working Papers 15-020, Rice University, Department of Economics.
    5. Zhang, Xingfa & Zhang, Rongmao & Li, Yuan & Ling, Shiqing, 2022. "LADE-based inferences for autoregressive models with heavy-tailed G-GARCH(1, 1) noise," Journal of Econometrics, Elsevier, vol. 227(1), pages 228-240.
    6. Yang, Yaxing & Ling, Shiqing, 2017. "Self-weighted LAD-based inference for heavy-tailed threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 197(2), pages 368-381.

    More about this item

    Keywords

    Stock Returns; Infinite Variance; Interquartile Range;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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