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Linear Scale Dilation of Asset Returns

Published: 2 April 2013
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Abstract

Comparing the order statistics of daily returns of the S&P 500 index from 03.01.1950 to 04.03.2013 with the corresponding rankits, a linear scale dilation is observed. This observation is used to derive a five-parameter density function for the parsimonious description of the unconditional distribution of stock returns. The typical graph of this density function looks like a wizard's hat. Its signature feature is the discontinuity at zero.

Published in American Journal of Theoretical and Applied Statistics (Volume 2, Issue 2)
DOI 10.11648/j.ajtas.20130202.15
Page(s) 38-41
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2013. Published by Science Publishing Group

Keywords

Discontinuity, Rankits, Stock Returns, Unconditional Distribution

References
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[3] A. Azzalini, The skew-normal distribution and related multivariate families, Scandinavian Journal of Statistics 32, pp. 159-188, 2005.
[4] F. M. Aparicio and J. Estrada, Empirical distributions of stock returns: European securities markets, 1990-95, The European Journal of Finance 7, pp. 1-21, 2001.
[5] T. Bollerslev, Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics 31, pp. 307-327, 1986.
[6] R. F. Engle, Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation, Econometrica 50, pp. 987-1007, 1982.
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[8] C. Fernandez and M. F. Steel, On Bayesian modeling of fat tails and skewness, Journal of the American Statistical Association 93, pp. 359–371, 1998.
[9] S. J. Kon, Models of stock returns - a comparison, The Journal of Finance 39, pp. 147-165, 1984.
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[14] H. T. Robertson and D. B. Allison, A novel generalized normal distribution for human longevity and other negatively skewed data, PLoS ONE 7, e37025, 2012.
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  • APA Style

    E. Reschenhofer. (2013). Linear Scale Dilation of Asset Returns. American Journal of Theoretical and Applied Statistics, 2(2), 38-41. https://doi.org/10.11648/j.ajtas.20130202.15

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    ACS Style

    E. Reschenhofer. Linear Scale Dilation of Asset Returns. Am. J. Theor. Appl. Stat. 2013, 2(2), 38-41. doi: 10.11648/j.ajtas.20130202.15

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    AMA Style

    E. Reschenhofer. Linear Scale Dilation of Asset Returns. Am J Theor Appl Stat. 2013;2(2):38-41. doi: 10.11648/j.ajtas.20130202.15

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  • @article{10.11648/j.ajtas.20130202.15,
      author = {E. Reschenhofer},
      title = {Linear Scale Dilation of Asset Returns},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {2},
      number = {2},
      pages = {38-41},
      doi = {10.11648/j.ajtas.20130202.15},
      url = {https://doi.org/10.11648/j.ajtas.20130202.15},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20130202.15},
      abstract = {Comparing the order statistics of daily returns of the S&P 500 index from 03.01.1950 to 04.03.2013 with the corresponding rankits, a linear scale dilation is observed. This observation is used to derive a five-parameter density function for the parsimonious description of the unconditional distribution of stock returns. The typical graph of this density function looks like a wizard's hat. Its signature feature is the discontinuity at zero.},
     year = {2013}
    }
    

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    T2  - American Journal of Theoretical and Applied Statistics
    JF  - American Journal of Theoretical and Applied Statistics
    JO  - American Journal of Theoretical and Applied Statistics
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    AB  - Comparing the order statistics of daily returns of the S&P 500 index from 03.01.1950 to 04.03.2013 with the corresponding rankits, a linear scale dilation is observed. This observation is used to derive a five-parameter density function for the parsimonious description of the unconditional distribution of stock returns. The typical graph of this density function looks like a wizard's hat. Its signature feature is the discontinuity at zero.
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Author Information
  • Department of Statistics and Operations Research, University of Vienna, Vienna, Austria

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