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A non-parametric and entropy based analysis of the relationship between the VIX and S&P500

Author

Listed:
  • D.E. Allen

    (School of Accounting Finance and Economics Edith Cowan University Joondalup Drive Joondalup Western Australia 6027)

  • A. Kramadibrata

    (School of Accounting Finance and Economics Edith Cowan University Joondalup Drive Joondalup Western Australia 6027)

  • Michael McAleer

    (Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam.)

  • R. Powell

    (School of Accounting Finance and Economics Edith Cowan University Joondalup Drive Joondalup Western Australia 6027)

  • A. K. Singh

    (School of Accounting Finance and Economics Edith Cowan University Joondalup Drive Joondalup Western Australia 6027)

Abstract

This paper features an analysis of the relationship between the S&P500 Index and the VIX using daily data obtained from both the CBOE website and SIRCA (The Securities Industry Research Centre of the Asia Pacific). We explore the relationship between the S&P500 daily continuously compounded return series and a similar series for the VIX in terms of a long sample drawn from the CBOE running from 1990 to mid 2011 and a set of returns from SIRCA's TRTH datasets running from March 2005 to-date. We divide this shorter sample, which captures the behaviour of the new VIX, introduced in 2003, into four roughly equivalent sub-samples which permit the exploration of the impact of the Global Financial Crisis. We apply to our data sets a series of non-parametric based tests utilising entropy based metrics. These suggest that the PDFs and CDFs of these two return distributions change shape in various subsample periods. The entropy and MI statistics suggest that the degree of uncertainty attached to these distributions changes through time and using the S&P500 return as the dependent variable, that the amount of information obtained from the VIX also changes with time and reaches a relative maximum in the most recent period from 2011 to 2012. The entropy based non-parametric tests of the equivalence of the two distributions and their symmetry all strongly reject their respective nulls. The results suggest that parametric techniques do not adequately capture the complexities displayed in the behaviour of these series. This has practical implications for hedging utilising derivatives written on the VIX, which will be the focus of a subsequent study.

Suggested Citation

  • D.E. Allen & A. Kramadibrata & Michael McAleer & R. Powell & A. K. Singh, 2012. "A non-parametric and entropy based analysis of the relationship between the VIX and S&P500," Documentos de Trabajo del ICAE 2012-19, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    • Handle: RePEc:ucm:doicae:1219
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    File URL: https://eprints.ucm.es/id/eprint/16222/1/1219.pdf
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    References listed on IDEAS

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    1. Sims, Christopher A., 2005. "Rational inattention: a research agenda," Discussion Paper Series 1: Economic Studies 2005,34, Deutsche Bundesbank.
    2. Chang, Chia-Lin & Jimenez-Martin, Juan-Angel & McAleer, Michael & Amaral, Teodosio Perez, 2013. "The rise and fall of S&P500 variance futures," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 151-167.
    3. Amos Golan & Esfandiar Maasoumi, 2008. "Information Theoretic and Entropy Methods: An Overview," Econometric Reviews, Taylor & Francis Journals, vol. 27(4-6), pages 317-328.
    4. Isao Ishida & Michael McAleer & Kosuke Oya, 2011. "Estimating the Leverage Parameter of Continuous-time Stochastic Volatility Models Using High Frequency S&P 500 and VIX," Documentos de Trabajo del ICAE 2011-17, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    5. Massimiliano Caporin & Michael McAleer, 2012. "Do We Really Need Both Bekk And Dcc? A Tale Of Two Multivariate Garch Models," Journal of Economic Surveys, Wiley Blackwell, vol. 26(4), pages 736-751, September.
    6. Esfandiar Maasoumi & Jeffrey Racine, 2009. "A Robust Entropy-Based Test of Asymmetry for Discrete and Continuous Processes," Econometric Reviews, Taylor & Francis Journals, vol. 28(1-3), pages 246-261.
    7. Carol Alexander & Dimitris Korovilas, 2011. "The Hazards of Volatility Diversification," ICMA Centre Discussion Papers in Finance icma-dp2011-04, Henley Business School, University of Reading.
    8. McAleer, Michael & Wiphatthanananthakul, Chatayan, 2010. "A simple expected volatility (SEV) index: Application to SET50 index options," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(10), pages 2079-2090.
    9. repec:eme:mfppss:v:37:y:2011:i:11:p:1048-1067 is not listed on IDEAS
    10. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, January.
    11. Ishida, I. & McAleer, M.J. & Oya, K., 2011. "Estimating the Leverage Parameter of Continuous-time Stochastic Volatility Models Using High Frequency S&P 500 VIX," Econometric Institute Research Papers EI 2011-10, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    12. Hayfield, Tristen & Racine, Jeffrey S., 2008. "Nonparametric Econometrics: The np Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i05).
    13. Golan, Amos, 2002. "Information and Entropy Econometrics--Editor's View," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 1-15, March.
    14. Maasoumi, Esfandiar & Racine, Jeff, 2002. "Entropy and predictability of stock market returns," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 291-312, March.
    15. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    16. C. W. Granger & E. Maasoumi & J. Racine, 2004. "A Dependence Metric for Possibly Nonlinear Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(5), pages 649-669, September.
    17. Anil Bera & Sung Park, 2008. "Optimal Portfolio Diversification Using the Maximum Entropy Principle," Econometric Reviews, Taylor & Francis Journals, vol. 27(4-6), pages 484-512.
    18. Racine, Jeffrey S., 2008. "Nonparametric Econometrics: A Primer," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(1), pages 1-88, March.
    19. Steve Pincus, 2008. "Approximate Entropy as an Irregularity Measure for Financial Data," Econometric Reviews, Taylor & Francis Journals, vol. 27(4-6), pages 329-362.
    20. Brenner, Menachem & Ou, Ernest Y. & Zhang, Jin E., 2006. "Hedging volatility risk," Journal of Banking & Finance, Elsevier, vol. 30(3), pages 811-821, March.
    21. Ebrahimi, Nader & Maasoumi, Esfandiar & Soofi, Ehsan S., 1999. "Ordering univariate distributions by entropy and variance," Journal of Econometrics, Elsevier, vol. 90(2), pages 317-336, June.
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    Cited by:

    1. Nektarios Aslanidis & Charlotte Christiansen & Christos S. Savva, 2021. "Quantile Risk–Return Trade-Off," JRFM, MDPI, vol. 14(6), pages 1-14, June.
    2. Athanasios P. Fassas & Nikolas Hourvouliades, 2019. "VIX Futures as a Market Timing Indicator," JRFM, MDPI, vol. 12(3), pages 1-9, July.

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    More about this item

    Keywords

    S&P500; VIX; Entropy; Non-Parametric Estimation; Quantile Regressions.;
    All these keywords.

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • E - Macroeconomics and Monetary Economics
    • F2 - International Economics - - International Factor Movements and International Business
    • F3 - International Economics - - International Finance
    • G - Financial Economics

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