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A Non-Parametric and Entropy Based Analysis of the Relationship between the VIX and S&P 500

Author

Listed:
  • David E. Allen

    (Edith Cowan University)

  • Michael McAleer

    (Erasmus University Rotterdam, Complutense University of Madrid, Spain, and Kyoto University, Japan)

  • Robert Powell

    (Edith Cowan University)

  • Abhay K. Singh

    (Edith Cowan University)

Abstract

This paper features an analysis of the relationship between the S&P 500 Index and the VIX using daily data obtained from both the CBOE website and SIRCA (The Securities Industry Research Centre of the Asia Pacic). We explore the relationship between the S&P 500 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&P 500 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

  • David E. Allen & Michael McAleer & Robert Powell & Abhay K. Singh, 2013. "A Non-Parametric and Entropy Based Analysis of the Relationship between the VIX and S&P 500," Tinbergen Institute Discussion Papers 13-018/III, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20130018
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    References listed on IDEAS

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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.
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    3. 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&P 500; VIX; Entropy; Non-Parametric Estimation; Quantile Regressions;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G24 - Financial Economics - - Financial Institutions and Services - - - Investment Banking; Venture Capital; Brokerage
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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