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

19 Pages Posted: 19 Aug 2012

See all articles by David E. Allen

David E. Allen

School of Mathematics and Statistics, The University of Sydney; Financial Research Network (FIRN); Department of Finance; School of Business and Law, Edith Cowan University

Michael McAleer

Erasmus University Rotterdam - Erasmus School of Economics, Econometric Institute; Tinbergen Institute; University of Tokyo - Centre for International Research on the Japanese Economy (CIRJE), Faculty of Economics

Robert J. Powell

Edith Cowan University - School of Accounting, Finance and Economics; Financial Research Network (FIRN)

Abhay Kumar-Singh

Edith Cowan University

Date Written: August 19, 2012

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 Pacific). 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.

Keywords: S&P 500, VIX, Entropy, Non-Parametric Estimation, Quantile Regressions

JEL Classification: C14, D80, G11, G13

Suggested Citation

Allen, David Edmund and McAleer, Michael and Powell, Robert J. and Kumar-Singh, Abhay, A Non-Parametric and Entropy Based Analysis of the Relationship between the VIX and S&P 500 (August 19, 2012). 25th Australasian Finance and Banking Conference 2012. Available at SSRN: https://ssrn.com/abstract=2132065 or http://dx.doi.org/10.2139/ssrn.2132065

David Edmund Allen (Contact Author)

School of Mathematics and Statistics, The University of Sydney ( email )

School of Mathematics and Statistics F07
University of Sydney
Sydney, New South Wales 2006
Australia

HOME PAGE: http://www.maths.usyd.edu.au

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

Department of Finance ( email )

Taiwan
Taiwan

School of Business and Law, Edith Cowan University

100 Joondalup Drive
Joondalup, WA 6027
Australia

HOME PAGE: http://www.dallenwapty.com

Michael McAleer

Erasmus University Rotterdam - Erasmus School of Economics, Econometric Institute ( email )

Rotterdam
Netherlands

Tinbergen Institute

Rotterdam
Netherlands

University of Tokyo - Centre for International Research on the Japanese Economy (CIRJE), Faculty of Economics

Tokyo
Japan

Robert J. Powell

Edith Cowan University - School of Accounting, Finance and Economics ( email )

Joondalup Campus
Perth
Joondalup 6027, WA
Australia

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

Abhay Kumar-Singh

Edith Cowan University ( email )

Mount Lawley Campus
Perth
Churchlands 6018 WA, Victoria
Australia

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