The Volatility-Return Relationship: Insights from Linear and Non-Linear Quantile Regressions

David Allen, Abhay K Singh, Robert Powell, Michael McAleer, James Taylor and Lyn Thomas
Additional contact information
Abhay K Singh: School of Accouting Finance & Economics, Edith Cowan University, Australia
James Taylor: Said Business School, University of Oxford, Oxford
Lyn Thomas: Southampton Management School, University of Southampton, Southampton

No 2012-24, Documentos de Trabajo del ICAE from Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico

Abstract: This paper examines the asymmetric relationship between price and implied volatility and the associated extreme quantile dependence using a linear and non-linear quantile regression approach. Our goal is to demonstrate that the relationship between the volatility and market return, as quantified by Ordinary Least Square (OLS) regression, is not uniform across the distribution of the volatility-price return pairs using quantile regressions. We examine the bivariate relationships of six volatility-return pairs, namely: CBOE VIX and S&P 500, FTSE 100 Volatility and FTSE 100, NASDAQ 100 Volatility (VXN) and NASDAQ, DAX Volatility (VDAX) and DAX 30, CAC Volatility (VCAC) and CAC 40, and STOXX Volatility (VS-TOXX) and STOXX. The assumption of a normal distribution in the return series is not appropriate when the distribution is skewed, and hence OLS may not capture a complete picture of the relationship. Quantile regression, on the other hand, can be set up with various loss functions, both parametric and non-parametric (linear case) and can be evaluated with skewed marginal-based copulas (for the non-linear case), which is helpful in evaluating the non-normal and non-linear nature of the relationship between price and volatility. In the empirical analysis we compare the results from linear quantile regression (LQR) and copula based non-linear quantile regression known as copula quantile regression (CQR). The discussion of the properties of the volatility series and empirical findings in this paper have significance for portfolio optimization, hedging strategies, trading strategies and risk management, in general.

Keywords: Return Volatility relationship; Quantile regression; Copula; Copula quantile regression; Volatility index; Tail dependence. (search for similar items in EconPapers)
JEL-codes: C14 C58 G11 (search for similar items in EconPapers)
Pages: 25 pages
Date: 2012-10
New Economics Papers: this item is included in nep-ecm, nep-fmk and nep-rmg
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https://eprints.ucm.es/id/eprint/16688/1/1224.pdf (application/pdf)

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Working Paper: The Volatility-Return Relationship:Insights from Linear and Non-Linear Quantile Regressions (2012)
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