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

Allen, David E. and Singh, Abhay K. and Powell, Robert J. and McAleer, Michael and Taylor, James (2012) The Volatility-Return Relationship: Insights from Linear and Non-Linear Quantile Regressions. [ Documentos de Trabajo del Instituto Complutense de Análisis Económico (ICAE); nº 24, 2012, ] (Unpublished)

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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 quantied by Ordinary Least Square (OLS) regression, is not uniform across the distribution of the volatility-price re-
turn 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 on-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 prop-erties of the volatility series and empirical ndings in this paper have signicance for portfolio optimization, hedging strategies, trading strategies and risk management, in general.


Item Type:Working Paper or Technical Report
Additional Information:

JEL Codes: C14, C58, G11,

Uncontrolled Keywords:Return Volatility relationship, Quantile regression, Copula, Copula quantile regression, Volatility index, Tail dependence.
Subjects:Social sciences > Economics > Econometrics
Series Name:Documentos de Trabajo del Instituto Complutense de Análisis Económico (ICAE)
Volume:2012
Number:24
ID Code:16688
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Deposited On:10 Oct 2012 12:29
Last Modified:09 Jan 2014 11:45

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