Template-type: ReDIF-Paper 1.0
Author-Name: D.E. Allen
Author-Email: d.allen@ecu.edu.au
Author-Person: pal66 
Author-Workplace-Name: School of Accounting Finance and Economics Edith Cowan University Joondalup Drive Joondalup Western Australia 6027 
Author-Name: Abhay K Singh
Author-Workplace-Name: School of Accouting Finance & Economics, Edith Cowan University, Australia
Author-Name: R. Powell
Author-Email: r.powell@unsw.edu.au 
Author-Person: ppo357 
Author-Workplace-Name: School of Accounting Finance and Economics Edith Cowan University Joondalup Drive Joondalup Western Australia 6027 
Author-Name: Michael McAleer
Author-Person: pmc90 
Author-Workplace-Name: Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam.
Author-Name: James Taylor
Author-Workplace-Name: Said Business School, University of Oxford, Oxford
Author-Name: Lyn Thomas
Author-Workplace-Name: Southampton Management School, University of Southampton, Southampton
Title: The Volatility-Return Relationship: Insights from Linear and Non-Linear Quantile Regressions
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.
Classification-JEL: C14, C58, G11.
Length: 25 pages 
Creation-Date: 2012-10  
Number: 2012-24 
X-File-Ref: http://america.sim.ucm.es/repec/ucm/ref/doicae1224.txt
File-URL: https://eprints.ucm.es/id/eprint/16688/1/1224.pdf
File-Format: Application/pdf
Handle: RePEc:ucm:doicae:1224