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

  • David E Allen

    (School of Accouting Finance & Economics, Edith Cowan University, Australia)

  • Abhay K Singh

    (School of Accouting Finance & Economics, Edith Cowan University, Australia)

  • Robert J Powell

    (School of Accouting Finance & Economics, Edith Cowan University, Australia)

  • Michael McAleer

    (Erasmus School of Economics, Erasmus University Rotterdam, Institute for Economic Research,Kyoto University, and Department of Quantitative Economics, Complutense University of Madrid)

  • James Taylor

    (Said Business School, University of Oxford, Oxford)

  • Lyn Thomas

    (Southampton Management School, University of Southampton, Southampton)

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 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 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.

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File URL: http://www.kier.kyoto-u.ac.jp/DP/DP831.pdf
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Paper provided by Kyoto University, Institute of Economic Research in its series KIER Working Papers with number 831.

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Length: 25pages
Date of creation: Nov 2012
Date of revision:
Handle: RePEc:kyo:wpaper:831
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  1. Chan, Louis K. C. & Lakonishok, Josef, 1992. "Robust Measurement of Beta Risk," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 27(02), pages 265-282, June.
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  8. Eide, Eric & Showalter, Mark H., 1998. "The effect of school quality on student performance: A quantile regression approach," Economics Letters, Elsevier, vol. 58(3), pages 345-350, March.
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  11. Ihsan Ullah Badshah, 2013. "Quantile Regression Analysis of the Asymmetric Return‐Volatility Relation," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 33(3), pages 235-265, 03.
  12. Moshe Buchinsky & Jennifer Hunt, 1999. "Wage Mobility In The United States," The Review of Economics and Statistics, MIT Press, vol. 81(3), pages 351-368, August.
  13. Hibbert, Ann Marie & Daigler, Robert T. & Dupoyet, Brice, 2008. "A behavioral explanation for the negative asymmetric return-volatility relation," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2254-2266, October.
  14. Dennis, Patrick & Mayhew, Stewart & Stivers, Chris, 2006. "Stock Returns, Implied Volatility Innovations, and the Asymmetric Volatility Phenomenon," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 41(02), pages 381-406, June.
  15. Ang, Andrew & Chen, Joseph, 2002. "Asymmetric correlations of equity portfolios," Journal of Financial Economics, Elsevier, vol. 63(3), pages 443-494, March.
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  17. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
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