The Volatility-Return Relationship: Insights from Linear and Non-Linear Quantile Regressions
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.
|Date of creation:||Oct 2012|
|Date of revision:|
|Contact details of provider:|| Phone: +34 913942604|
Web page: https://www.ucm.es/icae
More information through EDIRC
|Order Information:|| Postal: Facultad de Ciencias Económicas y Empresariales. Pabellón prefabricado, 1ª Planta, ala norte. Campus de Somosaguas, 28223 - POZUELO DE ALARCÓN (MADRID)|
Web: https://www.ucm.es/fundamentos-analisis-economico2/documentos-de-trabajo-del-icae Email:
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
- Roger Koenker & Kevin F. Hallock, 2001.
Journal of Economic Perspectives,
American Economic Association, vol. 15(4), pages 143-156, Fall.
- 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.
- John Y. Campbell & Ludger Hentschel, 1991.
"No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns,"
NBER Working Papers
3742, National Bureau of Economic Research, Inc.
- Campbell, John Y. & Hentschel, Ludger, 1992. "No news is good news *1: An asymmetric model of changing volatility in stock returns," Journal of Financial Economics, Elsevier, vol. 31(3), pages 281-318, June.
- Hentschel, Ludger & Campbell, John, 1992. "No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns," Scholarly Articles 3220232, Harvard University Department of Economics.
- 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.
- repec:ecu:wpaper:2009-11 is not listed on IDEAS
- Eric Bouye & Mark Salmon, 2009. "Dynamic copula quantile regressions and tail area dynamic dependence in Forex markets," The European Journal of Finance, Taylor & Francis Journals, vol. 15(7-8), pages 721-750.
- François Longin, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, 04.
- Robert F. Engle & Simone Manganelli, 2004.
"CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 22, pages 367-381, October.
- Robert Engle & Simone Manganelli, 2000. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Econometric Society World Congress 2000 Contributed Papers 0841, Econometric Society.
- Engle, Robert F & Manganelli, Simone, 1999. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," University of California at San Diego, Economics Working Paper Series qt06m3d6nv, Department of Economics, UC San Diego.
- 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.
- Jun Liu, 2005. "An Equilibrium Model of Rare-Event Premia and Its Implication for Option Smirks," Review of Financial Studies, Society for Financial Studies, vol. 18(1), pages 131-164.
- Andrew J. Patton, 2004.
"On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation,"
Journal of Financial Econometrics,
Society for Financial Econometrics, vol. 2(1), pages 130-168.
- Andrew J. Patton, 2002. "On the out-of-sample importance of skewness and asymetric dependence for asset allocation," LSE Research Online Documents on Economics 24951, London School of Economics and Political Science, LSE Library.
- 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.
- Cheekiat Low, 2004. "The Fear and Exuberance from Implied Volatility of S&P 100 Index Options," The Journal of Business, University of Chicago Press, vol. 77(3), pages 527-546, July.
- Ang, Andrew & Chen, Joseph, 2002. "Asymmetric correlations of equity portfolios," Journal of Financial Economics, Elsevier, vol. 63(3), pages 443-494, March.
- Wu, Guojun, 2001. "The Determinants of Asymmetric Volatility," Review of Financial Studies, Society for Financial Studies, vol. 14(3), pages 837-59.
- 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.
When requesting a correction, please mention this item's handle: RePEc:ucm:doicae:1224. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Águeda González Abad)
If references are entirely missing, you can add them using this form.