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

Author

Listed:
  • 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)

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 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 findings in this paper have significance for portfolio optimization, hedging strategies, trading strategies and risk management, in general.

Suggested Citation

  • David E Allen & Abhay K Singh & Robert J Powell & Michael McAleer & James Taylor & Lyn Thomas, 2012. "The Volatility-Return Relationship:Insights from Linear and Non-Linear Quantile Regressions," KIER Working Papers 831, Kyoto University, Institute of Economic Research.
  • Handle: RePEc:kyo:wpaper:831
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    References listed on IDEAS

    as
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    Cited by:

    1. Agbeyegbe, Terence D., 2015. "An inverted U-shaped crude oil price return-implied volatility relationship," Review of Financial Economics, Elsevier, vol. 27(C), pages 28-45.
    2. Badshah, Ihsan & Frijns, Bart & Knif, Johan & Tourani-Rad, Alireza, 2016. "Asymmetries of the intraday return-volatility relation," International Review of Financial Analysis, Elsevier, vol. 48(C), pages 182-192.

    More about this item

    Keywords

    Return Volatility relationship; quantile regression; copula; copula quantile regression; volatility index; tail dependence;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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