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. [Working Paper or Technical Report] (Unpublished)
Available under License Creative Commons Attribution Non-commercial.
Official URL: http://eprints.ucm.es/16688/
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)|
Alexander, C. (Ed.). (2008). Market Risk Analysis: Practical Financial Econometrics (Vol. II):Wiley Publishing.
Allen, D. E., Gerrans, P., Singh, A. K., and Powell, R. (2009). Quantile Regression and its application in investment analysis. The Finsia Journal of Applied Finance (JASSA), 7-12.
Allen, D., Singh, A. K., & Powell, R. J. (2011). Asset Pricing, the Fama-French factor Model and the Implications of Quantile Regression Analysis. In G. N. Gregoriou &
R. Pascalan (Eds.), Financial Econometrics Modeling: Market Microstructure, Factor Models and Financial Risk Measures: Palgrave Macmillan.
Ang, A., & Chen, J. (2002). Asymmetric Correlations of Equity Portfolios. Journal of Financial Economics, 63 (3), 443-494.
Badshah, I. U. (2012). Quantile Regression Analysis of the Asymmetric Return-Volatility Relation. Journal of Futures Markets.
Barnes, M. L., & Hughes, W. A. (2002) Quantile Regression Analysis of the Cross Section of Stock Market Returns. (Working Paper). Retrieved from Social Science Research Nework website: http://ssrn.com/abstract=458522 .
Black, F. (1976) Studies of stock market volatility changes. Proceedings of the American Statistical Association, Business and Economic Statistics Section, 177-81.
Black, F., & Scholes, M. (1973). The pricing of options and corporate liability. Journal of Political Economy, 81, 636-654.
Bouyé, E., & Salmon, M. (2009). Dynamic copula quantile regressions and tail area dynamic dependence in Forex markets. The European Journal of Finance, 15 (7-8), 721-750.
Buchinsky, M., Leslie, P., (1997). Educational attainment and the changing U.S. wage structure: Some dynamic implications. (Working Paper No. 97-13). Department of
Economics, Brown University.
Buchinsky, M., & Hunt, J. (1999). Wage Mobility In The United States. The Review of Economics and Statistics, 81 (3), 351-368.
Campbell, J. Y., & Hentschel, L. (1992). No news is good news: An asymmetric model of changing volatility in stock returns. Journal of Financial Economics, 31 (3), 281-318.
Christie, A. (1982). The stochastic behaviour common stock variances: Value, leverage and interest rate effects. Journal of Financial Economics, 10, 407-432.
Chan, L. K. C., & Lakonishok, J. (1992). Robust Measurement of Beta Risk. The Journal of Financial and Quantitative Analysis, 27 (2), 265-282.
Cheung, W. (2009). Copula: A Primer for Fund Managers. SSRN eLibrary.
Clayton, D. (1978). A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika, 65, 141-151.
Dennis, P., Mayhew, S., and Stivers, C (2006). Stock returns, implied volatility innovations, and the asymmetric volatility phenomenon. Journal of Financial and Quanti-
tative Analysis, 41 (2), 381-406.
Eide, E., & Showalter, M. H. (1998). The Effect of School Quality on Student Performance: A Quantile Regression Approach. Economics Letters, 58 (3), 345-350.
Engle, R. F., & Manganelli, S. (2004). CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles. Journal of Business & Economics Statistics, 22 (4), 367-381.
Erb, C. B., Harvey, C. R., & Viskanta, T. E. (1994). Forecasting International Equity Correlations. Financial Analysts Journal, 50, 32-45.
Fleming, J., Ostdiek, B., & Whaley, R. E. (1995). Predicting stock market volatility: A new measure. Journal of Futures Markets, 15 (3), 265-302.
Franke, J., Härdle, K. W., & Hafner, C. M. (2008). Statistics of Financial Market: An Introduction (II ed.): Springer-Verlag Berlin Heidelberg.
Gowlland, C., Xiao, Z. Zeng, Q. (2009). Beyond the Central Tendency: Quantile Regression as a Tool in Quantitative Investing. The Journal of Portfolio Management, 35 (3), 106-119.
Giot, P., (2005). Relationships between implied volatility indices and stock index returns. Journal of Portfolio Management, 31, 92-100.
Hibbert, A., Daigler, R., & Dupoyet, B. (2008). A behavioural explanation for the negative asymmetric return-volatility relation. Journal of Banking and Finance 32,
Joe, H. (Ed.). (1997). Multivariate Models and Dependence Concepts : Chapman and Hall.
Koenker, R. W., & Bassett, G. Jr. (1978). Regression Quantiles. Econometrica 46 (1), 33-50.
Koenker, R. (2005). Quantile Regression, Econometric Society Monograph Series: Cambridge University Press.
Kumar, S. S. S. (2012). A rst look at the properties of India's volatility index. International Journal of Emerging Markets, 7 (2),160 - 176.
Liu, J., Pan, J., & Wang, T. (2005). An equilibrium model of rare-event premia and its implication for option smirks. Review of Financial Studies, 18, 131-164.
Longin, F., & Solnik, B. (2001). Extreme correlation of international equity markets. Journal of Finance 56, 649-676.
Low, C. (2004). The fear and exuberance from implied volatility of S&P 100 index options. Journal of Business 77, 527-546.
Morillo, D. (2000). Income Mobility with Nonparametric Quantiles: A Comparison of the U.S. and Germany. Preprint.
Nelsen, R. B. (1999). Introduction to Copulas : Springer Verlag.
Patton, A. J. (2004). On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation. Journal of Financial Econometrics 2 (1), 130-168.
Patton, A. J. (2009) Copula-Based Models for Financial Time Series, in T.G. Andersen, R.A. Davis, J. P. Kreiss and T. Mikosch (eds.) Handbook of Financial Time Series, Springer Verlag.
Whaley, R. (2000). The investor fear gauge. Journal of Portfolio Management 26, 12-17.
Wu, G. (2001). The Determinants of Asymmetric Volatility. The Review of Financial Studies, 14 (3), 837-859.
|Deposited On:||10 Oct 2012 14:29|
|Last Modified:||09 Jan 2014 12:45|