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The Leverage Effect Puzzle: Disentangling Sources of Bias at High Frequency

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  • Yacine Ait-Sahalia
  • Jianqing Fan
  • Yingying Li

Abstract

The leverage effect refers to the generally negative correlation between an asset return and its changes of volatility. A natural estimate consists in using the empirical correlation between the daily returns and the changes of daily volatility estimated from high-frequency data. The puzzle lies in the fact that such an intuitively natural estimate yields nearly zero correlation for most assets tested, despite the many economic reasons for expecting the estimated correlation to be negative. To better understand the sources of the puzzle, we analyze the different asymptotic biases that are involved in high frequency estimation of the leverage effect, including biases due to discretization errors, to smoothing errors in estimating spot volatilities, to estimation error, and to market microstructure noise. This decomposition enables us to propose novel bias correction methods for estimating the leverage effect.

Suggested Citation

  • Yacine Ait-Sahalia & Jianqing Fan & Yingying Li, 2011. "The Leverage Effect Puzzle: Disentangling Sources of Bias at High Frequency," NBER Working Papers 17592, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:17592
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    Cited by:

    1. Sebastien Valeyre & Denis Grebenkov & Sofiane Aboura & Qian Liu, 2013. "The reactive volatility model," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1697-1706, November.
    2. Thilo A. Schmitt & Rudi Schafer & Holger Dette & Thomas Guhr, 2015. "Quantile Correlations: Uncovering temporal dependencies in financial time series," Papers 1507.04990, arXiv.org.
    3. Worapree Maneesoonthorn & Catherine S. Forbes & Gael M. Martin, 2013. "Inference on Self-Exciting Jumps in Prices and Volatility using High Frequency Measures," Monash Econometrics and Business Statistics Working Papers 28/13, Monash University, Department of Econometrics and Business Statistics.
    4. repec:eee:dyncon:v:79:y:2017:i:c:p:154-183 is not listed on IDEAS
    5. Thilo A. Schmitt & Rudi Schäfer & Holger Dette & Thomas Guhr, 2015. "Quantile Correlations: Uncovering Temporal Dependencies In Financial Time Series," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(07), pages 1-16, November.
    6. Linton, Oliver & Whang, Yoon-Jae & Yen, Yu-Min, 2016. "A nonparametric test of a strong leverage hypothesis," Journal of Econometrics, Elsevier, vol. 194(1), pages 153-186.
    7. repec:eee:jfinec:v:125:y:2017:i:1:p:72-98 is not listed on IDEAS
    8. repec:bla:jfnres:v:40:y:2017:i:3:p:401-427 is not listed on IDEAS
    9. Josselin Garnier & Knut Solna, 2015. "Correction to Black-Scholes formula due to fractional stochastic volatility," Papers 1509.01175, arXiv.org, revised Mar 2017.
    10. Jacod, Jean & Klüppelberg, Claudia & Müller, Gernot, 2017. "Testing for non-correlation between price and volatility jumps," Journal of Econometrics, Elsevier, vol. 197(2), pages 284-297.
    11. Vortelinos, Dimitrios I. & Lakshmi, Geeta, 2015. "Market risk of BRIC Eurobonds in the financial crisis period," International Review of Economics & Finance, Elsevier, vol. 39(C), pages 295-310.
    12. Choi, Jaewon & Richardson, Matthew, 2016. "The volatility of a firm's assets and the leverage effect," Journal of Financial Economics, Elsevier, vol. 121(2), pages 254-277.
    13. Lotfaliei, Babak, 2018. "The variance risk premium and capital structure," ESRB Working Paper Series 70, European Systemic Risk Board.
    14. Kleppe, Tore Selland & Yu, Jun & Skaug, Hans J., 2014. "Maximum likelihood estimation of partially observed diffusion models," Journal of Econometrics, Elsevier, vol. 180(1), pages 73-80.
    15. Hugonnier, Julien & Prieto, Rodolfo, 2015. "Asset pricing with arbitrage activity," Journal of Financial Economics, Elsevier, vol. 115(2), pages 411-428.
    16. M. Angeles Carnero Fernández & Ana Pérez Espartero, 2018. "Outliers and misleading leverage effect in asymmetric GARCH-type models," Working Papers. Serie AD 2018-01, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    17. repec:rjr:romjef:v::y:2017:i:3:p:37-53 is not listed on IDEAS
    18. Ericsson, Jan & Huang, Xiao & Mazzotta, Stefano, 2016. "Leverage and asymmetric volatility: The firm-level evidence," Journal of Empirical Finance, Elsevier, vol. 38(PA), pages 1-21.
    19. Li, Yingying & Xie, Shangyu & Zheng, Xinghua, 2016. "Efficient estimation of integrated volatility incorporating trading information," Journal of Econometrics, Elsevier, vol. 195(1), pages 33-50.
    20. Bibinger, Markus & Neely, Christopher J. & Winkelmann, Lars, 2017. "Estimation of the discontinuous leverage effect: Evidence from the NASDAQ order book," Working Papers 2017-12, Federal Reserve Bank of St. Louis.
    21. Li, Yong & Zeng, Tao & Yu, Jun, 2014. "A new approach to Bayesian hypothesis testing," Journal of Econometrics, Elsevier, vol. 178(P3), pages 602-612.
    22. El Euch Omar & Fukasawa Masaaki & Rosenbaum Mathieu, 2016. "The microstructural foundations of leverage effect and rough volatility," Papers 1609.05177, arXiv.org.
    23. Worapree Maneesoonthorn & Catherine S. Forbes & Gael M. Martin, 2016. "Inference on Self-Exciting Jumps in Prices and Volatility using High Frequency Measures," Monash Econometrics and Business Statistics Working Papers 8/16, Monash University, Department of Econometrics and Business Statistics.

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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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