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The Risk-Return Tradeoff and Leverage Effect in a Stochastic Volatility-in-Mean Model

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  • Bent Jesper Christensen

    (Aarhus University, School of Economics and Management, Bartholins Allé 10, Aarhus, Denmark & CREATES)

  • Petra Posedel

    (University of Zagreb)

Abstract

We study the risk premium and leverage effect in the S&P500 market using the stochastic volatility-in-mean model of Barndor¤-Nielsen & Shephard (2001). The Merton (1973, 1980) equilibrium asset pricing condition linking the conditional mean and conditional variance of discrete time returns is reinterpreted in terms of the continuous time model. Tests are performed on the risk-return relation, the leverage effect, and the overidentifying zero intercept restriction in the Merton condition. Results are compared across alternative volatility proxies, in particular, realized volatility from high-frequency (5-minute) returns, implied Black-Scholes volatility backed out from observed option prices, model-free implied volatility (VIX), and staggered bipower variation. Our results are consistent with a positive risk-return relation and a significant leverage effect, whereas an additional overidentifying zero intercept condition is rejected. We also show that these inferences are sensitive to the exact timing of the chosen olatility proxy. Robustness of the conclusions is verified in bootstrap experiments.

Suggested Citation

  • Bent Jesper Christensen & Petra Posedel, 2010. "The Risk-Return Tradeoff and Leverage Effect in a Stochastic Volatility-in-Mean Model," CREATES Research Papers 2010-50, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2010-50
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    References listed on IDEAS

    as
    1. Muller, Ulrich A. & Dacorogna, Michel M. & Olsen, Richard B. & Pictet, Olivier V. & Schwarz, Matthias & Morgenegg, Claude, 1990. "Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis," Journal of Banking & Finance, Elsevier, vol. 14(6), pages 1189-1208, December.
    2. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," Journal of Financial Econometrics, Oxford University Press, vol. 4(1), pages 1-30.
    3. Blundell,Richard & Newey,Whitney & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521871549.
    4. Blundell,Richard & Newey,Whitney & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521692106.
    5. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521871532.
    6. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521692090.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Financial leverage effect; implied volatility; realized volatility; risk-return relation; stochastic volatility; VIX;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • L12 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Monopoly; Monopolization Strategies

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