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

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    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 per-
    formed 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
    volatility proxy. Robustness of the conclusions is verified in bootstrap experiments.
    Original languageEnglish
    Place of publicationAarhus
    PublisherInstitut for Økonomi, Aarhus Universitet
    Number of pages25
    Publication statusPublished - 2010

    Keywords

    • Financial leverage effect, implied volatility, realized volatility, risk-return relation, stochastic volatility, VIX

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