## 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.

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 language | English |
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Place of publication | Aarhus |

Publisher | Institut for Økonomi, Aarhus Universitet |

Number of pages | 25 |

Publication status | Published - 2010 |

## Keywords

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