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Up- and Downside Variance Risk Premia in Global Equity Markets

This paper studies the variance risk premium from a new perspective by disaggregating the total premium into an upper and a lower semivariance premium. To this end, we provide novel tools for the computation of conditional expectations using traded options as well as moment generating functions.  Across a set of global stock market indices, we find that the variance premium is almost exclusively driven by downside risk, i.e., by the left tail of the index return distribution. We also consider the term structure of semivariance premia and condition the premia on several variables. Our results suggest that lower semivariance premia predominantly compensate investors for taking risks of large negative return innovations and remain large for horizons of several months.