August 23, 2019
We document that the term structures of risk-neutral expected squared negative (quadratic loss) and positive (quadratic gain) returns on the S&P 500 are upward sloping on average. These shapes mainly reflect the higher premium required by investors to hedge downside risk, and the belief that potential gains will increase in the long-run. The term structures exhibit substantial time series variation with large negative slopes during crisis periods. Through the lens of Andersen et al.