We introduce a new stylized fact: the hump-shaped behavior of slopes and coefficients of determination as a function of the aggregation horizon when running (forward/backward) predictive regressions of future excess market returns onto past economic uncertainty (as proxied by market variance,...

We argue that the predictive regression between implied volatility (regressor) and realized volatility over the remaining life of a European option (regressand) is likely to be a fractional cointegrating relation. Because cointegration is associated with long-run comovements, this classical...