When equity prices are determined as the discounted sum of current and expected future dividends, Shiller (1981) and LeRoy and Porter (1981) derived a relationship between the variance of the price of equities, p(t), and the variance of the ex post realized discounted sum of current and future...

We show that expected returns on US stocks and all major global stock market indices have a particular form of non-linear dependence on previous returns. The expected sign of returns tends to reverse after large price movements and trends tend to continue after small movements. The observed...