We show that there are some troubling differences between mean returns calculated using logarithmic returns and those calculated using simple returns. The mean of a set of returns calculated using logarithmic returns is less than the mean calculated using simple returns by an amount related to...

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...