Nonlinearity everywhere: implications for empirical finance, technical analysis and value at risk

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 market properties are consistent with various models of investor behaviour and can be captured by a simple polynomial model. We further discuss a number of important implications of our findings. Incorrectly fitting a simple linear model to the data leads to a substantial bias in coefficient estimates. We show through the polynomial model that well-known short-term technical trading rules may be substantially driven by the non-linear behaviour observed. The behaviour also has implications for the appropriate calculation of important risk measures such as value at risk.