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Abstract
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.
Highlights
It is fundamental in the study of asset markets to understand the cross-sectional and inter-temporal relationships between assets
We show through the polynomial model that well-known short-term technical trading rules may be substantially driven by the non-linear behaviour observed
Drawing on the literatures on reactions to large price movements and on trends in financial markets we show, using very comprehensive data for US stocks and world stock markets, that prices follow non-linear processes with reversals after large price changes and trend continuations after small price changes
Summary
It is fundamental in the study of asset markets to understand the cross-sectional and inter-temporal relationships between assets. Simple linear models of expected stock returns, cannot capture properties of the data which have been proposed in prior empirical and theoretical studies concerning stock behaviour. We use non-linear modelling to test whether stock price movements are, in general, consistent with the prior studies discussed above and investigate some important implications of this. There has been substantial prior work on nonlinear modelling of market returns [Moreno and Olmeda (2007) give a summary of inter-temporal work in this area. Our approach differs from prior work in being motivated by using the most parsimonious and tractable possible model that can directly capture and test for generalised stylised facts that have frequently been observed in prior research studies on particular and much less comprehensive data sets. We do not aim to find an optimal non-linear model for prediction or in-sample fit but instead to find whether a simple model can capture the salient features in which we are interested and to investigate some of the implications of this
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