Fear and its implications for stock markets

The value of stocks, indices and other assets, are examples of stochastic processes with unpredictable dynamics. In this paper, we discuss asymmetries in short term price movements that can not be associated with a long term positive trend. These empirical asymmetries predict that stock index drops are more common on a relatively short time scale than the corresponding raises. We present several empirical examples of such asymmetries. Furthermore, a simple model featuring occasional short periods of synchronized dropping prices for all stocks constituting the index is introduced with the aim of explaining these facts. The collective negative price movements are imagined triggered by external factors in our society, as well as internal to the economy, that create fear of the future among investors. This is parameterized by a ``fear factor'' defining the frequency of synchronized events. It is demonstrated that such a simple fear factor model can reproduce several empirical facts concerning index asymmetries. It is also pointed out that in its simplest form, the model has certain shortcomings.