Optimal investment horizons for stocks and markets

The inverse statistics is the distribution of waiting times needed to achieve a predefined level of return obtained from (detrended) historic asset prices [I. Simonsen, M.H. Jensen, A. Johansen, Eur. Phys. J. 27 (2002) 583; M.H. Jensen, A. Johansen, I. Simonsen, Physica A 234 (2003) 338]. Such a distribution typically goes through a maximum at a time coined the optimal investment horizon, , which defines the most likely waiting time for obtaining a given return ρ. By considering equal positive and negative levels of return, we reported in [M.H. Jensen, A. Johansen, I. Simonsen, Physica A 234 (2003) 338] on a quantitative gain/loss asymmetry most pronounced for short horizons. In the present paper, the inverse statistics for of the individual stocks presently in the DJIA is investigated. We show that this gain/loss asymmetry established for the DJIA surprisingly is not present in the time series of the individual stocks nor their average. This observation points towards some kind of collective movement of the stocks of the index (synchronization).