The inverse statistics is the distribution of waiting times needed to achieve a predefined level of return obtained from (detrended) historic asset prices \cite{ optihori,gainloss}. Such a distribution typically goes through a maximum at a time coined the { \em optimal investment horizon}, $\tau^*_\rho$, which defines the most likely waiting time for obtaining a given return $\rho$. By considering equal positive and negative levels of return, we reported in \cite{ gainloss} on a quantitative gain/loss asymmetry most pronounced for short horizons. In the present paper, the inverse statistics for 2/3 of the individual stocks presently in the DJIA is investigated. We show that this gain/loss asymmetry established for the DJIA surprisingly is { \em 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).
Categories: physics.soc-ph q-fin.ST