Assuming efficient markets, one cannot make money from buying/selling options without an edge about the direction of the underlying, so it seems to me that the long-term cost of insuring a security about which the owner has no edge or opinion is zero. But wouldn't this allow a "noise trader" to purchase a protective option and wait out the adverse moves (as opposed to getting stopped out) and take profits when the underlying moves in the "right" direction? And then repeat the process. The fact that the option was purchased as protection shouldn't make the option itself to be more or less likely to be profitable over the long run, and its average cost should converge to zero. I feel that this is the equivalent of a "perpetual motion machine", and should not be possible. What am I missing?