This paper examines the usefulness of concentration indices in characterizing the degree of competition in the motion picture industry. It shows that concentration ratios and the Herfindahl-Hirschman index give a misleading picture of the degree of competition in the industry. All these indices exhibit large fluctuations that make the common practice of calculating a static measure erroneous. Market shares are shown to follow a stochastic Pareto-Lévy motion in which the market shares of the leading distributors are unstable, and positions often change. We show that this stochastic industry structure implies that the expected value of the HHI is undefined (infinite!). The motion picture industry is (stochastically) concentrated but highly competitive. We argue that this is likely to be true of other industries with similar stochastic features.