Bicycle Industry

Topics: Normal distribution, Cumulative distribution function, Probability density function Pages: 40 (13104 words) Published: February 19, 2013
Uncertainty in the Movie Industry:
Does Star Power Reduce the Terror of the Box O±ce?¤
Arthur De Vany
Department of Economics
Institute for Mathematical Behavioral Sciences
University of California
Irvine, CA 92697
W. David Walls
School of Economics and Finance
The University of Hong Kong
Pokfulam Road
Hong Kong
Everyone knows that the movie business is risky. But how risky is it? Do strategies exist that reduce risk? We investigate these questions using a sample of over 2000 motion pictures. We discover that the movies are very risky indeed. Box-o±ce revenue dynamics are a Le'vy stable process and are asymptotically Pareto-distributed with in¯nite variance. The mean is dominated by rare blockbuster movies that are located in the far right tail. There is no typical movie because box o±ce revenue outcomes do not converge to an average, they diverge over all scales. Movies with stars in them have higher revenue ¤This paper was presented at the annual meeting of the American Economic Association, New York, January 1999. Walls received support from the Committee on Research and Conference Grants of the University of Hong Kong. De Vany received support from the Private Enterprise Research Center of Texas A&M University. 1

expectations, but in¯nite variance. Only 19 stars have a positive correlation with the probability that a movie will be a hit. No star is
\bankable" if bankers want sure things; they all carry signi¯cant risk. The highest grossing movies enjoy long runs and their total revenue is only weakly associated with their opening revenue. Contrary to conventional wisdom in Hollywood, the top stars are female and a star is

more important in extending a movie's run than in making it open. We conclude: (1) The studio model of risk management lacks a foundation in theory or evidence and revenue forecasts have zero precision. In other words, \Anything can happen." (2) Movies are complex products and the cascade of information among ¯lm-goers during the course of a ¯lm's run can evolve along so many paths that it is impossible to attribute the success of a movie to individual causal factors. In other words, \No one knows anything." (3) The audience

makes a movie a hit and no amount of \star power" or marketing can alter that. In other words, the real star is the movie.
\No one knows anything." Screenwriter William Goldman (1983). 1 Introduction
Everyone knows that motion pictures are uncertain products. In this paper we show that ¯lm makers must operate under such vague and uncertain knowledge of the probabilities of outcomes that \no one knows anything." The essence of the movie business is this: The mean of box-o±ce revenue is dominated by a few \blockbuster" movies and the probability distribution of box-o±ce outcomes has in¯nite variance! The distribution of box-o±ce revenues is a member of the class of probability distributions known as L¶evy stable distributions. These distributions are the limiting distributions of sums of random variables and are appropriate for modeling the box-o±ce revenues that motion pictures earn during their theatrical runs. L¶evy stable distributions have a \heavy" upper tail and may not have a ¯nite variance. Our parameter estimates of the asymptotic upper tail index reveal that the variance of box-o±ce revenue is in fact in¯nite: Motion pictures are among the most risky of products. Theoretically, the skewed shape of the L¶evy distribution means there is no natural scale or average to which movie revenues converge. Movie revenues diverge over all possible values of outcomes. One can forecast the mean of box-o±ce revenue since it exists and is ¯nite, but the con¯dence interval of the forecast is without bounds. The far-from-normal shape of the L¶evy probability distribution of box-o±ce revenue and its in¯nite variance are the sources of Hollywood's \terror of the box o±ce."

Our results explain heretofore puzzling aspects of the movie business. The average...
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