General stable models of the rate of return to Hollywood films

by Walls, W. D.

We use the non-symmetric stable distribution to quantify the returns to investments in motion pictures to properly account for asymmetry and infinite variance. We first quantify the unconditional distribution of returns using the normal distribution, the symmetric stable distribution, and the non-symmetric stable distribution and find that the normal and symmetric stable models can be rejected in favor of the non-symmetric stable model. We then model the parameters of the non-symmetric stable distribution---location, dispersion, skewness, and tail exponent---as functions of explanatory variables including a film's budget, presence of marquee (star) talent, and the number of screens on which a film is shown. The location of the returns distribution is increasing in budgets, marquee talent reduces dispersion, and the tail exponent is increasing in a film's budget. Even though the variance of film returns is infinite---so that point predictions have no precision---it is possible to model accurately the conditional probability distribution of film returns. Practical implications and applications of the results are discussed.

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