Using Extreme Value Theory to Improve Management Decision-Making with an Application to the Chinese Cinema in Hong Kong

This paper applies extreme value theory to the Cantonese movie business to demonstrate how these new statistical tools can be used to inform managerial decision making. We apply two competing statistical models from extreme value theory-the Pareto and the Weibull-to a sample of 2176 Cantonese movies produced and exhibited in Hong Kong between the years of 1973 and 1992. The statistical evidence leads to a rejection of the Pareto-based models in favour of the Weibull model. We show how the Weibull estimates can be used to make inference on the distribution of film success. 1. Introduction Managing risks quantitatively requires statistical knowledge about the possible outcomes and their associated probabilities. In most businesses, the range of outcomes is stationary. This is not so for the movie business or for any of the creative industries, all of which have a winner-take-all property about the distribution of success (Caves, 2000). So how can one begin to manage risks in the movie business? This paper begins to answer this question by identifying and estimating statistical models that capture the essential feature of the movie business, namely that financial returns are dominated by extreme events. Earlier papers by Walls (2000) and De Vany and Walls (2004) have fitted the stable Paretian distribution to motion picture returns in Hong Kong and North America, respectively. Their analyses confirm that the distribution of movie returns is highly skewed and has much heavier-than-Normal tails. Due to the enormous complexities of the statistical computation, their analysis is extremely difficult to apply in practice, especially when conditioning the distribution on a set of explanatory variables.1 The present paper complements and extends the earlier line of quantitative research: We combining easily estimable extreme value theory methods with practical management decision problems. Our goal is to provide a quantitative management tool that will be both useful and used in practice. To focus our analysis, the empirical application applies two competing statistical models of extreme values to the Hong Kong movie business.2 The Pareto power law model and the Weibull stretched exponential model are fitted to box-office revenue outcomes. The Weibull model is found to dominate the Pareto model. We show how the estimates of the Weibull model can be interpreted for use in practical management decisions. 2. Modeling the Distribution of Risks Before one can manage risks using modern analytics, those risks must be quantified. In a standard setting, one would assume that the distribution of outcomes follows a Normal distribution and proceed with the application of value-at-risk techniques. But in the movie business outcomes are not Normal. Instead, product success is characterized by extreme uncertainty. Movie outcomes are asymmetric and the probability of an extreme outcome-one far from the sample mean-is much larger than one would estimate from a Normal distribution. Power law distributions have been found useful in explaining the movie business because they allow for the heavy tails and skewness that are characteristic of box-office outcomes (De Vany and Walls, 1999, 2002). But for the purpose of managing large risks we are concerned with the extreme deviations that can occur when the probability density function extends to arbitrarily large values as set out by Frisch and Sornette (1997). In particular, we are interested in the tail behavior of the distribution. In statistics, one typically considers probabilities in the extreme 5% or 1% of the tails as extreme, but here we are concerned with much smaller tail probabilities because those are the risks that drive financial returns in the film industry. Recent empirical research has found significant deviations from power laws in nature and economy (LaHerrere and Sornette, 1998). 3 These deviations may occur because power laws are only observed asymptotically. …