Art De Vany explains some of the oddities of Motion Picture Finance:
It is not hard to see the non-Gaussian nature of the movies: Forrest Gump earned US theatrical revenues 10 standard deviations above the mean; Titanic earned revenues 20 standard deviations above the mean. These events would not occur in billions of reruns of the Earth’s history if events were Normally distributed. But, events occur on all scales, with no typical outcome in the movies. The mean is dominated by events of massive scale (“blockbusters”) and so is the sample average. The sample variance increases in the sample size and the theoretical variance is infinite. There is also a time-dependency in the statistics, partly because of the influence of extreme events. These and other properties are confirmation of Goldman’s proposition [that "nobody knows anything" in the movie industry]. The business is wildly uncertain and, for that reason, it offers unusual investment opportunities.
If you studied statistics in school, you likely did not study non-Gaussian distributions in great detail. Much of De Vany’s analysis revolves around Stable Distributions described by Mandelbrot, the mathematician famous for his work with fractals:
Mandelbrot was trying to model cotton prices. His analysis of historical data indicated that returns had sample distributions that were highly leptokurtic. They had “fat tails” that made extreme market moves more likely than would be predicted by the normal distribution. This phenomena has been observed before, and today we know it is typical of most asset returns—stock, bond, commodity and energy returns routinely exhibit leptokurtosis. This is particularly extreme for energy returns.Mandelbrot didn’t want to have to assume one distribution for daily returns, another for monthly returns, and still another for annual returns. This would reduce any model to mere empirical distribution fitting. He wanted a consistent, flexible model that could be fit to different asset returns irrespective of the unit of time over which returns were calculated. This was possible with a model that assumed normally distributed returns, but normal distributions didn’t fit historical data well.
The problem was the central limit theorem, which tells us that sums of random variables will converge to a normal random variable.
(Read the rest of that article if you want to understand stable distributions.)
Why should investors be interested?
Another factor that distorts studio decisions is that, in this business, the variance is the key to high returns. The Sharpe ratio, variance over mean, that determines a lot of financial decision-making is infinite in the movie business. So, perhaps a lot of hedge funds stay away from the business. But, this is an error. The heavy tails make for the infinite variance and the higher than Gaussian probabilities of large events in these tails drive the mean. Heavier tails, more variance, larger outcomes, higher mean. It is not a Gaussian world and that property can be used to give investors a piece of these hugely profitable upper tail events. In a world where arbitrage has driven prices to low Sharpe ratios, an industry like the movies offers one of the best opportunities to gain higher returns.
His solution is to sell potential “upper tail” revenue streams on financial markets — like call options. Currently, top directors earn pay contingent on performance, but their contracts are illiquid and can’t be sold on the open market:
An example from the contingent contracting used to compensate top directors is illustrative. Such a contract might have break points such as: 1. 16.25% of gross proceeds less than or equal to $150 million 2. 17.5% of gross proceeds between $150 and $165 million 3. 18.5% of gross proceeds between $165 and $172.5 million 4. 20% of gross proceeds between $172.5 and $180 million 5. 22.5% of gross proceeds above $180 million. A complicated, but easily managed, non-linear contract.