I would like to briefly revisit a problem that appeared on the problem set assigned for chapter 1:

On March 3, 2008, a revival of Gypsy, the Stephen Sondheim musical, opened at the St. James Theater in New York. Ticket prices ranged from $117 to $42 per seat. The show’s weekly gross revenues, operating costs, and profit were estimated as follows, depending on whether the average ticket price was $75 or $65: 

Average Price of $75

Average Price of $65

Gross revenues

$765,000

$680,000

Operating costs

600,000

600,000

Profit

165,000

80,000

With a cast of 71 people, a 30-piece orchestra, and more than 500 costumes, Gypsy cost more than $10 million to stage. This investment was in addition to the operating costs (such as salaries and theater rent). George Wachtel, director of research for the League of American Theaters and Producers, has said that about one in three shows opening on Broadway in recent years has at least broken even. Were the investors in Gypsy taking a substantial risk?

In the solutions that I distributed from the class website, I noted that “The investors in Gypsy were indeed taking a substantial risk. If only one in three shows breaks even, two out of three make losses.”

Clearly my “analysis” was rather subjective as well as limited in scope. It would be helpful in one’s risk assessment to know whether the low “success” rate (where only one in three shows at least breaks even) is good or bad for this kind of business activity. For what it’s worth, my sense from talking to some film industry friends and acquaintances is that hedge funds are typically a major source of capital for these kinds of creative ventures. I would imagine that hedge funds would not consider making such investments if they weren’t profitable on average.

What’s obviously missing in this problem is a description of the magnitude of potential losses and profits. For example, if there was a 2/3 chance of losing the entire investment of $10 million (i.e., the show is a total bust) and a 1/3 chance of not only paying back the $10 million investment but also earning an additional $30 million profit (i.e., the show is a huge success), then the expected value of profit would be positive; i.e., (2/3)(-$10 million) + (1/3)($30 million) = $3.33 million. The expected rate of return in this case would be quite generous; i.e., an expected profit of $3.33 million divided by the original investment of $10 million implies an expected rate of return of 33.33%, or an expected profit of $1 for every $3 invested.  However, the risk (as measured by standard deviation) would also be rather substantial; specifically, in dollar terms, the standard deviation of this investment is 18.9 million, and in terms of return, it comes out to 188.56%).  The coefficient of variation measure how many units of risk are being taken on per unit of return, and in this case this ratio comes out to 188.56%/33.33% = 5.66; i.e., nearly 6 units of risk have to be borne by investors for which they are rewarded with one unit of return.  Putting this into a broader empirical perspective, the long-run (1928–2008) coefficient of variation from investing in the U.S. stock market (as measured by the S&P500 index) is equal to 1.84; i.e., investors bear 1.84 units of risk for which they are rewarded on average with one unit of return.

Surely professional investors such as hedge funds track risk and reward from investing in creative ventures such as films and plays, and therefore would have a good sense whether or not this represents an attractive investment. Because of how risky this venture is, it provides about as clear of an example that I have ever seen concerning the notion that profit is, at least in part, a reward for risk bearing. We will formalize risk/reward concepts later this semester, and when we do that, it might be a good idea to bring this Broadway play example back up in light of that analysis. We’ll learn then, among other things, that a particularly compelling strategy involves pooling the risks of a number of different unrelated creative ventures, much like an insurance company pools the risks of car accidents, mortality and morbidity so that it is possible to credibly offer relatively “safe” insurance products such as auto insurance, life insurance, and health insurance.

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