Black-Scholes underpinned massive economic growth. By 2007, the international financial system was trading derivatives valued at one quadrillion dollars per year. This is 10 times the total worth, adjusted for inflation, of all products made by the world's manufacturing industries over the last century. The downside was the invention of ever-more complex financial instruments whose value and risk were increasingly opaque. So companies hired mathematically talented analysts to develop similar formulas, telling them how much those new instruments were worth and how risky they were. Then, disastrously, they forgot to ask how reliable the answers would be if market conditions changed.
Black and Scholes invented their equation in 1973; Robert Merton supplied extra justification soon after. It applies to the simplest and oldest derivatives: options. There are two main kinds. A put option gives its buyer the right to sell a commodity at a specified time for an agreed price. A call option is similar, but it confers the right to buy instead of sell. The equation provides a systematic way to calculate the value of an option before it matures. Then the option can be sold at any time. The equation was so effective that it won Merton and Scholes the 1997 Nobel prize in economics. (Black had died by then, so he was ineligible.)It's a genius act of advanced mathematics, which gives us predictability in an area of uncertainty and allows us to trade options at the level of ten times the total value of a century's production. There turns out to be just one little problem with it.
The Black-Scholes equation relates the recommended price of the option to four other quantities. Three can be measured directly: time, the price of the asset upon which the option is secured and the risk-free interest rate. This is the theoretical interest that could be earned by an investment with zero risk, such as government bonds. The fourth quantity is the volatility of the asset. This is a measure of how erratically its market value changes. The equation assumes that the asset's volatility remains the same for the lifetime of the option, which need not be correct.
Despite its supposed expertise, the financial sector performs no better than random guesswork.Oops. Guess that's why all those folks who used to have good jobs in construction are now raising their kids on the EITC. It wasn't because they didn't realize how dumb they were; it's because somebody else thought he was too smart.
This seems like a problem for our model too, though. We just finished a long talk about how markets make better decisions -- at least, when immediate information is available locally. Now, the financial sector is nothing if not a market. Isn't that right?