The Flaw of Averages: Why We Underestimate Risk in the Face of Uncertainty

CHAPTER 25

Options: Profiting from Uncertainty

A security whose value is derived from the value of another security is known as a derivative security, and the security that it is derived from is known as the underlying security. Derivative securities include such contracts as futures, forwards, options, and swaps. For most derivatives, the average value is not what you get by plugging in the average value of the underlying. They live in the land of the Strong Form of the Flaw of Averages.

If the portfolio theory of Markowitz and Sharpe is analogous to Newton’s laws of physics, simple enough to be taught in middle school, then the option theory of Fischer Black, Robert Merton, and Myron Scholes is more like the work of Einstein and is even related to it mathematically. Although almost no one knows how to derive Einstein’s famous E=MC², everyone can grasp the power of the atomic bomb that it unleashed. The famous Black-Scholes equation looks like this:

For most of us, including me, this is about as useful as the bicycle equations. However, as interpreted by computers and programmable calculators, it launched the trillion-dollar market in derivative securities. Furthermore, it is easy to gain a seat of the pants understanding of options. This in turn can allow you to actually benefit from uncertainty, rather than fear it.

Stock Options

One of the most basic derivatives is the ...