### When Exact Science Isn't

The Black-Scholes model of option pricing is probably the most relied-upon mathematical model in the investing world. A book review in the September 5, 2005, issue of Science ("Earning from Risks", vol. 309, p. 1678) states that:

When the refinancing craze was just about to begin, I bought a CMO which according to the standard and universally accepted model had an "average lifetime" of seven years. According to my guess as to how people were going to behave, half of the principle would likely be paid back in 12 years, not 7. The

By the time a mathematical model for investors has been around long enough to be tested and taken seriously, there's a good chance that investors' behavior will have changed, and the model is no longer worth much.

First, when Black, Scholes, and Merton published in 1973, their model's fit to real-world patterns of prices was only rough. The fit improved considerably in the 1970s, in part because the model was used in arbitrage.... Black was directly involved in this use. He set up a service selling sheets of theoretical option values to traders, .... [Think of the words 'self-fulfilling prophecy'.] The alignment of reality to the Black-Scholes-Merton model was not permanent. After the 1987 stock market crash, the fit between the model and patterns of option prices deteriorated sharply, with the emergence of a "volatility skew" (or "smile") in those prices that persists to this day.

When the refinancing craze was just about to begin, I bought a CMO which according to the standard and universally accepted model had an "average lifetime" of seven years. According to my guess as to how people were going to behave, half of the principle would likely be paid back in 12 years, not 7. The

*entire*CMO was paid back in*six months*.By the time a mathematical model for investors has been around long enough to be tested and taken seriously, there's a good chance that investors' behavior will have changed, and the model is no longer worth much.

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