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Myths 1

Once upon a time when I worked at Goldman, a trader friend of mine Dan O’Rourke and I used to sometimes talk about spelling out all the myths of option pricing that people believed in. The idea always appealed to me and about a year ago Nassim Taleb and I wrote a short piece in Quantitative Finance about some limitations of dynamic hedging.

One of the theories that always mystifies me a little is the Capital Asset Pricing Model. I learned options theory first and the CAPM much later, and options theory is much easier to understand.

In the latest issue of the Journal of Portfolio Management, Peter Bernstein, who wrote the book Capital Ideas, wrote an editorial from which I excerpted the following:

“CAPM has failed more empirical tests than any other element of the body of idea we usually call modern portfolio theory. Indeed, in 2004, Eugene Fama and Kenneth French put the situation this way: The CAPM,like Markowitz’s portfolio model on which it is built, is . . . a theoretical tour de force.We continue to teach the CAPM as an introduction to the fundamentals of portfolio theory and asset pricing . . . but we also warn students that, despite its seductive simplicity, the CAPM’s empirical problems probably invalidate its use in applications.”

So I suppose CAPM is a bit of a myth too, even though it’s sometimes taught as gospel you cannot contradict. Bernstein points out that the most enduring legacy of CAPM is the idea of systematic and unsystematic risk rather than the formula itself.

An aside: Black was a lifelong fan of CAPM, which opened his eyes to the possibilities of equilibrium valuation, and indeed discovered the options pricing PDE by applying CAPM to a market consisting of a stock and its option. I mentioned in my book that once, when I wrote a program to dynamically replicate a stock option and the program converged too slowly as the number of rehedgings increased — [because I coded delta as N(d_2) instead of N(d_1) — he briefly got quite excited about the (apparent) lack of convergence.

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