The Known, the Unknown, and the Unknowable in Financial Risk Management: Measurement and Theory Advancing Practice

By Francis X. Diebold; Neil A. Doherty et al. | Go to book overview

3. Mild vs. Wild Randomness
Focusing on Those Risks That Matter

Benoit B. Mandelbrot and Nassim Nicholas Taleb

Conventional studies of uncertainty, whether in statistics, economics, finance, or social science, have largely stayed close to the so-called bell curve, a symmetrical graph that represents a probability distribution. Used to great effect to describe errors in astronomical measurement by the 19th-century mathematician Carl Friedrich Gauss, the bell curve, or Gaussian model, has since pervaded our business and scientific culture, and terms like sigma, variance, standard deviation, correlation, R-square, and Sharpe ratio are all directly linked to it. Neoclassical finance and portfolio theory are completely grounded in it.

If you read a mutual fund prospectus, or a hedge fund's exposure, the odds are that information will incorporate some quantitative summary claiming to measure “risk.” That measure will be based on one of the above buzzwords that derive from the bell curve and its kin. Such measures of future uncertainty satisfy our ingrained human desire to simplify by squeezing into one single number matters that are too rich to be described by it. In addition, they cater to psychological biases and our tendency to understate uncertainty in order to provide an illusion of understanding the world.

The bell curve has been presented as “normal” for almost two centuries, even though its flaws have always been obvious to any practitioner with empirical sense.1 Granted, it has been tinkered with using such methods as complementary

1 There is very little of the “normal” in the Gaussian: we seem to be conditioned to justify nonGaussianity—yet, it is often Gaussianity that needs specific justification. To justify it in finance by a

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