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2 MASTERING UNCERTAINTY /WILD UNCERTAINTY A focus on the exceptions that prove the rule Traditional risk management tools focus on what is normal and consider extreme events as ancillaries. In a world characterised by volatility and uncertainty, Benoit Mandelbrot and Nassim Taleb argue that this approach is misguided, and propose an alternative methodology where large deviations dominate the analysis C onventional studies of uncer- tainty, 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-cen- tury 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. If you read a mutual fund prospectus, or a hedge fund’s exposure, the odds are that it will supply you, among other information, with 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 sat- isfy our ingrained 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 understand- ing the world. The bell curve has been presented as “nor- mal” for almost two centuries, despite its flaws being obvious to any practitioner with empirical sense. Granted, it has been tink- ered with using such methods as comple- mentary “jumps”, stress testing, regime switching or the elaborate methods known as GARCH, but while they represent a good effort, they fail to address the bell curve’s fundamental flaws. The problem is that measures of uncer- tainty using the bell curve simply disregard the possibility of sharp jumps or discontinui- ties and, therefore, have no meaning or conse- quence. Using them is like focusing on the grass and missing out on the (gigantic) trees. In fact, while the occasional and unpredicta-
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This note was uploaded on 04/05/2010 for the course FINANCE AN FRE6041 taught by Professor Taleb,nassimn during the Spring '09 term at NYU Poly.

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