we don't know what volatility

we don't know what volatility - We Dont Quite Know What We...

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Electronic copy of this paper is available at: http://ssrn.com/abstract=970480 We Don’t Quite Know What We Are Talking About When We Talk About Volatility Daniel G. Goldstein London Business School Nassim Nicholas Taleb Empirica Laboratory Limited DRAFT: 28 March 2007 Address all correspondence to: Professor Daniel Goldstein London Business School Regent’s Park London, NW1 4SA UK Phone: +44 (0)20 7000 8611 Fax: +44 (0) 20 7724 1145 Email: dgoldstein@london.edu
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Electronic copy of this paper is available at: http://ssrn.com/abstract=970480 ABSTRACT Finance professionals, who are regularly exposed to notions of volatility, seem to confuse mean absolute deviation with standard deviation , causing an underestimation of 25% with theoretical Gaussian variables. In some “fat tailed” markets the underestimation can be up to 90%. The mental substitution of the two measures is consequential for decision making and the perception of market variability.
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INTRODUCTION There is no particular normative reason to express or measure volatility in one of several possible ways, provided one remains consistent. However, once it is expressed, substituting one measure for another will lead to a consequential mistake. Suppose one measures “volatility” in root-mean-square deviations from the mean, as used by conventional statistics. It would be an error to substitute the definition and consider it mean deviation in the activity of decision-making, opinion formation, or verbal descriptions of the property of the process. Yet, to preview what we find in a survey of over 87 people trained to know the difference, people make this mistake. This brief note provides experimental evidence that participants, with varied backgrounds in financial markets (whether traders, quantitative analysts, graduate students in financial engineering, or portfolio managers) make the mistake of interpreting a physical description (in mean absolute returns per day) as a calculated measure (standard deviation). We illustrate the confusion experimentally and conclude by discussing implications for financial decision making and portfolio risk management. EXPERIMENTS To investigate common understanding of mean absolute deviation, we asked professionals and students of finance the following question: A stock (or a fund) has an average return of 0%. It moves on average 1% a day in absolute value; the average up move is 1% and the average down move is 1%. It does
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we don't know what volatility - We Dont Quite Know What We...

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