SSRN Author: Nassim Nicholas TalebNassim Nicholas Taleb SSRN Content
http://www.ssrn.com/author=475810
http://www.ssrn.com/rss/en-usSat, 23 Dec 2017 02:21:33 GMTeditor@ssrn.com (Editor)Sat, 23 Dec 2017 02:21:33 GMTwebmaster@ssrn.com (WebMaster)SSRN RSS Generator 1.0REVISION: Gini Estimation Under Infinite VarianceWe study the problems related to the estimation of the Gini index in presence of a fat-tailed data generating process, i.e. one in the stable distribution class with finite mean but infinite variance (i.e. with tail index α ∈ (1, 2)). We show that, in such a case, the Gini coefficient cannot be reliably estimated using conventional nonparametric methods, because of a downward bias that emerges in case of fat tails. This has important implications for the ongoing discussion about economic inequality.
We start by discussing how the nonparametric estimator of the Gini index undergoes a phase transition in the symmetry structure of its asymptotic distribution, as the data distribution shifts from the domain of attraction of a light-tailed distribution to that of a fat-tailed one, especially in the case of infinite variance. We show how the nonparametric Gini bias increases with lower values of α.
We then prove that maximum likelihood estimation outperforms nonparametric methods, ...
http://www.ssrn.com/abstract=3005184
http://www.ssrn.com/1653825.htmlFri, 22 Dec 2017 09:48:59 GMTREVISION: We Don't Quite Know What We are Talking About When We Talk About VolatilityFinance 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.
http://www.ssrn.com/abstract=970480
http://www.ssrn.com/1651840.htmlThu, 14 Dec 2017 15:20:15 GMTREVISION: The Problem is Beyond Psychology: The Real World is More Random than Regression AnalysesWhere the problem is not expert underestimation of randomness, but more: the tools themselves used in regression analyses and similar methods underestimate fat tails, hence the randomness in the data. We should avoid imparting psychological explanations to errors in the use of statistical methods.
http://www.ssrn.com/abstract=1941792
http://www.ssrn.com/1651839.htmlThu, 14 Dec 2017 15:16:47 GMTUpdate: The Problem is Beyond Psychology: The Real World is More Random than Regression AnalysesWhere the problem is not expert underestimation of randomness, but more: the tools themselves used in regression analyses and similar methods underestimate fat tails, hence the randomness in the data. We should avoid imparting psychological explanations to errors in the use of statistical methods.<br/><i>The Paper was removed</i>
http://www.ssrn.com/abstract=1941792
http://www.ssrn.com/1638492.htmlTue, 31 Oct 2017 10:33:47 GMTUpdate: We Don't Quite Know What We are Talking About When We Talk About VolatilityFinance 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.<br/><i>The Paper was removed</i>
http://www.ssrn.com/abstract=970480
http://www.ssrn.com/1638504.htmlTue, 31 Oct 2017 10:32:32 GMTREVISION: Gini Estimation Under Infinite VarianceWe study the problems related to the estimation of the Gini index in presence of a fat-tailed data generating process, i.e. one in the stable distribution class with finite mean but infinite variance (i.e. with tail index α ∈ (1, 2)). We show that, in such a case, the Gini coefficient cannot be reliably estimated using conventional nonparametric methods, because of a downward bias that emerges in case of fat tails. This has important implications for the ongoing discussion about economic inequality.
We start by discussing how the nonparametric estimator of the Gini index undergoes a phase transition in the symmetry structure of its asymptotic distribution, as the data distribution shifts from the domain of attraction of a light-tailed distribution to that of a fat-tailed one, especially in the case of infinite variance. We show how the nonparametric Gini bias increases with lower values of α.
We then prove that maximum likelihood estimation outperforms nonparametric methods, ...
http://www.ssrn.com/abstract=3005184
http://www.ssrn.com/1610305.htmlFri, 21 Jul 2017 04:45:09 GMTREVISION: Expected Shortfall Estimation for Apparently Infinite-Mean Models of Operational RiskStatistical analyses on actual data depict operational risk as an extremely heavy-tailed phenomenon, able to generate losses so extreme as to suggest the use of infinite-mean models. But no loss can actually destroy more than the entire value of a bank or of a company, and this upper bound should be considered when dealing with tail-risk assessment.
Introducing what we call the dual distribution, we show how to deal with heavy-tailed phenomena with a remote yet finite upper bound. We provide methods to compute relevant tail quantities such as the Expected Shortfall (ES), which is not available under infinite-mean models, allowing adequate provisioning and capital allocation. This also permits a measurement of fragility.
The main difference between our approach and a simple truncation is in the smoothness of the transformation between the original and the dual distribution.
Our methodology is useful with apparently infinite-mean phenomena, as in the case of operational risk, but it ...
http://www.ssrn.com/abstract=2681006
http://www.ssrn.com/1557602.htmlThu, 12 Jan 2017 14:24:57 GMT