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The book investigates the misapplication of conventional statistical techniques to fat tailed distributions and looks for remedies, when possible. Switching from thin tailed to fat tailed distributions requires more than "changing the color of the dress." Traditional asymptotics deal mainly with either n=1 or n=∞, and the real world is in between, under the "laws of the medium numbers"-which vary widely across specific distributions. Both the law of large numbers and the generalized central limit mechanisms operate in highly idiosyncratic ways outside the standard Gaussian or Levy-Stable basins of convergence. A few examples: - The sample mean is rarely in line with the population mean, with effect on "naïve empiricism," but can be sometimes be estimated via parametric methods. - The "empirical distribution" is rarely empirical. - Parameter uncertainty has compounding effects on statistical metrics. - Dimension reduction (principal components) fails. - Inequality estimators (Gini or quantile contributions) are not additive and produce wrong results. - Many "biases" found in psychology become entirely rational under more sophisticated probability distributions. - Most of the failures of financial economics, econometrics, and behavioral economics can be attributed to using the wrong distributions. This book, the first volume of the Technical Incerto, weaves a narrative around published journal articles.
As Ian Bremmer and Preston Keat reveal in this innovative book, volatile political events such as the 2008 Georgia-Russia confrontation--and their catastrophic effects on business--happen much more frequently than investors imagine. On the curve that charts both the frequency of these events and the power of their impact, the "tail" of extreme political instability is not reassuringly thin but dangerously fat. Featuring a new Foreward that accounts for the cataclysmic effects of the 2008 financial crisis, The Fat Tail is the first book to both identify the wide range of political risks that global firms face and show investors how to effectively manage them. Written by two of the world's leading figures in political risk management, it reveals that while the world remains exceedingly risky for businesses, it is by no means incomprehensible. Political risk is unpredictable, but it is easier to analyze and manage than most people think. Applying the lessons of world history, Bremmer and Keat survey a vast range of contemporary risky situations, from stable markets like the United States or Japan, where politically driven regulation can still dramatically effect business, to more precarious places like Iran, China, Russia, Turkey, Mexico, and Nigeria, where private property is less secure and energy politics sparks constant volatility. The book sheds light on a wide array of political risks--risks that stem from great power rivalries, terrorist groups, government takeover of private property, weak leaders and internal strife, and even the "black swans" that defy prediction. But more importantly, the authors provide a wealth of unique methods, tools, and concepts to help corporations, money managers, and policy makers understand political risk, showing when and how political risk analysis works--and when it does not. "The Fat Tail delivers practical wisdom on the impact of political risk on firms of every description and valuable advice on how to use it. Ian Bremmer and Preston Keat offer innovative thinking and useful insight that will help business decision-makers find fresh answers to questions they may not yet know they have." --Fareed Zakaria, best-selling author of The Post-American World "Political risk has become increasingly complex, and The Fat Tail provides a truly new way to quantitatively assess it in established and emerging markets. It is essential reading for any CEO with multinational interests." --Randall Stephenson, Chairman, CEO and President, AT&T Inc. "Should be essential reading for anyone involved in international business even--perhaps especially--in places that seem politically stable." --Bill Emmott, former editor-in-chief of The Economist
While mainstream financial theories and applications assume that asset returns are normally distributed, overwhelming empirical evidence shows otherwise. Yet many professionals don’t appreciate the highly statistical models that take this empirical evidence into consideration. Fat-Tailed and Skewed Asset Return Distributions examines this dilemma and offers readers a less technical look at how portfolio selection, risk management, and option pricing modeling should and can be undertaken when the assumption of a non-normal distribution for asset returns is violated. Topics covered in this comprehensive book include an extensive discussion of probability distributions, estimating probability distributions, portfolio selection, alternative risk measures, and much more. Fat-Tailed and Skewed Asset Return Distributions provides a bridge between the highly technical theory of statistical distributional analysis, stochastic processes, and econometrics of financial returns and real-world risk management and investments.
Heavy tails –extreme events or values more common than expected –emerge everywhere: the economy, natural events, and social and information networks are just a few examples. Yet after decades of progress, they are still treated as mysterious, surprising, and even controversial, primarily because the necessary mathematical models and statistical methods are not widely known. This book, for the first time, provides a rigorous introduction to heavy-tailed distributions accessible to anyone who knows elementary probability. It tackles and tames the zoo of terminology for models and properties, demystifying topics such as the generalized central limit theorem and regular variation. It tracks the natural emergence of heavy-tailed distributions from a wide variety of general processes, building intuition. And it reveals the controversy surrounding heavy tails to be the result of flawed statistics, then equips readers to identify and estimate with confidence. Over 100 exercises complete this engaging package.
Mason's World Encyclopedia of Livestock Breeds and Breeding describes breeds of livestock worldwide as well as a range of breed-related subjects such as husbandry, health and behaviour. This definitive and prestigious reference work presents easily accessible information on domestication (including wild ancestors and related species), genetics and breeding, livestock produce and markets, as well as breed conservation and the cultural and social aspects of livestock farming. Written by renowned livestock authorities, these volumes draw on the authors' lifelong interest and involvement in livestock breeds of the world, presenting a unique, comprehensive and fully cross-referenced guide to cattle, buffalo, horses, pigs, sheep, asses, goats, camelids, yak and other domesticants.
the mathematics of financial modeling & investment management The Mathematics of Financial Modeling & Investment Management covers a wide range of technical topics in mathematics and finance-enabling the investment management practitioner, researcher, or student to fully understand the process of financial decision-making and its economic foundations. This comprehensive resource will introduce you to key mathematical techniques-matrix algebra, calculus, ordinary differential equations, probability theory, stochastic calculus, time series analysis, optimization-as well as show you how these techniques are successfully implemented in the world of modern finance. Special emphasis is placed on the new mathematical tools that allow a deeper understanding of financial econometrics and financial economics. Recent advances in financial econometrics, such as tools for estimating and representing the tails of the distributions, the analysis of correlation phenomena, and dimensionality reduction through factor analysis and cointegration are discussed in depth. Using a wealth of real-world examples, Focardi and Fabozzi simultaneously show both the mathematical techniques and the areas in finance where these techniques are applied. They also cover a variety of useful financial applications, such as: * Arbitrage pricing * Interest rate modeling * Derivative pricing * Credit risk modeling * Equity and bond portfolio management * Risk management * And much more Filled with in-depth insight and expert advice, The Mathematics of Financial Modeling & Investment Management clearly ties together financial theory and mathematical techniques.
“An in-depth, well-researched, and thoughtful exploration of the ‘fat boom’ in America.” —TheBoston Globe Low carb, high protein, raw foods . . . despite our seemingly endless obsession with fad diets, the startling truth is that six out of ten Americans are overweight or obese. In Fat Land, award-winning nutrition and health journalist Greg Critser examines the facts and societal factors behind the sensational headlines, taking on everything from supersize to Super Mario, high-fructose corn syrup to the high costs of physical education. With a sharp eye and even sharper tongue, Critser examines why pediatricians are now treating conditions rarely seen in children before; why type 2 diabetes is on the rise; the personal struggles of those with weight problems—especially among the poor—and how agribusiness has altered our waistlines. Praised by the New York Times as “absorbing” and by Newsday as “riveting,” this disarmingly funny, yet truly alarming, exposé stands as an important examination of one of the most pressing medical and social issues in the United States. “One scary book and a good companion to Eric Schlosser’s Fast Food Nation.” —Seattle Post-Intelligencer
A homeless cat arrives in the neighborhood and is shunned by all but a housewife and her two young children. The father of the family is not a cat lover and both his wife and children set about trying to change his mind until the cat does it on his own. This story highlights the importance of not judging a book by its cover.
Taking due account of extreme events when constructing portfolios of assets or liabilities is a key discipline for market professionals. Extreme events are a fact of life in how markets operate. In Extreme Events: Robust Portfolio Construction in the Presence of Fat Tails, leading expert Malcolm Kemp shows readers how to analyse market data to uncover fat-tailed behaviour, how to incorporate expert judgement in the handling of such information, and how to refine portfolio construction methodologies to make portfolios less vulnerable to extreme events or to benefit more from them. This is the only text that combines a comprehensive treatment of modern risk budgeting and portfolio construction techniques with the specific refinements needed for them to handle extreme events. It explains in a logical sequence what constitutes fat-tailed behaviour and why it arises, how we can analyse such behaviour, at aggregate, sector or instrument level, and how we can then take advantage of this analysis. Along the way, it provides a rigorous, comprehensive and clear development of traditional portfolio construction methodologies applicable if fat-tails are absent. It then explains how to refine these methodologies to accommodate real world behaviour. Throughout, the book highlights the importance of expert opinion, showing that even the most data-centric portfolio construction approaches ultimately depend on practitioner assumptions about how the world might behave. The book includes: Key concepts and methods involved in analysing extreme events A comprehensive treatment of mean-variance investing, Bayesian methods, market consistent approaches, risk budgeting, and their application to manager and instrument selection A systematic development of the refinements needed to traditional portfolio construction methodologies to cater for fat-tailed behaviour Latest developments in stress testing and back testing methodologies A strong focus on the practical implementation challenges that can arise at each step in the process and on how to overcome these challenges “Understanding how to model and analyse the risk of extreme events is a crucial part of the risk management process. This book provides a set of techniques that allow practitioners to do this comprehensively.” Paul Sweeting, Professor of Actuarial Science, University of Kent “How can the likeliness of crises affect the construction of portfolios? This question is highly topical in times where we still have to digest the last financial collapse. Malcolm Kemp gives the answer. His book is highly recommended to experts as well as to students in the financial field.” Christoph Krischanitz, President Actuarial Association of Austria, Chairman WG “Market Consistency” of Groupe Consultatif