Financial Risk and Heavy Tails

Bradley, Brendan; Taqqu, Murad S.

doi:10.1016/b978-044450896-6.50004-2

Cited by 77 publications

(34 citation statements)

References 44 publications

(46 reference statements)

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“…6. Another case in which the MVO and the M-CVaR optimization are equivalent is the multivariate elliptical distribution with fat tails (see, e.g., Bradley and Taqqu 2003). 7.…”

Section: The Slight Variations Among the Mvo Results In Scenariosmentioning

confidence: 99%

The Impact of Skewness and Fat Tails on the Asset Allocation Decision

Xiong¹,

Idzorek²

2011

Financial Analysts Journal

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The authors modeled the non-normal returns of multiple asset classes by using a multivariate truncated Lévy flight distribution and incorporating non-normal returns into the mean-conditional value at risk (M-CVaR) optimization framework. In a series of controlled optimizations, they found that both skewness and kurtosis affect the M-CVaR optimization and lead to substantially different allocations than do the traditional mean-variance optimizations. They also found that the M-CVaR optimization would have been beneficial during the 2008 financial crisis.lthough numerous alternatives to the mean-variance optimization (MVO) framework have appeared in the literature, no clear leader has emerged. The lack of an agreed-upon alternative to MVO has slowed the development of practitioner-oriented tools. Moreover, the difficulty in estimating the required inputs-returns, standard deviations, and correlations-for MVO is well known, a problem that can be substantially more difficult with more advanced techniques. The future is hard to predict accurately, especially in detail.Asset class return distributions are not normally distributed, but the typical Markowitz MVO framework that has dominated the asset allocation process for more than 50 years relies on only the first two moments of the return distribution. Equally important, considerable evidence shows that investor preferences go beyond mean and variance to higher moments: skewness and kurtosis. Investors are particularly concerned about significant losses-that is, downside risk, which is a function of skewness and kurtosis.Recent research suggests that higher moments are important considerations in asset allocation. Patton (2004) showed that knowledge of both skewness and asymmetric dependence (higher correlations in downside markets) leads to economically significant gains, in particular, with no shorting constraints. Harvey, Liechty, Liechty, and Müller (2010) proposed a method for optimal portfolio selection involving a Bayesian decision theoretical framework that addresses both higher moments and estimation error. They suggested that incorporating higher-order return distribution moments in portfolio selection is important.The financial crisis of 2008 has led many investors to search for tools that minimize downside risk. In our study, we explored one of the promising alternatives to MVO that incorporates non-normal return distributions: mean-conditional value at risk (M-CVaR) optimization. Modeling Non-Normal ReturnsEmpirically, almost all asset classes and portfolios have returns that are not normally distributed. Many assets' return distributions are asymmetrical. In other words, the distribution is skewed to the left (or occasionally the right) of the mean (expected) value. In addition, most asset return distributions are more leptokurtic, or fatter tailed, than are normal distributions. The normal distribution assigns what most people would characterize as meaninglessly small probabilities to extreme events that empirically seem to occur approximately 10 times...

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“…6. Another case in which the MVO and the M-CVaR optimization are equivalent is the multivariate elliptical distribution with fat tails (see, e.g., Bradley and Taqqu 2003). 7.…”

Section: The Slight Variations Among the Mvo Results In Scenariosmentioning

confidence: 99%

The Impact of Skewness and Fat Tails on the Asset Allocation Decision

Xiong¹,

Idzorek²

2011

Financial Analysts Journal

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“…This leads to the intuitive 3 Indeed, let T be an orthonormal matrix then Σ = ΛΛ = ΛTT Λ = Λ * Λ * and therefore Λ and Λ * generate the same scatter matrix. 4 Hereafter we will skip the term multivariate. Nonetheless, the reader should always keep in mind that R is a random variable and U (k) is a random vector, thus X is a random vector as well.…”

Section: Elliptical Distributionsmentioning

confidence: 99%

“…3 Some important densities are embedded in the class of elliptical distributions: Gaussian, Student's t and ESD among others. 4 We obtain a Gaussian distribution if R = χ 2 k . Similarly, the Student's t is obtained if R = νχ 2 k /χ 2 ν where χ 2 k and χ 2 ν are stochastically independent.…”

Section: Elliptical Distributionsmentioning

confidence: 99%

“…As a consequence, stable distributions enjoy many of the properties of the Gaussian, including closeness under summation, and a number of theoretical results in asset allocation and option pricing are available (cf. Fama (1965a) and (1965b), Ortobelli, Huber and Schwartz (2002), Ortobelli and Rachev (2005), McCulloch (2003) and the survey by Bradley and Taqqu (2001)). …”

Section: Introductionmentioning

confidence: 99%

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Indirect estimation of elliptical stable distributions

Lombardi

Veredas

2009

Computational Statistics & Data Analysis

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We present an indirect estimation approach for elliptical stable distributions which relies on the use of a multivariate t distribution as auxiliary model. This distribution is also elliptical and we show that its parameters have a one-to-one relationship with those of the elliptical stable, therefore making the proposed indirect approach especially suitable. Standard asymptotic properties are also shown and we analyze the finite sample behavior of the estimators via a comprehensive Monte Carlo study. An application to 27 emerging markets stock indexes concludes the paper.

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“…In an attempt to model the unconditional distribution of stock returns several researchers have considered alternative approaches. See for example, Blattberg and Gonedes (1974), Bradley and Taqqu (2002), Clark (1973), Kon (1984, McDonald (1996), Mittnik and Rachev (1993), Panas (2001), Rachev and Mittnik (2000).…”

Section: R O L L I N G -S a M P L E D P A R A M E T E R S F R O M A Lmentioning

confidence: 99%