Higher Moments of Net Proton Multiplicity Distributions at RHIC

200 GeV corresponding to baryon chemical potentials (mu(B)) between 200 and 20 MeV. Our measurements of the products kappa sigma(2) and S sigma, which can be related to theoretical calculations sensitive to baryon number susceptibilities and long-range correlations, are constant as functions of collision centrality. We compare these products with results from lattice QCD and various models without a critical point and study the root s(NN) dependence of kappa sigma(2). From the measurements at the three beam energies, we find no evidence for a critical point in the QCD phase diagram for mu(B) below 200 MeV.

Optimal hedging with higher moments

This study proposes a utility-based framework for the determination of optimal hedge ratios (OHRs) that can allow for the impact of higher moments on hedging decisions. We examine the entire hyperbolic absolute risk aversion family of utilities which include quadratic, logarithmic, power, and exponential utility functions. We find that for both moderate and large spot (commodity) exposures, the performance of out-of-sample hedges constructed allowing for nonzero higher moments is better than the performance of the simpler OLS hedge ratio. The picture is, however, not uniform throughout our seven spot commodities as there is one instance (cotton) for which the modeling of higher moments decreases welfare out-of-sample relative to the simpler OLS. We support our empirical findings by a theoretical analysis of optimal hedging decisions and we uncover a novel link between OHRs and the minimax hedge ratio, that is the ratio which minimizes the largest loss of the hedged position. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark

Forecasting VaR using analytic higher moments for GARCH processes

It is widely accepted that some of the most accurate Value-at-Risk (VaR) estimates are based on an appropriately specified GARCH process. But when the forecast horizon is greater than the frequency of the GARCH model, such predictions have typically required time-consuming simulations of the aggregated returns distributions. This paper shows that fast, quasi-analytic GARCH VaR calculations can be based on new formulae for the first four moments of aggregated GARCH returns. Our extensive empirical study compares the Cornish–Fisher expansion with the Johnson SU distribution for fitting distributions to analytic moments of normal and Student t, symmetric and asymmetric (GJR) GARCH processes to returns data on different financial assets, for the purpose of deriving accurate GARCH VaR forecasts over multiple horizons and significance levels.

Do higher moments really matter in portfolio choice?

We present explicit formulas for evaluating the difference between Markowitz weights and those from optimal portfolios, with the same given return, considering either asymmetry or kurtosis. We prove that, whenever the higher moment constraint is not binding, the weights are never the same. If, due to special features of the first and second moments, the difference might be negligible, in quite many cases it will be very significant. An appealing illustration, when the designer wants to incorporate an asset with quite heavy tails, but wants to moderate this effect, further supports the argument.

A few more moments to finance theory: introducing higher moments in investment theory and econometrics

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Introducing higher moments in the CAPM: some basic ideas

We show how to include in the CAPM moments of any order, extending the mean-variance or mean-variance-skewness versions available until now. Then, we present a simple way to modify the formulae, in order to avoid the appearance of utility parameters. The results can be easily applied to practical portfolio design, with econometric inference and testing based on generalised method of moments procedures. An empirical application to the Brazilian stock market is discussed.

A CAPM with higher moments: theory and econometrics

We develop portfolio choice theory taking into consideration the first p~ moments of the underIying assets distribution. A rigorous characterization of the opportunity set and of the efficient portfolios frontier is given, as well as of the solutions to the problem with a general utility function and short sales allowed. The extension of c1assical meanvariance properties, like two-fund separation, is also investigated. A general CAPM is derived, based on the theoretical foundations built, and its empirical consequences and testing are discussed

On certain geometric aspects of portfolio optimisation with higher moments

We discuss geometric properties related to the minimisation of a portfolio kurtosis given its first two odd moments, considering a risk-less asset and allowing for short sales. The findings are generalised for the minimisation of any given even portfolio moment with fixed excess return and skewness, and then for the case in which only excess return is constrained. An example with two risky assets provides a better insight on the problems related to the solutions. The importance of the geometric properties and their use in the higher moments portfolio choice context is highlighted.

International stock portfolio selection and performance measures recognizing higher moments of return distributions

Since the seminal works of Markowitz (1952), Sharpe (1964), and Lintner (1965), numerous studies on portfolio selection and performance measure have been based upon the mean-variance framework. However, several researchers (e.g., Arditti (1967, and 1971), Samuelson (1970), and Rubinstein (1973)) argue that the higher moments cannot be neglected unless there is reason to believe that: (i) the asset returns are normally distributed and the investor's utility function is quadratic, or (ii) the empirical evidence demonstrates that higher moments are irrelevant to the investor's decision. Based on the same argument, this dissertation investigates the impact of higher moments of return distributions on three issues concerning the 14 international stock markets.^ First, the portfolio selection with skewness is determined using: the Polynomial Goal Programming in which investor preferences for skewness can be incorporated. The empirical findings suggest that the return distributions of international stock markets are not normally distributed, and that the incorporation of skewness into an investor's portfolio decision causes a major change in the construction of his optimal portfolio. The evidence also indicates that an investor will trade expected return of the portfolio for skewness. Moreover, when short sales are allowed, investors are better off as they attain higher expected return and skewness simultaneously.^ Second, the performance of international stock markets are evaluated using two types of performance measures: (i) the two-moment performance measures of Sharpe (1966), and Treynor (1965), and (ii) the higher-moment performance measures of Prakash and Bear (1986), and Stephens and Proffitt (1991). The empirical evidence indicates that higher moments of return distributions are significant and relevant to the investor's decision. Thus, the higher moment performance measures should be more appropriate to evaluate the performances of international stock markets. The evidence also indicates that various measures provide a vastly different performance ranking of the markets, albeit in the same direction.^ Finally, the inter-temporal stability of the international stock markets is investigated using the Parhizgari and Prakash (1989) algorithm for the Sen and Puri (1968) test which accounts for non-normality of return distributions. The empirical finding indicates that there is strong evidence to support the stability in international stock market movements. However, when the Anderson test which assumes normality of return distributions is employed, the stability in the correlation structure is rejected. This suggests that the non-normality of the return distribution is an important factor that cannot be ignored in the investigation of inter-temporal stability of international stock markets. ^

Evaluating predictive densities of U.S. output growth and inflation in a large macroeconomic data set

We evaluate conditional predictive densities for U.S. output growth and inflationusing a number of commonly used forecasting models that rely on a large number ofmacroeconomic predictors. More specifically, we evaluate how well conditional predictive densities based on the commonly used normality assumption fit actual realizationsout-of-sample. Our focus on predictive densities acknowledges the possibility that, although some predictors can improve or deteriorate point forecasts, they might have theopposite effect on higher moments. We find that normality is rejected for most modelsin some dimension according to at least one of the tests we use. Interestingly, however,combinations of predictive densities appear to be correctly approximated by a normaldensity: the simple, equal average when predicting output growth and Bayesian modelaverage when predicting inflation.

Distribución hiperbólica generalizada: una aplicación en la selección de portafolios y en la cuantificación de medidas de riesgo de mercado

En este trabajo se implementa una metodología para incluir momentos de orden superior en la selección de portafolios, haciendo uso de la Distribución Hiperbólica Generalizada, para posteriormente hacer un análisis comparativo frente al modelo de Markowitz.

Production risk, pesticide use and GM crop technology in South Africa

Technology involving genetic modification of crops has the potential to make a contribution to rural poverty reduction in many developing countries. Thus far, pesticide-producing Bacillus thuringensis (Bt) varieties of cotton have been the main GM crops under cultivation in developing nations. Several studies have evaluated the farm-level performance of Bt varieties in comparison to conventional ones by estimating production technology, and have mostly found Bt technology to be very successful in raising output and/or reducing pesticide input. However, the production risk properties of this technology have not been studied, although they are likely to be important to risk-averse smallholders. This study investigates the output risk aspects of Bt technology by estimating two 'flexible risk' production function models allowing technology to independently affect the mean and higher moments of output. The first is the popular Just-Pope model and the second is a more general 'damage control' flexible risk model. The models are applied to cross-sectional data on South African smallholders, some of whom used Bt varieties. The results show no evidence that a 'risk-reduction' claim can be made for Bt technology. Indeed, there is some evidence to support the notion that the technology increases output risk, implying that simple (expected) profit computations used in past evaluations may overstate true benefits.

Production risk, pesticide use and GM crop technology in South Africa

Technology involving genetic modification of crops has the potential to make a contribution to rural poverty reduction in many developing countries. Thus far, pesticide-producing Bacillus thuringensis (Bt) varieties of cotton have been the main GM crops under cultivation in developing nations. Several studies have evaluated the farm-level performance of Bt varieties in comparison to conventional ones by estimating production technology, and have mostly found Bt technology to be very successful in raising output and/or reducing pesticide input. However, the production risk properties of this technology have not been studied, although they are likely to be important to risk-averse smallholders. This study investigates the output risk aspects of Bt technology by estimating two 'flexible risk' production function models allowing technology to independently affect the mean and higher moments of output. The first is the popular Just-Pope model and the second is a more general 'damage control' flexible risk model. The models are applied to cross-sectional data on South African smallholders, some of whom used Bt varieties. The results show no evidence that a 'risk-reduction' claim can be made for Bt technology. Indeed, there is some evidence to support the notion that the technology increases output risk, implying that simple (expected) profit computations used in past evaluations may overstate true benefits.

Alocação dinâmica ótima com momentos de ordem superior para a estratégia de carry trade

O objetivo do presente trabalho é verificar se, ao levar-se em consideração momentos de ordem superior (assimetria e curtose) na alocação de uma carteira de carry trade, há ganhos em relação à alocação tradicional que prioriza somente os dois primeiros momentos (média e variância). A hipótese da pesquisa é que moedas de carry trade apresentam retornos com distribuição não-Normal, e os momentos de ordem superior desta têm uma dinâmica, a qual pode ser modelada através de um modelo da família GARCH, neste caso IC-GARCHSK. Este modelo consiste em uma equação para cada momento condicional dos componentes independentes, explicitamente: o retorno, a variância, a assimetria, e a curtose. Outra hipótese é que um investidor com uma função utilidade do tipo CARA (constant absolute risk aversion), pode tê-la aproximada por uma expansão de Taylor de 4ª ordem. A estratégia do trabalho é modelar a dinâmica dos momentos da série dos logartimos neperianos dos retornos diários de algumas moedas de carry trade através do modelo IC-GARCHSK, e estimar a alocação ótima da carteira dinamicamente, de tal forma que se maximize a função utilidade do investidor. Os resultados mostram que há ganhos sim, ao levar-se em consideração os momentos de ordem superior, uma vez que o custo de oportunidade desta foi menor que o de uma carteira construída somente utilizando como critérios média e variância.