Moments expansion densities for quantifying financial risk

We propose a novel semi-nonparametric distribution that is feasibly parameterized to represent the non-Gaussianities of the asset return distributions. Our Moments Expansion (ME) density presents gains in simplicity attributable to its innovative polynomials, which are defined by the difference between the nth power of the random variable and the nth moment of the density used as the basis. We show that the Gram-Charlier distribution is a particular case of the ME-type of densities. The latter being more tractable and easier to implement when quadratic transformations are used to ensure positiveness. In an empirical application to asset returns, the ME model outperforms both standard and non-Gaussian GARCH models along several risk forecasting dimensions

A new proposal for computing portfolio valueat-risk for semi-nonparametric distributions

This paper proposes a semi-nonparametric (SNP) methodology for computing portfolio value-at-risk (VaR) that is more accurate than both the traditional Gaussian-assumption-based methods implemented in the software packages used by risk analysts (RiskMetrics), and alternative heavy-tailed distributions that seem to be very rigid to incorporate jumps and asymmetries in the distribution tails (e.g. the Student’s t). The outperformance of the SNP distributions lies in the fact that Edgeworth and Gram-Charlier series represent a valid asymptotic approximation of any “regular” probability density function. In fact these expansions involve general and flexible parametric representations capable of featuring the salient empirical regularities of financial data. Furthermore these distributions can be extended to a multivariate context and may be estimated in several steps and thus we propose to estimate portfolio VaR in three steps: Firstly, estimating the conditional variance and covariance matrix of the portfolio consistently with the multivariate SNP distribution; Secondly, estimating the univariate distribution of the portfolio constrained to the portfolio variance obtained from the previous step; Thirdly, computing the corresponding quantile of the portfolio distribution by implementing straightforward recursive algorithms. We estimate the VaRs obtained with such methodology for different bivariate portfolios of stock indices and interests rates finding a clear underestimation (overestimation) of VaR measures obtained from the traditional Gaussian- (Student’s t-) based methods compared to our SNP approach

Higher-Order Risk Preferences, Constant Relative Risk Aversion and the Optimal Portfolio Allocation

We derive the conditions for optimal portfolio choice within an expected utility framework considering alternative probability distributions that are able to capture the stylized features of asset returns at different degrees of accuracy. We show the importance of higher-order moments in the optimal decision on liquidity and relate them with the risk preference properties of riskiness, prudence and temperance

Flexible distribution functions, higher-order preferences and optimal portfolio allocation

In this paper we show that flexible probability distribution functions, in addition to been able to capture stylized facts of financial returns, can be used to identify pure higher-order effects of investors' optimizing behavior. We employ the five-parameter weighted generalized beta of the second kind distribution and other density functions nested within it to determine the conditions under which risk averse, prudent and temperate agents are diversifiers in the standard portfolio choice theory. Within this framework, we illustrate through comparative statics the economic significance of higher-order moments in return's distributions

Portfolio Risk Assessment under Dynamic (Equi)Correlation and Semi-Nonparametric Estimation: An Application to Cryptocurrencies

The semi-nonparametric (SNP) modeling of the return distribution has been proved to be a flexible and accurate methodology for portfolio risk management that allows two-step estimation of the dynamic conditional correlation (DCC) matrix. For this SNP-DCC model, we propose a stepwise procedure to compute pairwise conditional correlations under bivariate marginal SNP distributions, overcoming the curse of dimensionality. The procedure is compared to the assumption of dynamic equicorrelation (DECO), which is a parsimonious model when correlations among the assets are not significantly different but requires joint estimation of the multivariate SNP model. The risk assessment of both methodologies is tested for a portfolio of cryptocurrencies by implementing backtesting techniques and for different risk measures: value-at-risk, expected shortfall and median shortfall. The results support our proposal showing that the SNP-DCC model has better performance for lower confidence levels than the SNP-DECO model and is more appropriate for portfolio diversification purposes

Multivariate Approximations to Portfolio Return Distribution

This article proposes a three-step procedure to estimate portfolio return distributions under the multivariate Gram-Charlier (MGC) distribution. The method combines quasi maximum likelihood (QML) estimation for conditional means and variances and the method of moments (MM) estimation for the rest of the density parameters, including the correlation coefficients. The procedure involves consistent estimates even under density misspecification and solves the so-called ‘curse of dimensionality’ of multivariate modelling. Furthermore, the use of a MGC distribution represents a flexible and general approximation to the true distribution of portfolio returns and accounts for all its empirical regularities. An application of such procedure is performed for a portfolio composed of three European indices as an illustration. The MM estimation of the MGC (MGC-MM) is compared with the traditional maximum likelihood of both the MGC and multivariate Student’s t (benchmark) densities. A simulation on Value-at-Risk (VaR) performance for an equally weighted portfolio at 1% and 5% confidence indicates that the MGC-MM method provides reasonable approximations to the true empirical VaR. Therefore, the procedure seems to be a useful tool for risk managers and practitioners

Altruismo y exclusión social

[ES]Este proyecto va dirigido al estudio de los conceptos y los patrones de la exclusión social desde una perspectiva económica. Desde el punto de vista teórico, se pretende plantear modelos que analicen las implicaciones del altruismo en relación a la lucha contra situaciones de pobreza y exclusión social, profundizando en el estudio con las herramientas que proporciona la economía experimental. Desde el punto de vista empírico, se analizan los factores que han llevado a retrocesos en la dimensión de pobreza y exclusión social de la estrategia Europa 2020. Los indicadores AROPE se basan únicamente en el recuento de excluidos y, en consecuencia, no incorporan el grado de intensidad de la exclusión que es la base de los indicadores multidimensionales de la pobreza como el IPM. Por ello, se plantea dar definiciones alternativas de medidas que permitan caracterizar la sensibilidad de los indicadores de pobreza y exclusión social, integrando en la medición la proporción de excluidos con la intensidad de la exclusión. Se pretende identificar patrones de exclusión y grupos de especial riesgo, estudiando la contribución de los posibles factores causales

On the stability of the constant relative risk aversion (CRRA) under high degrees of uncertainty

Growth models under uncertainty and constant relative risk aversion (CRRA) utility are fragile in explaining consumers’ choice, as equilibrium consumption is dependent on distributional assumptions. We show that, under semi-nonparametric distributions, general equilibrium models are stable, as the existence of expected utility is guaranteed

Semi-parametric density expansions: orthogonality vs simplicity

In this paper we introduce a family of densities based on a new type of expansions that we name General Moments Expansions. We argue that our approach presents theoretical advantages over Edgeworth and Charlier type of expansions, which are related to, on the one hand, the simplicity of their polynomials (i.e. the orthogonality property is not required yet), and on the other hand, their generality, since they can easily be applied to any distribution with finite moments up to the polynomial truncation order. We illustrate the usefulness of the proposed densities through an out-of-sample forecasting exercise for exchange-rate returns risk. Our results show that the proposed model provides fairly accurate volatility and VaR forecasts in comparison the ones obtained from the VaR procedure proposed in Engle (2001) and a GARCH model with Student's t errors