Trino-Manuel Ñíguez

Gram–Charlier densities: a multivariate approach

This paper introduces a new family of multivariate distributions based on Gram–Charlier and Edgeworth expansions. This family encompasses many of the univariate semi-non-parametric densities proposed in financial econometrics as marginal of its different formulations. Within this family, we focus on the analysis of the specifications that guarantee positivity to obtain well-defined multivariate semi-non-parametric densities. We compare two different multivariate distributions of the family with the multivariate Edgeworth–Sargan, Normal, Students t and skewed Students t in an in- and out-of-sample framework for financial returns data. Our results show that the proposed specifications provide a reasonably good performance, and would therefore be of interest for applications involving the modelling and forecasting of heavy-tailed distributions.

Multivariate Moments Expansion Density: Application of the Dynamic Equicorrelation Model

In this study, we propose a new semi-nonparametric (SNP) density model for describing the density of portfolio returns. This distribution, which we refer to as the multivariate moments expansion (MME), admits any non-Gaussian (multivariate) distribution as its basis because it is specified directly in terms of the basis density s moments. To obtain the expansion of the Gaussian density, the MME is a reformulation of the multivariate Gram-Charlier (MGC), but the MME is much simpler and tractable than the MGC when positive transformations are used to produce well-defined densities. As an empirical application, we extend the dynamic conditional equicorrelation (DECO) model to an SNP framework using the MME. The resulting model is parameterized in a feasible manner to admit two-stage consistent estimation, and it represents the DECO as well as the salient non-Gaussian features of portfolio return distributions. The in- and out-of-sample performance of a MME-DECO model of a portfolio of 10 assets demonstrates that it can be a useful tool for risk management purposes.

Forecasting Heavy-Tailed Densities with Positive Edgeworth and Gram-Charlier Expansions*

This article presents a new semi-nonparametric (SNP) density function, named Positive Edgeworth-Sargan (PES). We show that this distribution belongs to the family of (positive) Gram-Charlier (GC) densities and thus it preserves all the good properties of this type of SNP distributions but with a much simpler structure. The in- and out-of-sample performance of the PES is compared with symmetric and skewed GC distributions and other widely used densities in economics and finance. The results confirm the PES as a good alternative to approximate financial returns distribution, specially when skewness is not severe.

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

We derive the conditions for the optimal portfolio choice within a constant relative risk aversion type of utility function considering alternative probability distributions that are able to capture the asymmetric and leptokurtic features of asset returns. We illustrate the role —beyond risk aversion— played by higher-order moments in the optimal decision to form a portfolio of risky assets. In particular, we show that higher-order risk attitudes such as prudence and temperance associated with the third and fourth moments of the distribution define different optimal portfolios than those constrained under risk aversion.