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 demonstrate that it can be a useful tool for risk management purposes.

Exchange-Trade Funds Evaluation using Performance Measures Distribution

In this study we propose the use of the performance measure distribution rather than its punctual value to rank hedge funds. Generalized Sharpe Ratio and other similar measures that take into account the higher-order moments of portfolio return distributions are commonly used to evaluate hedge funds performance. The literature in this field has reported non-significant difference in ranking between performance measures that take, and those that do not take, into account higher moments of distribution. Our approach provides a much more powerful manner to differentiate between hedge funds performance. We use a non-semiparametric density based on Gram-Charlier expansions to forecast the conditional distribution of hedge fund returns and its corresponding performance measure distribution. Through a forecasting exercise we show the advantages of our technique in relation to using the more traditional punctual performance measures.

Multivariate Appoximations 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.