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.

Higher-order moments in the theory of diversifying and portfolio composition

This paper examines the role of higher-order moments in portfolio choice within an expected-utility framework. We consider two-, three-, four- and five-parameter density functions for portfolio returns and derive exact conditions under which investors would all be optimally plungers rather than diversifiers. Through comparative statics we show the importance of higher-order risk preference properties, such as riskiness, prudence and temperance, in determining plunging behaviour. Empirical estimates for the S&P500 provide evidence for the optimality of diversification.