Multivariate Return Decomposition: Theory and Implications

Abstract

In this paper, we propose a model based on multivariate decomposition of multiplicative—absolute values and signs—components of several returns. In the m-variate case, the marginals for the m absolute values and the binary marginals for the m directions are linked through a 2m-dimensional copula. The approach is detailed in the case of a bivariate decomposition. We outline the construction of the likelihood function and the computation of different conditional measures. The finite-sample properties of the maximum likelihood estimator are assessed by simulation. An application to predicting bond returns illustrates the usefulness of the proposed method.

Keywords: multivariate decomposition, multiplicative components, volatility and direction models, copula, dependence

JEL Classification: C13, C32, C51, G12