Multivariate asset return prediction with mixture models

Abstract

The use of mixture distributions for modeling asset returns has a long history in finance. New methods of demonstrating support for the presence of mixtures in the multivariate case are provided. The use of a two-component multivariate normal mixture distribution, coupled with shrinkage via a quasi-Bayesian prior, is motivated, and shown to be numerically simple and reliable to estimate, unlike the majority of multivariate GARCH models in existence. Equally important, it provides a clear improvement over use of GARCH models feasible for use with a large number of assets, such as constant conditional correlation, dynamic conditional correlation, and their extensions, with respect to out-of-sample density forecasting. A generalization to a mixture of multivariate Laplace distributions is motivated via univariate and multivariate analysis of the data, and an expectation–maximization algorithm is developed for its estimation in conjunction with a quasi-Bayesian prior. It is shown to deliver significantly better forecasts than the mixed normal, with fast and numerically reliable estimation. Crucially, the distribution theory required for portfolio theory and risk assessment is developed.

Keywords:

• density forecasting
• expectation–maximization algorithm
• fat tails
• mixture distributions
• multivariate Laplace distribution
• quasi-Bayesian estimation
• shrinkage estimation
• weighted likelihood

JEL Classification:

• C51
• C53
• G11
• G17

Acknowledgements

Part of this research has been carried out within the National Centre of Competence in Research ‘Financial Valuation and Risk Management’ (NCCR FINRISK), which is a research program supported by the Swiss National Science Foundation. The author thanks Pawel Polak and Maria Putintseva for assistance with programming the RSDC–GARCH and ADCC models, as well as the detailed discussions which led to a significantly improved paper. The paper has also benefited substantially from the extensive comments and suggestions provided by Christian Brownlees, Michael McAleer, Eric Renault and David Veredas on an earlier draft of this paper, as well as those from anonymous referees.