Portfolio optimization with mixture vector autoregressive models

TL;DR

This paper introduces mixture vector autoregressive models for improved portfolio optimization by capturing complex features like asymmetry and heteroskedasticity in multivariate financial time series, providing explicit predictive formulas.

Contribution

It proposes a novel MVAR modeling approach that effectively captures complex data features and offers explicit formulas for predictive distributions in portfolio optimization.

Findings

MVAR models outperform traditional models on real stock data.

Explicit formulas enable efficient computation of predictive distributions.

The approach effectively captures asymmetry and heteroskedasticity.

Abstract

Obtaining reliable estimates of conditional covariance matrices is an important task of heteroskedastic multivariate time series. In portfolio optimization and financial risk management, it is crucial to provide measures of uncertainty and risk as accurately as possible. We propose using mixture vector autoregressive (MVAR) models for portfolio optimization. Combining a mixture of distributions that depend on the recent history of the process, MVAR models can accommodate asymmetry, multimodality, heteroskedasticity and cross-correlation in multivariate time series data. For mixtures of Normal components, we exploit a property of the multivariate Normal distribution to obtain explicit formulas of conditional predictive distributions of returns on a portfolio of assets. After showing how the method works, we perform a comparison with other relevant multivariate time series models on real stock return data.