Analyzing Single-State and Multi-state Momentum Factors with VAR and MSVAR Models

The momentum factor has always been attracting great interest from investors, and recent studies has helped its implementation into portfolio constructions. We take a closer look at one of these studies, the paper by Moskowitz et al. (2012), and intend to further refine it as well as applying an extension in order to provide more insight regarding the momentum factor. We propose new estimation methods, namely the Generalized Least Squares (GLS) and the Maximum Likelihood Estimation (MLE), in addition to the Ordinary Least Squares (OLS) performed by Moskowitz et al. (2012). The new estimation methods are introduced as we find one of his assumptions regarding uncorrelated errors to be not as applicable in a real-world scenario, which is a requirement for the OLS they used. The model is then extended by introducing a multi-state approach, where we utilize Markov-switching processes for the momentum factor states. Our data spanned from 1982 to 2018 across 9 indices that are selected by Moskowitz et al. (2012), and our findings show different results once we implement our proposed GLS and MLE. As we introduce the multi-state model approach as an extension, we find links between the low-momentum and highmomentum states with the recession periods in the market. Based on these results, the momentum factor can still be utilized in portfolio construction although it may not be as straightforward as previously believed.