Can VAR models capture regime shifts in asset returns? a long-horizon strategic asset allocation perspective

In the empirical portfolio choice literature it is often invoked that through the choice of predictors that may closely track business cycle conditions and market sentiment, simple Vector Autoregressive (VAR) models could produce optimal strategic portfolio allocations that hedge against the bull and bear dynamics typical of financial markets. However, a distinct literature exists that shows that non-linear econometric frameworks, such as Markov switching, are also natural tools to compute optimal portfolios arising from the existence of good and bad market states. In this paper we examine whether and how simple VARs can produce empirical portfolio rules similar to those obtained under a range of multivariate Markov switching models, by studying the effects of expanding both the order of the VAR and the number/selection of predictor variables included. In a typical stock-bond strategic asset allocation problem on US data, we compute the out-of-sample certainty equivalent returns for a wide range of VARs and compare these measures of performance with those typical of non-linear models that account for bull-bear dynamics and characterize the differences in the implied hedging demands for a long-horizon investor with constant relative risk aversion preferences. We conclude that most (if not all) VARs cannot produce portfolio rules, hedging demands, or out-of-sample performances that approximate those obtained from equally simple non-linear frameworks.