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

It is often suggested that through a judicious choice of predictors that track business cycles 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 nonlinear econometric frameworks, such as Markov switching (MS), are also natural tools to compute optimal portfolios in the presence of stochastic good and bad market states. In this paper we examine whether simple VARs can produce portfolio rules similar to those obtained under MS, 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, 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 nonlinear models for a long-horizon investor with constant relative risk aversion. We conclude that most VARs cannot produce portfolio rules, hedging demands, or (net of transaction costs) out-of-sample performances that approximate those obtained from equally simple nonlinear frameworks. We also compute the improvement in realized performance that may be achieved adopting more complex MS models and report this may be substantial in the case of regime switching ARCH.