Portfolio strategies and estimation in a hidden Markov model using state dependent, state independent or no correlation

We consider portfolio optimization in a regime-switching market. The assets of the portfolio are modeled through a hidden Markov model (HMM) in discrete time, where drift and volatility are allowed to switch between different states. We consider different parametrizations of the involved asset covariances namely state-wise uncorrelated assets, which are though linked through the common Markov chain, assets correlated in a state-independent way, and assets where the correlation varies from state to state. As a control model, we also consider a model without regime switches. We utilize a filter-based EM-algorithm to obtain optimal parameter estimates within this multivariate HMM and develop parameter estimators in all three HMM settings. We discuss the impact of these different models on the performance of several portfolio strategies. Our findings show that for simulated returns our strategies often outperform naive investment strategies, like the equal weights strategy. Information criteria can be used to detect the best model for estimation as well as for portfolio optimization. A second study using real data confirms these findings.