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 of the single assets are allowed to switch between different states. We consider different parametrizations of the involved asset covariances: statewise uncorrelated assets (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 benchmark, we also consider a model without regime switches. We utilize a filter‐based expectation‐maximization (EM) algorithm to obtain optimal parameter estimates within this multivariate HMM and present 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 in many settings outperform naïve 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.

中文翻译：

---

HMM设置中基于过滤器的投资组合策略，具有不同的相关参数

我们考虑在体制转换市场中优化投资组合。投资组合的资产是通过离散时间的隐马尔可夫模型（HMM）建模的，其中允许单个资产的漂移和波动在不同状态之间切换。我们考虑了所涉及的资产协方差的不同参数化：状态无关资产（尽管通过共同的马尔可夫链进行链接），以独立于状态的方式相关的资产以及相关状态因州而异的资产。作为基准，我们还考虑了没有体制转换的模型。我们利用基于滤波器的期望最大化（EM）算法在此多元HMM中获得最佳参数估计，并在所有三个HMM设置中提供参数估计器。我们讨论了这些不同模型对几种投资组合策略的绩效的影响。我们的发现表明，对于模拟收益，我们的策略在许多情况下都优于单纯的投资策略，例如权重相等的策略。信息标准可用于检测最佳模型以进行估计以及投资组合优化。使用真实数据的第二项研究证实了这些发现。