Beyond static risk aversion: online multi-period mean-variance portfolio optimization using hidden Markov chains
摘要
Recognizing that investors’ risk preferences evolve in response to dynamically changing market conditions, which are often unobservable and exhibit regime-switching behavior, this paper addresses multi-period mean-variance (MMV) portfolio optimization with market-regime-dependent risk parameters and partially observed market information. The model incorporates a regime-switching framework represented by hidden Markov models (HMM) with Gaussian emission probabilities. This approach mirrors financial practice, where continuously observable variables, such as the Volatility Index (VIX), are used as proxies for underlying market information. HMM not only provides a tractable method for updating risk aversion and model parameters in an online learning fashion, but it also integrates seamlessly into the MMV solution framework. In the decision phase, we derive closed-form solutions for the MMV model in two scenarios: one with only risky assets and another that includes a risk-free asset. The proposed policies generalize several classical policies as special cases. Using real market data, we compare our model with alternatives that either ignore the regime-switching structure or assume constant risk aversion. Our experiments demonstrate that the proposed model consistently outperforms these benchmarks, highlighting the importance of incorporating dynamic market conditions and evolving risk preferences into practical portfolio management.