Quantitative Portfolio Optimization Framework with Market Regimes Classification, Probabilistic Time Series Forecasting, and Hidden Markov Models

This paper introduces a three-step methodology for optimizing an investment portfolio. The first step involves selecting the best performing Exchange-Traded Funds (ETFs) from a comprehensive list of assets for each phase of the market cycle. The second step builds on the first by promoting allocation through the maximization of risk-adjusted returns under uncertainty, using a probabilistic framework. The third step employs a Hidden Markov Model (HMM) approach to model the dynamics of asset returns and volatility, allowing the use of the Mean-Variance framework to optimize allocation. The objective is to propose a framework capable of outperforming the S\&P 500 benchmark by achieving higher risk-adjusted returns, as confirmed by experimental results, thereby contributing to efficient capital allocation. The third stage, which involves HMM-based allocation optimization, also proves to be very effective in redefining asset weights in stock indices, achieving good performance when applied to IBOVESPA, the main equity index in Brazil. In particular, all proposed steps individually contribute to improving portfolio performance and can be used together or separately. The framework is sufficiently generic to accommodate various time series forecasting methods with different levels of complexity, as well as enables integration with fundamentalist approaches. JEL Classification: C15 , G11