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Título

Multi-Period Optimal Allocation with Regime-Conditional Risk

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Palavras-chave

Multi-Period Allocation Regime-Conditional Risk Portfolio

Agradecimento: We thank FAPEMIG and CNPq.

Autores

Wanderci Alves Bitencourt

UNIVERSIDADE FEDERAL DE MINAS GERAIS (UFMG)
Robert Aldo Iquiapaza

UNIVERSIDADE FEDERAL DE MINAS GERAIS (UFMG)

Resumo

Introdução

Traditional portfolio allocation based on the Markowitz model is limited in dynamic markets. In response, models integrating Hidden Markov Models (HMM) for regime forecasting and Model Predictive Control (MPC) for multi-period optimization have gained prominence. However, the existing literature typically employs a fixed risk metric, ignoring that an investor's risk perception changes with market conditions. This study addresses this gap by proposing a risk management approach that dynamically adapts to the volatility regime, offering a solution for asset allocation and risk management.

Problema de Pesquisa e Objetivo

The core research problem is the rigidity of HMM-MPC models, which use fixed risk metrics and ignore the state-dependent nature of investor utility. The objective is to develop and test a dynamic allocation model that overcomes this limitation. The central innovation is the dynamic switching of the risk metric (Conditional Value-at-Risk - CVaR and Conditional Drawdown-at-Risk - CDaR) conditioned on the volatility regime. The hypothesis is that this adaptive approach yields superior risk-adjusted returns and utility compared to fixed-risk strategies

Fundamentação Teórica

The research builds upon Modern Portfolio Theory but advances it by using multi-period optimization via MPC, a tractable framework for sequential decisions. Hidden Markov Models (HMM) are used to identify market regimes (high and low volatility) and to forecast return behavior given the regime probability. The tail-risk metrics CVaR and CDaR are chosen for their robustness and convexity. The core theoretical basis is State-Dependent Utility Theory, where risk-switching serves as a practical approximation for optimizing an investor's changing preferences.

Metodologia

The adaptive HMM-MPC strategy was tested on ETFs in the Brazilian market (2020-2025). Both the HMM and MPC were implemented using a 252-day moving window. The portfolio optimization model assumes a regime-dependent risk function, employing CVaR when the HMM identifies low volatility and CDaR when high volatility is identified. The hyperparameters for risk aversion, transaction costs, and penalization were optimized via irace to maximize the Certainty Equivalent Return (CER). Statistical significance tests were performed using the Aligned Rank Transform (ART).

Análise dos Resultados

The empirical results show systematic superiority over fixed-risk benchmarks and the 1/n portfolio. Statistical significance was confirmed by the ART/ANOVA test. Conditional analysis reveals that the model used CVaR to capture gains in low-volatility periods and CDaR to protect capital during crises, validating the switching mechanism.

Conclusão

This study proposed and validated an HMM-MPC allocation model with an adaptive risk metric. The main theoretical contribution is the operationalization of a state-dependent utility function. Empirically, the strategy significantly outperformed benchmarks in the Brazilian market, achieving a superior CER (7.10%) even after transaction costs. The main limitation is the focus on a single market, suggesting future research to test the model's generalization in other contexts and with other asset classes.

Contribuição / Impacto

The main theoretical contribution is operationalizing a state-dependent utility function via risk metric switching, mitigating the misspecification error of static models. Empirically, the study validates that no single risk metric is universally optimal. In practice, the HMM-MPC framework offers a robust alternative for portfolio management, especially in emerging markets, as it controls drawdowns while enhancing risk-adjusted returns. The method is practical and reproducible.

Referências Bibliográficas

Boyd, S., Busseti, E., Diamond, S., & Kahn, R. N. (2017). Multi-period portfolio optimization with-and-without-transaction costs. Foundations and Trends in Optimization.
Jarrow, R. A., & Rungsuriyawiboon, S. (2021). Concavity and the portfolio choice problem. Mathematics and Financial Economics.
Nystrup, P., Hansen, B. W., Madsen, H., & Lindström, E. (2018). Dynamic portfolio optimization in a mean-variance framework with a hidden Markov-switching model. Quantitative Finance.
De Miguel, V., & Kourou, A. (2024). Multifactor portfolios with volatility conditioning. Journal of Banking & Finance.

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