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Título

Comparative Analysis of Volatility Proxies and Regime-Based Asset Allocation

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Palavras-chave

Hidden Markov Model Volatility 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

The vulnerability of global markets has exposed the limitations of static asset allocation strategies. Regime-switching models like the HMM are essential for identifying latent market states. A gap exists in the literature regarding the comparative effectiveness of different volatility measures for HMMs. This study fills this gap by comparing historical, implied, and conditional volatilities in the Brazilian and U.S.A. markets (2019-2024), offering practical implications for optimizing asset allocation in volatile environments.

Problema de Pesquisa e Objetivo

The literature lacks a comparative analysis of which volatility proxy is most effective for identifying and forecasting market regimes via HMMs. This study aims to fill this gap by empirically comparing historical, implied, and conditional volatilities in the Brazilian and U.S.A. markets (2019-2024). The objective is to determine the best proxy and, with it, to construct and evaluate a regime-based asset allocation strategy, offering practical implications for investors in volatile scenarios.

Fundamentação Teórica

The theoretical foundation stems from the critique of Modern Portfolio Theory (MPT), whose static models are inadequate for markets with regime changes. To overcome this limitation, the study employs Hidden Markov Models (HMM), a stochastic tool that identifies latent states (e.g., high/low volatility) from observable variables. The choice of the volatility proxy thus becomes crucial for the HMM's effectiveness and for the construction of dynamic allocation strategies.

Metodologia

This study employs daily ETF data from the Brazilian and U.S. markets (2019-2024). Volatility (historical, implied, and conditional) is used as an input proxy for Hidden Markov Models (HMMs). The HMM model (2 regimes) is fitted using 252-day moving windows and evaluated by RMSE/MAE. Conditional volatility was the most effective proxy. Using it, a regime-based asset allocation strategy is quadratically optimized for different risk aversions and transaction costs, and compared against static and naive benchmarks.

Análise dos Resultados

Conditional volatility was the better proxy for the HMM in both markets. In the U.S.A., the dynamic strategy outperformed the benchmarks, especially for risk-averse investors. In Brazil, the 1/n strategy was robust in terms of raw returns, but the dynamic strategy demonstrated superior risk control and better performance with higher risk aversion, addressing a "puzzle". A longer period of high volatility was observed in the U.S.A. than in Brazil. The high concentration in fixed income in Brazil reflected high real interest rates. Correlations between assets increase during high volatility.

Conclusão

This study identified conditional volatility as the most effective proxy for HMMs in detecting market regimes. The Dynamic Regime strategy offers superior risk control, outperforming benchmarks in the U.S., and its value increases with investor risk aversion. In Brazil, despite the resilience of the Naive strategy in terms of raw returns, the dynamic approach stands out for its ability to align risk exposure with the investor's profile and its superior control. The increase in correlations during high volatility is confirmed. There are practical implications for risk-averse investors.

Contribuição / Impacto

The main contribution is identifying conditional volatility as the most effective proxy for HMMs, providing a clear methodological guideline. The practical impact lies in the creation of a dynamic strategy with superior risk control. Even in markets where the naive strategy is robust, such as Brazil, the adaptive model adds value by aligning risk exposure with the investor's profile, with performance that improves with greater risk aversion. This offers a robust framework for adaptive asset management in volatile scenarios.

Referências Bibliográficas

Ang, A., & Bekaert, G. (2012). Regime switches in interest rates. Journal of Business & Economic Statistics.
De Jong, M. (2018). Portfolio optimisation in an uncertain world. Journal of Asset Management.
Hamilton, J. D. (1989). A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica.
Hwang, I., Xu, S., & In, F. (2018). Naive versus optimal diversification: Tail risk. European Journal of Operational Research.
Nystrup, P., et al. (2015). Regime-based versus static asset allocation: Letting the data speak. The Journal of Portfolio Management.

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