Regimes de volatilidade na gestão dinâmica de portfólio: estudos empíricos de medidas de risco

Abstract

Modern Portfolio Theory (MPT) seeks to optimize the risk-return tradeoff. Its foundational Mean-Variance model, pioneered by Markowitz, is the cornerstone of asset allocation. However, this approach’s reliance on variance as the sole risk measure presents limitations that have spurred the development of alternative risk metrics and a debate on their applicability. Numerous extensions have been proposed to mitigate the specification and estimation errors that compromise the robustness of static strategies and to better align models with investor needs. In this context, strategies that maximize downside risk-adjusted returns are gaining traction, featuring metrics like Conditional Value-at-Risk (CVaR) and Conditional Drawdown at Risk (CDaR). As market conditions switch between different regimes, the optimal risk measure becomes regime-dependent, a concept supported by State-Dependent Utility Theory. During high-volatility periods, for instance, rising asset correlations reduce the effectiveness of traditional diversification. This thesis, comprising three articles, evaluates whether adopting regime-adaptive risk functions enhances asset allocation performance. The first article assesses various volatility proxies (historical, conditional, and implied) for identifying market regimes via a Hidden Markov Model (HMM). The second article compares the performance of portfolios optimized with variance, CVaR, and CDaR within the HMM-identified low- and high-volatility regimes. The third article introduces a multi-period Model Predictive Control (MPC) framework that dynamically switches the risk function based on the prevailing regime—CVaR for low volatility and CDaR for high volatility. Results show that conditional volatility is the most effective proxy for regime identification. We find that CVaR performs best in low-volatility environments, whereas CDaR is superior in high-volatility scenarios. Crucially, the dynamic, regime-conditional risk strategy outperforms its static, single-regime counterpart, especially in terms of certainty equivalent return. These findings underscore the importance of dynamic risk management and provide practical guidance for investors aiming to build more adaptive portfolios in fluctuating market conditions.