Advancing Portfolio Optimization: Adaptive Minimum-Variance Portfolios and Minimum Risk Rate Frameworks

Abstract: This study presents the Adaptive Minimum-Variance Portfolio (AMVP) framework and the Adaptive Minimum-Risk Rate (AMRR) metric, innovative tools designed to optimize portfolios dynamically in volatile and nonstationary financial markets. Unlike traditional minimum-variance approaches, the AMVP framework incorporates real-time adaptability through advanced econometric models, including ARFIMA-FIGARCH processes and non-Gaussian innovations. Empirical applications on cryptocurrency and equity markets demonstrate the proposed framework's superior performance in risk reduction and portfolio stability, particularly during periods of structural market breaks and heightened volatility. The findings highlight the practical implications of using the AMVP and AMRR methodologies to address modern investment challenges, offering actionable insights for portfolio managers navigating uncertain and rapidly changing market conditions.