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

Abstract

We propose a computational portfolio optimization algorithm, the Adaptive Minimum-Variance Portfolio (AMVP), which iteratively constructs synthetic assets to obtain a fixed-point minimum-risk portfolio under non-Gaussian and long-memory dynamics. The algorithm converges to a stable minimum-variance solution while dynamically updating the covariance structure using ARFIMA-FIGARCH Normal Inverse Gaussian scenario generation. The expected return of the converged portfolio defines a shadow minimum-risk benchmark, termed the Adaptive Minimum-Risk Rate (AMRR). Unlike classical minimum-variance optimization, AMVP is robust to nonstationarity, heavy tails, and evolving dependence structures. We demonstrate convergence, numerical stability, and economic interpretability using Dow Jones equities and

major cryptocurrencies. The framework is extended to Conditional Value-at-Risk optimization. Our results highlight the computational advantages of adaptive portfolio learning for risk benchmarking and scenario-based portfolio construction.

Keywords: Adaptive portfolio optimization, Shadow risk-free rate, Long-range dependence, Computational asset pricing