We propose a clustering-based dimensionality reduction approach to minimum variance portfolio optimization. Rather than constructing the global minimum variance (GMV) portfolio over the full stock universe, which is subject to severe estimation error due to high-dimensionality, we apply Ward’s hierarchical clustering to partition stocks into groups of similarly behaving assets, select one representative per cluster, and optimize on the resulting low-dimensional sub-universe. We show theoretically that clustering preserves the factor structure and yields a better-conditioned covariance matrix than random selection. Empirically, on the Chinese A-share market, the proposed strategies substantially outperform the full-universe benchmark, with gains robust to transaction costs.