Understanding the Long-Only Minimum Variance Portfolio

Battle Count: 108

Highly relevant to quantitative portfolio construction. The paper provides actionable insights for practitioners building long-only minimum variance portfolios: (1) explicit threshold rule for single-factor models identifying which assets to include, (2) geometric characterization for multi-factor models, (3) empirical evidence showing only ~5-7% of assets are active in LOMV portfolios, (4) demonstration that low-beta and low-idiosyncratic-risk assets dominate. Directly applicable to index fund construction, risk-parity strategies, and minimum-variance ETF design.

Single-factor case is straightforward: sort betas, compute sequence R_i, find threshold k via bisection in O(log p) steps, then solve k-dimensional linear system. Multi-factor case requires convex optimization (cvxpy) or iterative methods since no closed-form exists. The JSE/JSM estimators add moderate complexity for covariance estimation. Overall, the theoretical framework is elegant but practical implementation for multi-factor requires numerical optimization.

The paper provides fully explicit formulas for the single-factor case (Theorem 2) and geometric characterizations for multi-factor (Theorem 3). Empirical data comes from CRSP via WRDS (subscription required). The JSE and JSM estimators are described algorithmically. The cvxpy package is used for multi-factor portfolio computation. Theoretical proofs are complete and self-contained.