Paper: arXiv 2603.07692

Authors: Nick L. Gunther, Alec N. Kercheval, Ololade Sowunmi

Abstract

For a covariance matrix coming from a factor model of returns, we investigate the relationship between the long-only global minimum variance portfolio and the asset exposures to the factors. In the case of a 1-factor model, we provide a rigorous and explicit description of the long-only solution in terms of the parameters of the covariance matrix. For $q>1$ factors, we provide a description of the long-only portfolio in geometric terms. The results are illustrated with empirical daily returns of US stocks.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 4.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper offers strong analytical proofs and geometric characterizations of long-only minimum variance portfolios under factor models, expanding on previous semi-explicit formulations. However, while it cites empirical illustrations using US stock data, the core value proposition is primarily theoretical rather than empirical backtesting.

Research Flowchart

  flowchart TD
    A[Research Goal: Map Long-Only Min Variance Portfolio to Factor Exposures] --> B[Data Inputs: 1-Factor & Multi-Factor Covariance Matrices + US Stock Returns]
    B --> C[Methodology: Solve Constrained Optimization under Long-Only Rules]
    C --> D[1-Factor Analysis: Derive Explicit Closed-Form Solution]
    C --> E[Multi-Factor Analysis: Formulate Geometric Description]
    D --> F[Key Outcomes: Exact Parametric Bounds for 1-Factor & Geometric Interpretation for Multi-Factor Models]
    E --> F

Cited References (14)

  1. Markowitz portfolio construction at seventy — → 2401.05080
  2. The optimization of a quadratic function subject to linear constraints (1956)
  3. Portfolio Selection (1952)
  4. Convex Optimization (2004)
  5. A simplified model for portfolio analysis (1963)
  6. James- S tein estimation of the first principal component (2022)
  7. Better betas (2020)
  8. James- S tein for the leading eigenvector (2023)
and 6 more
  1. The Dispersion Bias (2022)
  2. Portfolio Optimization via Strategy-specific Eigenvector Shrinkage (2025)
  3. Introduction to Nonlinear Optimization: Theory, Algorithms, and Applications with Python and MATLAB (2023)
  4. Minimum-Variance Portfolio Composition (2011)
  5. Honey, I shrunk the covariance matrix (2004)
  6. Portfolio selection revisited (2024)

1 of 14 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.