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Understanding the Long-Only Minimum Variance Portfolio

Author

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  • 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.

Suggested Citation

  • Nick L. Gunther & Alec N. Kercheval & Ololade Sowunmi, 2026. "Understanding the Long-Only Minimum Variance Portfolio," Papers 2603.07692, arXiv.org.
    • Handle: RePEc:arx:papers:2603.07692
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    File URL: http://arxiv.org/pdf/2603.07692
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