Understanding the Long-Only Minimum Variance Portfolio

Nick L. Gunther; Alec N. Kercheval; Ololade Sowunmi

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arXiv · 2603.07692

Understanding the Long-Only Minimum Variance Portfolio

Nick L. Gunther·Alec N. Kercheval·Ololade Sowunmi

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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.

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Nick L. Gunther, Alec N. Kercheval, Ololade Sowunmi. 2026-03-08. Understanding the Long-Only Minimum Variance Portfolio. https://arxiv.org/abs/2603.07692

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