An eigenvalue distribution derived ‘Stability Measure’ for evaluating Minimum Variance portfolios

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The Minimum Variance portfolio is subject to varying degrees of stability and robustness. We, therefore, propose a theoretical measure of its stability relative to a Marchenko–Pastur derived random correlation matrix. We demonstrate its practical use on the S&P 400, the S&P 500, the S&P 600 and the Russell 1000. Using historic market data from 2002 to 2021, we perform an optimisation on the empirical correlation matrix eigenvalue distribution to determine the implied variance ν(t) for the underlying data-generating process. Through monitoring its change over time Δν(t), we provide a Stability Measure for the Minimum Variance portfolio and thereby help researchers measure changes to estimation risk and manage rebalancing regimes.
Original languageEnglish
JournalQuantitative Finance
Issue number12
Early online date2 Dec 2022
Publication statusPublished online - 2 Dec 2022


  • Stability Measure
  • Minimum Variance portfolio
  • Modern portfolio theory
  • Covariance matrix
  • Marchenko–Pastur
  • General Economics, Econometrics and Finance
  • Finance


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