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

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  • William Smyth
  • Daniel Broby

Abstract

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 $ \nu (t) $ ν(t) for the underlying data-generating process. Through monitoring its change over time $ \Delta \nu (t) $ 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.

Suggested Citation

  • William Smyth & Daniel Broby, 2023. "An eigenvalue distribution derived ‘Stability Measure’ for evaluating Minimum Variance portfolios," Quantitative Finance, Taylor & Francis Journals, vol. 23(3), pages 521-537, March.
    • Handle: RePEc:taf:quantf:v:23:y:2023:i:3:p:521-537
    DOI: 10.1080/14697688.2022.2149420
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