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

William Smyth and Daniel Broby

Quantitative Finance, 2023, vol. 23, issue 3, 521-537

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.

Date: 2023
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DOI: 10.1080/14697688.2022.2149420

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