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

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