Paper shows minimum variance portfolio rankings are only weakly consistent for the mean
PtrPomorski · x · 2026-10-17
A finance paper, Minimum Variance Portfolios as Consistent Scoring Functions, analyzes the popular method of ranking covariance forecasts via out-of-sample minimum variance portfolio variance.
- The method implicitly defines a scoring (loss) function in the Bregman divergence family, robust to noise in the covariance proxy and homogeneous.
- However, it is only weakly consistent for the mean: the set of forecasts producing identical losses is large in realistic settings, so rankings can be misleading.
- Results extend to constrained portfolios (max Sharpe, short-sale limits); constraints act as loss function "shape parameters," and rankings of misspecified forecasts can be sensitive to that choice.
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