+Accurate estimation of the covariance matrix is essential for mean-variance portfolio optimisation, yet the sample covariance matrix isa notoriously noisy estimate, especially in high dimensions.Contemporary shrinkage methods attempt to mitigate this noisebut often retain significant estimation error in higher-dimensionalsettings or become computationally impractical in these scenarios.In this paper, we present a novel non-linear shrinkage method,Adaptive Beta Shrinkage. We also investigate an existing method,CorShrink, which has yet to be applied in a financial context. Inempirical studies, Adaptive Beta Shrinkage outperforms all surveyedcontemporary methods in terms of realised risk and risk-adjustedreturns for large asset universes. For smaller asset universes, thebest method is Munro’s (2010) equally-weighted blend estimator
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