Portfolio selection based on the spectral decomposition of the sample covariance matrix: A shrinkage-motivated basis-optimization strategy

The estimation of the covariance matrix and its inverse is crucial in portfolio selection. However, non-negligible estimation errors arise in practice, which has motivated a large literature on linear and nonlinear shrinkage methods for covariance and inverse covariance estimation. Among them, nonlinear shrinkage is generally more flexible and powerful than linear shrinkage. This paper proposes two portfolio construction methods motivated by linear and nonlinear shrinkage ideas and based on the spectral decomposition of the sample covariance matrix. After reparameterization, the proposed procedures are implemented as basis-coefficient optimization rules under an internally validated out-of-sample variance criterion, rather than as classical low-dimensional shrinkage estimators of portfolio weights. The first method is a generalized spectral-shrinkage-motivated portfolio rule, and the second is a double-target spectral-shrinkage-motivated portfolio rule. Empirical results based on real data show that the proposed methods can deliver competitive, and in some cases superior, out-of-sample mean and Sharpe ratio performance. At the same time, the additional diagnostics based on out-of-sample variance, turnover, and HHI concentration reveal important trade-offs in stability and implementability.