A Conditional Shrinkage Method for Portfolio Selection

We develop a conditional shrinkage method for portfolio selection. Our approach builds on a decomposition of the mean-variance portfolio into the 1/N portfolio and an alpha component that offers large efficiency gains but is exposed to substantial estimation risk. We show that a linear shrinkage covariance matrix determines the portfolio’s relative exposure to these components, and our framework allows the shrinkage intensity to depend on a state variable that predicts their relative performance. We implement the method using investor sentiment and find that the estimated relation predominantly leads to greater shrinkage toward 1/N when sentiment is low, improving mean-variance efficiency while maintaining low turnover. JEL Classification: G11, G12.