Sampling Error in Mean–Variance Portfolios

Derive the global minimum-variance portfolio weights from a covariance matrix under a full-investment constraint.

Compute unconstrained mean–variance portfolio weights for a specified risk-aversion parameter.

Explain why inversion amplifies estimation error along low-variance sample eigenvectors.

Quantify the dimensional ratio q = N/T for a return matrix and interpret its effect on covariance estimation.

Determine when a sample covariance matrix is singular from the relationship between N and T.

Use Python to compare oracle and sample-covariance minimum-variance portfolios on simulated Gaussian returns.