Covariance Matrix Comparisons
Compare empirical, shrinkage, and GARCH covariance matrices.
Covariance Matrix Comparison
Three covariance matrices are produced, each with different properties: empirical (backward-looking, high estimation error), shrinkage (regularized, stable), and GARCH (forward-looking, captures current volatility). The choice of matrix depends on the investment application.
Key Steps:
Condition Number:
$$
\kappa(Q) = \frac{\lambda_{\max}}{\lambda_{\min}}
$$
Portfolio Variance:
$$
\sigma_p^2 = w^\top Q w
$$