This paper constructs a new estimator for large covariance matrices by drawing a bridge between the classic Stein (1975) estimator in finite samples and recent progress under large-dimensional asymptotics. Our formula is quadratic: it has two shrinkage targets weighted by quadratic functions of...

This paper introduces a nonlinear shrinkage estimator of the covariance matrix that does not require recovering the population eigenvalues first. We estimate the sample spectral density and its Hilbert transform directly by smoothing the sample eigenvalues with a variable-bandwidth kernel....

Second moments of asset returns are important for risk management and portfolio selection. The problem of estimating second moments can be approached from two angles: time series and the cross-section. In time series, the key is to account for conditional heteroskedasticity; a favored model is...

This paper injects factor structure into the estimation of time-varying, large-dimensional covariance matrices of stock returns. Existing factor models struggle to model the covariance matrix of residuals in the presence of time-varying conditional heteroskedasticity in large universes....

Many applied problems require a covariance matrix estimator that is not only invertible, but also well-conditioned (that is, inverting it does not amplify estimation error). For large-dimensional covariance matrices, the usual estimator--the sample covariance matrix--is typically not...

We develop an estimation method for the Diagonal Multivariate GARCH model. For a vector of size N unidimensional GARCH processes for the diagonal elements of the conditional covariance matrix, and N(N-1)/2 bivariate GARCH processes for the off-diagonal elements of the conditional covariance...

The central message of this paper is that nobody should be using the sample covariance matrix for the purpose of portfolio optimization. It contains estimation error of the kind most likely to perturb a mean-variance optimizer. In its place, we suggest using the matrix obtained from the sample...

This paper constructs a new estimator for large covariance matrices by drawing a bridge between the classic Stein (1975) estimator in finite samples and recent progress under large-dimensional asymptotics. The estimator keeps the eigenvectors of the sample covariance matrix and applies shrinkage...