Covariance Matrices, Estimation, and Why They Break foundational

How a covariance matrix summarizes co-movement, why the sample version becomes unstable in high dimensions, and why shrinkage is the default repair.

How a covariance matrix summarizes co-movement, why the sample version becomes unstable in high dimensions, and why shrinkage is the default repair.

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References

Improved estimation of the covariance matrix of stock returns with an application to portfolio selection
Olivier Ledoit, Michael Wolf (2003) — Journal of Empirical Finance
The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Second Edition
Trevor Hastie, Robert Tibshirani, Jerome Friedman (2009) — Springer-Verlag
Optimal Versus Naive Diversification: How Inefficient is the 1/N Portfolio Strategy?
Victor DeMiguel, Lorenzo Garlappi, Raman Uppal (2009) — The Review of Financial Studies