medium · Quantitative Finance prob-stats
Which property of a covariance matrix Σ is utilized when using Principal Component Analysis (PCA) to decompose portfolio risk?
- The determinant of covariance matrix Sigma always equals one.
- Sigma always has a trace of zero, meaning total portfolio risk is fully eliminated.
- The covariance matrix Sigma is always structured as upper triangular.
- Σ is a symmetric matrix, allowing for an orthogonal basis of eigenvectors.
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