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FRM Part II · FRM Exam Part II · Regression Hedging and Principal Component Analysis

A analyst runs PCA on the same eight US Treasury yield changes using (i) the covariance matrix and (ii) the correlation matrix. Short-maturity yields have much higher volatility than long-maturity ones. Which conclusion is most accurate?

The results generally differ. Correlation-matrix PCA standardizes each yield to unit variance, giving all rates equal weight, while covariance-matrix PCA lets the most volatile rates dominate the leading components. So eigenvectors and variance proportions are not identical across the two approaches.

  1. AThe eigenvectors and the proportion of variance explained will be identical under both approaches
  2. BThe correlation-matrix PCA gives equal weight to each rate, so the covariance-matrix first component tends to be dominated by the most volatile rates, and results generally differCorrect
  3. CThe correlation-matrix PCA explains more variance in the first component by mathematical necessity
  4. DCovariance-matrix PCA cannot be applied to yields because the components would be correlated

Explanation

Correlation PCA standardizes each series to unit variance, so every rate has equal influence; covariance PCA lets high-volatility rates dominate. Hence eigenvectors and variance shares generally differ. No result guarantees a larger first-component share for the correlation approach, and components are uncorrelated in both cases.

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