Skip to content

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

A bank hedges a bond portfolio's term structure risk using the first three principal components of yield changes, which together explain 97% of variance. Compared with hedging each of the ten key rates separately, what is the main advantage of the PCA approach?

The main advantage is dimension reduction: three uncorrelated factors capture 97% of variance, so fewer hedges are needed than for ten separate key rates. It does not remove the residual 3% risk, and the covariance matrix must still be estimated.

  1. AIt eliminates all interest rate risk, including that from the omitted components
  2. BIt reduces the number of risk factors to hedge while capturing most variance, using uncorrelated factorsCorrect
  3. CIt ensures the hedge ratios are stable whenever the correlation structure changes
  4. DIt removes the need to estimate a covariance matrix

Explanation

PCA reduces dimensionality: three uncorrelated factors replace ten correlated rates while retaining most variance. The residual 3% remains unhedged, so it does not eliminate all risk. PCA still requires a covariance or correlation matrix, and instability of that matrix is a limitation.

Did you get it right without looking?

One question tells you little. A timed set on Regression Hedging and Principal Component Analysis shows your real accuracy, how long you take and where you lose marks.

Practise Regression Hedging and Principal Component AnalysisFree diagnostic mock

More Regression Hedging and Principal Component Analysis questions