Skip to content

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

A portfolio has exposures to two PCA factors. Factor 1 has a standard deviation of 8 bp per day and factor 2 has a standard deviation of 3 bp per day. The portfolio's sensitivities are USD 50,000 per bp for factor 1 and USD 100,000 per bp for factor 2. Principal components are uncorrelated. What is the portfolio's one-day standard deviation of P&L?

The one-day P&L standard deviation is USD 500,000. Factor contributions are 400,000 and 300,000, and because principal components are uncorrelated they combine as the square root of the sum of squares, not by simple addition.

  1. AUSD 500,000Correct
  2. BUSD 700,000
  3. CUSD 300,000
  4. DUSD 1,200,000

Explanation

Factor 1 P&L sd = 50,000 x 8 = 400,000. Factor 2 sd = 100,000 x 3 = 300,000. Uncorrelated, so total = sqrt(400,000^2 + 300,000^2) = 500,000. Simply adding gives 700,000, which wrongly assumes perfect correlation.

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