Skip to content

FRM Part II · FRM Exam Part II · Correlation Basics: Definitions, Applications, and Terminology

A portfolio manager observes that two assets have a Pearson correlation near zero, and concludes the assets are statistically independent. Which statement best evaluates this conclusion?

The conclusion is incorrect. Pearson correlation captures only linear dependence, so two assets can show near-zero correlation while being nonlinearly dependent, such as one being a squared function of the other. Independence implies zero correlation, but zero correlation does not generally imply independence.

  1. AIt is correct, because zero correlation always implies independence
  2. BIt is incorrect, because zero correlation implies perfectly negative dependence
  3. CIt is incorrect, because Pearson correlation measures only linear dependence, and nonlinear dependence can exist with zero correlationCorrect
  4. DIt is correct only if the assets have equal variances

Explanation

Independence implies zero correlation, but the converse is false in general. For example, Y = X² with symmetric X has zero linear correlation yet is fully dependent. The converse holds in special cases such as the bivariate normal, which is not assumed here.

Did you get it right without looking?

One question tells you little. A timed set on Correlation Basics: Definitions, Applications, and Terminology shows your real accuracy, how long you take and where you lose marks.

Practise Correlation Basics: Definitions, Applications, and TerminologyFree diagnostic mock

More Correlation Basics: Definitions, Applications, and Terminology questions