Skip to content

FRM Part II · FRM Exam Part II · Empirical Properties of Correlation: How Do Correlations Behave in the Real World?

An analyst notes that the correlation between two stock returns is zero, and concludes the two stocks are statistically independent. Which is the best critique of this conclusion?

Zero correlation does not guarantee independence. Pearson correlation captures only linear dependence, so two variables may be related nonlinearly, for example one being the square of the other, while correlation is zero. Independence follows only in special cases such as joint normality.

  1. AZero correlation implies independence only if the relationship is linear and the variables are jointly normal; nonlinear dependence can exist with zero correlationCorrect
  2. BZero correlation always implies independence for any distribution
  3. CZero correlation implies a perfect negative relationship
  4. DCorrelation is invalid for returns and can only be used for prices

Explanation

Pearson correlation measures only linear dependence. Variables can be strongly nonlinearly dependent (e.g., Y = X squared with symmetric X) with zero correlation. Independence follows from zero correlation only in special cases such as joint normality.

Did you get it right without looking?

One question tells you little. A timed set on Empirical Properties of Correlation: How Do Correlations Behave in the Real World? shows your real accuracy, how long you take and where you lose marks.

Practise Empirical Properties of Correlation: How Do Correlations Behave in the Real World?Free diagnostic mock

More Empirical Properties of Correlation: How Do Correlations Behave in the Real World? questions