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FRM Part I · FRM Exam Part I · Measuring Return, Volatility, and Correlation

An analyst computes the Pearson correlation between daily returns of two equity indices and obtains 0.05. She concludes the two indices are statistically independent. Which statement best evaluates this conclusion?

The conclusion is invalid because Pearson correlation captures only linear dependence. Variables can be strongly related in a nonlinear way, such as one being the square of the other, and still show near-zero correlation. Zero correlation implies independence only under joint normality.

  1. AIt is valid, because a correlation near zero implies independence for any joint distribution
  2. BIt is invalid, because zero or near-zero linear correlation does not rule out nonlinear dependenceCorrect
  3. CIt is valid, because correlation of 0.05 is below the significance threshold for all sample sizes
  4. DIt is invalid, because correlation can only be computed for prices and not for returns

Explanation

Pearson correlation measures only linear association. Two variables can have strong nonlinear dependence (for example Y = X squared with X symmetric about zero) and still have zero correlation. Independence implies zero correlation, but the converse holds in general only for jointly normal variables.

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