FRM Part I · FRM Exam Part I · Measuring Return, Volatility, and Correlation
An analyst finds that the Pearson correlation between daily returns of two equity indices is 0.05, and concludes the two indices are independent. Which statement best describes the flaw in this conclusion?
Low Pearson correlation does not prove independence because correlation measures 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. Independence implies zero correlation, but not the reverse.
- AZero or low linear correlation does not rule out nonlinear dependence, so independence cannot be inferredCorrect
- BA correlation of 0.05 is statistically always significant with daily data, so the indices are dependent
- CPearson correlation measures only the sign of dependence, not its magnitude
- DCorrelation is undefined for returns measured over daily horizons
Explanation
Pearson correlation captures only linear association. Two variables can have near-zero correlation yet be strongly dependent, for example Y = X^2 with symmetric X. Independence implies zero correlation, but the converse is false.
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