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

An analyst finds that the Pearson correlation between two asset returns is 0.02 and concludes the assets are independent. Which statement best describes the flaw in this conclusion?

Pearson correlation measures only linear dependence, so a near-zero value does not prove independence. Variables can be strongly related nonlinearly, such as a variable and its square, and still show almost no linear correlation. Independence follows from zero correlation only for jointly normal variables.

  1. APearson correlation captures only linear dependence, so zero or low correlation does not rule out nonlinear dependenceCorrect
  2. BPearson correlation is always biased toward zero in small samples, so independence cannot be tested
  3. CA correlation below 0.05 is statistically indistinguishable from one, so dependence is likely
  4. DPearson correlation is defined only for normally distributed returns, so the value is meaningless

Explanation

Pearson correlation measures linear association only. Two variables can be strongly dependent in a nonlinear way (for example Y = X^2 with X symmetric) and still have near-zero correlation. Zero correlation implies independence only in special cases such as the bivariate normal.

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