CFA Level I · CFA Level I Exam · Statistical Characteristics of Asset Returns
A scatter plot of the returns of two assets shows a clear U-shaped pattern, and the sample correlation coefficient is close to zero. Which conclusion is most appropriate?
The assets may have a strong nonlinear relationship. Correlation captures only linear association, so a U-shaped pattern can yield a correlation near zero even though the variables are clearly related; zero correlation does not mean independence.
- AThe assets have no relationship of any kind
- BThe assets have a strong linear relationship with a negative slope
- CThe assets may have a strong nonlinear relationship that correlation fails to captureCorrect
Explanation
Correlation measures only the strength and direction of a linear relationship. A U-shaped pattern is a systematic nonlinear relationship that can produce a correlation near zero. So a zero correlation does not imply independence or no relationship.
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