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Answer: Correlation and the regression slope are closely related.
The correct answer is C. Correlation and the slope of the regression are intimately related, as regression explains the sense in which correlation measures linear dependence. Pearson's correlation coefficient is a statistical measure that quantifies the strength and direction of the linear relationship between two variables. The slope of the regression line, which is derived from the correlation coefficient, indicates the rate of change of one variable with respect to the other. In the context of financial assets, correlation is used to assess the degree to which the returns of two assets move together. A positive correlation indicates that both assets tend to increase or decrease together, while a negative correlation suggests that one asset increases as the other decreases. However, it's important to note that correlation does not imply causation. Option A is incorrect because financial assets are often interdependent and can exhibit both linear and nonlinear relationships. Option B is incorrect because Pearson's correlation specifically measures linear dependence, not nonlinear dependence. Option D is incorrect because the rank correlation, which is a measure of the monotonic relationship between two variables, is virtually identical to Pearson's correlation for normally distributed variables. This is because, under normality, the relationship between variables is linear.
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A financial risk analyst is tasked with examining the relationship between the returns of two financial assets to determine if there is any interdependence between them. To understand this relationship, the analyst considers the concept of correlation. Correlation measures the strength and direction of a linear relationship between two variables, in this case, the returns of the two assets. Based on this, which of the following statements accurately describes the correlation and its implication for the interdependence of the asset returns?
A
Returns on financial assets tend to be independent.
B
Pearson's correlation measures both linear and nonlinear dependence.
C
Correlation and the regression slope are closely related.
D
If the returns of the two assets are normally distributed, their rank correlation and Pearson's correlation would not be equal.