Financial Risk Manager Part 1

Explanation

Correct Answer: B

A zero correlation (ρ = 0) between two variables specifically indicates that there is no linear relationship between them. However, this does not necessarily mean the variables are independent.

Key Points:

• Correlation measures linear relationships only - It quantifies how well two variables can be described by a straight line
• Independence vs. Zero Correlation:
  • If two variables are independent, they must have zero correlation
  • However, zero correlation does NOT guarantee independence
  • Variables can have zero correlation but still be related through nonlinear relationships

Example:

Consider the relationship between X and Y = X². If X is symmetric around zero (e.g., normally distributed), the correlation between X and X² will be zero, but they are clearly not independent - Y is completely determined by X.

Therefore, option B is correct because zero correlation specifically means no linear relationship exists, while option A is incorrect because zero correlation doesn't guarantee independence.