Financial Risk Manager Part 1
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Which of the following properties of covariance is INCORRECT?
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NNikitesh
A
Covariance measures how one random variable moves with another random variable.
B
Covariance of (R,R) = Variance of R
C
Covariance ranges from -1 to +1.
D
None of the above.
Explanation:
Explanation:
Covariance has the following properties:
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Option A is correct: Covariance measures the linear relationship between two random variables - how one variable moves with another.
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Option B is correct: The covariance of a random variable with itself equals its variance: Cov(R,R) = Var(R).
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Option C is incorrect: Covariance does NOT range from -1 to +1. Covariance can take any value from negative infinity to positive infinity. The range is unbounded because it depends on the scale of the variables.
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Option D is incorrect: Since option C is incorrect, 'None of the above' cannot be the correct answer.
Key distinction: Correlation (specifically, Pearson's correlation coefficient) ranges from -1 to +1, not covariance. Correlation is a standardized version of covariance that removes the scale effect by dividing by the product of the standard deviations.
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