FRM Part I · FRM Exam Part I · Sample Moments
An analyst estimates the sample covariance between the monthly returns of two assets at 24 (in squared percentage points). The sample standard deviations are 4 and 10 percentage points respectively. What is the sample correlation?
The sample correlation is 0.60. Correlation equals covariance divided by the product of the two standard deviations, so 24 divided by 4 times 10 gives 0.60. Using variances or the sum of standard deviations in the denominator gives incorrect values.
- A0.60Correct
- B2.40
- C0.15
- D1.71
Explanation
Correlation = covariance / (σx × σy) = 24 / (4 × 10) = 0.60. Dividing by the product of variances (16 × 10 = 160) gives 0.15, which mixes variance with standard deviation. Dividing by the sum of standard deviations gives 1.71, which is also invalid, since correlation must lie within -1 and 1.
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