CFA Level I · CFA Level I Exam · Statistical Characteristics of Asset Returns
An analyst doubles every return in a data series for Asset M while leaving the returns of Asset N unchanged. Compared with the original values, the covariance and correlation between M and N will most likely:
The covariance doubles while the correlation stays the same. Covariance depends on the scale of the returns, so doubling M doubles it. Correlation divides by the standard deviations, including M's doubled one, so the scaling cancels out.
- Aboth double
- Bcovariance double and correlation stay the sameCorrect
- Cboth stay the same
Explanation
Covariance scales with the units of each variable, so multiplying M by 2 doubles the covariance. Correlation divides by both standard deviations, and the standard deviation of M also doubles, so the correlation is unchanged.
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