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CFA Level I · CFA Level I Exam · The Return and Risk of a Financial Portfolio

An analyst doubles every return of Asset A (multiplies each by 2) and adds 1% to every return of Asset B, then recomputes the covariance and correlation of A and B. Compared with the original values, the covariance and correlation most likely:

Covariance doubles and correlation is unchanged. Multiplying one series by two scales the covariance by two, while adding a constant to the other has no effect. Correlation divides by the standard deviations, which also scale, so it stays the same.

  1. Acovariance doubles and correlation is unchangedCorrect
  2. Bcovariance and correlation both double
  3. Ccovariance is unchanged and correlation doubles

Explanation

Cov(2A, B+0.01) = 2·Cov(A,B) because adding a constant does not affect covariance and scaling by 2 multiplies it. Correlation is scale- and shift-invariant for positive multipliers, so it is unchanged. The other options wrongly let correlation scale.

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