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CFA Level I · CFA Level I Exam · Statistical Characteristics of Asset Returns

The sample standard deviation of Asset M's returns is 12% and that of Asset N's returns is 5%. The correlation between the two is -0.40. If every return of Asset M is doubled while Asset N is unchanged, the new covariance in squared percent units is closest to:

The new covariance is -48. The original covariance is -0.40 times 12 times 5, or -24. Doubling one series scales covariance by two, giving -48, while correlation is unaffected by the change of scale and remains -0.40.

  1. A-48Correct
  2. B-24
  3. C-12

Explanation

Original covariance = -0.40 × 12 × 5 = -24. Doubling M's returns doubles its deviations, so covariance doubles to -48. The correlation stays at -0.40 because it is scale-free; using the original covariance (-24) ignores the scaling.

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