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

Compared with the sample standard deviation, the mean absolute deviation of a return series is most likely to:

The mean absolute deviation is typically equal to or smaller than the standard deviation. Standard deviation squares deviations, which gives large deviations more weight, while the mean absolute deviation weights all deviations equally. It is based on the mean, so outliers still affect it.

  1. Abe equal to or smaller than it, because squaring deviations gives more weight to large deviationsCorrect
  2. Bbe larger than it, because absolute values remove the offsetting of signs
  3. Cbe unaffected by outliers, because it uses the median

Explanation

Squaring gives extreme deviations more weight, so the standard deviation is generally at least as large as the mean absolute deviation, which treats all deviations linearly. The mean absolute deviation uses the mean, not the median, and so still reacts to outliers.

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