- CFA Exams
- CFA Level I Exam
- Study Session 18. Portfolio Management (1)
- Reading 52. Portfolio Risk and Return: Part I
- Subject 1. Major Return Measures

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**CFA Practice Question**

Compared to geometric mean, the arithmetic return is typically ______ if the holding period returns are not equal.

B. biased downward

C. the same as the arithmetic return

A. biased upward

B. biased downward

C. the same as the arithmetic return

Correct Answer: A

The bias is especially severe if the holding period returns are a mix of both positive and negative returns.

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**User Contributed Comments**
6

User |
Comment |
---|---|

czar |
won't it be biased downward? can somebody please help? |

michlam14 |
found the answer, unless R is the same every period, the geometric mean will always be smaller than Arithmetic mean. IMO i think because for arithmetic mean it is reduced by N whereas Geometric mean is reduced exponetially by nth. You should look up the formula of Geometric mean in the text book for negative value return. |

jonan203 |
arithmetic mean does NOT take into account compounding, which is why geometric (compounded rate of return) mean will typically be smaller |

Admir |
Geometric mean is always equal to or lower than the arithmetic mean. Never higher. |

robbiecow |
If not equal A (arithmetic) > G (geometric) > H (harmonic) Like in the alphabet A before G before H |

pigletin |
essentially a math problem |