- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 2. Organizing, Visualizing, and Describing Data
- Subject 6. Measures of Central Tendency

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**CFA Practice Question**

When using stock return data, a geometric mean return calculation is most likely preferred over a geometric mean calculation because ______.

A. return data can be less than one.

B. return data can be negative.

C. the geometric mean return is closer in value to the arithmetic mean.

**Explanation:**Taking the nth root of a negative number, when n is an even number, cannot be done (unless one uses imaginary numbers). As returns can be negative, it might not be possible to find their geometric means. However, returns cannot be lower than -100%. By adding one to each return, as is done in the geometric mean return calculation, we create a series of numbers greater than or equal to zero. The product of such terms must therefore also be positive and the nth root can always be found.

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**User Contributed Comments**
2

User |
Comment |
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saadbhatty |
Typo in this question. |

myron |
No there is no typo. A geometric mean return calculation [(1 + r1)(1 + r2)...(1+rn)]^(1/n) is different from a geometric mean calculation [(r1)(r2)...(rn)]^(1/n) because ri can be negative. |