- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 3. Statistical Measures of Asset Returns
- Subject 1. Measures of Central Tendency

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**CFA Practice Question**

Suppose that four different portfolios have produced the following returns over the past year: 10%, 30%, 5% and 15%.

II. The range is 25%.

III. The mean absolute deviation is 7.5%.

IV. The variance is 0.875%.

V. The standard deviation is 9.354%.

I. The mean return is 15%.

II. The range is 25%.

III. The mean absolute deviation is 7.5%.

IV. The variance is 0.875%.

V. The standard deviation is 9.354%.

Which statement(s) is (are) FALSE?

A. II and IV only

B. III and V only

C. None of the above

**Explanation:**All the statements were true and can be computed as follows:

Mean return = (10 + 30 + 5 + 15) / 4 = 15%

Range = 30 - 5 = 25%

Mean absolute deviation (MAD) = [ |10 - 15| + | 30 - 15 | + | 5 - 15 | + | 15 - 15 |] / 4 = 7.5%

Variance s

^{2}= [(10% - 15%)

^{2}+ (30% - 15%)

^{2}+ (5% - 15%)

^{2}+ (15% - 15%)

^{2}] / 4 = 0.875%

Standard deviation = (0.875%)

^{0.5}= 9.354%

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**User Contributed Comments**
9

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

Eckhardt1978 |
but variance is 116,66 and therefore standard deviation is 10,8 %, isn't it? Sum(Ri-R')^2/(n-1) |

Eckhardt1978 |
ok, i'm false. it's a sample so divided by n and not by n-1. |

tenny45 |
If st.dev is 9.354, then variance is 9.354^2 = 87.5. |

shayu |
It's just a convention for the unit (unit^2). Nothing wrong. |

tabulator |
No, Eckhardt, this is population; therefore divide by n (in this case 4). |

achu |
A minor aside is that, since this is a POPULATION as tabulator mentions, it should be sigma^2, not s^2. |

panvino |
Why is this a population? I'm lost! |

NickPash |
Since it take smore than 1.5 min. Use POE, You know choice 2 is coreect without any calculation, so A is correct. Now check MAD, Mad is correct. Therefore, answer must be C. |

soukhov |
good way for calculation stdev for population on calc, is adding one more number from a row, use 10% 30% 5% 15% 15% for example |