- CFA Exams
- CFA Exam: Level I 2021
- Study Session 2. Quantitative Methods (1)
- Reading 7. Statistical Concepts and Market Returns
- Subject 6. Measures of Dispersion

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**CFA Practice Question**

The risk-free rate of return is 4.25%. Based on the following information about a common stock portfolio, what is the coefficient of variation?

Geometric mean return: 12.7%

Variance of returns: 380

Portfolio beta: 1.35

B. 1.25

C. 1.36

Arithmetic mean return: 14.3%

Geometric mean return: 12.7%

Variance of returns: 380

Portfolio beta: 1.35

A. 0.86

B. 1.25

C. 1.36

Correct Answer: C

380

^{0.5}/14.3 = 19.49/14.3 = 1.36###
**User Contributed Comments**
7

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

Kevdharr |
Standard deviation is equal to the square root of the variance. The variance here is 380. The square root of 380 is 19.494. Once you have standard deviation, you can find the coefficient of variation by dividing the standard deviation (19.49) by the arithmetic mean (14.3). 19.49/14.3=1.36 |

sungryongl |
how to know which mean return to use based on risk-free rate of return? |

kaichan91 |
In question twelve the mean return was calculated in decimals to get 1.4% (or 144%% as the answer stated). Why do we divide by 14.3 here instead of .143? |

choas69 |
where are you senpai? |

Huricane74 |
@sungryongl - The risk free rate of return has no being on this question. You use the Arithmetric mean in the denominator when calculating the coefficient of variation. |

Huricane74 |
I got 136.31. Why are we using 14.3 instead of .143 when the mean was 14.3%? |

gc1210 |
You are dividing 14.3 instead of .143 because the standard diviation also has a unit (%) the two unit canceled out. The variance with unit should be 380%% The standard diviation with unit should be 19.494% Hence CV should be 19.494% / 14.3% = 19.494 / 14.3 |