- CFA Exams
- CFA Exam: Level I 2021
- Study Session 2. Quantitative Methods (1)
- Reading 7. Statistical Concepts and Market Returns
- Subject 10. Kurtosis in Return Distributions

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**CFA Practice Question**

The following data represents the annualized total returns (in percentages) for twelve bond funds.

B. -0.85

C. -1.73

14.2, 12.7, 11.7, 11.5, 11.2, 10.8, 10.0, 9.2, 9.1, 8.4, 7.9, -2.1

If mean = 9.55 and standard deviation = 4.10, what is the relative measure of skewness?

A. -2.27

B. -0.85

C. -1.73

Correct Answer: C

Use the formula: Sigma (xi - u)

^{3}= -1431.62. divided by 12 x 4.1^{3}= -1.73###
**User Contributed Comments**
20

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

willeen |
can anyone tell me what numbers to input to get -1431.62? thanks |

Rotigga |
You're kidding right? Take every single (X - 9.55)^3 and sum them up to get -1,431.62; it's a pain to do. |

cp24 |
...but skewness is different from kurtosis. Why was the kurtosis formula used? Or is kurtosis one of the measures of skewness? If so, for questions involving "skewness" how do we know the term pertains to kurtosis? |

arkot90 |
the skewness formula is used.... skewness= (x-m)^3/ NSigma^3 kurtosis= (x-m)^4/NSigma^4 |

mchu |
really time consuming |

bobert |
In addition to arkot90's formula of kurtosis, kurtosis= [(x-m)^4]/(NSigma^4) +3 |

mordja |
im not sure bobert is correct. Normal Dist has Kurtosis of 3. Thus [(x-m)^4]/(NSigma^4)is the kurtosis [x-m)^4]/(NSigma^4) -3 is the excess kurtosis |

JKiro |
you can cut the calculation time in by utilizing HP12c: the numerator can be calculated and summed quite easily by NOT clearing the register, seperating the individual sums by [ENTER] and ofcourse accumulating the sums by [+] |

strike |
Jkiro what are the functions to be pressed on the hp 12c? |

viannie |
according to the LOS, there is no calculation for kurtosis ... so ... just understand, but please correct me if I'm wrong ok ;) |

tschorsch |
for hp12c 9.55 sto 1 14.7 enter rcl 1 - 3 y^x 12.7 enter rcl 1 - 3 y^x + ... 7.9 enter rcl 1 - 3 y^x + 2.1 chs enter rcl 1 - 3 y^x + 12 div 4.1 enter 3 y^x div |

8thlegend |
I am not quiet understanding why Sigma (xi - u)^3 formula was used. I thought the formula was Sigma 1/n * (xi - u)^4/Std^4 -3. |

thekid |
8thlegend... B/C the question asks about "the relative measure of SKEWNESS" ...NOT Kurtosis... hence we use the skewness formula... Hope this helps. |

dcfa |
i do not have the curiculum in front of me now, but i am pretty sure that the LOS does not ask for "calculating" skewness/kurtosis. yes, you would have to understand/interpret it. |

anniepass |
Does anyone know which function can be used to calculate on the BA IIplaus |

soilnewyork |
Why are we not using N/(N-1*N-2) then multiplying this with (sum of the cubed deviations/4.1 cubed)= Skewness?? |

soilnewyork |
n/(n-1*n-2) = 12/110 = 0.10909 then multiply by -1431.64/68.921= -20.772 Therefore 0.10909 * -20.772 = -2.266 Shouldn't A be correct?? |

dmfz |
A. Should be the correct answer, even when you enter the values in excel and use =SKEW(range) it gives you A. Any thoughts? |

schweitzdm |
Calculating kurtosis is not in this LOS. Skip this question. |

choas69 |
my teacher told me to not study any formulas here ten times. |