CFA Practice Question

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CFA Practice Question

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

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 4.13 = -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.
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