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# P1.T2.203. Skew and kurtosis (Stock & Watson)

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
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Skew and kurtosis can get pretty technically actually. For example, sample skew and kurtosis are variously defined (e.g., skew in Excel is likely different from our calc due to its small sample adjustment). How much do you *need* to know? Historically, GARP has approached them qualitatively rather than requiring a calculation. My third below is a tweak of a question in the 2012 GARP sample paper - David

AIM: Define, calculate, and interpret the skewness, and kurtosis of a distribution

Questions:

203.1. Let random variable W be distributed normally as N(0,10). What are, respectively, the following: i. The fourth moment of W, E[W^4]; and ii. The kurtosis of W?

a. 30.0 (4th moment) and zero (kurtosis)
b. 100.0 and 3.0
c. 300.0 and zero
d. 300.0 and 3.0

203.2. A random variable (X) has three possible outcomes: 90.0 with 40% probability; 100.0 with 50% probability; and 110.0 with 10% probability. What is the skewness of the variable's distribution?

a. -1.82
b. -0.95
c. 0.37
d. 0.74

203.3. An analyst gather information about the return distribution for two portfolios during the same period: Portfolio A shows skewness of 0.9 and kurtosis of 3.7; Portfolio B shows skewness of 1.3 and kurtosis of 2.1. The analyst asserts "Portfolio A is more peaked--that is, has a higher peak--than a normal distribution and Portfolio B has a long right tail."

a. The analyst is correct about both portfolios