1.2 the shape of the distributions Flashcards
what does it mean for a distribution to be symmetric
the left side is a mirror image of the right side
normal distribution has which characteristics?
Its mean and median are equal.
The mean and variance completely describe the distribution
skeweness
An asymmetrical distribution is skewed
A positively skewed distribution
long right tail
has frequent small losses and a few extreme gains
The mode is less than the median, which is less than the mean
A negatively skewed distribution
long left tail
has frequent small gains and a few extreme losses.
The mean is less than the median, which is less than the mode
Investors should be concerned if returns have this distribution
skeweness formula
the average cubed deviation from the mean divided by the cubed standard deviation
Skeweness =
(1/n) * (Sum of all (Xi - Xmean)^3)/s^3
Kurtosis
measures if a return is more or less peaked than a normal distribution
what is the kurtosis for a normal distribution?
3
mesokurtic
A kurtosis distribution that is peaked just like a normal distribution
leptokurtic
A kurtosis distribution that is more peaked than the normal distribution
kurtosis measure greater than 3
described as having fat tails
Most equity returns fall under which type of kurtosis?
leptokurtic
extreme returns are more common than would be expected if they were normally distributed
platykurtic
A less peaked kurtosis distribution that has a kurtosis of less than 3
described as having thin tails
Excess kurtosis
kurtosis minus 3
This measures kurtosis relative to the kurtosis of a normal distribution
how to approximate excess kurtosis in a large (100+) sample?
KE = [ (1/n) * (Sum of all Xi - Xmean)^4))/s^4] - 3
A mesokurtic distribution is most likely characterized by:
A no excess kurtosis.
B positive excess kurtosis.
C negative excess kurtosis.
A: no excess kurtosis.
An analyst examined a cross-section of annual returns for 252 stocks and calculated the following statistics:
Arithmetic Average 9.986%
Geometric Mean 9.909%
Variance 0.001723
Skewness 0.704
Excess Kurtosis 0.503
Compared to the normal distribution, this sample’s distribution is best described as having tails of the distribution with:
A: less probability than the normal distribution.
B: the same probability as the normal distribution.
C: more probability than the normal distribution.
C: more probability than the normal distribution.
If a distribution is positively skewed, which of the following measures of central tendency most likely has the lowest value?
A: Mean
B: Mode
C: Median
B: Mode
describe the Excess Kurtosis, Tail, and Distribution for a Kurtosis greater than 3
Excess Kurtosis: Greater than 0
Tail: Fatter-tailed than normal
Distribution: Leptokurtic
describe the Excess Kurtosis, Tail, and Distribution for a Kurtosis equal to 3
Excess Kurtosis: equals 0
Tail: Similar tails to normal
Distribution: Mesokurtic
describe the Excess Kurtosis, Tail, and Distribution for a Kurtosis less than 3
