7.3: Skew and Kurtosis Flashcards
What is Chebyshev’s inequality? What is most important about it?
Chebyshev’s inequality states that for any set of observations, the percentage of the observations that lie within k standard deviations of the mean is at least 1 - 1/k^2 for all k > 1.
The most important part of Chebyshev’s inequality:
- applies to any distribution
- applies to both sample and population data
What is relative dispersion and how is it commonly measured? Why is it useful?
Relative dispersion is the amount of variability in a distribution relative to a reference point or benchmark.
It is commonly measured with the coefficient of variation (CV), which is computed as standard deviation of x / average value of x. It is useful because it helps to make a direct comparison of dispersion across different sets of data.
What is coefficient of variation used to measure in an investment setting?
Risk (variability) per unit of expected return (mean).
Why is a symmetrical distribution important?
Symmetry is important because the degree of symmetry tells analysts if deviations form the mean are more likely to be positive or negative (skewness).
What is skewness? What are the two types of skewness?
Skewness refers to the extent to which a distribution is not symmetrical as a result of outliers in the observation.
Two types of skewness:
- Left tail/negatively skewed distribution
- Right tail/positively skewed distribution
Another term for left tail skewness
Negatively skewed distribution.
Another term for right tail skewness
Positively skewed distribtion.
What is the relationship between mean, median, and mode in a symmetrical distribution?
Mean = mode = median
What is the relationship between mean, median, and mode in a positive/right tail skewness?
Mean > median > mode
What is the relationship between mean, median, and mode in a negative/left tail skewness?
Mean < median < mode
What is kurtosis? What are the three types of kurtosis (LPM)?
Kurtosis is a measure of the degree to which a distribution is more or less peaked than a normal distribution.
Leptokurtic describes a distribution that is more peaked than a normal distribution.
Platykurtic describes a distribution that is less peaked than a normal distribution.
Mesokurtic describes a distribution that has the same kurtosis as a normal distributions.
What is leptokurtic? What is its characteristics? What are the two other types of kurtosis?
Leptokurtic describes a distribution that is more peaked than a normal distribution. Characteristics: more returns clustered around the mean and more returns with large deviations from the mean (fatter tails) indicating lower returns with small deviations from the mean.
Platykurtic describes a distribution that is less peaked than a normal distribution.
Mesokurtic describes a distribution that has the same kurtosis as a normal distributions.
What is platykurtic? What are the two other types of kurtosis?
Platykurtic describes a distribution that is less peaked than a normal distribution.
Leptokurtic describes a distribution that is more peaked than a normal distribution.
Mesokurtic describes a distribution that has the same kurtosis as a normal distributions.
What is mesokurtic? What are the two other types of kurtosis?
Mesokurtic describes a distribution that has the same kurtosis as a normal distributions.
Platykurtic describes a distribution that is less peaked than a normal distribution.
Leptokurtic describes a distribution that is more peaked than a normal distribution.
What is excess kurtosis? What does a positive value of excess kurtosis indicate? Negative value?
Excess kurtosis is if a distribution has more or less kurtosis than the normal distribution.
Positive value of excess kurtosis indicate a distribution that is leptokurtic (more peaked, fat fails). Negative value of excess kurtosis indicate a distribution that is platykurtic (less peaked, thin tails)
