Module 7.3: Skew and Kurtosis Flashcards
What is Chebyshev’s inequality?
For any ser of observations, the percentage of the observations that lie within “k” standard deviations of the mean is at least 1 - 1/k^2
For example - What is the minimum percantage of any distribution that will lie within 2 SD’s of the mean?
1 - 1k^2 = 1 - 1/2^2 = 1-1/4 = 75%
What is the coefficient of variation?
Measure of relative dispersion between two data sets. Relative dispersion is the amount of variability in a distribution relative to a reference point or benchmark.
What is the formula for coefficient of variation?
Standard deviation of X / Average value of X
remember, measurement of variation so standard deviation goes on the top
Explain distribution symmetry, what does it mean and why is it significant?
Symmetrical distribution is when the likelihood of return being -6 and +6 are equal. The degree of symmetry tells analysts if deviations from the mean are more likely to be positive or negative.
Explain Skewness? What causes skewness?
What is positively skewed and negatively skewed?
Skewness is when the distribution is not symmetrical, it is caused by the occurrence of outliers int he data set.
Outliers are observations with extraordinarily large values.
Positive / Negative skewed means that the distribution has positive outliers and negative outliers
Explain Mean, Median, and Mode of a symmetrical distribution
For a symmetrical distribution, the mean, median, and mode are all equal.
Explain Mean, Median, and Mode for a positively skewed distribution?
Mode is less than the median, which is less than the mean.
Explain Mean, Median, and mode for a negatively skewed distribution?
Mean is less than the median, which is less than the mode.
What is Kurtosis? Leptokurtic? Platykurtic? Mesokurtic?
Kurtosis is the measure of the degree to which a distribution is more or less “peaked” than a normal distribution.
Leptokuric - more peaked than a normal distribution. Has higher change for returns around the mean, and extremely large deviations from the mean.
Platykuric - distribution that is less peaked
mesokurtic - same kurtosis as a normal distribution
What is excess kurtosis? how is it calculated?
more or less kurosis than a normal distribution, which has a kurtosis of 3. therefore, excess kurtosis for a normal distribution is 0. Leptokurtic has excess kurtosis greater than 1, and platykurtic will have excess kurtosis less than zero.
What is the formula for sample skewness?
Sum of cubed deviations from the mean / cubed standard deviation and the number of observations.
What is the formula for sample kurtosis
Sum of deviations from the mean to the fourth power / standard deviation to the fourth power and the number of observations.
When should you use arithmetic mean and geometric mean to analyze investment returns?
Arithemtic mean is the statistically best estimators of the next year’s return. If we’re calculating multi-year return, then geometric mean would be a better calculation.
