Quantitative Methods - Data - Skewness, Kurtosis and Correlation Flashcards
when is a distribution considered symmetrical?
if it is shaped identially either side of its mean
what does distributional symmetry imply?
intervals of losses and gains will exhibit the same frequency
why is the extent to which a returns distribution being symmetrical important?
the degree of symmetry tells analysts if deviations from the mean are more likely to be positive or negative
what does skewness refer to?
the extent to which a distribution is not symmetrical
a +vely skewed distribution is said to be skewed to which direction and why? vice versa for -vely skewed
to the right because of its relatively long upper (right) tail
how are the mean, median and mode affected by skewness of a distribution? symmetrical, +ve and -ve
symmetrical - all the same
+ve (unimodal) - mode < median < mean.
-ve (unimodal) - mean < median < mode
- the mean is the most affecfted by outliers followed by the median and than the mode
when calculating sample skewness, are the numerator and denominator +ve or -ve?
denominator is always positive but the numerator can be either depending on whether observations above the mean or observations below the mean tend to be farther from the mean on average
what is sample skewness equal to?
the sum of the cubed deviations from the mean divided by the cubed standard deviation and by the number of observations
when calculating the sample skewness, what allows the interpretation of the skewness measure?
dividing by standard deviation cubed (this standardises the statistic)
values of sample skewness over what value are considered significant?
in excess of 0.5 in absolute value
what is kurtosis?
a measure of the degree to which a distribution is more or less peaked than a normal distribution
what is leptokurtic? talk about how this looks graphically and the probability of observations being close/far from the mean
distribution that is more peaked than a normal distribution. i.e. more returns clustered around the mean and more returns with large deviations from the mean (fatter tails). There is relatively greater probability of an observed value being either close to the mean or far from the mean.
what is platykurtic?
a distribution that is less peaked, or flatter than a normal distribution (less peak, thin tails)
what is mesokurtic?
the same kurtosis as a normal distribution
how might a leptokurtic distribution be interpreted from a financial risk perspective?
a greater likelihood of a large deviation from the mean return is often perceived as an increase in risk
