Standard Deviation Skewness

 Q1

Mean (): It is the average value of the observation, which is calculated by taking the sum of observed values (X) divided by the number of observations (N). [pic 1]

Variance (σ2): It is a measure of the difference between observed values from the mean or the spread of values from the mean.  It is referred to as the second moment and is denoted as:

[pic 2]

Standard deviation (σ): the most popular estimator of standard deviation is the sample standard deviation. It is the measure of the dispersion of a set of data from the mean of the data set.  Higher dispersion results in higher standard deviation.  The advantage of using standard deviation is that it is simple to use and widely accepted.  The disadvantage of standard deviation is that it does not work for comparing the variation of items of different units, in addition to this it doesn’t work well when comparing if two mean levels of a price series are different.  Higher price levels will result in higher standard deviations (double a price series results in double the standard deviation despite variation not doubling).   Standard deviation is calculated as below:

[pic 3]

Skewness: Skewness is a measure of asymmetry from the normal distribution; a negatively skewed distribution in the case of a stock return distribution would have a long thin tail to the left of the distribution. This would indicate large negative returns or high risk. The advantage of skewness when analyzing stock data is that it measures large losses, which are of greatest importance to risk managers.  Skewness is referred to as the third moment.

Kurtosis: Kurtosis is a measure that describes the shape of the distribution’s tails, positive kurtosis means there are fat tails and peak when compared to a normal distribution.  If we find positive kurtosis then the distribution has fatter tails, then the normal distribution.  

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