Module 3: Statistical Measures of Asset Returns

Absolute dispersion

The amount of variability present without comparison to any reference point or benchmark

Arithmetic mean

The sum of the observations divided by the number of observations

Bimodal

A distribution that has two most frequently occurring values

Box and Whisker plot

A graphic for visualising the dispersion of data across quartiles. It consists of a box with “whiskers” connected to the box

Coefficient of variation

The ratio of set of observations’ standard deviation to the observations’ mean value

Correlation

A measure of the linear relationship between two random variables

Deciles

Values that divide a distribution ranked smallest to largest into 10 equal partsD

Dispersion

The variability of a population or sample of observations around the central tendency

Downside risk

The potential for loss

Excess kurtosis

Degree of kurtosis (fatness of tails) relative to the kurtosis of the normal distribution

Fat-Tailed

Describes a distribution that has fatter tails than a normal distribution (also called leptokurtic)In

Interquartile range

The difference between the third and first quartiles of a dataset

Kurtosis

The statistical measure that indicates the combined weight of the tails of a distribution relative to the rest of the distribution

Leptokurtic

Describes a distribution that has fatter tails than a normal distribution (also called fat-tailed)

Mean absolute deviation

With reference to a sample, the mean of the absolute values of deviation from the sample mean.

Measure of central tendency

A quantitative measure that specifies where data are centered.

Measures of location

Quantitative measures that describe the location or distribution of data. They include not only measures of central tendency but also other measures, such as percentiles.

Median

The “middlemost” observation

Mesokurtic

Describes a distribution with kurtosis equal to that of the normal distribution, namely, kurtosis equal to three.

Mode

The most frequently occuring value in a distribution

Percentiles

Values that divide a distribution into 100 equal parts

Platykurtic

Describes a distribution that has relatively less weight in the tails than the normal distribution.

Quantile

A value at or below which a stated fraction of the data lies.

Quartiles

Quantiles that divide a distribution into four equal parts

Quintiles

Quantiles that divide a distribution into five equal parts

Range

The difference between the maximum and minimum values in a dataset.

Relative dispersion

The amount of dispersion relative to a reference value or benchmark.

Sample correlation coefficient

A standardised measure of how two variables in a sample move together. It is the ratio of the sample covariance to the product of the two variables’ standard deviations.

Sample covariance

A measure of how two variables in a sample move together

Sample excess kurtosis

A sample measure of the degree of a distribution’s kurtosis in excess of the normal distribution’s kurtosis

Sample mean

The sum of the sample observations divided by the sample size

Sample skewness

A sample measure of the degree of asymmetry of a distribution

Sample standard deviation

The positive square root of the sample variance

Sample variance

The sum of squared deviations around the mean divided by the degrees of freedom

Scatter plot

A two dimensional graphical plot of paired observations of values for the independent and dependent variables in a simple linear regression.

Skewed

Not symmetrical

Skewness

A quantitative measure of skew. It is computed as the average cubed deviation from the mean standardised by dividing by the standard deviation cubed.

Spurious correlation

Correlation between two variables arising not from a direct relation between them but from their relation to a third variable

Standard deviation

The positive square root of the variance; a measure of dispersion in the same units as the original data.

Target semideviation

A measure of downside risk, calculated as the square root of the average of the squared deviations of observations below the target

Thin-tailed

Describes a distribution that has relatively less weight in the tails than the normal distribution

Trimmed mean

A mean computed after excluding a stated small percentage of the lowest and highest observations

Unimodal

A distribution with a single value that is most frequently occurring.

Variance

The expected value of squared deviations from a random variable’s expected value

Winsorised mean

A mean computed after assigning a stated percentage of the lowest values equal to one specified low value and a stated percentage of the highest values equal to one specified high value