Chapter 3: Statistical Measures of Asset Returns

Question 1

Scatter plot

Answer 1

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

Question 2

Correlation

Answer 2

A measure of the linear relationship between two random variables.

Question 3

Sample covariance

Answer 3

A measure of how two variables in a sample move together.

Question 4

Sample correlation coefficient

Answer 4

A standardized 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.

Question 5

Spurious correlation

Answer 5

Refers to: 1) correlation between two variables that reflects chance relationships in a particular dataset; 2) correlation induced by a calculation that mixes each of two variables with a third variable; and 3) correlation between two variables arising not from a direct relation between them but from their relation to a third variable.

Question 6

Measure of central tendency

Answer 6

A quantitative measure that specifies where data are centered.

Question 7

Measures of location

Answer 7

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.

Question 8

Median

Answer 8

The value of the middle item of a set of items that has been sorted into ascending or descending order (i.e., the 50th percentile).

Question 9

Mode

Answer 9

The most frequently occurring value in a distribution.

Question 10

Arithmetic mean

Answer 10

The sum of the observations divided by the number of observations.

Question 11

Sample mean

Answer 11

The sum of the sample observations divided by the sample size.

Question 12

Unimodal

Answer 12

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

Question 13

Bimodal

Answer 13

A distribution that has two most frequently occurring values.

Question 14

Trimmed mean

Answer 14

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

Question 15

Quantile

Answer 15

A value at or below which a stated fraction of the data lies. Also referred to as a fractile.

Question 16

Quartiles

Answer 16

Quantiles that divide a distribution into four equal parts.

Question 17

Quintiles

Answer 17

Quantiles that divide a distribution into five equal parts.

Question 18

Deciles

Answer 18

Quantiles that divide a distribution into 10 equal parts.

Question 19

Percentiles

Answer 19

Quantiles that divide a distribution into 100 equal parts that sum to 100.

Question 20

Interquartile range

Answer 20

The difference between the third and first quartiles of a dataset.

Question 21

Box and whisker plot

Answer 21

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

Question 22

Dispersion

Answer 22

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

Question 23

Range

Answer 23

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

Question 24

Mean absolute deviation

Answer 24

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

Question 25

Variance

Answer 25

The expected value (the probability-weighted average) of squared deviations from a random variable’s expected value.

Question 26

Standard deviation

Answer 26

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

Question 27

Downside risk

Answer 27

Risk of incurring returns below a specified value.

Question 28

Target semideviation

Answer 28

A measure of downside risk, calculated as the square root of the average of the squared deviations of observations below the target (also called target downside deviation).

Question 29

Coefficient of variation

Answer 29

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

Question 30

Skewness

Answer 30

A quantitative measure of skew (lack of symmetry); a synonym of skew. It is computed as the average cubed deviation from the mean standardized by dividing by the standard deviation cubed.

Question 31

Kurtosis

Answer 31

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

Question 32

Leptokurtic

Answer 32

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

Question 33

Platykurtic

Answer 33

Describes a distribution that has relatively less weight in the tails than the normal distribution (also called thin-tailed).

Question 34

Mesokurtic

Answer 34

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

Question 35

Excess kurtosis

Answer 35

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