I. FUNDAMENTALS -- A. Statistics and Methods

Question 1

Mean

Answer 1

A measure of central tendency. The arithmetic average of a sample or population, or the expected value of set of probabilities.

Question 2

Formula of Sample Mean

Answer 2

Question 3

Formula of Population Mean

Answer 3

Question 4

Formula of Expected Value of a Set of Probabilities

Answer 4

Question 5

Median

Answer 5

A measure of central tendency. The value at the 50th percentile (midpoint) of a sample or population.

Question 6

Mode

Answer 6

A measure of central tendency. The value that occurs most frequently in a sample or population.

Question 7

Standard deviation

Answer 7

A measure of spread of a sample, population, or set of probabilities. The square root of variance. Empirical rule says that, for a normal distribution, approximately 68% of observations are within +/- 1 standard deviation of the mean, and approximately 95% of observations are within +/- 2 standard deviations of the mean.

Question 8

Formula of Sample Standard Deviation

Answer 8

Question 9

Formula of Population Standard Deviation

Answer 9

Question 10

Formula of Standard Deviation of a Set of Probabilities

Answer 10

Question 11

Variance

Answer 11

A measure of spread of a sample, population, or set of probabilities. Standard deviation squared. Cannot be negative.

Question 12

Formula of Sample Variance

Answer 12

Question 13

Formula of Population Variance

Answer 13

Question 14

Formula of Variance of a Set of Probabilities

Answer 14

Question 15

Covariance

Answer 15

A measure of how things move together. Just a directional measure (positive value means that things move in the same direction and negative value means that things move in opposite directions).

Question 16

Correlation

Answer 16

A measure of how things move together. Between -1 and +1. Indicates the strength of the relationship.

Question 17

Skewness

Answer 17

A departure from the normal distribution.

Left or negatively skewed is where mean < median < mode.

Right or positively skewed is where mean > median > mode.

Stock returns are positively skewed due to survivorship bias.

Standard deviation overestimates risk for negatively skewed distributions and underestimates risk for positively skewed distributions.

Question 18

Range

Answer 18

The difference between the largest and smallest value in a sample or population.

Question 19

Absolute Deviation

Answer 19

Mean absolute deviation is the average of the absolute values of differences between each value and a measure of central tendency. The measure of central tendency used can be the mean, median, or mode.

Question 20

Semi-variance

Answer 20

Variance formula but only including observations below the mean or other target value (such as MAR or minimum acceptable return).

Question 21

Normal distribution

Answer 21

Symmetric: the probability of any positive devation above the mean is equal to that of a negative deviation of the same magnitude.

Stable: when assets with normally distributed returns are mixed to construct a portfolio, the portfolio return is also normally distributed.

Only two parameters – mean and standard deviation – need to be estimated to obtain the probabilities of future scenarios.

When securities are normally distributed, the statistical relation between returns can be summarized with a single correlation coefficient.