Reading 8: Statistical Concepts and Market Returns

Question 1

Descriptive Statistics

Answer 1

Are used to summarize important characteristics of a large data set

Question 2

Inferential Statistics

Answer 2

Procedures used to make judgments about a larger data set based on the statistical characteristics of a smaller set (a sample)

Question 3

Population

Answer 3

A set of all possible members of a stated group e.g. all stocks on NYSE

Question 4

Sample

Answer 4

A subset of the population of interest

Question 5

Types of Measurement Scales

Answer 5

Nominal
Ordinal
Interval
Ratio

Question 6

Nominal Scales

Answer 6

Data put into categories that have no particular order (range with the least amount of information)

Question 7

Ordinal Scales

Answer 7

Data is put into categories that can be ordered according to some characteristics

Reveals nothing about performance differences

(Higher level of measurement than nominal)

Question 8

Interval Scale

Answer 8

Temperature

Relative ranking like ordinal with differences in data values being meaningful, however ratios, such as twice as much/large are not meaningful

Measurement of zero does not mean the absence of what we are measuring

Question 9

Ratio Scale

Answer 9

Most refined level of measurement (Money)

Ratios of values (twice as much etc.) are meaningful, and zero measures the complete absence of the characteristics being measured

Question 10

Parameter

Answer 10

Numerical measure used to describe a characteristic of a population
E.g. mean or standard deviation of returns

Question 11

Sample Statistic

Answer 11

Characteristic of a Sample

Question 12

Frequency Distribution

Answer 12

Groups observations into a classes or intervals. An interval is a range of values

Question 13

Relative Frequency

Answer 13

The percentage of total observations that fall within each interval

Question 14

Cumulative Relative Frequency

Answer 14

The sum of all relative frequencies up to and including the given interval

Question 15

Histogram

Answer 15

Graphical presentation of absolute frequency distribution (Bar Chart)

Benefit: Allows us to see where most observations are concentrated

Question 16

Frequency Polygon

Answer 16

Midpoint of each interval is plotted on the horizontal axis and the absolute frequency is plotted on the vertical axis (Line Chart)

Question 17

Measures of Central Tendency

Answer 17

Used to identify the center or average of a data set. Can be used to represent the expected value of a dataset

Question 18

Population Mean

Answer 18

Sum of all values in a population divided by the total number of observations in the population (only one possible mean)

Question 19

Sample Mean

Answer 19

Sum of all values in a sample divided by the total number of observations in the sample (used to make inferences about the population)

Question 20

Arithmetic Means (Properties)

Answer 20

• All interval and ratio data sets have an arithmetic mean
• All data values are considered and included
• Only one mean
• Sum of all deviations of each observation always equals zero

Question 21

Arithmetic Mean (Negative)

Answer 21

Outliers can have a disproportionate effect

Question 22

Arithmetic Mean (Positive)

Answer 22

Uses all information available from observations

Question 23

Weighted Mean

Answer 23

Recognizes that outliers have a disproportionate effect

Used to calculate portfolio returns (weighted average return of the individual assets in the portfolio)

Question 24

Median

Answer 24

Middle number

Helps eliminate disproportionate effect of outliers

Calculate the arithmetic mean if there is an even number of observations

Question 25

Mode

Answer 25

Number that occurs most frequently in a dataset. Unimodal, Bimodal, Trimodal

Question 26

Geometric Mean

Answer 26

Used to calculate investment returns over multiple periods Measures compound growth rates Always less than or equal to the arithmetic mean

Question 27

Harmonic Mean

Answer 27

Average cost of shares purchased over time

Question 28

Dollar Cost Averaging

Answer 28

Purchasing the same dollar amount of mutual fund shares each month or each week

Question 29

Modal Interval

Answer 29

The interval with the greatest frequency

Question 30

Quantile

Answer 30

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

Question 31

Quartiles

Answer 31

Distribution of data into quarters

Question 32

Quntile

Answer 32

Fifths

Question 33

Decile

Answer 33

Tenths

Question 34

Percentile

Answer 34

100ths

Question 35

Quartile (Formula)

Answer 35

Ly = (n+1) * y/100 Where: n = # of data points y = given percentile

Question 36

Measures of Locaiton

Answer 36

Quantiles and Measures of central tendency collectively

Question 37

Dispersion

Answer 37

Variability around the central tendency (mean etc.)

Question 38

Range

Answer 38

Max - Min

Question 39

Mean Absolute Deviation (MAD)

Answer 39

Average distance between each data value and the mean. (Use absolute values e.g. ignore the mean)

Question 40

[Population] Variance

Answer 40

Average of the squared deviations from the mean

Question 41

[Population] Square Root

Answer 41

Positive square root of the population variance | NB: Standard Deviation > MAD (in general)

Question 42

Sample Variance (Difference)

Answer 42

N-1 as a denominator to ensure there is not an unbiased overestimation

Question 43

Chebyshev's Inequality

Answer 43

1-1/k2 | - the minimum percentage of the population that will lie within k standard deviations from the mean

Question 44

Coefficient Variation

Answer 44

The ratio of the standard deviation of the sample to its mean e.g. risk per unit of return

Question 45

Sharpe Ratio

Answer 45

Excess return per unit of risk (Rp - Rf)/standard deviation Large positive Sharpe ratios are preferred to smaller ratios (e.g. higher return)

Question 46

Limitations of the Sharpe Ratio

Answer 46

1. Two negative ratios. Higher one doesn't necessarily imply better returns (e.g. more risk moves it closer to zero) 2. Asymmetric Returns e.g. investment strategies with option characteristics (standard deviation not a good measure of risk)

Question 47

Explain skewness

Answer 47

Refers to the extent to which a distribution is not symmetrical

Question 48

Positive Skew

Answer 48

Many outliers in the upper region (or right tail) so skewed right and has a longer upper right tail

Question 49

Negative Skew

Answer 49

Outliers in the lower region (left tail) so skewed left

Question 50

Where is the mean/median/mode for a positively skewed unimodal distribution?

Answer 50

Mean is greater than median, which is greater than mode

Question 51

Where is the mean/median/mode for a negatively skewed unimodal distribution?

Answer 51

Mean is less than median which is less than mode

Question 52

Kurtosis

Answer 52

Measure of peakedness relative to a normal distribution and the probability of extreme outcomes e.g. thickness of tails

Question 53

Excess Kurtosis

Answer 53

Excess Kurtosis with an absolute value greater than 1 is considered significant Sample Kurtosis - 3

Question 54

Leptokurtic

Answer 54

More peaked Greater probability of being close to the mean or far from the mean (Riskier investment) Positive Excess Kurtosis

Question 55

Platykurtic

Answer 55

Less peaked Negative Excess Kurtosis Kurtosis

Question 56

Mesokurtic

Answer 56

Same as peakedness relative to normal

Question 57

Sample Skewness

Answer 57

Cubed (3) deviations from the mean divided by the cubed (3) standard deviation and by the number of observations

Question 58

Sample Kurtosis

Answer 58

Measured relative to the kurtosis of a normal distribution Excess kurtosis values exceeding 1 in absolute values are considered large

Question 59

Geometric Mean / Arithmetic Mean

Answer 59

Arithmetic Mean = Forecasting single period returns in future periods Geometric Mean = Forecasting future compound returns over multiple periods