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Book 1: Quantitative Methods > Reading 8: Statistical Concepts and Market Returns > Flashcards

Reading 8: Statistical Concepts and Market Returns Flashcards

1
Q

Descriptive Statistics

A

Are used to summarize important characteristics of a large data set

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2
Q

Inferential Statistics

A

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

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3
Q

Population

A

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

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4
Q

Sample

A

A subset of the population of interest

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5
Q

Types of Measurement Scales

A

Nominal
Ordinal
Interval
Ratio

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6
Q

Nominal Scales

A

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

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7
Q

Ordinal Scales

A

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

Reveals nothing about performance differences

(Higher level of measurement than nominal)

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8
Q

Interval Scale

A

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

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9
Q

Ratio Scale

A

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

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10
Q

Parameter

A

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

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11
Q

Sample Statistic

A

Characteristic of a Sample

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12
Q

Frequency Distribution

A

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

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13
Q

Relative Frequency

A

The percentage of total observations that fall within each interval

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14
Q

Cumulative Relative Frequency

A

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

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15
Q

Histogram

A

Graphical presentation of absolute frequency distribution (Bar Chart)

Benefit: Allows us to see where most observations are concentrated

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16
Q

Frequency Polygon

A

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

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17
Q

Measures of Central Tendency

A

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

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18
Q

Population Mean

A

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

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19
Q

Sample Mean

A

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

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20
Q

Arithmetic Means (Properties)

A
  • 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
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21
Q

Arithmetic Mean (Negative)

A

Outliers can have a disproportionate effect

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22
Q

Arithmetic Mean (Positive)

A

Uses all information available from observations

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23
Q

Weighted Mean

A

Recognizes that outliers have a disproportionate effect

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

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24
Q

Median

A

Middle number

Helps eliminate disproportionate effect of outliers

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

25
Q

Mode

A

Number that occurs most frequently in a dataset.

Unimodal, Bimodal, Trimodal

26
Q

Geometric Mean

A

Used to calculate investment returns over multiple periods

Measures compound growth rates

Always less than or equal to the arithmetic mean

27
Q

Harmonic Mean

A

Average cost of shares purchased over time

28
Q

Dollar Cost Averaging

A

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

29
Q

Modal Interval

A

The interval with the greatest frequency

30
Q

Quantile

A

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

31
Q

Quartiles

A

Distribution of data into quarters

32
Q

Quntile

A

Fifths

33
Q

Decile

A

Tenths

34
Q

Percentile

A

100ths

35
Q

Quartile (Formula)

A

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

36
Q

Measures of Locaiton

A

Quantiles and Measures of central tendency collectively

37
Q

Dispersion

A

Variability around the central tendency (mean etc.)

38
Q

Range

A

Max - Min

39
Q

Mean Absolute Deviation (MAD)

A

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

40
Q

[Population] Variance

A

Average of the squared deviations from the mean

41
Q

[Population] Square Root

A

Positive square root of the population variance

NB: Standard Deviation > MAD (in general)

42
Q

Sample Variance (Difference)

A

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

43
Q

Chebyshev’s Inequality

A

1-1/k2

- the minimum percentage of the population that will lie within k standard deviations from the mean

44
Q

Coefficient Variation

A

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

45
Q

Sharpe Ratio

A

Excess return per unit of risk
(Rp - Rf)/standard deviation

Large positive Sharpe ratios are preferred to smaller ratios (e.g. higher return)

46
Q

Limitations of the Sharpe Ratio

A
  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)
47
Q

Explain skewness

A

Refers to the extent to which a distribution is not symmetrical

48
Q

Positive Skew

A

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

49
Q

Negative Skew

A

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

50
Q

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

A

Mean is greater than median, which is greater than mode

51
Q

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

A

Mean is less than median which is less than mode

52
Q

Kurtosis

A

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

53
Q

Excess Kurtosis

A

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

Sample Kurtosis - 3

54
Q

Leptokurtic

A

More peaked

Greater probability of being close to the mean or far from the mean
(Riskier investment)

Positive Excess Kurtosis

55
Q

Platykurtic

A

Less peaked

Negative Excess Kurtosis Kurtosis

56
Q

Mesokurtic

A

Same as peakedness relative to normal

57
Q

Sample Skewness

A

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

58
Q

Sample Kurtosis

A

Measured relative to the kurtosis of a normal distribution

Excess kurtosis values exceeding 1 in absolute values are considered large

59
Q

Geometric Mean / Arithmetic Mean

A

Arithmetic Mean = Forecasting single period returns in future periods

Geometric Mean = Forecasting future compound returns over multiple periods

Book 1: Quantitative Methods (10 decks)

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