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Quantitative Methods > Statistical Measures of Asset Returns > Flashcards

Statistical Measures of Asset Returns Flashcards

1
Q

What is a measure of central tendency?

A

A measure that specifies where the data are centered.

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2
Q

What is a drawback of the Arithmetic Mean?

A

Sensitive to outliers

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3
Q

What are the mean, median and mode?

A

Mean = average
Median = middle observation
Mode = most occurring value

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4
Q

What is unimodal or bimodal?

A

Unimodal = when a dataset has a single mode
Bimodal = when a dataset has multiple modes

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5
Q

What are three options to deal with outliers?

A

1: Use the original data without adjustments
2: Delete all outliers (trimmed mean)
3. Replace outliers (winsorized mean)

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6
Q

What are measures of location?

A

Measure to describe the location of data that involves identifying values at or below which specified proportions of the data lie.

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7
Q

Name the four quantiles and state what they are.

A

Quartiles into quarters.
Quintiles into fifths.
Deciles into tenths.
Percentiles into hundredths.

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8
Q

What is a box and whisker plot?

A

Diagram to visualize the dispersion of data across quartiles

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8
Q

What is the interquartile range (IQR) ?

A

Difference between the third and first quartile

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8
Q

What is dispersion?

A

The variability around the central tendency. If central tendency addresses reward, dispersion addresses risk and uncertainty.

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9
Q

What are the most common measures of dispersion?

A

Range, mean absolute deviation, variance, and standard deviation

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10
Q

What does absolute dispersion mean?

A

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

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11
Q

What is the range?

A

The difference between maximum and minimum values in a dataset.

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12
Q

What is the mean absolute deviation?

A

Sigma (Observed Value - Mean Value) / n

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13
Q

What is the variance and how to calculate it?

A

The average of the squared deviations around the mean.
Sigma (Observed Value - Mean Value)^2 / (n - 1)

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14
Q

What is an advantage and disadvantage of the variance?

A

Advantage:
No problem of negative deviations by squaring
Disadvantage:
Difficult to interpret because it is squared.

15
Q

What is standard deviation?

A

The square root of the variance. Easily interpretable

16
Q

What is target downside deviation or target semideviation?

A

A measure of dispersion of the observations below a certain threshold to picture the downside risk.

17
Q

What is the relative dispersion?

A

The amount of dispersion relative to a reference value or benchmark

18
Q

What is the coefficient of variation (CV)?

A

The ratio of standard deviation of a set of observations to their mean value. s/X

19
Q

What are characteristics of a normal distribution?

A

Symmetrical, bell-shaped graph where mean, median, mode are equal, it is completely described by two parameters (mean and standard deviation)

20
Q

What is skewness?

A

A distribution that is not symmetrical but leans to one side. Positively skewed leans left and negatively skewed leans right.

21
Q

How to calculate the sample skewness?

A

(1/n) * (Sigma)(Observed Value - Average Value)^3 / Standard Deviation ^ 3

22
Q

What is kurtosis?

A

A measure that tells how fat the tails are. Leptokurtic is fat-tailed and platykurtic is thin-tailed. Otherwise, it is mesokurtic.

23
Q

How to calculate kurtosis and how to interpret kurtosis?

A

(1/n) * (Sigma)(Observed Value - Mean Value)^4 / Standard Deviation^4 ) -3

Normal distribution has a kurtosis of 3 and everything above this is fat-tailed and below is thin-tailed.

24
Q

What is correlation and name its properties?

A

A measure of the linear relationship between two random variables.
Between -1 and 1. Correlation of 0 means uncorrelated. Correlation close to 1 is strong positive relationship. Correlation close to -1 is strong negative relationship.

25
Q

What is covariance?

A

Measure of how two variables move together.

Calculated as (X - Average X)(Y - Average Y) / n - 1

26
Q

How to calculate correlation?

A

Covariance / Standard Deviation A * B

27
Q

What is an advantage of correlation?

A

Expresses strength and direction of relationship

28
Q

What are limitations of correlation?

A

Doesn’t measure nonlinear relationships and sensitive to outliers. Also, correlation does not imply causation.

29
Q

What is spurious correlation?

A

Chance relationships or wrongfully calculated relationships

Quantitative Methods (9 decks)

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