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CFA Lvl.1 > Module 3.1 Central Tendency And Dispersion > Flashcards

Module 3.1 Central Tendency And Dispersion Flashcards

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1
Q

What is the main focus when calculating downside risk?

A

Outcomes less than a specific value or mean

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2
Q

What is target downside deviation also known as?

A

Target semideviation

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3
Q

How is target downside deviation calculated?

A

By measuring deviations from a target value only for outcomes below that target

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4
Q

What is the formula for target downside deviation?

A
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5
Q

In the formula for target downside deviation, what does ‘B’ represent?

A

The target value

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6
Q

True or False: Target downside deviation includes all outcomes in its calculation.

A

False

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7
Q

What is the denominator in the target downside deviation formula?

A

n - 1

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8
Q

Fill in the blank: Target downside deviation focuses on deviations from the target value for outcomes _______.

A

below that target

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9
Q

What does variance or standard deviation measure in the context of risk?

A

Risk based on outcomes both above and below the mean

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10
Q

Why is a direct comparison of dispersion not meaningful between retail stocks and real estate portfolios?

A

Due to the relatively large difference in their means.

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11
Q

What must be used to make a meaningful comparison of dispersion?

A

A relative measure of dispersion.

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12
Q

What is relative dispersion?

A

The amount of variability in a distribution around a reference point or benchmark.

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13
Q

How is relative dispersion commonly measured?

A

With the coefficient of variation (CV).

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14
Q

What is the formula for calculating the coefficient of variation (CV)?

A

CV = Sx / average value of x.

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15
Q

What does the coefficient of variation (CV) measure?

A

The amount of dispersion in a distribution relative to the distribution’s mean.

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16
Q

Why is the coefficient of variation (CV) useful?

A

It enables comparison of dispersion across different sets of data.

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17
Q

In an investments setting, what does the CV measure?

A

The risk (variability) per unit of expected return (mean).

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18
Q

Is a lower coefficient of variation (CV) better or worse?

A

Better.

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19
Q

Why is variance difficult to interpret?

A

It is in terms of squared units of measurement

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20
Q

How is the sample standard deviation denoted?

A

s

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21
Q

What is the relationship between sample standard deviation and sample variance?

A

The sample standard deviation is the square root of the sample variance

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22
Q

What is the sample variance, s²?

A

The measure of dispersion that applies when evaluating a sample of n observations from a population.

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23
Q

What is the formula for calculating sample variance?

Study These Flashcards
A

s² = Σ(Xᵢ - X̄)² / (n - 1)

24
Q

Why is the denominator for sample variance n - 1 instead of n?

Study These Flashcards
A

Using n - 1 prevents systematic underestimation of the population variance, especially for small sample sizes.

25
How does using n - 1 in the denominator affect the sample variance?
It improves the statistical properties of s² as an estimator of the population variance.
26
Fill in the blank: The sample variance is calculated using the formula s² = Σ(Xᵢ - X̄)² / _______.
n - 1
27
True or False: Using the entire number of sample observations, n, is preferred for calculating sample variance.
False
28
What does MAD stand for?
Mean Absolute Deviation
29
How is the Mean Absolute Deviation (MAD) calculated?
Average of the absolute values of the deviations of individual observations from the arithmetic mean
30
Why are absolute values used in the computation of MAD?
The sum of the actual deviations from the arithmetic mean is zero
31
What is dispersion?
Dispersion is defined as the variability around the central tendency. ## Footnote Dispersion measures how spread out the values are in a dataset.
32
What does the central tendency measure in finance and investments?
The central tendency measures the reward. ## Footnote Common measures of central tendency include mean, median, and mode.
33
In finance, what is the relationship between reward and variability?
The common theme is the tradeoff between reward and variability. ## Footnote Higher potential rewards often come with higher variability (risk).
34
What does dispersion measure in the context of investments?
Dispersion is a measure of risk. ## Footnote It indicates how much the returns on an investment can vary.
35
What is the general term for a value at or below which a stated proportion of the data in a distribution lies?
Quantile ## Footnote Quantiles are used to understand the distribution of data points within a dataset.
36
What is a quartile?
A quantile that divides the distribution into quarters ## Footnote Quartiles are specific types of quantiles.
37
What is a quintile?
A quantile that divides the distribution into fifths ## Footnote Quintiles help in analyzing data by segmenting it into five equal parts.
38
What is a decile?
A quantile that divides the distribution into tenths ## Footnote Deciles are useful for understanding the distribution of data in smaller segments.
39
How can any quantile be expressed?
As a percentile ## Footnote This allows for a standard way to compare different quantiles.
40
What does the third quartile represent in terms of percentile?
The 75th percentile ## Footnote The third quartile indicates that three-fourths of the observations fall below this value.
41
What is the interquartile range?
The difference between the third quartile and the first quartile (25th percentile) ## Footnote The interquartile range measures the spread of the middle 50% of the data.
42
What is the mode in a dataset?
The value that occurs most frequently in a dataset ## Footnote A dataset may have more than one mode or even no mode.
43
What is a unimodal distribution?
A distribution with one value that appears most frequently ## Footnote In a unimodal distribution, there is only one mode.
44
What is a bimodal distribution?
A dataset with two values that occur most frequently ## Footnote Bimodal distributions have two modes.
45
True or False: A dataset can have no mode.
True ## Footnote This occurs when no value repeats in the dataset.
46
What is a trimmed mean?
A trimmed mean excludes a stated percentage of the most extreme observations ## Footnote For example, a 1% trimmed mean discards the lowest 0.5% and the highest 0.5% of observations.
47
How is a 1% trimmed mean calculated?
By discarding the lowest 0.5% and the highest 0.5% of observations
48
What is a winsorized mean?
A winsorized mean substitutes a value for the highest and lowest observations instead of discarding them ## Footnote This technique allows the dataset to retain its size while reducing the influence of extreme values.
49
How is a 90% winsorized mean calculated?
Determine the 5th and 95th percentile, substitute the 5th percentile for values lower than it, substitute the 95th percentile for values higher than it, and then calculate the mean of the revised dataset
50
What are percentiles?
Measures of location
51
Fill in the blank: A trimmed mean excludes a stated percentage of the most ________ observations.
extreme
52
True or False: A winsorized mean involves discarding the highest and lowest observations.
False
53
What is the purpose of using a trimmed mean?
To exclude outliers from a measure of central tendency
54
What happens to extreme values in a winsorized mean?
They are substituted with values from the percentiles
55
What type of plot is used to visualize a dataset based on quantiles?
Box and whisker plot ## Footnote A box and whisker plot is useful for displaying the distribution and identifying outliers in the data.
56
In a box and whisker plot, what does the box represent?
The central portion of the data, such as the interquartile range ## Footnote The interquartile range is the range between the first quartile (Q1) and the third quartile (Q3).
57
What does the vertical line in a box and whisker plot represent?
The entire range of the data ## Footnote This includes the smallest and largest observations in the dataset.

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