1.2 Measures of Dispersion, Downside Deviation, and Coefficient of Variation Flashcards

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1
Q

dispersion (or variability) around the mean

A

addressing risk

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2
Q

the most common measures of absolute dispersion

A

range

mean absolute deviation (MAD)

variance

standard deviation

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3
Q

The range

A

the difference between the maximum and minimum values

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4
Q

Mean Absolute Deviation (MAD)

A

It uses all the observations in the sample, which makes it better than the range

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5
Q

Variance

A

the average of the squared deviations around the mean

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6
Q

standard deviation

A

the positive square root of the variance

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7
Q

sample variance

A

it is often very challenging to collect data on an entire population

It is more common to calculate the sample statistic and use it to draw inferences about the population statistic

In other words, to estimate the variance of a population, we first need to calculate the variance of a sample

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8
Q

sample variance formula

A

s^2 = (sum of all ((Xi - MeanX)^2))/(n-1)

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9
Q

the degrees of freedom

A

n - 1 in a sample

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10
Q

The sample standard deviation formula

A

s = square root of s^2

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11
Q

The sample standard deviation has a special relationship with the arithmetic mean and the geometric mean

explain

A

Geometric mean is almost equal to (the arithmetic mean - (s^2)/2)

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12
Q

do investors care about symmetric risk measures or downside risk?

A

downside risk

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13
Q

Target semideviation, or target downside deviation

A

captures dispersion of observations below a specified target value (e.g., 10%)

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14
Q

Target semideviation formula

A

Starget = square root of ((sum of all Xi <= B * (Xi - B)^2)/(n-1))

where B
is the target and n
is the total number of sample observations

sum of all Xi <= B indicates that only the observations no greater than B are included in the summation

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15
Q

The coefficient of variation (CV)

A

a relative dispersion measure

allows comparisons between data sets with very different means

has no units of measurement

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16
Q

The coefficient of variation (CV) formula

A

CV = s / MeanX

17
Q

what does it mean if the coefficient of variation is negative?

A

it is useless