1.2 Measures of Dispersion, Downside Deviation, and Coefficient of Variation Flashcards
dispersion (or variability) around the mean
addressing risk
the most common measures of absolute dispersion
range
mean absolute deviation (MAD)
variance
standard deviation
The range
the difference between the maximum and minimum values
Mean Absolute Deviation (MAD)
It uses all the observations in the sample, which makes it better than the range
Variance
the average of the squared deviations around the mean
standard deviation
the positive square root of the variance
sample variance
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
sample variance formula
s^2 = (sum of all ((Xi - MeanX)^2))/(n-1)
the degrees of freedom
n - 1 in a sample
The sample standard deviation formula
s = square root of s^2
The sample standard deviation has a special relationship with the arithmetic mean and the geometric mean
explain
Geometric mean is almost equal to (the arithmetic mean - (s^2)/2)
do investors care about symmetric risk measures or downside risk?
downside risk
Target semideviation, or target downside deviation
captures dispersion of observations below a specified target value (e.g., 10%)
Target semideviation formula
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
The coefficient of variation (CV)
a relative dispersion measure
allows comparisons between data sets with very different means
has no units of measurement
