Book 1_Quan_Statistical measures of asset returns

Question 1

• Measures of Central Tendency

Answer 1

o arithmetic mean
o median

Question 2

• Methods for Dealing With Outliers

Answer 2

o 1% trimmed mean: remove 0.5% highest and 0.5% lowest
o 10% winsorized mean: Replace 5% highest and 5% lowest

Question 3

Measures of Location (Quantile)

Answer 3

is the general term for a value at or below which a stated proportion of the
data in a distribution lies
- Quartile. The distribution is divided into quarters.
- Quintile. The distribution is divided into fifths.
- Decile. The distribution is divided into tenths
- Percentile. The distribution is divided into hundredths (percentages).

Question 4

• Dispersion

Answer 4

o the variability around the central tendency

Question 5

coefficient of variation

Answer 5

• Compare dispersion across different sets
  of data
  = Sx/ mean = std deviation of x/average value of x

Question 6

• The range

Answer 6

o range = maximum value − minimum value

Question 7

• mean absolute deviation (MAD)

Answer 7

o the average of the absolute values of the deviations of individual observations from the arithmetic mean

Question 8

• sample variance, s^2:

Answer 8

s2 = Sum (Xi-X!)^2/(n-1)

Question 9

• standard deviation

Answer 9

S = Căn Simple variance

Question 10

• Covariance

Answer 10

+ is a measure of how two variables move together
Sxy = Sum (Xi - X!)(Yi - Y!)/ (n-1)

Question 11

target downside deviation

Answer 11

• Only include deviations from the target value in
  our calculation if the outcomes are below that target
  S (target) = Can [sum(xi - B)^2]/(n-1)

B: the target

Question 12

• Correlation

Answer 12

+ measures the strength of the linear relationship between two random variables.
+ does not imply that changes in one variable cause changes in the other.
+ The correlation ranges from −1 to +1
+ Pxy = Sxy/ (SxSy)

Question 13

• Spurious correlation

Answer 13

refers to correlation that is either the result of chance or present due to changes in both variables over time that is caused by their
association with a third variable

Question 14

Skewness

Answer 14

+ describes the degree to which a distribution is not symmetric about its
mean
+ A right-skewed distribution: the mean is greater than the median,
which is greater than the mode
+ A left-skewed distribution : the mean is less than the median, which is less than the mode.

Question 15

Kurtosis

Answer 15

measures the peakedness of a distribution and the probability of extreme
outcomes (thickness of tails):
- Excess kurtosis is measured relative to a normal distribution, which has a kurtosis of 3.
- Positive values of excess kurtosis indicate a distribution that is leptokurtic (fat tails, more peaked), so the probability of extreme outcomes is greater than for a
normal distribution.
+ Negative values of excess kurtosis indicate a platykurtic distribution (thin tails, less peaked).