Statistical Measures of Asset Returns Flashcards
What is a measure of central tendency?
A measure that specifies where the data are centered.
What is a drawback of the Arithmetic Mean?
Sensitive to outliers
What are the mean, median and mode?
Mean = average
Median = middle observation
Mode = most occurring value
What is unimodal or bimodal?
Unimodal = when a dataset has a single mode
Bimodal = when a dataset has multiple modes
What are three options to deal with outliers?
1: Use the original data without adjustments
2: Delete all outliers (trimmed mean)
3. Replace outliers (winsorized mean)
What are measures of location?
Measure to describe the location of data that involves identifying values at or below which specified proportions of the data lie.
Name the four quantiles and state what they are.
Quartiles into quarters.
Quintiles into fifths.
Deciles into tenths.
Percentiles into hundredths.
What is a box and whisker plot?
Diagram to visualize the dispersion of data across quartiles
What is the interquartile range (IQR) ?
Difference between the third and first quartile
What is dispersion?
The variability around the central tendency. If central tendency addresses reward, dispersion addresses risk and uncertainty.
What are the most common measures of dispersion?
Range, mean absolute deviation, variance, and standard deviation
What does absolute dispersion mean?
The amount of variability present without comparison to any reference point or benchmark.
What is the range?
The difference between maximum and minimum values in a dataset.
What is the mean absolute deviation?
Sigma (Observed Value - Mean Value) / n
What is the variance and how to calculate it?
The average of the squared deviations around the mean.
Sigma (Observed Value - Mean Value)^2 / (n - 1)
What is an advantage and disadvantage of the variance?
Advantage:
No problem of negative deviations by squaring
Disadvantage:
Difficult to interpret because it is squared.
What is standard deviation?
The square root of the variance. Easily interpretable
What is target downside deviation or target semideviation?
A measure of dispersion of the observations below a certain threshold to picture the downside risk.
What is the relative dispersion?
The amount of dispersion relative to a reference value or benchmark
What is the coefficient of variation (CV)?
The ratio of standard deviation of a set of observations to their mean value. s/X
What are characteristics of a normal distribution?
Symmetrical, bell-shaped graph where mean, median, mode are equal, it is completely described by two parameters (mean and standard deviation)
What is skewness?
A distribution that is not symmetrical but leans to one side. Positively skewed leans left and negatively skewed leans right.
How to calculate the sample skewness?
(1/n) * (Sigma)(Observed Value - Average Value)^3 / Standard Deviation ^ 3
What is kurtosis?
A measure that tells how fat the tails are. Leptokurtic is fat-tailed and platykurtic is thin-tailed. Otherwise, it is mesokurtic.
How to calculate kurtosis and how to interpret kurtosis?
(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.
What is correlation and name its properties?
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.
What is covariance?
Measure of how two variables move together.
Calculated as (X - Average X)(Y - Average Y) / n - 1
How to calculate correlation?
Covariance / Standard Deviation A * B
What is an advantage of correlation?
Expresses strength and direction of relationship
What are limitations of correlation?
Doesn’t measure nonlinear relationships and sensitive to outliers. Also, correlation does not imply causation.
What is spurious correlation?
Chance relationships or wrongfully calculated relationships
