Statistical Concepts and Market Returns Flashcards
We explore four properties of return distributions:
- where the returns are centered (______);
- how far returns are dispersed from their center (______);
- whether the distribution of returns is symmetrically shaped or lopsided (______); and
- whether extreme outcomes are likely (______).
central tendency
dispersion
skewness
kurtosis
The study of how data can be summarized
effectively to describe the important aspects of large data sets.
Descriptive statistics
Making forecasts, estimates, or judgments about a larger group from the smaller group actually observed
Statistical inference
Any descriptive measure of a population characteristic is called a _________
parameter
A quantity computed from or used to describe a sample
sample statistic (or statistic)
All data measurements are taken on one of four major measurement scales: (4)
nominal, ordinal,
interval, or ratio
The strongest level of measurement.
They have all the characteristics of interval measurement scales as well as a true zero point as the origin.
Ratio scales
tabular display of data summarized into a relatively small number of intervals.
frequency distribution
The actual number of observations in a given interval is called the
The absolute frequency,
The absolute frequency of each interval divided by the total number of observations
Relative frequency
The ________ cumulates (adds up) the relative frequencies as we move from the first to the last interval.
cumulative relative frequency
bar chart of data that have been grouped into a frequency distribution.
A histogram
Two other graphical tools for displaying data (besides the histogram) are the _____ and the _______.
frequency polygon
cumulative frequency distribution
the sum of the observations divided by the number of observations.
The arithmetic mean
Most frequently used to average rates of change over time or to compute the growth rate of a variable
Geometric mean
How to calculate geometric mean?
Convert to decimal form and add 1. Take the root and substract the result by 1.
How to calculate the harmonic mean?
The value obtained by summing the reciprocals of the observations—terms of the form 1/Xi
—then averaging that sum by dividing it by the number
of observations n, and, finally, taking the reciprocal of the average
When is the harmonic used in investing?
appropriate when averaging ratios
(“amount per unit”) when the ratios are repeatedly applied to a fixed quantity to yield
a variable number of units. The concept is best explained through an illustration.
What is MAD?
mean absolute deviation
How do you take the variance?
You compute the average of the squared deviation around the mean
What is special with the sample variance and the sample standard deviation?
Soustraite 1 au dénominateur
What is the average squared deviation below the mean?
The semivariance. The semideviation is the square root of this number.
The average squared deviation below a stated target.
A target semivariance.
What does the Chebyshev’s Inequality give?
The inequality gives the proportion of values
within k standard deviations of the mean
What is the coefficient of variation?
The ratio of the standard deviation of a set of observations to their mean value
How is skewness computed?
The average cubed deviation from the mean standardized by dividing by the standard deviation cubed to make the measure free of
scale.
a measure of the combined weight of the tails of a distribution relative
to the rest of the distribution
Kurtosis
A distribution that has fatter tails than the normal distribution is called
leptokurtic
Distribution that has thinner tails than the normal distribution is called
platykurtic
a distribution identical to the normal distribution as concerns relative
weight in the tails is called
mesokurtic
For all normal distributions, kurtosis is equal to
3
the use of _______ rather than arithmetic scales is more appropriate when graphing past performance
semilogarithmic
The more uncertain the returns, the more _____
exists between
the arithmetic and geometric means
divergence
Chebyshev’s inequality
1 - 1/(k^2) -> % contained in k standard deviations from the mean
Formula for location
Ly = (n+1) X (y/100)
Coefficient of variation formula
Standard deviation/mean
