Statistical Sampling and Market Returns Flashcards
2 broad meanings of stats?
Data
Method
What is the foundation for statistical inference?
Probability theory
Define:
Population
A population is defined as all members of a specified group.
Define:
Parameter
Any descriptive measure of a population characteristic
Define:
Sample
A subset of a population
Define:
Sample statistic
A descriptive measure of a sample characteristic
A sample statistic is a quantity computed from or used to describe a sample.
What are the four major measurement scales?
Nominal, ordinal, interval, or ratio.
We are examining cross-sectional data when…
We examine the characteristics of some units at a specific point in time.
Four types of ‘means’…
Arithmetic
Weighted
Geometric
Harmonic
Define:
Dispersion
Dispersion is the variability around the central tendency.
What are the 4 most common measures of absolute dispersion?
- Range
- Mean absolute deviation
- Variance
- Standard deviation
Define”
Absolute deviation
Amount of variability present without comparison to any reference point or benchmark.
How does one compute the mean absolute deviation?
- Sum the absolute difference between observations and the mean.
- Divide by n.
What is the main technical drawback of MAD?
It is difficult to manipulate mathematically compared with - variance…
What is the population variance?
Variance is defined as the arithmetic average of the squared deviations around the mean.
What is the population standard deviation?
Standard deviation is defined as the square root of the variance.
Why is the standard deviation easier to interpret than the variance?
Standard deviation is expressed on the same unit of measurement as the observations.
4 steps to calculating sample variance?
- Calculate the sample mean
- Calculate each observation’s squared deviation from the sample mean
- Sum the squared deviations from the mean
- Divide the sum of the squared deviations from the mean by n - 1
What is relative dispersion?
Most common way to measure…?
Relative dispersion is the amount of dispersion relative to a reference value or benchmark.
Coefficient of variation
Define:
Coefficient of variation
It is the ratio of the standard deviation of a set of observations to their mean value.
Why is the coefficient of variation so useful?
By expressing the magnitude of variation among observations relative to their average size, it allows direct comparison of dispersion across different datasets.
It is a scale-free measure.
What does Chebyshev’s inequality state?
The proportion of observations within K standard deviations of the arithmetic mean is atleast
1 - 1/k^2 for all k > 1
What are the three general characteristics of normal distributions?
- Its mean and median are equal.
- It is completely described by two parameters - its mean and variance.
- Roughly 68% of its observations lie between plus and minus one standard deviation from the mean; 95 percent lie between plus and minus 2 standard deviations and 99 percent lie between plus and minus 3 standard deviations.
If the distribution is not symmetrical it is called ______________.
Skewed
A return distribution with _______ ________ has frequent small gains and a few extreme losses.
Positive skew
When a distribution is skewed to the right it is said to be _______ skewed.
Positively
When a distribution is skewed to the left it is said to be _______ skewed.
Negatively
For the positively skewed unimodal distribution, the _______ is less than the ________, which is less than the ________.
Mode
Median
Mean
How does one calculate skewness?
Find the sum of the cubed deviations from the mean, divide by the standard deviation cubed, and then multiply that result by n/(n-1)(n-2)
What does kurtosis tell us?
Tell us when a distribution is more or less peaked than a normal distribution.
What does it mean for a distribution to be leptokurtic?
The distribution is more peaked than normal.
What does it mean for a distribution to be platykurtic?
The distribution is less peaked than normal.
For normal distributions, kurtosis is equal to _______
three (3)
A leptokurtic distribution has excess kurtosis _______ than 0.
greater
A platykurtic distribution has excess kurtosis _______ than 0.
less
Leptokurtic distributions have more frequent ________ ___________ deviations from the mean than a normal distribution.
extremely large
Normal distribution is a better approximation for U.S. equity returns for _______ holding periods than for ________ holding periods, which tend to be __________.
annual
monthly
leptokurtic
How does one calculate excess kurtosis?
Find the sum of the deviations from the mean raised to the fourth power, divide that by the standard deviation raised to the fourth power, and multiply that result by n(n+1)/[(n-1)(n-2)(n-3)]. This calculation determines kurtosis.
Excess kurtosis is kurtosis minus 3(n-1)^2/[(n-2)(n-3)]
In general, the geometric mean is appropriate for making investment statements _____________.
about past performance
In general, the arithmetic mean is appropriate for making investment statements _____________.
in a forward looking context.
The arithmetic mean is always ________ or ________ the geometric mean.
Greater than or equal to
