Statistical Sampling and Market Returns

Question 1

2 broad meanings of stats?

Answer 1

Data

Method

Question 2

What is the foundation for statistical inference?

Answer 2

Probability theory

Question 3

Define:

Population

Answer 3

A population is defined as all members of a specified group.

Question 4

Define:

Parameter

Answer 4

Any descriptive measure of a population characteristic

Question 5

Define:

Sample

Answer 5

A subset of a population

Question 6

Define:

Sample statistic

Answer 6

A descriptive measure of a sample characteristic

A sample statistic is a quantity computed from or used to describe a sample.

Question 7

What are the four major measurement scales?

Answer 7

Nominal, ordinal, interval, or ratio.

Question 8

We are examining cross-sectional data when…

Answer 8

We examine the characteristics of some units at a specific point in time.

Question 9

Four types of ‘means’…

Answer 9

Arithmetic
Weighted
Geometric
Harmonic

Question 10

Define:

Dispersion

Answer 10

Dispersion is the variability around the central tendency.

Question 11

What are the 4 most common measures of absolute dispersion?

Answer 11

1. Range
2. Mean absolute deviation
3. Variance
4. Standard deviation

Question 12

Define”

Absolute deviation

Answer 12

Amount of variability present without comparison to any reference point or benchmark.

Question 13

How does one compute the mean absolute deviation?

Answer 13

1. Sum the absolute difference between observations and the mean.
2. Divide by n.

Question 14

What is the main technical drawback of MAD?

Answer 14

It is difficult to manipulate mathematically compared with - variance…

Question 15

What is the population variance?

Answer 15

Variance is defined as the arithmetic average of the squared deviations around the mean.

Question 16

What is the population standard deviation?

Answer 16

Standard deviation is defined as the square root of the variance.

Question 17

Why is the standard deviation easier to interpret than the variance?

Answer 17

Standard deviation is expressed on the same unit of measurement as the observations.

Question 18

4 steps to calculating sample variance?

Answer 18

1. Calculate the sample mean
2. Calculate each observation’s squared deviation from the sample mean
3. Sum the squared deviations from the mean
4. Divide the sum of the squared deviations from the mean by n - 1

Question 19

What is relative dispersion?

Most common way to measure…?

Answer 19

Relative dispersion is the amount of dispersion relative to a reference value or benchmark.

Coefficient of variation

Question 20

Define:

Coefficient of variation

Answer 20

It is the ratio of the standard deviation of a set of observations to their mean value.

Question 21

Why is the coefficient of variation so useful?

Answer 21

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.

Question 22

What does Chebyshev’s inequality state?

Answer 22

The proportion of observations within K standard deviations of the arithmetic mean is atleast

1 - 1/k^2 for all k > 1

Question 23

What are the three general characteristics of normal distributions?

Answer 23

1. Its mean and median are equal.
2. It is completely described by two parameters - its mean and variance.
3. 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.

Question 24

If the distribution is not symmetrical it is called ______________.

Answer 24

Skewed

Question 25

A return distribution with _______ ________ has frequent small gains and a few extreme losses.

Answer 25

Positive skew

Question 26

When a distribution is skewed to the right it is said to be _______ skewed.

Answer 26

Positively

Question 27

When a distribution is skewed to the left it is said to be _______ skewed.

Answer 27

Negatively

Question 28

For the positively skewed unimodal distribution, the _______ is less than the ________, which is less than the ________.

Answer 28

Mode Median Mean

Question 29

How does one calculate skewness?

Answer 29

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)

Question 30

What does kurtosis tell us?

Answer 30

Tell us when a distribution is more or less peaked than a normal distribution.

Question 31

What does it mean for a distribution to be leptokurtic?

Answer 31

The distribution is more peaked than normal.

Question 32

What does it mean for a distribution to be platykurtic?

Answer 32

The distribution is less peaked than normal.

Question 33

For normal distributions, kurtosis is equal to _______

Answer 33

three (3)

Question 34

A leptokurtic distribution has excess kurtosis _______ than 0.

Answer 34

greater

Question 35

A platykurtic distribution has excess kurtosis _______ than 0.

Answer 35

less

Question 36

Leptokurtic distributions have more frequent ________ ___________ deviations from the mean than a normal distribution.

Answer 36

extremely large

Question 37

Normal distribution is a better approximation for U.S. equity returns for _______ holding periods than for ________ holding periods, which tend to be __________.

Answer 37

annual monthly leptokurtic

Question 38

How does one calculate excess kurtosis?

Answer 38

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)]

Question 39

In general, the geometric mean is appropriate for making investment statements _____________.

Answer 39

about past performance

Question 40

In general, the arithmetic mean is appropriate for making investment statements _____________.

Answer 40

in a forward looking context.

Question 41

The arithmetic mean is always ________ or ________ the geometric mean.

Answer 41

Greater than or equal to