(R7) Quantitative Methods: Statistical Concepts and Market Returns

Question 1

Population definition

Answer 1

All members of a specified group; all descriptive measures are called parameters

Question 2

Sample definition

Answer 2

Subset of a population; all descriptive measures are called sample statistics

Question 3

Definition of Parameter

Answer 3

Any descriptive measure of a population

Question 4

Definition of Sample statistic

Answer 4

Any descriptive measure of a sample

Question 5

Inferential statistics

Answer 5

involves making forecasts, estimates, or judgements about a larger group (population) from the smaller group (sample) actually observed

Question 6

4 Types of measurement scales

Answer 6

1. Nominal
2. Ordinal
3. Interval
4. Ratio

These are ordered from weakest to strongest level of measurement

Question 7

Nominal Measurement Scale

Answer 7

Categorical data that is not ranked; weakest level of measurement

Question 8

Ordinal Measurement Scale

Answer 8

Ranking system due to some characteristic; but this tells us nothing about the difference between the rankings

Question 9

Interval Measurement Scale

Answer 9

Provides ranking but also assurance that the difference between scale values are equal; I.e. temperature

Question 10

Ratio Measurement scale

Answer 10

They have all the characteristics of interval measurement scales as well as a true zero point as the origin; strongest level of measurement

Question 11

Frequency Distribution

Answer 11

a tabular display of data grouped into intervals; works with all measurement scales

Question 12

Absolute frequency

Answer 12

Number of observations in each interval

Question 13

How to construct a frequency distribution

Answer 13

1. Sort the data in ascending order
2. Calculate the range of the data, defined as range = maximum value - minimum value
3. Choose the number of intervals (k)
4. Determine the interval width (max - min)/k

Question 14

Relative frequency

Answer 14

Absolute frequency of each interval divided by the total number of observations

Question 15

Cumulative relative frequency

Answer 15

Adds up the relative frequencies as we move from the first to the last interval

Question 16

Histogram definition

Answer 16

Bar chart of data that have been grouped into a frequency distribution

Question 17

Frequency Polygon

Answer 17

Plot the midpoint of each interval on the x-axis and the absolute frequency on the y-axis; then connect the points with a straight line

Question 18

Three methods to display data graphically

Answer 18

1. Histogram
2. Frequency polygon
3. Cumulative frequency distribution

Question 19

Measures of central tendency (Definition and types)

Answer 19

Specifies where the data is centered; Ex: arithmetic mean, median, mode, weighted mean, geometric mean

Question 20

Arithmetic mean definition

Answer 20

Is the sum of all observations divided by the number of observations (the scribble m notation represents the population mean; the x with the bar on top is the notation for a sample mean); the best estimate of a single period return

Question 21

Cross-sectional data

Answer 21

Examining the characteristics of some units at a specific point in time (Ex: comparing the 2020 class averages in the morning or afternoon times for the year)

Question 22

Time-series data

Answer 22

Comparing data over multiple years (Ex: comparing the class averages from 2015 to 2020)

Question 23

Median

Answer 23

Number in the middle; (n+1)/2

Question 24

Only measure of central tendency that can be used with nominal data is

Answer 24

Mode

Question 25

Weighed mean

Answer 25

different weights for different observations; Ex: You have 70% in equities and 30% in bonds. Equities has a 10% ROI and bonds has 8% ROI. What is the average ROI? average = .7(.1) + .3(.08)

Question 26

Geometric mean

Answer 26

most used measure to average rates of change (i.e. growth rate of a variable); excellent measure of past performance and multi period returns; aka average annual compound return

Question 27

Which mean will always be lower than the other? Geometric or arithmetic

Answer 27

Geometric Mean

Question 28

Quartiles, quintiles, deciles, and percentiles

Answer 28

Quartiles - divide data into quarters Quintiles - divide data into fifths Deciles - divide into tenths Percentiles - divide into hundredths

Question 29

Formula for locating a percentile is

Answer 29

(n+1)(y/100) n equals the number of observations y is the percentage point at which we are dividing the distribution

Question 30

Measures of dispersion

Answer 30

Range, mean absolute deviation, variance, and standard deviation

Question 31

Mean absolute deviation =

Answer 31

Take absolute value of the following: (Each data point - arithmetic mean); then divide by the total number of observations

Question 32

Population variance =

Answer 32

(each data point - arithmetic mean) ^2 / number of observations

Question 33

Population standard deviation =

Answer 33

The square root of [(each data point - mean) ^2 / number of observations]

Question 34

Sample variance =

Answer 34

(each data point - arithmetic mean) ^2 / (number of observations - 1)

Question 35

Sample standard deviation =

Answer 35

The square root of [(each data point - mean) ^2 / (number of observations - 1)]

Question 36

Standard deviation definition

Answer 36

measures dispersion around the arithmetic mean

Question 37

Chebyshev's inequality definition and equation

Answer 37

Definition - minimum proportion of observations within a certain amount of standard deviations of the arithmetic mean Formula = 1 - (1/(k^2))

Question 38

Relative dispersion

Answer 38

Is the amount of dispersion relative to a reference value or benchmark

Question 39

Coefficient of Variation formula

Answer 39

= s / X bar S = standard deviation X bar = sample mean

Question 40

Coefficient of variation definition

Answer 40

Measures relative dispersion to the mean

Question 41

Skewness

Answer 41

degree of symmetry in a return distribution

Question 42

Normal distribution (symmetrical)

Answer 42

Mean = median Completely described by two parameters (mean and variance) Skewness = 0

Question 43

Non-symmetrical distributions

Answer 43

``` Positive skew (taller on the left; mean>median>mode) Negative skew (taller on the right; mean ```

Question 44

What is considered a large skew

Answer 44

When observations are greater than 100 and the skewness is +/- 0.5

Question 45

Kurtosis definition

Answer 45

Measure of the combined weight of the tails of a distribution relative to the rest of the distribution

Question 46

Leptokurtic

Answer 46

kurtosis is greater than the normal distribution (normal is when K = 3); Distribution has fatter tails, which means greater number of extreme returns

Question 47

Mesokurtic

Answer 47

kurtosis equal to normal (K = 3)

Question 48

Platykurtic

Answer 48

kurtosis less than normal (K <3)

Question 49

Geometric mean formula =

Answer 49

Take the nth root of : (data point + 1) x (data point + 1)...; subtract this total - 1 to get percentage

Question 50

What kind of distribution (negative or positive) has frequent small gains and few extreme losses?

Answer 50

Negative skew

Question 51

What kind of distribution (negative or positive) has frequent small losses and few extreme gains

Answer 51

Positive skew

Question 52

Sharpe Ratio formula

Answer 52

(Mean return on the portfolio - Mean return on a risk free asset) / standard deviation of return on the portfolio 30 day T-bill is an example of a risk free asset