(R7) Quantitative Methods: Statistical Concepts and Market Returns Flashcards
Population definition
All members of a specified group; all descriptive measures are called parameters
Sample definition
Subset of a population; all descriptive measures are called sample statistics
Definition of Parameter
Any descriptive measure of a population
Definition of Sample statistic
Any descriptive measure of a sample
Inferential statistics
involves making forecasts, estimates, or judgements about a larger group (population) from the smaller group (sample) actually observed
4 Types of measurement scales
- Nominal
- Ordinal
- Interval
- Ratio
These are ordered from weakest to strongest level of measurement
Nominal Measurement Scale
Categorical data that is not ranked; weakest level of measurement
Ordinal Measurement Scale
Ranking system due to some characteristic; but this tells us nothing about the difference between the rankings
Interval Measurement Scale
Provides ranking but also assurance that the difference between scale values are equal; I.e. temperature
Ratio Measurement scale
They have all the characteristics of interval measurement scales as well as a true zero point as the origin; strongest level of measurement
Frequency Distribution
a tabular display of data grouped into intervals; works with all measurement scales
Absolute frequency
Number of observations in each interval
How to construct a frequency distribution
- Sort the data in ascending order
- Calculate the range of the data, defined as range = maximum value - minimum value
- Choose the number of intervals (k)
- Determine the interval width (max - min)/k
Relative frequency
Absolute frequency of each interval divided by the total number of observations
Cumulative relative frequency
Adds up the relative frequencies as we move from the first to the last interval
Histogram definition
Bar chart of data that have been grouped into a frequency distribution
Frequency Polygon
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
Three methods to display data graphically
- Histogram
- Frequency polygon
- Cumulative frequency distribution
Measures of central tendency (Definition and types)
Specifies where the data is centered; Ex: arithmetic mean, median, mode, weighted mean, geometric mean
Arithmetic mean definition
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
Cross-sectional data
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)
Time-series data
Comparing data over multiple years (Ex: comparing the class averages from 2015 to 2020)
Median
Number in the middle; (n+1)/2
Only measure of central tendency that can be used with nominal data is
Mode
Weighed mean
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)
Geometric mean
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
Which mean will always be lower than the other? Geometric or arithmetic
Geometric Mean
Quartiles, quintiles, deciles, and percentiles
Quartiles - divide data into quarters
Quintiles - divide data into fifths
Deciles - divide into tenths
Percentiles - divide into hundredths
Formula for locating a percentile is
(n+1)(y/100)
n equals the number of observations
y is the percentage point at which we are dividing the distribution
Measures of dispersion
Range, mean absolute deviation, variance, and standard deviation
Mean absolute deviation =
Take absolute value of the following: (Each data point - arithmetic mean); then divide by the total number of observations
Population variance =
(each data point - arithmetic mean) ^2 / number of observations
Population standard deviation =
The square root of [(each data point - mean) ^2 / number of observations]
Sample variance =
(each data point - arithmetic mean) ^2 / (number of observations - 1)
Sample standard deviation =
The square root of [(each data point - mean) ^2 / (number of observations - 1)]
Standard deviation definition
measures dispersion around the arithmetic mean
Chebyshev’s inequality definition and equation
Definition - minimum proportion of observations within a certain amount of standard deviations of the arithmetic mean
Formula = 1 - (1/(k^2))
Relative dispersion
Is the amount of dispersion relative to a reference value or benchmark
Coefficient of Variation formula
= s / X bar
S = standard deviation
X bar = sample mean
Coefficient of variation definition
Measures relative dispersion to the mean
Skewness
degree of symmetry in a return distribution
Normal distribution (symmetrical)
Mean = median
Completely described by two parameters (mean and variance)
Skewness = 0
Non-symmetrical distributions
Positive skew (taller on the left; mean>median>mode) Negative skew (taller on the right; mean
What is considered a large skew
When observations are greater than 100 and the skewness is +/- 0.5
Kurtosis definition
Measure of the combined weight of the tails of a distribution relative to the rest of the distribution
Leptokurtic
kurtosis is greater than the normal distribution (normal is when K = 3); Distribution has fatter tails, which means greater number of extreme returns
Mesokurtic
kurtosis equal to normal (K = 3)
Platykurtic
kurtosis less than normal (K <3)
Geometric mean formula =
Take the nth root of : (data point + 1) x (data point + 1)…; subtract this total - 1 to get percentage
What kind of distribution (negative or positive) has frequent small gains and few extreme losses?
Negative skew
What kind of distribution (negative or positive) has frequent small losses and few extreme gains
Positive skew
Sharpe Ratio formula
(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
