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Level 1 CFA 2020 > (R7) Quantitative Methods: Statistical Concepts and Market Returns > Flashcards

(R7) Quantitative Methods: Statistical Concepts and Market Returns Flashcards

1
Q

Population definition

A

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

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2
Q

Sample definition

A

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

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3
Q

Definition of Parameter

A

Any descriptive measure of a population

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4
Q

Definition of Sample statistic

A

Any descriptive measure of a sample

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5
Q

Inferential statistics

A

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

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6
Q

4 Types of measurement scales

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

These are ordered from weakest to strongest level of measurement

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7
Q

Nominal Measurement Scale

A

Categorical data that is not ranked; weakest level of measurement

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8
Q

Ordinal Measurement Scale

A

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

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9
Q

Interval Measurement Scale

A

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

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10
Q

Ratio Measurement scale

A

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

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11
Q

Frequency Distribution

A

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

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12
Q

Absolute frequency

A

Number of observations in each interval

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13
Q

How to construct a frequency distribution

A
  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
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14
Q

Relative frequency

A

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

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15
Q

Cumulative relative frequency

A

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

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16
Q

Histogram definition

A

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

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17
Q

Frequency Polygon

A

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

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18
Q

Three methods to display data graphically

A
  1. Histogram
  2. Frequency polygon
  3. Cumulative frequency distribution
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19
Q

Measures of central tendency (Definition and types)

A

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

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20
Q

Arithmetic mean definition

A

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

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21
Q

Cross-sectional data

A

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)

22
Q

Time-series data

A

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

23
Q

Median

A

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

24
Q

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

A

Mode

25
Q

Weighed mean

A

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)

26
Q

Geometric mean

A

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

27
Q

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

A

Geometric Mean

28
Q

Quartiles, quintiles, deciles, and percentiles

A

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

29
Q

Formula for locating a percentile is

A

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

30
Q

Measures of dispersion

A

Range, mean absolute deviation, variance, and standard deviation

31
Q

Mean absolute deviation =

A

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

32
Q

Population variance =

A

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

33
Q

Population standard deviation =

A

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

34
Q

Sample variance =

A

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

35
Q

Sample standard deviation =

A

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

36
Q

Standard deviation definition

A

measures dispersion around the arithmetic mean

37
Q

Chebyshev’s inequality definition and equation

A

Definition - minimum proportion of observations within a certain amount of standard deviations of the arithmetic mean

Formula = 1 - (1/(k^2))

38
Q

Relative dispersion

A

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

39
Q

Coefficient of Variation formula

A

= s / X bar

S = standard deviation
X bar = sample mean

40
Q

Coefficient of variation definition

A

Measures relative dispersion to the mean

41
Q

Skewness

A

degree of symmetry in a return distribution

42
Q

Normal distribution (symmetrical)

A

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

43
Q

Non-symmetrical distributions

A 
Positive skew (taller on the left; mean>median>mode)
Negative skew (taller on the right; mean
44
Q

What is considered a large skew

A

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

45
Q

Kurtosis definition

A

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

46
Q

Leptokurtic

A

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

47
Q

Mesokurtic

A

kurtosis equal to normal (K = 3)

48
Q

Platykurtic

A

kurtosis less than normal (K <3)

49
Q

Geometric mean formula =

A

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

50
Q

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

A

Negative skew

51
Q

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

A

Positive skew

52
Q

Sharpe Ratio formula

A

(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

Level 1 CFA 2020 (25 decks)

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