Statistical Concepts and Market Returns Flashcards Preview

CFA Level 1 - Quantitative Methods > Statistical Concepts and Market Returns > Flashcards

Flashcards in Statistical Concepts and Market Returns Deck (47)
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1
Q

Statistics used to summarize important characteristics of large data sets

A

Descriptive Statistics

2
Q

The procedures used to make forecasts, estimates or judgments about large data sets on the basis of the statistical characteristic of a smaller set (sample).

A

Inferential Statistics

3
Q

The set of all possible members of a stated group

A

Population

4
Q

A subset of the population of interest

A

Sample

5
Q

A measurement scale that contains the least information. Observations are classified or counted with no particular order. (i.e. binary)

A

Nominal Scale

6
Q

A measurement scale that has every observation assigned to one of several categories. Then the categories are ordered with respect to certain characteristics. (I.e. Top 100 stocks of SP500)

A

Ordinal Scale

7
Q

A measurement scale that provides relative ranking, plus the assurance that the differences between scale values are equal. (i.e. temperature )

A

Interval Scale

8
Q

A measurement scale that provides ranking and equal differences between scale values and a true zero point at the origin. (i.e. money purchasing power)

A

Ratio Scale

9
Q

A measure used to describe a characteristic of a population

A

parameter

10
Q

used to measure a characteristic of a sample

A

Sample Statistic

11
Q

A tabular presentation of statistical data that aids the analysis of large data sets. (For frequency distributions, the interval with the greatest frequency is the modal interval)

A

Frequency Distribution

12
Q

Calculated by dividing the absolute frequency of each return interval by the total number of observations

A

Relative Frequency

*The percentage of total observation that fall within each interval

13
Q

Summing the absolute frequencies starting at the lowest interval and progressing through the highest

A

Cumulative Absolute Frequencies

14
Q

Calculation for Population/Sample Mean

A

SUM(Xi) / N

15
Q

Calculation for Sum of Mean Deviations

A

Sum(Xi-Xbar) = 0

16
Q

Calculation for Weight Mean

A

Sum(wi*Xi) = 1
wi == weight for each Xi

  • example is a portfolio weight by %stock, bond, cash
17
Q

Calculation for Geometric Mean

A

G = (X1X2…*Xn)^(1/n)

*Always less than arithmetic mean

18
Q

Calculation for Geometric Mean Return

A

1 + Rg = ((1+Rg1)(1+Rg2)…*(1+Rgn))^(1/n)

19
Q

Calculation for Harmonic Mean

A

N / SUM(1/Xi)

*ex. average cost per share
harmonic mean < geometric mean < arithmetic mean

20
Q

Percentile Calculation

A

Ly = (n+1) *(y/100) == the number below which observation is the quartile

21
Q

The variability around the Central Tendency

A

Dispersion

22
Q

Mean Absolute Deviation

A

SUM(abs(Xi-Xbar)) / N

23
Q

Population Variance Calculation

A

sigma^2 = SUM(Xi- u)^2 / N

24
Q

Calculation for Population Standard Deviation

A

sigma = ((SUM(X-u)^2) / N)^(1/2)

25
Q

Calculation for Sample Variance

A

s^2 = SUM(Xi-Xbar)^2 / (n-1)

26
Q

If n is used, not (n-1), the sigma squared is systematically underestimated

A

biased estimator

27
Q

Sample Standard Deviation

A

s = (SUM(Xi-Xbar)^2/(n-1))^(1/2)

28
Q

States that for any set of observations, whether sample or population data and regardless of the shape of the distribution, the percentage of the observations that lie within k standard deviations of the mean is at least (1-(1/k^2)) for all k > 1

A

Chebyshev’s Inequality

29
Q
36% of all observations lie within +- 1.25 sdev's of mean
56% "" +/- 1.5 sdev's of mean 
75%  " " +/- 2 sdev's of mean 
89% "" +/- 3 sdev's of mean 
94% "" +/- 4 sdev's of mean
A

Using Chebyshev’s Inequality

30
Q

The amount of variability in a distribution relative to a reference point or benchmark. It is measured with coefficient of variation

A

Relative Dispersion

31
Q

Coefficient of Variation Calculation

  • measures the amount of dispersion in a distribution relative to its mean
    • risk per unit of return
A

CV = sx/ Xbar = (Std. Dev of x) / (avg. value of x)

32
Q

Sharpe Ratio Calculation

*measures excess return per unit

A

s = (Rpbar - Rf) / sigmap

Rpbar = portfolio return 
Rf = risk-free return
sigmap = std. dev. of portfolio returns

*T-bills are convention for risk free return

33
Q

2 limitations of Sharpe Ratio

A
  1. If 2 portfolios have negative Sharpe Ratios, it is not necessarily true that the higher Sharpe Ratio implies superior risk-adjusted performance. Increasing Risk moves a negative Sharpe Ratio closer to Zero.
  2. Investment strategies with the option characteristics produce Sharpe Ratios to high and underestimate risk because of asymmetric return distributions
34
Q

Skewness refers to the extent to which a distribution is not symmetrical

A
  • positively skewed == many outliers in the upper region, or right tail
  • *negatively skewed == many outliers in the lower region, or left tail.
35
Q

In positively skewed distribution, (organize mean, median and mode)

A

mode < median < mean

36
Q

In negatively skewed distribution, (organize mean, median and mode)

A

mean < median < mode

37
Q

The measure of the degree to which a distribution is more or less “peaked” than a normal distribution

A

Kurtosis

38
Q

Leptokurtic

A

More peaked

39
Q

Platykurtic

A

less peaked

40
Q

Mesokurtic

A

equal or same as normal

41
Q

This distribution will have more returns clustered around the mean and more return with large deviation from the mean (fatter tails). This is perceived as risk increasing.

A

Leptokurtic Distribution

42
Q

If it has more or less kurtosis than the normal distribution

A

excess kurtosis

43
Q

Kurtosis for normal kurtosis = 3
Excess Kurtosis = kurtosis - 3

*Generally, more positive kurtosis and more negative skew signify increased risk.

A

excess kurtosis:
leptokurtic if >0
platykurtic if < 0

44
Q

Sample Skewness Calculation

A

Sk = (1/n) * (SUM(Xj-Xbar)^3 / s^3)

s = sample standard deviation

45
Q

Sample Kurtosis Calculation

A

== (1/n) * (SUM(Xi-Xbar)^4 / s^4)

46
Q

Excess kurtosis > +/- 1 is considered large

A

””

47
Q

Geometric Mean when measuring the past

A

Arithmetic Mean when measuring the future.