Statistical Concepts and Market Returns

Question 1

Descriptive vs. inferential statistics

Answer 1

Summarize data to describe aspects vs. forecasting, estimating to larger group based on smaller group

Question 2

Population vs. sample

Answer 2

All members of group vs. subset of group

Question 3

Types of measurement scales

Answer 3

Nominal (categorize, no rank)

Ordinal (categorize with order, e.g. stars) - lack relativity

Interval (rank with equal differences in scale values) - lack true zero so no ratios

Ratio (rank with equal differences in scale values, with true zero)

Question 4

Parameter

Answer 4

Any descriptive measure of population

Question 5

sample statistic

Answer 5

Quantity computed from or use to describe sample

Question 6

frequency distribution

Answer 6

Table of data summarized into small number of intervals. e.g. x occur in y range, a occur in b range, etc. Interval width depends on usefulness of size.

Question 7

calculate and interpret relative and cumulative frequencies

Answer 7

Relative frequency = absolute frequency / total observations

Cumulative frequency adds up relative frequencies as move from first to last interval

Question 8

describe properties of data presented as histogram or frequency polygon

Answer 8

Histogram is bar chart grouped by frequency distribution while frequency polygon is graph with midpoint of interval on x axis and frequency on y axis

Question 9

measures of central tendency

Answer 9

Specifies where data centered

Question 10

quartiles, quintiles, deciles, percentiles

Answer 10

Measures of location

Question 11

proportion of observations within X standard deviations using Chebyshev’s inequality

Answer 11

Proportion of observations within k standard deviations is AT LEAST 1-1/k^2

Question 12

Coefficient of variation

Answer 12

CV = s/Xbar

Question 13

sharpe ratio

Answer 13

S = mean return portfolio - mean risk free return / std dev. portfolio

Good for portfolio with symmetric returns, not asymmetric (options)

Question 14

skewness - positive vs. negative

Answer 14

positive - frequent small losses and few extreme gains

negative - frequent small gains, few extreme losses

Question 15

relative locations of mean, median, mode for unimodal, nonsymmetrical distribution

Answer 15

Locations will vary depending on skewness and kurtosis

Positive skew - mean > median

Question 16

measures of kurtosis

Answer 16

Degree of peakedness of distribution. More peak, fatter tails (less in middle).

Leptokurtic - more peaked than normal = greater than 3
Platykurtic - less peaked than normal = less than 3
Mesokurtic - normal = 3

Normal distribution = 3

Excess kurtosis is kurtosis minus 3

Question 17

arithmetic vs. geometric mean in investment returns

Answer 17

Geometric mean is preferable to computing change or growth over time. Arithmetic mean has benefits for single period performance.

Question 18

Population mean, sample mean, arithmetic mean

Answer 18

All arithmetic means. u is population mean, Xbar is sample mean.

Upshot: mean takes account of al values but can be distorted by extreme values

Question 19

Median

Answer 19

Value of middle item or sorted data. Ignores extremes but ignores magnitude largely. Good for skewed data.

Odd number set media = (n+1)/2
Even numbered set media = average of n/2 and (n+2)/2

Question 20

Mode

Answer 20

Most frequently occurring value. Multiple or none possible.

Question 21

Weighted mean

Answer 21

Use whenever asset not equally represented in sample/pop. Multiply observation by weight and add up.

Weighted average of forward-looking data = expected value.

Question 22

Geometric mean

Answer 22

nth root of the product of all values multiplied together.

Question 23

Harmonic mean

Answer 23

n/(sigma (1/x))

Used in cost averaging.

Question 24

Location of percentile formula

Answer 24

L = (n+1)(y/100)

y is percentage point

Question 25

Range

Answer 25

max value minus min value

Question 26

Mean absolute deviation

Answer 26

(sigma | xi - x | ) / n

those are absolute value bars

Question 27

Population Variance

Answer 27

[sigma (xi - u)^2 ] / n

Question 28

Population Standard deviation

Answer 28

square root of [ sigma (x - u)^2 ] / n

Question 29

sample variance

Answer 29

[sigma (xi - x)^2] /(n-1)

Question 30

Sample standard deviation

Answer 30

square root of [sigma (xi - x)^2]/(n-1)

Question 31

Downside risk measures

Answer 31

Semivariance, semideviation - deviation below the mean

Target semivariance, target semideviation - deviation below target