Statistical Concepts and Market Returns Flashcards
Descriptive vs. inferential statistics
Summarize data to describe aspects vs. forecasting, estimating to larger group based on smaller group
Population vs. sample
All members of group vs. subset of group
Types of measurement scales
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)
Parameter
Any descriptive measure of population
sample statistic
Quantity computed from or use to describe sample
frequency distribution
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.
calculate and interpret relative and cumulative frequencies
Relative frequency = absolute frequency / total observations
Cumulative frequency adds up relative frequencies as move from first to last interval
describe properties of data presented as histogram or frequency polygon
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
measures of central tendency
Specifies where data centered
quartiles, quintiles, deciles, percentiles
Measures of location
proportion of observations within X standard deviations using Chebyshev’s inequality
Proportion of observations within k standard deviations is AT LEAST 1-1/k^2
Coefficient of variation
CV = s/Xbar
sharpe ratio
S = mean return portfolio - mean risk free return / std dev. portfolio
Good for portfolio with symmetric returns, not asymmetric (options)
skewness - positive vs. negative
positive - frequent small losses and few extreme gains
negative - frequent small gains, few extreme losses
relative locations of mean, median, mode for unimodal, nonsymmetrical distribution
Locations will vary depending on skewness and kurtosis
Positive skew - mean > median
measures of kurtosis
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
arithmetic vs. geometric mean in investment returns
Geometric mean is preferable to computing change or growth over time. Arithmetic mean has benefits for single period performance.
Population mean, sample mean, arithmetic mean
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
Median
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
Mode
Most frequently occurring value. Multiple or none possible.
Weighted mean
Use whenever asset not equally represented in sample/pop. Multiply observation by weight and add up.
Weighted average of forward-looking data = expected value.
Geometric mean
nth root of the product of all values multiplied together.
Harmonic mean
n/(sigma (1/x))
Used in cost averaging.
Location of percentile formula
L = (n+1)(y/100)
y is percentage point
Range
max value minus min value
Mean absolute deviation
(sigma | xi - x | ) / n
those are absolute value bars
Population Variance
[sigma (xi - u)^2 ] / n
Population Standard deviation
square root of [ sigma (x - u)^2 ] / n
sample variance
[sigma (xi - x)^2] /(n-1)
Sample standard deviation
square root of [sigma (xi - x)^2]/(n-1)
Downside risk measures
Semivariance, semideviation - deviation below the mean
Target semivariance, target semideviation - deviation below target
