Statistical Concepts & Market Returns Flashcards
Parameter
A descriptive measure of a population characteristic.
Population
All members of a specified group
Sample
A subset of a population.
Sample statistic
A quantity computed from or used to describe a sample.
Nominal scale
Categories according to style, rather than rank. (Weakest level; ie. small cap, large cap)
Ordinal scales
Sorts data into ranked categories, but not necessarily equal, or scaled categories (S&Ps star ratings)
Interval scales
Provide not only ranking, but assurance that the difference between scales are equal.
Ratio scales
Interval scale, but with a true zero, true scale.
Mesokurtic
Distribution identical to normal distribution.
Platykurtic
A distribution that is less peaked than normal.
Leptokurtic
A distribution that is more peaked than normal.
Kurtosis
Statistical measure that tells us when a distribution is more or less peaked than a normal distribution.
Negatively skewed distribution
Long tail on left side. Mean is less than median is less than mode.
Positively skewed distribution
Long tail on its right side. Mode is less than median is less than mean.
Sharpe ratio formula
Mean return of portfolio minus mean return of risk free asset. Divided by standard deviation of portfolio.
Target semideviation
The positive square root of target semi variance.
Target semivariance
The average squared deviation below a target value.
Linear interpolation
Estimating an unknown value on the basis of two values around it.
Percentile
L = (n+1) y/100
y
Y= percentage at which we divide distribution Ly= location of percentile N= number of samples in distribution
Dispersion
The variability around the central tendency. If mean addresses reward, then dispersion measures risk.
Range
Maximum value minus minimum value.
Histogram
A bar chart of data that have been grouped into a frequency distribution.
Frequency polygon
A group of frequency distributions obtained by drawing straight lines joining successive points representing the class frequencies.
Measure of central tendency
Specifies where the data are centered.
Arithmetic mean
Sum of observations divided by the number of observations.
Population mean
The arithmetic value of a population
Sample mean
Arithmetic mean of a sample.
Cross sectional data
Observations over individual units at a point in time.
Time series data
Observations of a variable over time
Median
The value of the middle item of a ordered set.
Mode
Most frequently occurring value in a distribution
Weighted mean
An average in which each observation is weighted by an index of its relative importance.
Expected value
The weighted average of forward looking data
Chebyshev’s inequality
For any distribution with finite variance, the proportion of the observations within k standard deviations of the arithmetic mean is at least 1 - 1/k2
Coefficient of variation
Used to find relative dispersion. The ratio of the standard deviation of a set of observations to their mean value.
Frequency distribution
A tabular display of summarized data in a relatively small number of intervals. Frequency distributions permit us to evaluate how data are distributed.
Relative frequency of observations
The number of observations in the interval divided by the total number of observations.
Cumulative relative frequency
Summed relative frequencies as we move from the first interval to the last, thus giving the fraction of the observations that are less than the upper limit of each value.
