Statistical Concepts and Market Returns Flashcards
Statistics that summarize the characteristics of a data set
Descriptive statistics
Statistics that are used to make probabilistic statements about a population based on a sample
Inferential statistics
Data is put into categories that have no particular order
Nominal scale
Data is put into categories that can be ordered with respect to some characteristic
Ordinal scale
Differences in data values are meaningful, but ratios, such as twice as much or twice as large, are not meaningful
Interval scale
Ratios of values are meaningful, and zero represents the complete absence of the characteristic being measured
Ratio scale
Any measurable characteristic of a population
Parameter
A characteristic of a sample
Sample statistic
The percentage of total observations falling within an interval
Relative frequency
The sum of the relative frequencies for all values less than or equal to that interval’s maximum value
Cumulative relative frequency
Arithmetic Mean
Mean = Sum of all values / n
Geometric Mean (compound growth rate)
Mean = (1+X1 x 1+X2….)^1/n
Harmonic Mean
Mean = N / (1/x1) + (1/x2)…
Mean Absolute Deviation
MAD = Σ (|X1 - Mean| + |X2 - Mean|) / n
*Absolute values
The mean of the squared deviations from the arithmetic mean or from the expected value of a distribution
Variance
Population Variance
= Σ (Xi - μ)^2 / N
Sample Variance
= Σ (Xi - x-bar)^2 / n - 1
Chebyshev’s inequality
= 1 - (1/k^2)
The proportion of the observations with k standard deviations of the mean
Coefficient of Variation
= s / x-bar
The degree to which a distribution is not symmetric about its mean
Skewness, > .5 = significantly different from 0
The measure of peakedness of a distribution and the probability of extreme outcomes
Kurtosis, normal is = 3, excess kurtosis > 1 = significant
Leptokurtic
Positive excess kurtosis (fat tails, more peaked) = probability of extreme outcomes is greater than a normal distribution
Platykurtic
Negative values of kurtosis (thin tails, less peaked)
When is the arithmetic mean appropriate? When is the geometric return appropriate?
Mean = forecasting single period returns in future periods
Geometric = forecasting future compound returns over multiple periods
