Statistical Concepts and Market Returns
8 important questions on Statistical Concepts and Market Returns
In which two broad meanings do we use statistics?
2) Statistical inference (making forecasts/estimates from a smaller group that is observed, based on probability theory)
How do we define a population vs. a sample?
What measurement scales do we use?
- Ordinal scale: can be ranked, but the scale can't tell us anything about the difference (e.g. between 1 and 2 compared to 4 and 5).
- Interval scale: differences between a scale are equal but there is no zero point (zero celsius is not the absence of temperature)
- Ratio: strongerst version, true zero point (e.g. money).
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What is a histogram, frequency polygon and CFD (cumulative frequency distribution) ?
A polygon is a straight line between the midpoints of the intervals, in which the height is determined by the absolute frequency.
A CFD or CDF is the cumulative version of a polygon, but uses the upper interval limit instead of the midpoint. Mainly useful if a statement about at least X% is above Y. In essence the slope at any point is proportional to the number of observations in the interval.
What measures of dispersion do we use?
We have multiple absolute dispersion measures (no reference point or benchmark):
- Range (which is the maximum - minimum)
- Mean absolute deviation (sum would otherwise be zero)
- Variance (average of squared deviations from the arithmatic mean)
- Standard deviation (positive square root of the variance), often interpreted as an assets risk.
How do we calculate a semivariance/semideviation?
Semideviation - - > positive square root of the semivariance
Calculate by:
- Sample mean
- Identify observations smaller than or equal to the mean
- Compute the sum of all these squared negative deviations
- Divide by the number of observations in the sample - 1.
We can use something else than the mean as well, then it turns into target semivariance and target semideviation.
What does Chebyshev inequality present us?
1,25 - - > 36%
1,5 - - > 56%
2 - - > 75%
2,5 - - > 84%
3 - - > 89%
4 - - > 94%
Importance is because of generality as it holds for any shape of distribution, continuous or discrete data.
Why do we use the coefficient of variation?
IMPORTANT: if we use returns we measure the amount of risk (standard deviation) per unit of mean return. Which expresses the magnitude of variation among observations relative to their average size. This enables us to compare portfolios and stocks, as it is a scale free measure!! No units of measurement.
The question on the page originate from the summary of the following study material:
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