Statistical Measures of Asset Returns

How to summarise a return series and judge what the summary is worth: where the data are centred and located, how widely they spread, what shape they have, and how two series move together, plus the pitfalls of each measure.

1. 1. Mean, median, mode and outliersA measure of central tendency condenses a return series into one number for where it is centred; which measure you trust depends on outliers and on the type of data.Free14 min
2. 2. Quantiles, box plots and their usesQuantiles mark the values at or below which a given share of the sorted data lies, so they show where any observation stands relative to the rest.14 min
3. 3. Range, mean absolute deviation, variance and standard deviationDispersion measures how widely returns scatter around their mean; if the mean is the reward, dispersion is the risk.14 min
4. 4. Target downside deviation and coefficient of variationTarget downside deviation measures only the risk of falling short of a target, and the coefficient of variation scales risk by return so that different assets can be compared.Video · 7 min13 min
5. 5. Skewness and kurtosisSkewness shows whether big surprises lean toward gains or losses; kurtosis shows how often big surprises occur compared with a normal distribution.Video · 6 min15 min
6. 6. Scatter plots, covariance and correlationCovariance shows whether two variables move together; correlation rescales it to a unit-free number between −1 and +1 that measures the strength of the linear link.14 min
7. 7. Limits of correlation analysisA correlation coefficient is only as good as the data behind it: it misses non-linear links, bends to outliers, can be spurious, and never proves causation.12 min
8. 8. Integrated cases: describing one return series from raw dataA single table of monthly returns supports a whole chain of questions: centre and shape, spread, downside risk and co-movement. The case is won by choosing the right divisor and the right reference point for each statistic.15 min