Lesson 8 of 8 · All lessons in this module
  1. Mean, median, mode and outliers
  2. Quantiles, box plots and their uses
  3. Range, mean absolute deviation, variance and standard deviation
  4. Target downside deviation and coefficient of variationVideo lesson
  5. Skewness and kurtosisVideo lesson
  6. Scatter plots, covariance and correlation
  7. Limits of correlation analysis
  8. Integrated cases: describing one return series from raw data

Lesson 8 of 8 · 15 min

Integrated cases: describing one return series from raw data

A 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.

In short

  • Compare mean and median first: a mean below the median hints at a left tail (negative skew), and a mean above the median at a right tail.
  • A sample variance divides by n−1n-1. A reported population variance converts with s2=σ2⋅n/(n−1)s^2 = \sigma^2\cdot n/(n-1); take the square root last.
  • Target downside deviation uses only the returns below the target, but divides by n−1n-1 with n counting all returns.
  • The coefficient of variation s/Xˉs/\bar X puts risk per unit of mean return; a negative or near-zero mean makes it meaningless.
  • Covariance carries the units of both series; correlation divides by both standard deviations and sits between −1 and +1.

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