Lesson 6 of 11 · All lessons in this module
- Mean, median, mode and outliers
- Quantiles, box plots and their uses
- Range, mean absolute deviation, variance and standard deviation
- Median absolute deviation, semivariance and estimator bias
- Target downside deviation and coefficient of variationVideo lesson
- Returns not prices, data frequency and volatility scaling
- Skewness and kurtosisVideo lesson
- Scatter plots, covariance and correlation
- Limits of correlation analysis
- The four moments, benchmark correlation and spreadsheet functions
- Integrated cases: describing one return series from raw data
This lesson is part of the 2027 curriculum. You are following the 2026 curriculum, where it is not taught in this form. Switch if you are sitting the exam under the 2027 curriculum.
Lesson 6 of 11 · 13 min
Returns not prices, data frequency and volatility scaling
Statistics should be computed on returns rather than prices, and how often the data are sampled changes the numbers, which the square-root-of-time rule (roughly) translates between horizons.
In short
- Prices are usually non-stationary: their mean and variance drift over time. Returns are much closer to stationary, so analyse returns.
- The longer the interval between observations, the larger the typical return and the larger the variance per observation.
- Root-of-time law: variance scales linearly with time, standard deviation with the square root of time (about 22 trading days a month, 252 a year).
- In practice longer-horizon variance often grows more slowly than the rule predicts, because of market frictions, changing regimes, jumps and fat tails.
- The inverse of the CV (mean ÷ s) is return per unit of risk; with high-frequency data, annualize the mean and standard deviation before comparing.
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