Glossarytaught in QD1.02, DA1.04, QM1.03
Z-score
Also called z-scores, z score, standard score.
How many standard deviations an observation sits from the mean: the observation less the mean, divided by the standard deviation. It puts numbers measured in different units on one scale.
A stock returning 16% in a year when its peer group averaged 10% with a standard deviation of 4 points has a z-score of 1.5. When a margin is 2 standard deviations below its own ten-year average, it's unusually low for that company, whatever its level compared with other companies.
Under a normal distribution about 68% of observations fall within one standard deviation of the mean and about 95% within two, so a z-score beyond 2 is unusual. Financial data has fatter tails than that, so treat the probabilities as rough. Do not confuse it with the Altman Z-score, a different measure that shares only the letter: a bankruptcy-risk model built from five ratios.
Standardise before you compare.
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