ATLASNormal distribution
Investing glossary · Models and probabilities
The symmetric bell-shaped distribution fully described by its mean and standard deviation.
Definition
The normal distribution, or bell curve, is symmetric around its average, with most values near the middle and fewer further out. It is fully described by two numbers: the mean and the standard deviation. About 68% of values fall within one standard deviation of the mean, about 95% within two and about 99.7% within three.
Many risk tools assume returns are normal because it makes the maths simple. But real stock returns have fat tails: extreme days happen far more often than the bell curve predicts. A normal approximation is good for rough sizing and can badly understate the risk of rare, severe moves.
Formula
P(|X − μ| ≤ kσ) = 68.3% (k=1), 95.4% (k=2), 99.7% (k=3)
k = number of standard deviations from the mean; the percentages are the share of values within ±kσ.
Worked example
Microsoft (MSFT) trades at $534.57. With a monthly standard deviation of about 6.8%, the normal rule gives a one-sigma range of $498.25 to $570.89 (about 68% of outcomes) and a two-sigma range of $461.93 to $607.21 (about 95%).
Treat these as rough bands: because of fat tails, moves beyond them happen more often than 32% and 5% of the time would imply for a perfect bell curve.
How ATLAS uses it
ATLAS replaces the normal curve with a fat-tailed distribution calibrated on past forecasts, so that a range labeled 90% contains the outcome about 90% of the time.
Related in ATLAS: Stock analysis →Browse all ATLAS tools →See it on a real stock
The example above uses these companies. Open their pages for the full numbers:
Frequently asked questions
Are stock returns normally distributed?
Only approximately. Daily returns have fatter tails and sometimes skew, so extreme moves are more common than a normal distribution implies.
What is the 68-95-99.7 rule?
For a normal distribution, about 68%, 95% and 99.7% of values fall within one, two and three standard deviations of the average.
Related terms
Put the idea to work on your own stocks
Open any company in ATLAS to see its fair value, its odds of rising and its risk numbers side by side.
Try ATLAS →Not investment advice. ATLAS estimates are produced by statistical models from public data; they can be wrong and past performance does not predict future results. Consider your own situation before investing. Disclaimer