Normal Distribution: Overview, Concepts, and Financial Uses

What Is Normal Distribution?

By Kristi Waterworth – Updated Nov 3, 2025 at 11:21 PM EST | Fact-checked by Frank Bass

Key Points

The normal distribution is a concept in statistics that assumes all values are distributed in the same pattern.
It requires symmetry and consistent proportions in the distribution of values.
Normal distributions underlie many statistical models, and can help determine how best to balance a portfolio using Modern Portfolio Theory.

Depending on what kind of investor you are, you may find yourself dealing with a lot of math and statistical models. When you're an investor more interested in the numbers, understanding the concept of a "normal distribution" is invaluable. We'll explore this topic and how to use it as an investor in this article.

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About the Author

Kristi Waterworth has been a contributing real estate and financial expert at The Motley Fool, covering real estate, investing, and personal finance topics, since 2020. Kristi has been interviewed by various TV media outlets and podcasts for her real estate investing expertise – from residential real estate to digital real estate and everything in between. Kristi’s journalist career spans over 25 years, and she has written about real estate investing, homeownership, and home construction specifically for the last decade. She was also previously a licensed Realtor and general building contractor before the Great Recession and housing market collapse. She holds a bachelor’s degree in American history from Columbia College in Missouri.

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Consistent proportions. There's a constant proportion of distance under the curve between the mean and any specific number of standard deviations from the mean, positive or negative, known as empirical rule. So, for example, 95% of cases may fall within two standard deviations from the mean in either direction.

Skewness and kurtosis. The coefficients known as skewness and kurtosis describe how different any distribution is from the normal distribution. Skewness is a measure of symmetry, and kurtosis measures the thickness of the ends of the distribution, all in relation to the normal distribution.

Where is the normal distribution used?

The normal distribution is the basis of many important ways of evaluating your portfolio or individual stocks. Here are a few ways it's used in investing:

Modeling stock returns. By assuming that stock returns follow a normal distribution, it's easier to predict the probability of different returns and the likelihood of a gain or loss.

Risk management. Both value at risk (VaR) and volatility are based on the normal distribution.

Pricing options. Models like Black-Scholes, which are used to determine how much an option should be worth today, are based on normal distributions.

Benchmarking portfolios. Comparing your portfolio to a benchmark can help you estimate how well you're doing, both in luck and skill. This requires a normal distribution underneath the model to determine the probability of each.

Modern Portfolio Theory (MPT). This portfolio construction theory is used to build portfolios that are optimized for specific returns based on risk tolerance. It requires a normal distribution to help calculate correlations and covariances.

What Is Normal Distribution?

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