Volatility Primer 3: The Normal Distribution

The random variation of monthly or annual asset returns conform to a probability distribution known as the normal (Gaussian) distribution or bell curve. The probability distribution for the asset is described by its average return, or mean, and its volatility, or standard deviation.

Standard deviation is the square root of the average of the squared deviations from their average value and is a measure of the dispersion of the data. A low standard deviation means the data is close to the average while a high standard deviation means the data is spread across a wide range of values.

For example, the plot below shows the probability distributions for both the S&P 500 total return and the 10-year US Treasury from 12/31/71 through 1/31/17.

The average monthly return for the S&P500 during this time period was 0.94% with a monthly standard deviation of 4.38%. The 10-year US Treasury had an average monthly return of 0.62% with a monthly standard deviation of 2.06%. Clearly the bonds have lower dispersion or volatility than the stocks, but also a lower average return.

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Disclosure:

The information presented here is the opinion of the author and may quickly become outdated and is subject to change without notice. All material presented in this article are compiled from sources believed to be reliable, however accuracy cannot be guaranteed. No person should make an investment decision in reliance on the information presented here.

The information presented here is distributed for education purposes only and is not an offer to buy or sell or a solicitation of an offer to buy or sell any security or participate in any particular trading strategy.

Performance data showing past performance results is no guarantee of future returns.