# Standard Deviation

**Meaning and definition of Standard Deviation **

The general definition of **standard deviation** can be given as a measure of the dispersion of a set data from its mean. A higher dispersion in the data indicates a higher deviation. In finance, standard deviation is applied to the annual rate of return of an investment for measuring the volatility of an investment. Standard deviation is also referred as historical volatility and is used by investors as an estimate for the amount of expected volatility.

Investopedia explains standard deviation as a statistical measurement that throws light on historical volatility. For instance, a volatile stock features a high standard deviation whereas deviation of a stable blue chip stock will be comparatively lower. A large distribution indicates how much return on the fund is being deviated from the expected normal returns.

**Calculating Standard Deviation **

The standard deviation for a data set is calculated as the square root of its variance. Let us presume that an investor has $600 to invest and is considering investing all of it in a single firm’s shares, trading currently at $30. The investor assesses a 0.75 probability that the shares will rise in market value to $33 over the coming period and a 0.25 probability that the share will fall in its market value to $26. Presume that the firm will pay $1 dividend per share at the closing of the year.

The payoffs from the proposed investment are as listed below:

If shares rise: $33 x 20 shares + $20 dividend = $680

If shares decline: $26 x 20 shares = $540

**Formula **

Being computed as the square root of its variance, the general formula used for computing Standard Deviation is:

**Application of Standard Deviation **

In finance, standard deviation is used in determination of risk involved in an investment. Putting it simple, standard deviation provides the investors with a mathematical basis for their decisions related to investments. Standard deviation is a common term used in context with deals involving trade of stocks, stock options, bonds, property, mutual funds, ETFs, and index mutual funds. Standard deviation is also, commonly, referred as volatility.

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