# Volatility

## What is volatility?

Volatility is a measure of how much an asset fluctuates over time. It refers to the degree of uncertainty about the value of an asset or security. For example, stocks that move quickly up and down are considered volatile.

Oxford Languages

1. liability to change rapidly and unpredictably, especially for the worse.

“the succession of new rulers contributed to the volatility of the situation”

1. tendency of a substance to evaporate at normal temperatures.

“the volatility of chemicals in an indoor environment”

Merriam Webster Online

the quality or state of being volatile: such as

a: a tendency to change quickly and unpredictably

“price volatility”

“the volatility of the stock market”

Wikipedia

In finance, volatility (usually denoted by σ) is the degree of variation of a trading price series over time, usually measured by the standard deviation of logarithmic returns.

Volatility does not measure the direction of price changes, merely their dispersion. This is because when calculating standard deviation (or variance), all differences are squared, so that negative and positive differences are combined into one quantity. Two instruments with different volatilities may have the same expected return, but the instrument with higher volatility will have larger swings in values over a given period of time.

For example, a lower volatility stock may have an expected (average) return of 7%, with annual volatility of 5%. This would indicate returns from approximately negative 3% to positive 17% most of the time (19 times out of 20, or 95% via a two standard deviation rule). A higher volatility stock, with the same expected return of 7% but with annual volatility of 20%, would indicate returns from approximately negative 33% to positive 47% most of the time (19 times out of 20, or 95%). These estimates assume a normal distribution; in reality stocks are found to be leptokurtotic.

## Historical volatility

Historical volatility is the average rate at which the price of an asset has changed over time.

## Implied volatility

Implied volatility is a measure of how much investors expect the price of an asset will fluctuate over the life of its options.