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Annualized Volatility: Definition & Formula

Instructor: David Bartosiak

Dave draws off his years of experience as a Financial Advisor and Analyst to teach others all about finance and the investing world.

This lesson will detail how to annualize volatility by first calculating daily volatility and then annualizing this number. It explains the calculation and gives a couple examples of how to work through the formula.

Extrapolating Volatility Over a Year

When measuring financial performance, it's important to give a frame of reference. As with returns, volatility can be annualized to help provide this frame of reference and give some perspective. To annualize volatility, it's necessary to measure volatility over a shorter period of time and extrapolate it over the course of a year. It's very similar to annualizing returns -- compounding a shorter period's returns to show what returns would hypothetically be for a year. Put simply, annualizing a figure assumes observations over a short time frame will continue over the course of a year.

Let's say that XYZ Fund has returned 1% in 6 months. To annualize that return, take the 12 months in a year and divide by the 6 months XYZ made its return. There are 2 periods in a year where XYZ would have hypothetically returned 1%. $10,000 in XYZ Fund would have grown to $10,100 the first six months, ($10,000 * (1 + 1%)), then to $10,201 the next six months. Dividing $10,201 by $10,000 and subtracting 1 gives the annualized return of 2.01%.

Annualizing volatility is a little more complicated than simply calculating returns. Volatility is a measure of the variance of returns over a period of time. In order to figure out what the variance of returns is, the daily returns must first be calculated. After these daily returns are calculated, then the standard deviations of these returns can be calculated to give the daily volatility. Standard deviation is the measure of variance from the mean of a data set. Once this variance, or volatility, is calculated, it can then be annualized over the course of a year.

Annualized Volatility Calculation

Annual volatility = daily volatility times the square root of 252

Where Vol D = Daily volatility and 252 represents the typical number of trading days in a year

Assume ABC Stock has experienced the following daily changes:

{ 1%, 2%, 3%, 4%, 5% }

Using an online standard deviation calculator or Excel function =STDEV(), you can find that the standard deviation of the data set is 1.58%. Multiplying 1.58% by the square root of 252 gives 25.08%, which is the annualized volatility for ABC Stock given the assumed daily returns.

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