How to Calculate Annualized Volatility on Stock Prices
The annualized volatility of stock prices measures how much a stock price has fluctuated from its initial price over the course of a year. It is calculated using the daily logarithmic return, taking its standard deviation, and then dividing by the square root of the time period of returns. As the calculation involves a large set of data, a spreadsheet program is practical.
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Instructions
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Obtain the data necessary for your calculation of the annualized volatility on stock prices. You will need not only the initial value of your investment, which is the price of the stock when bought, but also its value every trading day for the year of your calculation. Organize your data into a spreadsheet, with the daily stock prices for each trading day in the first column, A, and the initial value of the investment in the second column, B.
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Divide the data in the first column by the data in the second column. Put the results of this calculation into column C.
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Take the natural log of the results in column C. Most spreadsheet programs have a formula for this. The opposite of an exponential function, the natural log is a mathematical function that makes big numbers easier to compare, and is written as "ln" or "LN" by convention. In Excel, this formula is written as "=LN(n)," without the quote marks, where "n" represents the number for which you want to take the log. The result in column C represents the daily logarithmic returns of your investment.
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Take the mean of the daily logarithmic returns in column C by first adding them and then dividing by the number of observations. If there are 252 trading days in a year, which is the norm, your number of observations should be 252.
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Subtract the mean of daily logarithmic returns from the daily logarithmic returns in column C. This calculation is performed 252 times, if there are 252 observations. Put these results in column D.
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Raise the results in column D to the power of two, divide by the number of observations, and then take the square root. This figure represents the standard deviation of the daily logarithmic returns.
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Divide one by the number of trading days in the year, which, like the number of observations, is often equal to 252. Take the square root. This is called the square root of the time period of returns.
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Divide the standard deviation of daily logarithmic returns by the square root of the time period of returns. This gives you the annualized volatility on stock prices.
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References
- 25 Years of Programming: Stock Price Volatility Calculator for Option Valuation Formulas
- Microsoft Support; Formulas to Find the Log and Inverse Log of a Number; 18 June, 2010
- Barcelona Field Studies Centre: Mimimum Sample Size Calculation
- Aetheling; The Mathematics of Volatility; Loren Cobb; 9 July 2006
- Aenorm; The Worst Case Scenario for Next Year's Stock Return; Oct. 2007
- Purple Math: The Common and Natural Logarithims
