# How to Calculate Historical Volatility for Stock Prices

by Ben Taylor ; Updated April 19, 2017To calculate a stock's historical volatility, which is based on actual recorded performance, first establish its statistical mean price for a period of time, then compute its standard deviation. Market prices that represent a higher standard deviation indicate higher volatility, and volatility decreases as market prices trend toward the stock's statistical mean. Computing historical volatility can help an investor understand trends in a stock's movement, and can help interpret current fluctuations

## Computing Standard Deviation

Record the closing price for a particular stock in a computer spreadsheet. Some computer spreadsheets can download stock data from the Internet by connecting to sites such as Yahoo Finance or Google Finance. Order the data by date from most recent to oldest.

Compute the statistical mean for the stock's market prices you have recorded. Total each closing price, then divide the sum by the number of days for which you have recorded a price. For example, if you have a population of 100 stock prices, total each market price then divide the sum by 100. Calculate and square the difference between each stock's market price and the statistical mean to begin determining standard deviation.

Compute the average of all differences, then take the square root, and the result is the standard deviation for the entire population. Use the sample standard deviation, which divides the average of all differences using a denominator that is one less than the total number of data points in the population - if the market prices represents only a sample of the entire population. Standard deviation, or sample standard deviation, is one way to quantify the historical volatility of a stock.

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