How to Calculate Historical Volatility

Historical volatility measures how much an asset’s price has fluctuated over a specific period. It quantifies the dispersion of returns, offering insight into an investment’s stability or instability.

Key Concepts for Volatility Calculation

Historical volatility is determined using past price data, focusing on the asset’s closing prices over a chosen timeframe. Financial analysis often uses “returns” to measure price changes, typically calculated as daily logarithmic returns. Logarithmic returns normalize price movements, making them comparable across various assets and different time periods.

Volatility is commonly expressed as an annualized standard deviation of these returns. Standard deviation quantifies the dispersion of data points around their average, indicating how widely values are spread out. A higher standard deviation suggests greater price fluctuations and higher historical volatility.

The accuracy of historical volatility calculations relies on consistent historical price data, usually daily closing prices. The selected period for this data, known as the lookback period, influences the resulting volatility figure.

The Calculation Steps

Calculating historical volatility involves several steps, starting with data acquisition. Gather historical closing prices for the asset over your chosen period, such as 20 days, 60 days, or 252 trading days.

Next, calculate the periodic returns from these prices. Financial professionals commonly use logarithmic returns, which are derived using the natural logarithm of the ratio of the current day’s closing price to the previous day’s closing price. The formula for logarithmic returns is: ln(Current Price / Previous Price). For example, if a stock closed at $100 yesterday and $101 today, the logarithmic return is ln(101/100).

Once you have a series of periodic returns, you will calculate their standard deviation. This involves determining the average of the returns, then finding the difference between each individual return and this average. Each of these differences is then squared, summed, and divided by the number of observations minus one (for a sample standard deviation), before taking the square root of the result. This standard deviation represents the daily volatility of the asset.

Finally, to make the volatility comparable across different assets and timeframes, you must annualize it. This process involves multiplying the daily standard deviation by the square root of the number of trading days in a year. While the exact number can vary, 252 trading days is a widely accepted figure for annualization in the United States.

Practical Application and Tools

While historical volatility calculations can be performed manually, spreadsheet software offers efficient methods for practical application. Programs like Microsoft Excel or Google Sheets include built-in functions that streamline the process. For instance, the LN() function calculates natural logarithms for returns, STDEV.S() computes the sample standard deviation of the return series, and SQRT() is used for the annualization step.

Within a spreadsheet, you would typically set up columns for dates, closing prices, and then a column for the calculated logarithmic returns. Subsequently, you apply the standard deviation function to the returns column, and finally, multiply that result by the square root of the annualization factor, such as 252, to obtain the annualized historical volatility. This systematic approach simplifies what would otherwise be a complex manual calculation.

Many financial data providers and software platforms also offer pre-calculated historical volatility figures. Services from entities like Bloomberg, Cboe, or specialized data providers often include this metric as part of their comprehensive financial datasets. These tools allow users to quickly access volatility data without performing the detailed calculations themselves.

Choosing an appropriate lookback period for historical volatility is a practical consideration. Common choices include 20-day, 60-day, or 252-day periods, with the selection depending on the specific analytical objective. A shorter period will reflect more recent price movements, while a longer period provides a smoother, broader view of past fluctuations.