# Historical volatility : an indicator of long-term risk An indicator of the level of risk and return of an asset, historical volatility is a tool regularly used in technical analysis.

Many investors specializing in technical analysis and chartism tend to emphasize short-term tools such as RSI or Stochastic in their trading strategy. Despite this, it is wise to take a complementary, longer-term view of an asset's performance: that's where historical volatility comes in!

Here is a complete summary of everything you need to know about historical volatility in order to use this tool in the best conditions.

## What is Historical Volatility ?

Historical volatility is a form of volatility used to evaluate the risk of a security in a financial market in relation to the magnitude of its variations over a given period. Although it can take into account any time scale, it is generally the year that is chosen as the period of study for its calculation, hence the use of the so-called "historical" graph of the security in question. Proportional to the measured risk, but without mentioning the direction of the historical variation of the price, historical volatility measures the deviation from the average of the variations of said price.

Please note : historical volatility does not represent the variations of a stock, but its volatility! It is quite possible for a stock to have low variations and a high historical volatility.

This indicator can be used to study the assets of financial markets such as :

## How to Calculate Historical Volatility

Four steps are required to calculate historical volatility :

1. Obtaining the average of the price variations over a given period
2. Subtracting this average from each closing price over the same period
3. Calculating the average of the results obtained
4. Taking the square root of this result.

In plainer language, the formula for historical volatility is Historical volatility = √ (365 . [ ∑ ( r (t) )² / ( n - 1 ) ] ) in which

• 365 is the number of days taken into account in the period;
• r(t) is the return on the asset, whose formula is r(t) = Ln (P(t)/P(t-1)).

In this way, volatility is expressed as a percentage that indicates the probability of an increase or decrease over the given period. The magnitude of the changes over the same period is measured symmetrically.

Please note : although generally used on a one-year basis, historical volatility can also be calculated in minutes, hours, days or months.

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## Using Historical Volatility in Trading

The percentage thus obtained gives two possible indications :

• If the percentage is low, then the risk is low, as is the potential for profitability of the asset
• If the percentage is high, then the risk is high, as is the potential for profitability

The dilemma then lies in your investor profile. Depending on whether you have a passive or aggressive trading style, on your trading strategy and on the goals you have set for yourself, a high percentage will be a signal to enter the market (or not). In addition, historical volatility is similar to Average True Range (ATR) except that the latter uses an Arithmetic Moving Average and not an Exponential Moving Average. Historical volatility is also complementary to implied volatility, which looks at price changes in the near future.

Note : for financial derivatives, historical volatility is not the tool to use. Implied volatility is preferred.

Historical volatility can be put to use in the following contexts :

• to analyze the risk of a single asset
• to compare the risk of several assets
• to compare the risk of several asset classes
• to compare risk across multiple industries

Because long-term volatility often differs from short-term volatility, it is best to couple the use of historical volatility with other shorter-term technical indicators.

## Conclusion

Historical volatility is an indicator of risk, but also of the profit potential of an asset or several securities over the long term. Thus, it provides reliable information that is anchored in time; however, to optimize your trading strategy, particularly with regard to technical analysis, it is wise to use it in addition to more reactive technical indicators. 