# Historical Volatility Uses & Calculation

The three most common questions I get regarding historical volatility are:

• What is Historical Volatility?
• How do you calculate Historical Volatility?
• And what’s the best number of days to use?

### WHAT IS HISTORICAL VOLATILITY?

Historical Volatility is the Standard Deviation of price returns (daily percentage price changes). Historical Volatility calculates the probability of the magnitude of price changes in the future rather than the direction of price changes.

For this article the closing price of the asset is used.  While this is easily defined when speaking about equities or other exchange traded products which have a closing price used for mark-to-market.

When speaking about Foreign Exchange or other OTC traded markets, decisions as to the closing time has to be made.

Typically two closes will be used depending on location. For the United States the two closing times are: 11AM New York time (4PM London Time) & 4PM New York Time.  Best workflow practice says to make your decision prior to creating your time series and remain consistent to your rules.

### HOW DO YOU CALCULATE HISTORICAL VOLATILITY?

The table below takes the reader through the historical volatility calculation step by step.

### TABLE 1 10 day historical volatility

Table 1 shows the closing price in column C.  As you move to the right you can see all the calculations.  Each step is shown separately for educational purposes.  In practice you can nest the equations down to three columns.

From Column C (the closing price of the asset) we continue..

In Column D  you see the NATURAL LOGARITHM of the daily percentage change

In Column E  you see the 10 day average of Column D

In Column F  you can see the deviation from the mean(average)

In Column G  you can see the deviation squared followed by

In Column H  the sum of the squared deviations

In Column I  The result of Column H is divided by the number of changes in the sample (9)

In Column J  The Square Root of Column I brings us to the daily volatility (based on the last 10 days of closing prices)

In Column K  The daily volatility multiplied by the Square Root of the number of Trading days in a year (roughly 252) results in the ANNUALIZED 10 DAY HISTORICAL VOLATILITY

Today’s 10 day historical volatility is 32.48% (annualized).  In practice,  one typically looks at a time series of historical volatility numbers to ensure the current 10 day sample doesn’t have an outlier event (or a very slow period).  Historical Volatility such as you would see on Bloomberg by pressing HVT [go] or HVG [go] is calculated like a moving average using the number of days one desires.

### WHAT NUMBER OF DAYS SHOULD BE USED FOR  HISTORICAL VOLATILITY?

It’s best to avoid time periods too short or too long.  Using a short time period or too long of a time period each have their own problems.

A 5 day historical volatility chart will have a lot of noise, with extreme highs and extreme lows.

Consider 5 day historical volatility: Each day = 20% of the final number; each CHANGE is 25% of the final number (4 changes)

A 200 day historical volatility chart will have very little noise, smooth with no extreme highs or lows.

Consider 200 day historical volatility.  Each day = .5% of the final number; each CHANGE is also .5% of the final number (199 changes)

When using a very long sample like 200 day historical volatility you stand the risk of including the distant past which may not reflect the current market.

### IS THERE ONE NUMBER WE CAN LOOK AT?

If the purpose is to get a general sense of the assets volatility you can begin with the study which will show the range and average volatility.

Use 5 years of daily closing price data and Calculate 20 day historical volatility for 5 years.

To calculate the range:

Create a histogram:

Using Excel you’ll need the high and low 20 day historical volatility number over the past 5 yrs.

Calculate the range of the 20 day volatility “most of the time”.  This answer depends on your strategy and risk management so I will leave that variable up to you to play with but something greater than 75% – 80% of the time.

To calculate the average:

Throw out observations which occurred less than 4 times and calculate the AVERAGE from the rest of the data series.

### There are plenty of sites that sell historical volatility data

Words of Caution: Know how the data provider is calculating their result and how they handle such things as rollovers (for continuous front month futures) and stock splits.

If what you REALLY want to know is the probable range of prices at expiration,  use a RANGE CALCULATOR like the one available on this site. Range Calculators are quite useful and easy to use.  If you’re looking for the probability associated with a specific date and a specific volatility, a range calculator may be all you need.

### Other Types of Volatility

There are several other TYPES of volatility used in the market. You will find blogs on this site and others.  The Types of Volatility you want to know are:

Historical Volatility:  Range Volatility; Overnight Volatility;

Implied Volatility: The Markets expectation of volatility of the underlying asset to expiration day. There are several Implied Volatility Figures we work with to make what is called The Volatility Surface

Forecast Volatility: Your forecast of the volatility of the underlying asset over some future time period.

Event Volatility: Calculated for both historical and implied volatility around earnings dates, economic release dates and other market impacting events.

### Volatility Studies

There are a handful of studies I like to use.  From those studies I can determine the risk/reward of an options strategy.  The way each study is used will differ depending on my goals. A volatility will use the studies to determine whether to trade gamma or skew.  For my personal account my strategies portfolio based: selling calls versus stock, trading for earnings, etc.

Authors