# Volatility, Range, True Range, and ATR

## Using Range for Measuring Volatility

The easiest way to quickly measure market’s volatility during a particular trading day or week is by calculating the **Range**. Price Range is simply the **absolute difference between the highest and the lowest price** reached during a particular time period (e.g. a trading day).

- Range = High – Low

## S&P500 Futures Daily Range Example

For example, the daily high of S&P500 index futures was 1,151.75 and the daily low was 1,139.50. The **Range of that particular trading day** was 1,151.75 less 1,139.50, which equals 12.25 points.

When you **follow the trading range of a market on a regular basis** (you know that the average daily range of S&P500 futures has been let’s say 18 points), you can tell whether **this particular day’s volatility was high or low**. You can observe the development in trading range over multiple days and use it as one of the tools for describing market conditions and making trading decisions.

## The Problem with Gaps and Limit Moves

**Range as a measure of volatility** over a series of trading days has one significant weakness. It **only looks at every single trading day in isolation** and without any regard to overnight price changes. You only look at the high and the low, but you don’t care where the market is trading relative to the previous day.

While markets usually open near the level where they closed the previous day, sometimes there are **gaps** (for example when important news come out during the night). This has been characteristic for some commodity futures markets, where spikes in supply or demand sometimes push prices to their daily price limits, which may result in gaps and limit moves over multiple days in a row.

In case of gaps and limit moves, **range as a measure of volatility is misleading**, as it **understates the volatility**. It only measures **intraday volatility**, but it ignores **overnight volatility**.

## Range vs. True Range

In the 1970’s, when commodity futures markets were showing limit moves and gaps often, *J. Welles Wilder Jr.* invented the concept of True Range, which addressed this problem. Compared to the traditional Range, **True Range takes into consideration both intraday and overnight component of price volatility**.

## How to Determine True Range

**True Range is defined as** the greatest of the following three:

**Current bar’s High less current bar’s Low**(the traditional Range – it is the greatest of the three when the previous bar’s close is within the current bar’s range)**Current bar’s High less previous bar’s Close**(this one is the greatest when current bar’s low is higher than previous bar’s close)**Previous bar’s Close less current bar’s Low**(this one is the greatest when current bar’s high is lower than previous bar’s close)

Here you can see more details about true range calculation, including visual examples: True Range.

## Average True Range

True Range is then used to calculate Average True Range (ATR), which is the (simple, exponential, or other) **moving average of True Range** (usually with a period of 14 or 20). Average True Range is a reliable indicator of price volatility, taking both intraday and overnight price changes into consideration. **ATR is often used for risk management purposes**, e.g. for determining position size or stop loss order distance based on market’s volatility.