The Average True Range (ATR) has many different uses in trading and was developed by Welles Wilder. It was included in his groundbreaking book New Concepts in Technical Trading Systems, released in 1978. Wilder developed the ATR so that he could more accurately measure the volatility in the commodity markets. Since many commodities have gap openings and limit moves other volatility measures would not accurately reflect the true volatility. The first part of the calculation is to determine the true range (TR) which he defined as the greatest one of the following three values:

• The current High less the current Low.
• The absolute value of the current High less the previous Close.
• The absolute value of the current Low less the previous Close.

Many use a 14-period moving average of the TR to calculate the ATR, and this is used in a variety of ways by traders and money managers. One method that has become more popular in recent years is the use of the ATR to help refine one's approach to money management by adjusting the position size.

Let's look at an example to see how the ATR can be useful. The ATR is often used as a method of determining an initial stop value, as the probability of an issue moving beyond two to three times the Average True Range in one period is quite low. One of the standard concepts in money management is to not risk more than 2% of your trading portfolio on any one trade. In this hypothetical example, let's assume that after the test of the lows on March 17th of 2008 you decided to buy stock and you wanted to initially use a stop that was two times the ATR below the close. The two stocks I have selected are Microsoft (MSFT) and Jinpan International Ltd. (JST). As noted first in the table below, we have the closing price and the beta value. The beta value has been used to compare the volatility of an individual stock to the market. A beta value of 1.0 means it has the same volatility as the market, while a value of more than 1.0 means it is more volatile, and a value under 1.0 means it is less volatile. As you can see from the numbers below, JST is more volatile than MSFT as it has a beta of 3.46 compared to 1.59 for MSFT.

Table 1

Therefore, if we assume a \$100,000 account, and using the 2% guideline, one would not want to risk more that \$2000 on any one trade. As of 3/17 there was a wide difference in the ATR with a value of 0.91 for MSFT and 1.34 for JST. Now using a stop of two times the ATR (2ATR), barring any earnings reports or other shocks, should give one a decent number of days to stay in a trade. The difference between the closing price and the stop is noted as the risk on the table. By dividing \$2000 by the risk, you can calculate the number of shares you should trade; for MSFT this was almost 1100, for JST it was about 746. If instead you had purchased 1100 shares of JST and your stop was hit, the loss would have been around \$2950 almost 50% above the \$2000 limit.

Forex traders often use the ATR for short-term trading. For example, if you are trading the Euro/\$ with an ATR of .0130 you might use it in the following manner. Let's say your system or methodology says that you should be buying the Euro at 1.5640. For our example the day's high so far is 1.5720 and the day's low is 1.5610. Assuming no new highs, the expected low should not be below 1.5590 (high minus ATR) to match the daily ATR.

Figure 1

The ATR is often also used to calculate trailing stops. One trailing stop method using the ATR with daily data is to look at the highest high (for longs) or the lowest low (for shorts) over the past 20 periods and then subtracting or adding three times the 14-MA of the ATR from this value. Now though many use this after a position has been established, it can also be used as a guideline for initial stops. The 20-period history reflects approximately a month of trading using daily data. The 3ATR was my choice but some will use a larger or smaller value and some attempt to optimize the multiplier for a specific market. The chart above is a daily chart of the SPY that begins in May of 2006 and covers up through March of 2007. In addition to the price, the trailing stop (ATRLS) has been plotted. On the daily chart, I have identified a nice bottoming formation (lines a and b). It is not the purpose of this article to look at the reasons for taking a trade, but towards the end of the formation, there were a number of positive signals from a wide range of indicators. After the breakout above resistance at line a, the SPY rallied for over a week before dropping back to the breakout level (circle c). With the close on August 10th at 127.37 the ATRLS stood at 125.05 so the risk was 1.8%. The SPY stayed above the ATRLS until November 3rd when it dropped below the stop by half a point before closing back above it. Now for position traders, you can use this on a close-only basis, but as you will soon see, once we look at the price action in February 2007, the benefits of intra-day stops will also be evident. SPY made a new closing high just three days later and the SPY stayed above the ATRLS until the price collapse on February 27. This was one of the largest percentage one-day declines in modern history as the stop at 142.04 was hit with the SPY closing at 139.50. Of course the gap opening on February 27th that was below the prior eight days' lows was a clear indication that something had changed.

Figure 2

One concern I have had about using the highest high or lowest low of the past 20 days is that in especially strong trending markets, the stop might be moved in too tight, therefore, stopping one out on a pullback within the major trend. An example of this occurred on November 3rd as indicated by point 1. In Figure 2, I have added a modified formula of the original trailing stop ATRLS. This variation, called ATRLSma (plotted in red), uses a 20-period MA of the highest high to smooth out the data and is plotted in red. During the period I have selected, there are only a few significant differences. During the bottoming process (circle c), the stop using the ATRLSma would have been slightly tighter (.40 of a point), dropping the risk based on the prior days' close to 1.5% from 1.8%. More significantly, in November, while the ATRLS was hit, the SPY stayed above the ATRLSma as the low of the day was 135.62 and the ATRLSma was at 135.55. The other main difference occurred in early 2007 (circle d) as the ATRLSma was broken for four consecutive days while the SPY held above its ATRLS. And even though the SPY did eventually move five points higher, the intra-day exits on February 27th were similar, using either stop value.

Figure 3

Before moving on to how this works on the short side, let us look at another market to see how the two approaches compare. One of the wildest and most difficult markets to trade in 2007 was China, as epitomized by the iShares FTSE/Xinhua China 25 Index (FXI). The daily chart above covers all of 2007 with both the ATRLS and ATRLSma plotted in a similar manner as in Figure 2. On the lower half of the chart, I have also plotted the 14-period ATR. FXI hit a low of \$22 in mid-2006 and then spiked to a high of \$39 in early 2007. This became an area of resistance (line a) in 2007, which was decisively overcome in June (point 1). By late July, FXI was trading above \$49, where the rally stalled; FXI then plunged in mid-August with most of the world markets. The exits based on either stop were about the same. Seven days after the lows at \$37, FXI had broken out above the previous highs (line b) as noted by point 2. FXI was able to stay above both the ATRLS and ATRLSma for the next two months until October 19th when the ATRLS was violated (point 3). FXI made one more marginal new high at \$73.18 on October 31st, then gapped to the downside three days later breaking both stop levels (point 4).

So what is one to make of how these stop formulas performed with FXI? Certainly it was not nearly as clean as the examples we discussed using SPY, but does this mean that it should not be considered as a stop method? One factor that might help explain the action in FXI is found by examining the 14-day ATR, which is plotted on the bottom of the chart. The ATR moved above the 1.14 level (line c) in late July (point 5), consistent with a major increase in volatility, as the ATR had never exceeded this level. As you can see on the chart, the ATR continued to rise sharply into November, so the wide swings were possibly not that surprising. In the next part of this article, I will look at how these stop methods work with short positions and also explore other ways the behavior of the ATR can be used to help your trading.

As always I welcome your feed back on these articles and I can be contacted at tomaspray@intershow.com. I would also appreciate any suggestions you may have for future articles.

Tom Aspray, professional trader and analyst, serves as video content editor for InterShow's MoneyShow.com Video Network. Mr. Aspray joined InterShow full time in June of 2007 where he also does other editorial work for the site, including the bi-weekly trading lessons and the weekly charts to watch. Mr. Aspray has written widely on technical analysis and has given over 60 presentations around the world. Over the years, he has applied his methodologies not only to the stock and commodity markets but also the global markets, mutual funds, and foreign exchange. Many of the technical indicators that Mr. Aspray wrote about in the 1980s, such as the MACD, have since gained worldwide acceptance. He was originally trained as a biochemist but began using his computer expertise to analyze the financial markets in the early 80s. As a consultant, Mr. Aspray wrote daily institutional reports for firms such as Fleming Jardine and Barings Bank and was noted by the Wall Street Journal as one of the "top bond market technicians."